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Europe|Istanbul Explosion Kills 10 Tourists, and ISIS Is Blamed
https://nyti.ms/1mTrXtw
Istanbul Explosion Kills 10 Tourists, and ISIS Is Blamed
Witness Recalls the Moment of Blast
A man who saw the explosion in Istanbul's central district of Sultanahmet on Tuesday recounts what he saw.
ISTANBUL, TURKEY (JANUARY 12, 2016) (REUTERS - ACCESS ALL) TURKISH EYEWITNESS, MURAT MANAZ, SAYING: "It was a suicide bomb, yes. I went there and saw it and came back to the hotel. There was chaos. Everybody was running somewhere. Policemen did not see this coming. They were sad but at the same time they were trying to evacuate the area because they said there was a possibility that a second bomb could go off. The square was completely evacuated."
A man who saw the explosion in Istanbul's central district of Sultanahmet on Tuesday recounts what he saw.CreditCredit...Osman Orsal/Reuters
By Ceylan Yeginsu and Tim Arango
ISTANBUL — On any given day, the heart of this city's historic district, where the monuments of three empires — Roman, Byzantine and Ottoman — collide with a mix of majesty and tranquillity, is a bustling center of tourism, one of the world's most visited places.
Mixing among German tourists on Tuesday morning, not far from the celebrated Blue Mosque, the authorities said, was an Islamic State operative from Syria in his late 20s, wearing a vest of explosives and determined to kill as many people as possible.
The attack left 10 tourists dead, all foreigners, and like other terrorist strikes in recent months in Paris; Beirut, Lebanon; Mali; Egypt; and Baghdad, it resonated far beyond Turkey as civilians were again cut down while going about their daily lives.
"Today, Istanbul was hit," said Angela Merkel, the German chancellor, in a statement. "Paris has been hit. Tunisia has been hit. Ankara has been hit before."
She continued, "Once again, international terrorism is showing its cruel and inhuman face today."
The attack at a center of tourism here underscored what security and political analysts say is an inevitable and grim byproduct of the fight against terrorism and the self-declared Islamic State: Attacks against so-called "soft targets," while few in number, are likely to continue with chilling regularity.
Tuesday's bombing came as the Islamic State faces increasing pressure from an international military coalition — of which Turkey and Germany are members — that has accelerated attacks on the group's oil infrastructure and has recently driven it from one of its key cities in Iraq, the provincial capital Ramadi.
Emergency workers and a dead body near the Blue Mosque in the Sultanahmet district in Istanbul, the site of a suicide bombing on Tuesday.Credit...Deniz Toprak/European Pressphoto Agency
"It's clear that they've diversified their strategy and are determined to target more soft targets outside their areas, that is, in Syria and Iraq," said Daniel Benjamin, a scholar at Dartmouth and a former coordinator for counterterrorism at the State Department during President Obama's first term.
He added, "There is a paradoxical situation where they seem to be inflicting more pain while at the same time they are suffering setbacks."
As the bomber struck on Tuesday morning in Sultanahmet, the heart of Istanbul's old city, workers in Baghdad were still clearing away the wreckage and blood from an Islamic State attack Monday night on a shopping mall that brought with it the return of old fears for the city's residents. Almost daily for years, the city faced the type of attack that hit Istanbul.
Erdogan Says Bomber Was From Syria
President Recep Tayyip Erdogan of Turkey condemned the suicide bombing in Istanbul and said the attack was carried out by a person with Syrian origins.
(SOUNDBITE) (Turkish) TURKISH PRESIDENT, TAYYIP ERDOGAN, SAYING: "I strongly condemn the terror incident in Istanbul's Sultanahmet District, assessed to be an attack by a suicide bomber with Syrian origins." (SOUNDBITE) (Turkish) TURKISH PRESIDENT, TAYYIP ERDOGAN, SAYING: "Unfortunately, so far, we have 10 dead in this terrorist attack, including foreigners and Turkish nationals." (SOUNDBITE) (Turkish) TURKISH PRESIDENT, TAYYIP ERDOGAN, SAYING: "I express my condolences to those who were killed in the blast and hope for a quick recovery for those who are wounded. Around 15 people were wounded." (SOUNDBITE) (Turkish) TURKISH PRESIDENT, TAYYIP ERDOGAN, SAYING: "This incident showed us once again that we need to stand in solidarity. We need to stand as one as a nation against terror attacks."
President Recep Tayyip Erdogan of Turkey condemned the suicide bombing in Istanbul and said the attack was carried out by a person with Syrian origins.CreditCredit...Reuters
Ahmed Saadawi, a prominent Iraqi writer, received a top Arabic literary prize in 2014 for his novel "Frankenstein in Baghdad," which delved into the effects such random violence can have on a society, by breaking down social bonds as fear prevails. Iraq is an extreme case, and in previous years, the violence led to all-out sectarian conflict.
But in Turkey, Europe, the United States and elsewhere, the rising anxiety about terrorism is eroding empathy and compassion while stoking xenophobia and intolerance.
"When fear controls a society, it will distract and confuse people's minds, and it will erase the lines between enemies and friends," Mr. Saadawi said. His honored novel, he said, is largely about fear: "How it makes people scared to walk in the streets, thinking, who is the enemy? Who is the friend?"
The Islamic State, also known as ISIS or ISIL, did not immediately claim credit for the attack Tuesday, but Prime Minister Ahmet Davutoglu said it appeared that the attacker — whom President Recep Tayyip Erdogan identified as Syrian — had connections with the terrorist group.
For Mr. Erdogan, the participation of a Syrian is likely to complicate his government's cooperation with the European Union in stemming the flow of migrants from Turkey's shores to Europe, while also steeling his resolve to keep Syrians out of Turkey altogether.
The country has already effectively shut its southern border with Syria to new refugees. Last week, it instituted new visa regulations for Syrians arriving by air, a decision that stranded hundreds of Syrians at the airport in Beirut.
It is unclear if the bomber looked specifically for Germans to kill. "By targeting Germans, ISIS seems intent on creating an anti-refugee backlash in Europe, hoping to fuel already rising anti-Islam sentiments on the Continent," said Soner Cagaptay, an expert on Turkey at the Washington Institute for Near East Policy.
For Turkey, the attack was the latest spillover from the Syrian civil war. In October, two suicide bombers who the authorities say were working for the Islamic State struck a rally in Ankara, the Turkish capital. Nearly 100 people were killed in a crowd of mostly Kurds gathering to demand an end to the conflict between Turkey and Kurdish militants in the southeast.
Tuesday's attack, while less deadly, was by some accounts more resonant, as it seemed unconnected to Turkish domestic politics and designed to deal a blow to the country's $30 billion tourism industry.
Merkel Voices Sympathy and Resolve
Chancellor Angela Merkel of Germany expressed sympathy for the victims of the suicide bombing in Istanbul and said the fight against terrorism would prevail.
BERLIN, GERMANY (JANUARY 12, 2016 GERMAN CHANCELLOR, ANGELA MERKEL, SAYING: I am sad for our people and I think and feel about them. They have to live with the terrible pain that their beloved ones who had hoped to have a beautiful holiday in Istanbul, are not going to come back." "Terrorists are enemies of all free people. Yes, they are enemies of all humanity, whether they are in Syria, Turkey, France or Germany. It is exactly this freedom and our determination to fight these terrorists together with our international partners that will prevail."
Chancellor Angela Merkel of Germany expressed sympathy for the victims of the suicide bombing in Istanbul and said the fight against terrorism would prevail.CreditCredit...Fabrizio Bensch/Reuters
As the Syrian civil war metastasized over the last five years, Turkey, in its determination to see Syria's president, Bashar al-Assad, ousted, supported rebel groups, offering its territory as a transit route for fighters and weapons. Turkey has faced heavy criticism from its Western allies, including the United States, for enabling the rise of the Islamic State.
Only recently, analysts say, has Turkey seemed determined to clamp down on the group, conducting raids against cells in Turkey and building a wall on a portion of its southern border with Syria, opposite territory controlled by the Islamic State.
Many critics say that those efforts came too late and that in recent years the group was able to build up networks in Turkey that are now targeting the country as retaliation for the recent clampdown.
Where ISIS Has Directed and Inspired Attacks Around the World
More than a dozen countries have had attacks since the Islamic State, or ISIS, began to pursue a global strategy in the summer of 2014.
"It's very difficult to stop suicide bombers, especially if you have allowed an infrastructure to grow in your country," said Mr. Benjamin, the scholar at Dartmouth and former American counterterrorism official.
The explosion in Sultanahmet occurred close to the German Fountain, a gazebo-style structure that commemorates a visit by Kaiser Wilhelm II in 1898. The blast left several bodies around the base of an Egyptian obelisk that was carved around 1490 B.C. and was brought to the city in A.D. 390 by the Roman emperor Theodosius.
The Germans reported that at least eight Germans died, while the Turkish government put the number at nine. The other tourist who died was Peruvian, according to news agencies. At least 15 other people were wounded, including nine Germans, along with citizens of Norway, Peru, South Korea and Turkey. The suicide bomber also died.
More than three hours after Tuesday's explosion, a group of waiters stood in shock outside a nearby restaurant.
"I don't know what to say — I guess we were expecting this, but not an explosion this big," said one of the workers, who gave his name only as Ibrahim, his eyes fixed on the Blue Mosque, an early-17th-century landmark.
On a usual day, the restaurant would be busy with customers, with lines forming outside.
"Tourism had already dried up after last year's explosion, but after this, it's game over," said Ayse Demir, 36, a shopkeeper at an arts and crafts shop, referring to an attack at a police station that killed an officer. "No one is going to risk their lives for shopping and history."


God gave us memories, so we might have roses in December.
I think that God is proud of those that bear a sorrow bravely.
to find Him there and kneel in faith to touch His garment's hem.
He who knows all sorrow and how hard grief is to bear.
each finds his hurt heart strangely comforted.
when the world will be at peace.
The dead are merely sleeping.
All who have ever lived, or will live, will be resurrected.
and come unto the knowledge of the truth.
All mankind will live together in peace and happiness, forever.
God will dwell with men, and wipe away all tears.
There will be no more death, sorrow, crying, or pain (Rev. 21:3–4).


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text:
\section{Introduction}

Electric control of magnetism in nanostructures must be viewed as an
important milestone  on our road map for successful realization of
spintronic devices. Although most of the operations in such devices
ultimately should be based on spin--only processes, i.e., processes
not associated with (highly dissipative) electric charge transport,
to gain best benefits from such designs, spin must be manipulated
both during the input, control, and read--out stage and eventually be
coupled to charge.  Several schemes achieving this goal have been
explored both at the quantum and semi-classical level, such as the
electric distortion of the orbital wave function of spin carriers in
inhomogeneous (effective) magnetic fields \cite{Shin2010:PRL},
electric g-tensor control \cite{Roloff2010:NJP,Kroutvar2004:N}, or
spin torque transfer.\cite{Myers1999:S, Ralph2008:JMMM,Wenin2010:JAP}
Here we explore, on theoretical grounds,  the influence of an electric bias on the ferromagnetic state
and  feasibility of electric control of ferromagnetism in
Ga$_{1-x-y}$Al$_y$Mn$_x$As multiple quantum wells.  Structural design, including effective potential profiling and
doping to position emitter and collector quasi--Fermi levels, as well as
tunneling is used to control hole density and spin polarization within the Mn doped layers.

Dilute magnetic semiconductors (DMS) have been realized by doping of
conventional ZnS--structured  semiconductors with elements providing open
electronic $d$ or $f$ shells.  This  has added yet another degree of
freedom to the rich spectrum of physical phenomena in semiconductors
available for material design with potential for technological applications.\cite{Jungwirth2006:RMP}
A prominent example is bulk Ga$_{1-x}$Mn$_x$As where Mn on the Ga sites
provides both an open d-shell with a local magnetic moment and
a hole which may establish ferromagnetic ordering among the
Mn d--electrons, a mechanism known as carrier--mediated
ferromagnetism.\cite{Ohno1996:APL,VanEsch1997:PRB,Dietl2000:Science}
The preferentially anti--parallel alignment  of the 3/2  spin of the
mobile holes with the 5/2 spin of the localized Mn d--electrons
promotes ferromagnetic ordering of the latter below a critical
temperature of  up to  $\sim 150$ K.
Theoretical work  has confirmed strong hybridization between the 5d Mn and  3p electrons
in the ground state.\cite{Jain2001:PRB}
The effective
hole--concentration--dependent exchange field lifts the spin
degeneracy of the holes' energy bands and thus goes hand in hand with hole spin polarization.
The Mn ions sitting on Ga sites act as acceptors and are believed to give rise to acceptor levels which lie about 100 meV above the valence band edge.\cite{Jungwirth2006:RMP,VanEsch1997:PRB,Schneider1987:PRL}
Photoluminescence experiments indicate the co-existence of
holes bound to Mn sites and itinerant holes which participate in establishing magnetic order amongst the Mn ions below $T_c$.\cite{Sapega2009:PRB}

Since structural defects  of bulk and confined layers of Ga$_{1-x}$Mn$_x$As  depend on grow conditions, Mn concentration $x$ , and annealing procedures it is not too surprising that experiments have come up with somewhat different  conclusions regarding the ``electronic structure of bulk Ga$_{1-x}$Mn$_x$As".  More recent work seems to hint at the existence of an impurity band which forms at Mn concentrations above ~ 1.5~\% leading to a metal--insulator transition in high--quality GaMnAs.\cite{Burch2006:PRL,Richardella2010:S,Ohya2011:NP}
The Fermi level in these samples is reported to lie in the impurity band
and  the valence--band properties remain largely GaAs--like.\cite{Ohya2011:NP}
The radius of the Mn acceptor wave function has been  measured to be about 2~nm, indicating that Mn$_{Ga}$ is not a shallow acceptor.\cite{Richardella2010:S}
In contrast, other studies rather hint at a disordered top valence
band edge containing the Fermi energy, but no isolated impurity band is present.\cite{Jungwirth2006:RMP}   Recent theoretical work has led to the conclusion  that  a tight--binding approach (within the coherent-potential approximation for disorder) and local--density functional theory + Hubbard U correction cannot account for an isolated impurity band.\cite{Masek2010:PRL}
Other theoretical work has lead to the conclusion that  disorder may enhance ferromagnetic stability.\cite{Lee2007:PRB,Berciu2002:PhysicaB}
Ionized impurity scattering seems to play the dominant role in explaining Hall resistivity data.\cite{Yoon2004:JAP}

Controlled growth of heterostructures containing  crystalline  layers of GaMnAs of high structural quality has remained a challenge up to date.  Nevertheless, tunneling spectroscopy has confirmed size quantization effects in GaMnAs quantum well layers.\cite{Ohya2007:PRB,Ohya2010:PRL,Ohya2011:NP}   However, compared to crystalline GaAs well layers, in an otherwise identical structure,  the signature appears to be rather weak and in no sample yet, apparently, has one observed negative differential conductivity due to resonances associated with GaMnAs well layers.   This hints at a significant concentration of defects, reminiscent of thin layers of amorphous Si where similar transport studies have revealed size quantization effects but, to our knowledge, not negative differential conductivity.\cite{Miyazaki1987:PRL,Li1993:PRB}
 Experimental evidence indicating a coexistence of localized and extended Bloch--like states in bulk GaMnAs, in general, allows
 the prediction that, in thin layers, certainly for $\leq 3$ nm,  of GaMnAs extended states will be subjected to confinement effects
(quantization and energy shifts) while localized states will remain largely unaffected.  This is similar to external magnetic--field effects on point defects or quantization effects in amorphous Si.\cite{Poetz1983:SSC, Li1993:PRB}
Assuming that no significant additional defects arise  in GaMnAs heterostructures,  this makes plausible experimental reports on quantum confinement effects arising from (ferromagnetic) GaMnAs layers in thin heterostructures.\cite{Ohya2007:PRB,Ohya2010:PRL,Ohya2011:NP}
Indeed, when one succeeds to incorporate high--quality magnetic layers
in semiconductor heterostructures  strongly
spin-dependent carrier transmission can be predicted due to spin-selective
tunneling.\cite{Sankowski2007:PRB} In magnetic resonant tunneling
structures of high structural quality this spin splitting may be used for a realization of spin
valves, spin filtering, and spin switching devices
\cite{Likovich2009:PRB,Slobodskyy2003:PRL,Slobodskyy2007:APL,Petukhov2002:PRL,Ohya2007:PRB,Ohya2010:APL,Ertler2006a:APL,Ertler2007a:PRB}, all representing  important
ingredients for spintronic-based device technology.

In several experiments ferromagnetism has been generated in bulk GaMnAs
by,  electrically or
optically, tailoring the hole density.\cite{Ohno2000:N, Boukari2002:PRL}
In 2d-confined systems
containing layers of Ga$_{1-x}$Mn$_x$As  the magnetic order depends
strongly on the local spin density, which can be influenced by the
tunneling current, resulting in a bias-dependent exchange
splitting.\cite{Dietl1997:PRB,Jungwirth1999:PRB}
A spin-density dependent
exchange splitting in ferromagnetic structures enriches the dynamic
complexity by offering a mechanism for  external electrical
control of the ferromagnetic state.
This is in contrast
to structures comprising paramagnetic DMS, such as ZnMnSe, in which
a giant Zeeman splitting of the bands is induced by applying an
external magnetic field of the order of a few Tesla.

Already nonmagnetic multi--well heterostructures exhibit interesting
dynamic nonlinear effects which are based, however, on different physical
mechanisms, such as the formation of electric field domains and the
motion of charge dipoles through the structure.\cite{Eaves1989:SSE, Poetz1990:PRB, Stegemann2007:NJP,Bonilla2005:RPP}
Recently it has
been predicted that, in heterostructures containing paramagnetic DMS
wells, this kind of phenomena can be controlled by an external
magnetic field.\cite{Sanchez2001:PRB, Bonilla2007:APL,Escobedo2009:PRB}  Using an incoherent, sequential tunneling model
we have proposed that {\em ferromagnetic} multi--well structures can
generate ac spin currents, a phenomenon which originates from
time--dependent inversion of the spin population in adjacent
wells.\cite{Ertler2010:APL}

In this article we investigate spin--selective hole transport in
GaAs/AlGaAs/GaMnAs heterostructures within the limit of moderately thin samples
with predominantly {\em coherent} transport characteristics.  We apply a
non-equilibrium Green's function formalism based on a tight--binding
Hamiltonian for the electronic structure, including self-consistency
regarding the charge density and the exchange splitting of the
effective potential, as well as charge transfer to the contacts.
Both the carriers' Coulomb interaction and the exchange coupling
with the magnetic ions are described within a mean-field picture.
Details of our model are exposed in Sect.~\ref{sec:model}.  The
mechanism of electric control of magnetization switching is
explored for two generic structures containing, respectively,  one
and two layers of Ga$_{1-x}$Mn$_x$As.  Results are given in
Sect.~\ref{sec:results}. We also provide a qualitative explanation
for the occurrence of spin-polarized current oscillations, predicted
in an earlier paper \cite{Ertler2010:APL}, and investigate the
influence of spin flip processes at the interfaces on the total
current spin polarization.  Since disorder seems to play a major role in actual samples
we study the effect of substitutional  disorder on a qualitative level and discuss the robustness of the effects predicted here.
Relevance to experiment is discussed.   In particular, we can give an explanation for the absence of exchange splitting (magnetization) under resonance bias condition reported in a recent experiment and identify
characteristic features which may be explored in future experiments.
Summary and conclusions are given in Sect.~\ref{sec:sum}.

\section{Physical Model}\label{sec:model}

The magnetic semiconductor heterostructure  is described by a two--band tight-binding Hamiltonian
for the heavy holes $(J_3=\pm 3/2)$.  It is
given in the form
\begin{eqnarray}
H_s &=& \sum_{i,\sigma} \varepsilon_{i,\sigma} |i,\sigma\rangle\langle
i,\sigma|\nonumber\\
&&+\sum_{i,\sigma\sigma'}t_{i,\sigma\sigma'}|i,\sigma\rangle\langle
i+1,\sigma'|+ \mathrm{h.c.},
\end{eqnarray}
where  $\varepsilon_{i,\sigma}$ is the spin-dependent ($\sigma
=\uparrow,\downarrow \equiv \pm 1$) onsite energy at lattice site $i$,
$t_{i,\sigma\sigma'}$ denotes the hopping-matrix between
neighboring lattice sites, and $\mathrm{h.c.}$ abbreviates the Hermitian conjugate term. Spin conserving hopping gives a diagonal
matrix $t_{i,\sigma,\sigma'} = t\delta_{\sigma\sigma'}$, whereas spin flip processes can be taken into account
by introducing off-diagonal elements. The hopping parameter $t = -\hbar^2/(2 m^* a^2)$ depends on the effective mass $m^*$ and the lattice spacing $a$ between to neighboring
lattice sites. The onsite energy
\begin{equation}
\varepsilon_{i,\sigma} = U_i - e \phi-\frac{\sigma}{2}\Delta_i
\end{equation}
includes the intrinsic hole band profile $U_i$ due to the band
offset between different materials, the electrostatic potential
$\phi$ with $e$ denoting the elementary charge, and the local
exchange splitting $\Delta_i$.  Near the band-edges this model is
equivalent to an effective--mass model, however, it has the
advantage that structural imperfections and spin--flip processes can
readily be incorporated.  Moreover, it can be extended to arbitrary
sophistication by introducing a larger set of basis
functions.\cite{Sankowski2007:PRB, Schulman1983:PRB,Poetz1989:SM,DiCarlo1994:PRB}

Within a mean-field approach the exchange coupling between holes and magnetic
impurities can be described by two interrelated effective
magnetic fields,
respectively, originating from  a nonvanishing mean spin
polarization of the ions' d--electrons  $\langle S_z\rangle$ and from the hole
spin density $\langle s_z\rangle = (n_\uparrow-n_ \downarrow)/2$.\cite{Dietl1997:PRB,Jungwirth1999:PRB, Fabian2007:APS}  The exchange splitting of the hole bands is then given
by
\begin{equation}\label{eq:delta}
 \Delta(z) = -J_\mathrm{pd} n_\mathrm{imp}(z) \langle S_z\rangle(z)~,
\end{equation}
with $z$ being the longitudinal (growth) direction of the structure,
$J_\mathrm{pd} > 0 $  is the coupling strength between the impurity
spin and the carrier spin density (in case of GaMnAs p-like holes
couple to the d-like impurity electrons), and $n_\mathrm{imp}(z)$ is
the impurity density profile of magnetically active ions. Since the
magnetic order between the impurities is mediated by the holes, the
effective impurity spin polarization depends on the mean hole spin
polarization via
\begin{equation}\label{eq:Szgen}
  \langle S_z\rangle= - S B_S\left( \frac{S J_\mathrm{pd} \langle s_z \rangle}{k_B T}\right),
\end{equation}
where $k_B$ denotes Boltzmann's constant, $T$ is the lattice
temperature, and $B_S$ is the Brillouin function of order $S$, here with
$S = 5/2 $ for the Mn impurity spin. Combining Eq.~(\ref{eq:delta}) and
Eq.~(\ref{eq:Szgen}) leads to a self-consistent effective Hamiltonian
for the holes $H_\mathrm{eff} = -\sigma \Delta(z)/2$ with
\begin{equation}\label{eq:delta1}
 \Delta(z) = J_\mathrm{pd} n_\mathrm{imp}(z)
S B_S\left\{\frac{S J_\mathrm{pd} [n_\uparrow(z)-
n_\downarrow(z)]}{2 k_B T}\right\}.
\end{equation}
Note that in thermodynamic equilibrium of a quasi 2D-systems, such
as a quantum well,  the hole spin density polarization $\langle
s_z\rangle$ is the key figure of merit for the appearance of
ferromagnetism.

Within a Hartree mean-field picture space-charge effects are taken into account
self-consistently  by calculating the electric potential from the Poisson equation,
\begin{equation}\label{eq:poisson}
 \frac{\mathrm{d}}{\mathrm{d}z} \epsilon \frac{\mathrm{d}}{\mathrm{d}z}\phi =
e\left[ N_a(z) - n(z)\right],
\end{equation}
where $\epsilon$ denotes the dielectric constant and $N_a$ is the
acceptor density. The
local hole density at site $|i\rangle$ is given by
\begin{equation}\label{eq:n}
 n(i) = \frac{-i}{A a}\sum_{k_{||},\sigma}\int\frac{\mathrm{d}E}{2\pi} G^<(E;i\sigma,i\sigma)~,
\end{equation}
with $A$ being the in-plane cross sectional area of the structure, and $k_{||}$
denotes the in-plane momentum. The non-equilibrium ``lesser''
Green's function $G^<$ is calculated from the equation of motion
\begin{equation}\label{eq:gless}
 G^< = G^R\Sigma^<G^A
\end{equation}
where $G^R$ and $G^A = [G^R]^+$ denotes the retarded and advanced Green's function, respectively.
The scattering function $\Sigma^<=\Sigma^<_l+\Sigma^<_r$ describes the inflow of
particles from the left $(l)$ and right $(r)$ reservoirs \cite{Datta:1995}
\begin{equation}
\Sigma^<_{l,r} = f_0(E-\mu_{l,r})(\Sigma^A_{l,r}-\Sigma^R_{l,r})~,
\end{equation}
where $f_0(x) = [1+\exp(x/k_B T)]^{-1}$ is the Fermi distribution function and
$\mu_l$ and $\mu_r$, respectively, denote the quasi--Fermi energies in the contacts.
The retarded and advanced self-energy terms $\Sigma^R = \Sigma_l^R+\Sigma_r^R$ and $\Sigma^A = [\Sigma^R]^+$
account for the coupling of the system region to the left and right semi--infinite chains, for which an
analytic expression can be derived.\cite{Datta:1995, Economou:1983}
The retarded Green's function is then given by
\begin{equation}\label{eq:gr}
 G^R = \left[E+i\eta-H_s-\Sigma^R\right]^{-1}~,
\end{equation}
with $i\eta$ being a positive infinitesimal imaginary part of the
energy.

Together with adjusting the Fermi energies relative to the band
edges in the leads to ensure asymptotic charge
neutrality \cite{Poetz1989:JAP}, the band splitting given by
Eq.~(\ref{eq:delta1}),
 the Poisson equation Eq.~(\ref{eq:poisson},\ref{eq:n}),
and the kinetic equations Eqs.~(\ref{eq:gless}) and (\ref{eq:gr})
have to be solved self-consistently until convergence to a
steady--state solution is reached. Nonlinearities in both Hartree
and exchange term can give rise to multi--stable behavior, as will
be discussed below.  If this selfconsistency loop terminates with ferromagnetic ordering in the system, the effective one--particle potential
is different for spin--up and spin--down holes, thus leading to spin filtering in transmission.

After obtaining the self-consistent potential profile
the spin-dependent transmission probability $T_{\sigma'\sigma}(E)$
from the left to the right reservoir, as a matrix element of the structure's S-matrix,  can be calculated
from special matrix elements of the retarded Green's function \cite{DiCarlo1994:PRB}
\begin{equation}
T_{\sigma'\sigma}= T_{\sigma'\leftarrow\sigma}(E) =
\frac{v_{r,\sigma'}|G^R(E;r\sigma',l\sigma)|^2}{v_{l,\sigma}
|G^0(E;l\sigma,l\sigma)|^2}
\end{equation}
with $G_0$ denoting the free Green's function of the asymptotic
region, and $v_{l,\sigma}$ and $v_{r,\sigma}$, respectively, are the
spin-dependent group velocities in the leads.
$G^R(E;r\sigma',l\sigma)$ is computed most conveniently by adding
one layer after another which requires merely 2x2 matrix inversions
for the present two--band model.\cite{Economou:1983}

Finally, the steady--state current
is obtained from scattering theory (generalized Tsu-Esaki formula),
\begin{eqnarray}
 j_{\sigma'\sigma} & = & \frac{e m^* k_B T}{(2\pi)^2\hbar^3}
\int_0^\infty \mathrm{d} E\: T_{\sigma'\sigma } g(E)\nonumber\\
g(E) & = & \ln\left\{\frac{ 1 + \exp\left[(\mu_l-E)/k_B T\right]}{
1 + \exp\left[(\mu_r-E)/k_B T\right]}\right\}.
\end{eqnarray}
The applied bias $V=(\mu_l-\mu_r)/e$ is determined by the difference in quasi-Fermi levels of the contacts.

We would like to point out that we conduct a genuine non--equilibrium study whereby the quasi--Fermi level positions are associated with the contacts.  Self--consistency then leads to an effective, in general, spin--dependent one--particle potential.  Thus one is not confronted with the question where to place the Fermi level in the GaMnAs layers.   Essential to confinement effects  is the existence of states near the top of the valence band edge of GaMnAs which have a coherence length of at least the layer thickness.   Highly localized states,  whether separated from or attached to the top valence band edge, will not be very sensitive  to
finite layer width.
While in the bulk and thermal equilibrium the itinerant hole exchange model firmly relates hole density to T$_c$ and the Fermi energy, in a non-equilibrium tunneling situation this is different.   The key question is whether tunneling can induce a net hole spin polarization or not.  As is shown below, we find that this depends on structural properties as well as on the applied bias.

\section{\label{sec:results} Results}

We start with a symmetric double--barrier structure containing a  single GaMnAs  quantum well
and investigate the role of resonant hole tunneling on the magnetic state of the device.
For the simulation we use generic parameters for GaMnAs and GaAs:
 $m^* = 0.4\:m_0$, $\epsilon_r = 12.9$, $V_\mathrm{bar} = 400$ meV, $\mu_l =\mu_r= 80$ meV, $d = 20 \AA$,
$w = 25 \AA$, $n_\mathrm{imp} = 1\times10^{20} $cm$^{-3}$,
$J_{\mathrm{pd}} = 0.15$ eV nm $^3$ \cite{Lee2000:PRB}, $T = 4.2$~K,
where $m_0$ denotes the free electron mass,  $\epsilon_r$ is the
relative permittivity, $V_\mathrm{bar}$ is the bare barrier height
of AlGaAs relative to GaAs, $d$ and $w$, respectively, are the
barrier and quantum well width.
The thermal equilibrium position of the Fermi energies $\mu_l =\mu_r$ was deliberately chosen close to the first resonance to promote ferromagnetic
ordering in the well region at zero bias.
The background charge $N_a$ is
assumed to be only about 10\% of the Mn doping $n_\mathrm{imp}$
since GaMnAs is a heavily compensated system, most likely  due to Mn interstitial
or antisite defects.\cite{VanEsch1997:PRB,DasSarma2003:PRB}
The hole densities in the quantum well can be adjusted by the Mn doping level and the quasi-Fermi levels in the contacts.
As can be seen from Eq.~(\ref{eq:delta1}) the exchange splitting increases with the hole density in the case of a steady
particle spin polarization. The value of the exchange coupling constant varies in literature to some extend
$J_{\mathrm{pd}}\approx 0.04 - 0.16$ eV nm. Since we use an optimistic value for $J_{\mathrm{pd}}$, we assume only moderate Mn$_\mathrm{Ga}$ doping in the well. Higher Mn$_\mathrm{Ga}$ densities and smaller values of $J_\mathrm{pd}$ will give  very similar results.

Disorder effects in the GaMnAs layers are modeled by performing a configurational average over structures with randomly
selected onsite and hopping matrix elements of the tight-binding
Hamiltonian in the Mn doped region. For each specific Hamiltonian the transport problem (I-V curve) is solved self--consistently.  The
final result is obtained by averaging over all configurations.   Typically 300 configurations are used for one I-V curve.
For the numerical simulation we assume a fixed 5\% Mn concentration in the well and model substitutional disorder.  If a Mn ion is present at a given  lattice site
in the well the onsite energy is shifted according to a Gaussian distribution
around  a mean onsite energy--shift of 40 meV and a standard deviation of 20 meV, which are reasonable
values according to experimental results which indicate either an impurity band slightly above the valence band edge or a defect--induced  valence band tail.\cite{Ohya2011:NP,Richardella2010:S,Masek2010:PRL}
The nearest--neighbor hopping matrix elements for such a site are sampled according to a Gaussian between  5\% and 25\% standard deviation
($\sigma_t$) of its bulk value $t$. This model for substitutional disorder leads to a hybridization of quantum confined hole states, associated with bulk like valence band states, and localized defect states arising from Mn$_{Ga}$ sites.   The degree of hybridization depends on
layer thickness since it controls the position of the quantized heavy hole band relative to the energy of the localized Mn acceptor levels.    This hybridization and the experimentally found Mn acceptor radius of about 2 nm calls for rather thin GaMnAs layers to ensure quantization effects in transport.\cite{Ohya2011:NP}

\begin{figure}[!t]
\centering
\includegraphics[width=0.95\linewidth]{Tdis.eps}
\caption{(Color online) Spin-dependent transmission probability of the double barrier structure at zero bias with
and without disorder ($\sigma_t = 5 \%$).}
\label{fig:T}
\end{figure}

The calculated spin-filtering effect via distinct tunneling probabilities for
spin-up and spin-down holes arising  from the exchange term is
displayed in Fig.~\ref{fig:T} in which  the transmission
probability at zero bias is plotted versus energy of incidence $E$.    This figure also gives a qualitative account of the density of states in the GaMnAs well region discussed above.
For an idealized GaMnAs layer which,  at the valence band edge, is modeled as a GaAs layer plus exchange term,  one obtains sharp spin doublets
which are exchange--split  by  about 25-30 meV (see dashed versus solid lines in Fig.~\ref{fig:T}).
The state of zero spin polarization of holes represents  an unstable
equilibrium since, below T$_c$, the slightest perturbation in
spin--polarization drives the system into a partially ordered lower
energy state (spontaneous symmetry breaking) due to the exchange
interaction.  The latter, in turn,  accounts for different
effective barrier profiles for spin--up and spin--down holes.  It is
this nonlinear effect that can be utilized to control the hole spin
polarization and thus the favorable Mn spin orientation by
structural design and applied bias.  Placing the Fermi level near the first heavy--hole resonance
promotes this effect, similar to  the formation of Cooper pairs near the Fermi edge of an interacting electron gas.

Spin--selective tunneling into and out of the Mn doped wells, regardless of whether sequential or resonant, promotes hole spin polarization and, thus, alignment of the Mn spins as long as spin-depolarizing processes in the heterostructure are slow compared to the effective tunneling rates.  Furthermore, disorder which leads to spectral broadening of the resonances may suppress spin--selective tunneling.   Inspection of Fig.~\ref{fig:T} shows an asymmetric broadening and significant overlap of the
transmission peaks under substitutional disorder, modeled as discussed above, which is particularly pronounced for the first heavy--hole resonance since it is most sensitive to potential fluctuations.  The asymmetric (``anti--bonding") shift towards higher energies is due to  hybridization with
Mn acceptor levels below the conduction band edge.   The latter do not contribute to resonant transport.  Even at the moderate disorder for the effective hopping matrix element of 5 percent, a significant
overlap in spin-up and spin--down resonance is obtained.  Increased disorder and/or spin--flip scattering will eventually wash out spin--selectivity in transmission and a destruction of ferromagnetic ordering under bias  must be expected  since {\em unpolarized} holes are steadily fed into the GaMnAs regions.   Exchange splitting at zero bias for 5\% and 25\%, respectively,  is reduced  to 33~meV and 23~meV.

Clearly, our effective one--dimensional modeling of (substitutional)  disorder must be viewed as a limited estimate since it corresponds to a  cross--sectional average of  transport though
uncorrelated effective linear chains.  Correlations from disorder parallel to the heterointerface will play a role in the establishing of coherence and ferromagnetic order in real structures relative to the idealized
homogeneous mean--field model adopted here, since both ferromagnetic order and disorder effects are highly dependent upon spatial dimensionality.\cite{Kaxiras:2003, Ashcroft:1976}  Additional types of disorder from Mn clustering, Mn interstitials, etc. may be present in real structures.  The role of disorder in the formation of ferromagnetic order in diluted magnetic semiconductors has been explored theoretically and, remarkably, certain form of disorder has been predicted to promote ferromagnetic ordering.\cite{Lee2007:PRB, Berciu2002:PhysicaB}
In experiment, STM studies have given information on the nature of defects near the surface of GaMnAs samples.\cite{Burch2006:PRL,Richardella2010:S}

\begin{figure}[!t]
\centering
\includegraphics[width = 0.9\linewidth]{IVdis.eps}
\caption{(Color online) $IV$-characteristics of a magnetic double barrier structure due to heavy--hole associated bands with and
without disorder. The solid (dashed) lines refer to a voltage up (down)-sweep without disorder (black lines) and moderate disorder of $\sigma_t = 5 \%$ (blue lines). The $IV$-curve is flattened at higher defect concentrations as indicated by the red dotted
line  $\sigma_t = 25 \%$ assuming a voltage up-sweep.
As shown in the inset in the voltage range of $V = 0.07 - 0.09$ V for the case of a high-quality sample no steady state is
reached, suggesting the occurrence of dynamic effects.}
\label{fig:IVgreen}
\end{figure}

\begin{figure}[!t]
\centering
\includegraphics[width= 0.9\linewidth]{Deltadis.eps}
\caption{(Color online) The configuration averaged spin splitting $|\Delta|$ in the quantum well
 as a function of the applied bias with and without disorder.}
\label{fig:Delta}
\end{figure}

\begin{figure}[!t]
\centering
\includegraphics[width=0.9\linewidth]{Pjdis.eps}
\caption{(Color online) Averaged current spin polarization $|P_j|$ versus
applied bias $V$ with and without disorder.}
\label{fig:Pjdis}
\end{figure}

The current-voltage I--V characteristics, plotted in
Fig.~\ref{fig:IVgreen}, reveals the typical hysteretic behavior of
resonant tunneling diodes for an up- and down-sweep
of the applied bias. This well known intrinsic bistability
occurs due to different charging of the well depending on the
bias--sweep direction.   Since our model ignores contributions from the light--hole band, associated resonances
are missing in the plot.  The latter are important due to in--plane non--parabolicity effects in narrow layers,  however, low--lying resonances associated with heavy and  light holes generally are  clearly
separated in energy.  For the present structure a light--hole--band resonance would be expected between the first two heavy--hole--associated resonances, thus strongly reducing the peak--to valley ratio and  contributing spin $\pm 1/2$ holes to the Mn--doped layers.   It should be observed that only single resonance peaks are observed in the I--V characteristics in spite of spin doubles in the (zero--bias) transmission spectra.  Furthermore, the drop in
current beyond the first heavy--hole peak value (see insert in Fig.~\ref{fig:IVgreen}), unlike in ballistic models for nonmagnetic tunneling structures (see second peak), is gradual even in the absence of disorder.  This broadening of the resonance can be attributed to ferromagnetic ordering away from the first resonance peak which tends to widen the bias window for meeting the resonance condition.

Disorder effects  diminish the peak--to valley ratio  but
regions of negative differential resistance are maintained for weak  disorder.   Since experiments have not shown negative differential conductivity in such a structure we have increasing disorder and find its disappearance at relatively high
hopping disorder of about $\sigma_t = 25$~\% (see Fig.~\ref{fig:IVgreen}).   This indicates that defects other than Mn acceptors are present in real samples.
Further numerical studies regarding this issue will be published elsewhere.\cite{Ertler2011:JCE}

In Fig.~\ref{fig:Delta} the  average
exchange band spin splitting $|\Delta|$ in the quantum well, characterizing its magnetic state,  is plotted versus applied bias.  It shows that ferromagnetism can be controlled by the applied bias in this
structure  near the first current peak, remarkably, even when disorder is sufficiently strong to suppress negative differential conductivity.
At zero bias ferromagnetic ordering is energetically preferred since the Fermi $\mu_l=\mu_r$ level is located close to the edge of the first heavy--hole subband.  As the bias is increased tunneling into the upper doublet state
becomes allowed from the emitter side reducing the net hole--spin polarization (in spite of increasing hole density) and the effective exchange field decreases to zero and both spin--up and spin--down subbands go into resonance.  Note that under moderate bias both emitter and collector contribute to the population of the well region.  As the bias increases resonant population from the emitter gets shut off and hole polarization is determined by the collector leading once more to a build-up of the exchange field for a bias regime between 0.08~V and 0.2~V, when finally the collector quasi-Fermi level drops below the hole subbands and the well region becomes almost depleted of holes.  For higher bias no further
spontaneous magnetization has been obtained within our self--consistency loop.  The overall feature of the bias dependence of the
exchange splitting thus somewhat resembles its behavior versus temperature, with ``$T=T_c$" corresponding to a bias of about 0.18~V.   It arises from the fact that it is the number of {\it spin--polarized} holes which determines the maximum spontaneous magnetization for given Mn$_Ga$ concentration.  A simple model for the dependence of the Curie temperature in resonant tunneling systems has been given by one of us before.\cite{Ertler2008:APL} The voltage-dependence of the Curie temperature under resonant tunneling has also been studied before.\cite{Ganguly2005:PRB}

The displayed build--up and
destruction of ferromagnetic order as a function of applied bias
can be further understood by the exchange interaction which is mediated by
spin--polarized holes.  In an ideal 2D particle system with parabolic dispersion there is no energy gain by magnetic ordering due to the constant density of states associated with each spin subband: energy gained by lowering one subband is exactly cancelled by raising the other.
However, here we deal with  a 3D heterostructure which
favors a spin ordered state when the quasi--Fermi level lies
near (within about half of the maximal exchange splitting)  the bottom of a well subband resonance.
If the temperature in the
contacts is sufficiently low, one subband after the other will go
through resonance.  Thus, when only the lower spin--subband is in
resonance holes in the magnetic well will tend to be be spin--polarized.
However, as bias is increased eventually the subband with opposite
spin orientation will also go into resonance thus reducing spin
polarization and magnetic ordering in the GaMnAs layer.
When, for a given bias,  the well region cannot be populated  (lack of hole density of states) or no energy gain can be drawn from ferromagnetic ordering,   loss of the latter
will result.

\begin{figure}[!t]
\centering
\includegraphics[width=0.9\linewidth]{ldos1.eps}
\caption{(Color online) Logarithmic local density of states (LDOS)
as a function of energy at the bias $V = 0.085$ V. The
self-consistent band profile is indicated by the solid line. The
spin-splitting of the quasi--bound states is clearly visible.}
\label{fig:ldos}
\end{figure}

Interestingly, in the voltage range of $V = 0.07 - 0.09$ V no steady
state solution can be found for the low disorder sample case. Instead the solution for the
magnetization is oscillating, as shown in Fig.~\ref{fig:Delta}, suggesting the occurrence of dynamic
effects. This behavior can be understood qualitatively as follows:
Figure~\ref{fig:ldos} shows a contour plot of the local density of
states, for an applied bias
$V=0.085$ V lying in the critical voltage range. The self--consistent band profile is indicated by the solid line.
For the emitter Fermi energy of
$\mu_l = 0.08$ eV only the two
ground state (potentially spin--split) subbands in the quantum well
participate in the tunneling transport.  At this bias condition and
hole spin polarization the lowest (spin--up) subband may be
populated by holes from the collector side, whereas the spin--down
level is almost empty since it cannot be reached elastically by
either emitter or collector. Since the (steady--state) band
splitting $\Delta$ is proportional to the spin polarization
$(n_\uparrow - n_\downarrow)$ the well magnetization increases with
spin polarization, pushing the spin--down level upwards in energy.
At some point holes can start to tunnel from the emitter side into
the spin--down level.  This in turn decreases the total spin
polarization  and, hence, effectively pushes the spin--down level
back  below the emitter's band edge. From there, the process starts
anew, leading to an oscillatory behavior in well magnetization,
tunneling current, and spin polarization.\cite{Ertler2010:APL}

\begin{figure}[!t]
\centering
\includegraphics[width=0.9\linewidth]{Pj.eps}
\caption{(Color online) Current spin polarization $P_j$ versus
applied bias $V$ taking into account spin flips at the
hetero-interfaces. The polarization is diminished for an increasing
spin flip probability $p$ becoming unpolarized for $p = 1/2$.}
\label{fig:pflip}
\end{figure}

Although the I-V curves in Fig.~\ref{fig:IVgreen} do not display spin-split resonance peaks,  but merely a broadening of the resonance,
the steady--state current at low bias is spin polarized as shown in Fig.~\ref{fig:Pjdis}.
As the bias is increased from zero, current spin polarization is reduced and reversed before it drops to zero through resonance.  Above resonance current spin polarization reemerges (due to the action of the collector)
and once more changes sign before dropping and remaining at zero in one-to-one agreement with the behavior of the exchange field.   Although resonance peaks in the I-V curve my be suppressed by disorder, see Fig.~\ref{fig:IVgreen},
the bias--dependence of spin polarization in the current may persist and may be observed in experiment as a bias--dependent spin valve.

In order to study qualitatively the influence of spin flip processes at the
hetero--interfaces on the total current spin polarization at the collector side, $P_j =
(j_{\uparrow\uparrow}+j_{\uparrow\downarrow}-j_{\downarrow\uparrow}-j_{\downarrow\downarrow})/j$
with $j = \sum_{\sigma\sigma'} j_{\sigma\sigma'}$, we introduce
off-diagonal hopping matrices $V_{i,\sigma\sigma'}$ in the
tight-binding Hamiltonian. In general for $N$ interfaces there are
$2^N$ different flip configurations.  For each of them a simulation
is performed and the results are finally averaged by weighting with
the probability for the occurrence of the configuration. In the case
of a double-barrier structure we have four hetero-interfaces, giving
$16$ configurations. However, flipping at the first barrier
interfaces is inefficient, since it does not change the total
current or spin polarization. Single flipping at the third or fourth
interface does also not modify the total current density but inverts
the spin polarization to $-P_j$. By introducing single spin flip
probabilities $p_i, (i=1,\ldots,N)$ at the interface $i$, the
probability of a flipping process at the second barrier is then
given by $p_{\mathrm{flip}} = p_3(1-p_4)+(1-p_3)p_4$. Hence, the
mean spin polarization results in
\begin{equation}
\langle P_j\rangle = P_j(1-2p_\mathrm{flip}).
\end{equation}
The bias-dependent current spin polarization for different spin flip
probabilities (assuming $p_3 = p_4 = p$) is plotted in
Fig.~\ref{fig:pflip}. The spin polarization decreases  for
increasing $p$ with $\langle P_j\rangle [p] = \langle
P_j\rangle[1-p]$ reaching its minimum $\langle P_j\rangle = 0$ for $p
= 1/2$.  From this analysis we conclude that our results will not be altered significantly when the spin--orbit interaction is taken into account in the analysis.

\begin{figure}[!t]
\centering
\includegraphics[width=0.95\linewidth]{IVqws1.eps}
\caption{IV-characteristics of a three-barrier
structure with two coupled quantum wells made of GaMnAs. At the
current maxima resonance conditions are fulfilled, i.e., the
quasi--bound states of the adjacent wells become energetically aligned.
The inset shows the local density of states at the applied bias $V =
0.03$ corresponding to the first current maxima. } \label{fig:IVqws}
\end{figure}

\begin{figure}[!t]
\centering
\includegraphics[width=0.9\linewidth]{Dqws.eps}
\caption{(Color online) Maximum exchange splitting
$\Delta_{\mathrm{max}}$ in the first (solid) and second well (dashed
line) as a function of the applied bias.} \label{fig:Dqws}
\end{figure}

While spin--selective hole tunneling may allow electric control of ferromagnetic order, tunneling spectroscopy, in turn, provides a sensitive experimental tool  for exploring the electronic structure of
mesoscopic semiconductor systems.\cite{Smoliner1996:SST}
Recently, tunneling spectroscopy experiments have been performed on thin layers of GaMnAs.\cite{Ohya2011:NP}   The authors have verified ferromagnetic ordering in their samples
 (with Mn concentration of typically $x\approx $5 to 15~$\%$ and layer thickness ranging from 4 to 20 nm)
and have measured their respective Curie temperature.  Their measurements indicate that Mn induced defect states remain separated from the GaAs--like valence band edge as evidenced by a pinning of the Fermi level.   Furthermore, they find clear signatures of quantization effects in the transmission spectra of their samples and report an absence of spin-splitting in the resonances which they can fit to a GaAs-like k.p model, including light-hole states.  We believe that these experimental findings compare favorably with the general features of our results.   Moreover, we have provided an explanation for the observed absence of  ferromagnetic ordering near resonance in spite of ferromagnetic behavior of the sample at zero bias.
It would be interesting to perform spin--sensitive tunneling spectroscopy on these samples since, according to Fig.~\ref{fig:pflip},  such a measurement gives more detailed information about the bias dependence of ferromagnetic ordering than the I-V curve and its derivatives.   This can test the prediction that ferromagnetic order which can be achieved at zero bias is destroyed near resonance would be verified, and that electric switching back and forth between the ferromagnetic and paramagnetic state can be achieved.

We now explore feasibility of selective magnetization switching
among several magnetic layers of high structural quality.  We investigate a three-barrier
structure with two adjacent GaMnAs quantum wells, choosing an
asymmetric structure with the second well being thinner than the
first one ($w_1 = 25 \AA$, $w_2 = 20\AA$).  All other parameters are
as in the previous structure. Quantum confinement gives rise to a
higher ground state energy in the second quantum well at zero bias.
The resonant alignment of the ground state subbands of the two wells
is therefore achieved at a finite voltage as shown in the inset of
Fig.~\ref{fig:IVqws}, corresponding to the first maximum  in the
current-voltage characteristics at about $V=0.02$ V which is plotted
in Fig.~\ref{fig:IVqws}. The second current maximum result from the
resonance of the first excited state subbands of both wells. Next to
possible exchange splitting the finite separating barriers cause the
energy levels in the two quantum wells to further split into bonding
and antibonding subband states. However, for our structure the
middle barrier is too thick and the natural energy broadening of the
quasi--bound states is too large for resolving this additional
splitting in the local density of states.

Having two coupled quantum wells allows one to realize several
magnetic configurations. The maximum (steady--state) exchange
splitting of the two wells as a function of the applied bias is
plotted in Fig.~\ref{fig:Dqws}, revealing three different regions.
For low voltages both wells are magnetized due to the build--up of
spin polarization in the wells due to resonance of the ground state
subband levels with populated reservoir states.  Exchange causes a
relative shift in the  density of states for spin--up and spin--down
holes which, in turn, stabilizes ferromagnetism in both layers. When
the second well goes off resonance at around  $V > 0.03$ V the
accumulated spin polarization in the second well is preserved, since
for voltages up to $V \approx 0.1$ V the collector Fermi energy
$\mu_r$ is still higher than the bottom of its ground state subbands
thus maintaining spin polarization. For voltages in the interval
$0.12$ V$ < V < 0.33$ V the first well remains magnetic, whereas the
second well becomes nonmagnetic, since the ground state subbands are
no longer filled from the collector side.
 At sufficiently high
bias,   $V > 0.33$ V,  also the first well becomes demagnetized
since holes can no longer resonantly populate its two lowest (now
degenerate) subbands from either emitter or collector thus resulting
in a completely nonmagnetic structure.

Several simplifying assumptions have been made in the present
analysis which should, just as well as experimental aspects,  be
discussed. The present model is based on an effective-mass-like
two--band approach for the heavy holes in the structure.   This
approximation should at least  qualitatively be correct since the
applied bias is kept below typically  0.2~V and most of the phenomena
discussed here occur at lower bias.   Thus it can be expected, that
this model describes  effects qualitatively correct.    We are
currently working on more realistic tight--binding formulations
using a significantly increased number of basis states in
conjunction with density functional plus dynamic mean-field models
to arrive at a more detailed and realistic electronic
structure.\cite{Chioncel2011:PRB}
 Impurity scattering effects  have been accounted for on a phenomenological level within the TB model.
Our ballistic model neglects
electron--phonon scattering within the heterostructure altogether
and the electron--electron interaction is described within
mean--field theory.  In thin structures, such as the ones studied
here where effective tunneling rates are higher than carrier--phonon
scattering rates and optical phonon transitions are suppressed
energetically the former assumption should be rather well fulfilled
and not alter significantly subband population within the
heterostructure.   Electron--electron scattering may play role,
however, as long as it does not involve spin--flip processes should
not influence our basic conclusions much.

 Clearly the effects studied here require low temperatures,
for one to favor ferromagnetic ordering and, secondly, to preserve
strong hole--spin polarization in the carrier injection process.  It
is well known that, at least at low temperatures, structural
imperfections are the main source for reduction of nonlinear
effects, such as the peak--to--valley--ratio in the IV
curve.\cite{Poetz1989:SM, Poetz1989:SSE, Chevoir1990:SS,
Mizuta:1995} It is most likely the difficulty in clean sample
preparation which has slowed experimental progress on thin--layer
semimagnetic semiconductor heterostructures.   High quality doping
profiles and high quality interfaces must be achieved within one
growth process.\cite{Ohya2007:PRB,Likovich2009:PRB,Ohya2010:APL}
Growth of good quality DMS layers needs low temperature molecular
beam epitaxy which, however,  adversely  affects interface quality.
Usually thin GaAs spacer layers are inserted to smooth the
surfaces.\cite{Ohya2007:PRB,Ohya2010:APL}  Furthermore, GaMnAs
layers must be thick enough to support ferromagnetism.
Qualitatively, all structural imperfections lead to broadening of
resonances.  Once the latter becomes comparable to the (theoretical)
maximum  of the exchange energy induced spin--splitting,
spin--selective tunneling and, hence, tunneling--induced control of
magnetic ordering may be suppressed.   Even in the presence
of disorder, as long as it does not go hand in hand with strong
spin--flip processes, achieving bias--control of hole--spin polarization in
the GaMnAs layers should allow one to manipulate magnetization.

\section{Conclusions and Outlook}\label{sec:sum}

In summary, we have used a ballistic steady--state transport model
to investigate bias--induced magnetic multi--stability in
AlGaAs/MnGaAs quantum well structures. Ferromagnetic exchange, as
well as the hole Coulomb interaction are treated within
self--consistent mean--field approximation.  Substitutional disorder is treated phenomenologically within a tight--binding model.

Our studies indicate  that in these systems ferromagnetic ordering
can be controlled selectively by an externally applied bias.  The
underlying mechanism is found in spin--selective tunneling due to
the anti--ferromagnetic exchange interaction between itinerant heavy
holes and localized Mn d--electrons. In structurally  suitably
designed heterostructures the applied electric bias allows control
of the ferromagnetic state, as well as electric and  spin current
density.

 In the simplest structural case in form of a double barrier structure containing a GaMnAs well, we predict that ferromagnetic ordering in the well, when present at zero bias, is lost under bias near the first  heavy-hole resonance, allowing a switching back and forth between the magnetic and nonmagnetic state in the well.    In GaMnAs multi-well structures we predict that the loss of ferromagnetic order can be engineered structurally to occur at different applied bias for the individual layers.

Within our model we are able to provide a possible explanation for the absence of exchange splitting near resonances,
as observed in recent tunneling spectroscopy measurements on thin GaMnAs layers.\cite{Ohya2011:NP}   We generally predict that ferromagnetic order which may be achieved in
GaMnAs quantum well layers under zero bias tends to be destroyed under resonance condition since the well region then is swept by unpolarized holes.   Under favorable conditions detailed in the main text,
ferromagnetic order may be reestablished above resonance.  Such a behavior should be revealed experimentally by  spin--sensitive tunneling spectroscopy.\cite{Ando2005:APL}

In previous work based on a complementary time--dependent sequential tunneling
model including intra--well scattering we have predicted that,  under specific bias conditions,  the interplay of transport and
magnetic properties can result in robust self-sustained charge and
magnetization oscillations.\cite{Ertler2010:APL}   The present model, albeit based on the resonant--tunneling picture,
backs the possibility of such phenomena by predicting bias regions in which no steady--state solution for the current exists.

Disorder and spin--flip effects have been modeled on a phenomenological level.  We find that disorder due to Mn taking a Ga site alone should not  suffice to destroy spin--selective tunneling, nor should spin flips at a rate expected in these structures, for example from the spin--orbit interaction, significantly suppress spin polarization of the steady--state current.  As expected, our analysis does show that disorder and spin flip processes do reduce  the total average current spin polarization, however, not as efficiently as the resonance peaks in the I--V curve.

We conclude that multi--well structures containing GaMnAs layers
may allow one to realize various bias-dependent magnetic configurations.
While the current investigation of bias induced effects considers
only bias in longitudinal direction, i.e., a 2--terminal
configuration, applying additional gates in transverse direction
(multi--terminal configuration)  should allow for an additional
control knob to move spin--split subbands in and out of resonance with the contact states and/or to inject spin--polarized holes into the Mn--doped regions.  Such a structure has been studied in a
recent experiment.\cite{Ohya2010:APL}

\section{Acknowledgment}

This work has been supported by the FWF project P21289-N16.

redpajama_set_name: RedPajamaArXiv


Wahl aus: Fries, Coleslaw, Corn on the cob, Coleslaw, Corn on the cob, Fries, Pepsi Max und mehr.
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Wahl aus: Fries, Coleslaw, Corn on the cob, Coleslaw, Corn on the cob, Fries, Ketchup und mehr.
Wahl aus: 4 chocolate chip cookies, 4 double chocolate chip cookies, 6 Hot Wings, 6 Crispy Strips und mehr.
Wahl aus: Cheese, Fries, Coleslaw, Corn on the cob, Coleslaw, Corn on the cob, Fries und mehr.
Wahl aus: Fries, Coleslaw, Corn on the cob, Coleslaw, Fries, Corn on the cob, Pepsi und mehr.
Wahl aus: Fries, Coleslaw, Corn on the cob, Pepsi, Pepsi Max, Sisi, 7UP, Earth water und mehr.
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Wahl aus: Fries, Chocolate chip cookie, Double chocolate chip cookie, 1 Original Recipe chicken und mehr.
Wahl aus: Cheese, Fries, Corn on the cob, Coleslaw, Pepsi, Pepsi Max, Sisi, 7UP und mehr.
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Wahl aus: Cheese, Fries, Chocolate chip cookie, Double chocolate chip cookie, 1 Original Recipe chicken piece und mehr.
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Wahl aus: Fries, Coleslaw, Corn on the cob, Chocolate chip cookie, Double chocolate chip cookie und mehr.
Wahl aus: Cheese, Chocolate chip cookie, Double chocolate chip cookie, 1 Original Recipe chicken piece und mehr.
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Wahl aus: 1 small popcorn chicken, 1 crispy burger, 2 Crispy Strips, 1 drumstick, Fries und mehr.


This is the seventeenth SS. To understand this SS the students are expected to have working knowledge up to SS 16. You can confirm their knowledge by taking them through the Level Selector Test.
This exercise comprises of 5 categories. Each category consists of a number of exercises.
Noun + Preposition phrase (pp) i.e. pp modifies the noun.
Example: The boy with the red shirt, the girl from Chandigarh. This use of pp is seen in the subject and object columns of all the tables.
5. I don't know how to answer your questions. I can't think ….
7. The number of people without jobs fell last month. Last month there was a fall….
Fill in the blank with one of the following options +the appropriate preposition.
· There has been a ……….. our system. We're trying to find a ……….. it. Do you have any …….. what we can do?
· I think examining the ………. Code X and Code Y will give you your answers.
· Yes! You're right! How come we didn't think of this before?
· Good Morning, Sir! Our NGO works to educate underprivileged kids. We wish to add a new building to our school so that we can reach out to more children. We have already consulted an architect and have a ……. the building ready. We now have a …….. funds.
· How much money do you require?
· We estimate a ………. Rs 25 lakh.
· I'm sorry I can't afford such a large amount but I'll gladly write you a ……… 1 lakh.
· We are grateful for your contribution. Thank you!
Complete the following sentences by using one of the following nouns + a correct preposition.
1. On the wall there were some pictures and a _____ the world.
2. Thank you for the ________ your party next week.
3. Since she left home two years ago, she has had little ____ her family.
4. I can't open this door. Have you got a _ the other door?
5. The ____ the fire last night at the hotel is still unknown.
6. I wrote to Aashay last week, but I still haven't got a _____ my letter.
7. Devansh showed me some old _____ the city as it looked some hundred years ago.
8. Charvi has decided to give up her job. I don't know her ___________ doing this.
9. The two companies are completely independent. There is no _____ them.
10. It wasn't a bad accident. The ________ the car wasn't serious.
1. There are some differences in/between British and American English.
2. Everything can be explained. There is a reason in/for everything.
3. Money isn't the solution to/of every problem.
4. The advantage in/of having a car is that you don't have to rely on public transport.
6. Anika showed me a photograph of/with the house she lived in as a child.
7. What was Anu's reaction to/about the news?
8. Kartik and I used to be good friends. Sadly, I don't have much contact with/between him any more.
9. There has been a sharp rise in/on the cost of living in the last three years.
10. The company has rejected the workers' demand for /of a raise in/of pay.
Example: afraid of, happy with etc. Table 3 is exclusively made for this purpose.
Complete the sentence using one of the following adjectives + the correct preposition. Some of the options need not to be used (extra to confuse).
1. We're all ____ going on holiday next week.
2. I was surprised when I met her the first time. She was ___ what I had expected.
3. Thank you for all your help. You have been very ____me.
4. I wouldn't like to be in her position. I feel ____her.
5. Mrs. Mehta is a very keen gardener. She is very _____ her garden.
6. Why do you always get so __________ little things.
7. The editor is the person _____ what appears in a newspaper.
8. I wasn't very ________ the service in the restaurant. We had to wait for ages before our food arrived.
9. Don't worry, I will look after you. There is nothing to be ____.
10. Mayur isn't happy at college. He says he is _________the course he is doing.
12. I had never seen so many people before. I was _____ the crowds.
13. I think she is arriving this evening but I'm not _______that.
1. I was delighted by/with the present you gave me.
2. It was a bit careless by/of you to leave the door unlocked when you went out.
3. Are you angry with/about what happened?
4. Are you still upset with/about what I said to you yesterday?
5. The teacher wasn't very satisfied by/with his progress.
6. We always have the same food every day. I am fed up with/of it.
7. We were a little disappointed in/with the hotel on our holiday.
8. He said he was sorry about/for the situation.
9. Sagar starts his new job next week. He is quite excited about/for it.
10. Tapan does not look very well. I am worried for/about him.
3. I don't like the sport very much. I am not very keen _____________.
4. We haven't got enough time. We're a bit short _______.
5. I'm not a very good tennis player. I'm not very good ___________.
6. Devika's husband is a Maharashtrian. Devika is married ___________.
7. I don't trust Manoj. I am suspicious _________.
Imagine you have moved to a new city . Tell us how you feel. Use preposition phrases to answer the questions given below.
NOTE: The material in the bracket is a pointer for teachers only. She may decide if she wants to give students the hints as to which preposition to use in each answer or not.
Complete the sentence on the right with the help of the adjective given in the bracket + an appropriate preposition.
3. He lost the match (narrow margin). I am (sorry) him.
4. He's a very talented boy. Yes. Even the headmaster is (impressed) him.
5. Do you think dogs are scary. Yes, I'm (terrified) them.
6. Did you know he was married? No, I wasn't (aware) that.
7. Can you lend me some cash? I'm a bit (short) money.
All the conversations make use of the wrong preposition after adjectives. identify them and correct the errors.
· Are you happy in the UK's decision to exit the EU?
· Not really. I'm really disappointed in it, in fact. I'm also apprehensive of the consequences of the decision.
· Me too! I'm also amazed with the number of people who voted without thinking the consequences through. I'm very angry on these mindless people. Did they think the referendum was a joke?
· Are you interested with our new volunteer program?
· I am. I would love to associate with you. Unfortunately, I don't have the time to spare currently.
However, I would love to contribute in some way and would request you to accept a donation cheque on Rs4000.
· Thank you. That's very kind for you.
· Are you aware on the implications in your decision?
· Yes, I am aware that the road ahead will be full with difficulties but I think I am capable for overcoming them.
· That's good. I too believe that you will succeed because you really are good in what you do and interested with what you are doing. Also your product is different to the ones the market currently offers.
· Exactly! I have always been keen for bringing something new to the table and being responsible about bringing innovation to the company.
· Are you happy with the UK's decision to exit the EU?
· Not really. I'm really disappointed with it, in fact. I'm also apprehensive about the consequences of the decision.
· Me too! I'm also amazed by the number of people who voted without thinking the consequences through. I'm very angry at these mindless people. Did they think the referendum was a joke?
· Are you interested in our new volunteer program?
· I have, and I would love to associate with you. Unfortunately, I don't have the time to spare currently.
· However, I would love to contribute in some way and would request you to accept a donation cheque for Rs 4000.
· Thank you. That's very kind of you.
· Are you aware of the implications of your decision?
· Yes, I am aware that the road ahead will be full of difficulties but I think I am capable of overcoming them.
· That's good. I too believe that you will succeed because you really are good at what you do. and interested in what you are doing. Also your product is different from the ones the market currently offers.
· Exactly! I have always been keen on bringing something new to the table and being responsible for bringing innovation to the company.
Write sentences about yourself. Use the words in the brackets.
1 (interested) I'm interested in sport.
This is covered in table 2.
Complete the following sentences by choosing the correct alternative from the box given below.
Example: look at, find out, start with etc. Table 4 contains example of this.
Fill in the blanks with one of the following verbs ( in the correct form) + the correct preposition.
1. A man escaped from prison. The police are __________ him.
2. We're still ______ a reply to our letter. We still have not heard anything.
4. Kavya is unemployed. She has ________ many jobs but she hasn't had any luck.
6. Sushruta's car is very old. Still it is in good condition. She _______it well.
8. I look stupid in this haircut. Everybody will _____me.
9. I don't understand this story. Can you ______it ______ me.
11. We've been _________the party. Unfortunately we cannot go.
12. Please _____ me! I've got something important to tell you.
13. Don't ________stones___the birds. It's cruel.
14. If you don't want to eat the sandwich, ________it _______the dogs. They will eat it.
15. Tapan and Yashada had an argument and now they are not ___________each other.
16. I __________ Aashna last week. She hasn't replied to my letter yet.
1. His parents don't ___________ his choice.
2. Did you _______the tickets?
3. The poor boy was _______ something he didn't do.
5. Things are very cheap there. You can ________very little money.
6. I ________ Alark ________ passing his driving test.
7. You were very rude to Reva. You should __________ her.
8. Kartik _______ on accompanying me home at night. He felt it was unsafe for me to travel alone.
9. What has ________ Jasmine? She doesn't seem to look alright?
10. The drunk man _____his car ___ wall.
11. It's a very long novel. Its ____________four parts.
12. I don't _______ghosts. I think they're a myth.
13. Awanti gave me an empty bucket. She asked me to _______it _____ water.
14. Don't try and do too many things at once. __________one thing at a time.
15. The police ____________nabbing the culprit.
1. I've never ______ Dhanush. Who is he?
2. I haven't ________ Shivani in a long time.
4. I live in a very small town in rural Rajasthan. You have probably never _________it.
1. You look serious. What are you ___________.
2. He's very selfish. He only ________ himself.
3. We are ________ going out for a meal this evening. Would you like to come?
4. Naira is very homesick. She is always _______ her family back home.
5. I don't know what to get Yash for his birthday. Have you ______something special?
6. I don't _______much___ coffee. It's like water.
7. I like to have time to make decisions. I prefer ______things carefully.
1. He was very selfish. He didn't ________ others.
2. Are you hungry? Would you ___________something to eat.
3. Please let me borrow your camera. I promise I'll take good ____________it.
4. I want to have a good holiday. I don't _______the cost.
D. Complete the sentences using 'look for' and 'look after'. Use the correct form of look.
1. Aishwarya is __________ a job. I hope she finds one.
3. I'm ___________ Yashvi. Have you seen her?
4. A babysitter ________ people's children.
Complete the second sentence so that it means the same as the first.
1. She said I was selfish. She accused me…………………….
2. The misunderstanding was my fault. I apologized. I apologized……………..
3. There are 11 players in a football team. A football team consists………..
4. She eats only salads and fruits. She lives…………………………….
5. Do you think the economic crisis is the fault of the government? Do you blame the government……?
6. I think the increase in violent crime is because of television. I blame the increase in……..
Choose the correct alternative to complete the sentences below.
1. Shamika and Sagar are touring Himachal right now. Currently they are in Naggar. Tomorrow they leave for/to Shimla.
2. I don't want to go out yet. I am waiting for/since the post to arrive.
3. We discussed about/no preposition the problem in detail. We couldn't find a solution.
4. I don't want to talk on/about what happened. Let's forget it.
5. Atharva apologized to/no preposition Chinmay for the misunderstanding.
6. I explained the task to/for everybody.
7. She was so angry she threw a chair on/at him.
8. They invited only a few people in/to their wedding.
9. We warned our children of/for the dangers of playing in the street.
10. Mr. Mehta has been complaining of/about pain in his chest. He must visit the doctor.
11. Nandita is often unwell. She suffers with/from severe headaches.
13. She hasn't got a job. She depends on/off her parents for money.
14. A strange thing happened with/to me a few days ago.
15. There was an awful noise as the car crashed into/in the tree.
10. Mr. Mehtas has been complaining of/about pain in his chest. He must visit the doctor.
11. Nandita is often unwell. She suffers from/with severe headaches.
14. A strange thing happened to/with me a few days ago.
A. Fill in the blanks with preposition phrases.
I don't mind big cities but I prefer small towns. I prefer……..
I got all the information I needed from Zinnia. Zinnia provided…..
Use your own ideas to complete these sentences. Use preposition phrases.
Prepositional Phrases occurring anywhere in the sentence to give it a more nuanced meaning.
Example: After the match, we ate ice-cream. I play cricket every day before sunset. . This is seen in several places in Table 2, 3 and 4.
First complete the following sentences by choosing the correct alternative. Thereafter rewrite the sentences by shifting the part of the sentence with the second preposition phrase to the front.
1. The busy city of/in Mumbai is the capital of/for Maharashtra.
2. They are citizens of/ from Mauritius unlike/dislike me.
3. The ladies in/with that group are her best friends despite of/ in spite of the distance between them.
5. The decision taken by/with the people of/from UK is not wise according to/according with my sister.
7. Since/Until childhood her weight has been in/on the higher side.
2. Unlike me they are citizens of Mauritius.
3. In spite of the distance between them, the ladies in that group are her best friends.
4. For the next activity, the boy with the red specs is her partner.
5. By 12 o clock tomorrow, the astronaut from Russia will be on the moon.
6. According to my sister, the decision taken by the people of UK is not wise.
7. Just beside the store across the street, is the house with the red roof.
This category contains prepositions from all the previous 5 categories.
NOTE: Very basic. May be skipped if the teacher so wishes, but it is a good way to ensure that students are clear with the concept of Prepositional phrases.
A prepositional phrase is made by putting together a preposition with the object of that preposition. To identify a prepositional phrase in a sentence you need to find the preposition, then the object of that preposition. Then you just have to put two together and you will have the preposition phrase.
Example:" Gia ran towards the finish line."
The object of the preposition is "the finish line".
The prepositional phrase is "towards the finish line".
1. Harshika ran up the hill.
2. Nihaar was only allowed to play football after he finished his chores.
3. Dhruv hid his sister's toy above his wardrobe.
Underline the prepositional phrase in each sentence. Circle the preposition.
1. The confused foreign exchange student walked through the school halls.
2. My cousin Tanishk wore a bandage on his nose to cover the wound.
3. Our crazy dog escaped and wandered all around the neighbourhood.
4. Your little brother had surgery and must stay in the hospital.
5. Mr.Thakur had to drive through the large puddles.
6. Anvita came to visit from France.
7. We walked up the stairs.
8. My mom took a walk around the block.
9. I looked under my bed.
10. The girl looked behind the door for her friend.
11. Don't leave without your coat.
12. During lunch we had a basketball tournament.
13. The car travelled at a high speed.
14. For a fraction of the cost you can buy a watermelon.
15.The boy tried to finish the race at any cost.
Read each sentence. Identify the complete prepositional phrase. Circle your response.
1. Fighter-Truck jumped over a burning pile of cars.
2. Lugnut landed hard on the dirt track and made a big dust cloud.
3. King Crush was tied with Lugnut as they crossed the finish line.
4. King Crush's truck had a gold crown on the roof and it shined as he drove.
5. Destructor raced around the corner as he tried to catch King Crush.
6. Truckavore grabbed a small car with its claw and ate it.
7. When King Crush drove into the arena, all the kids cheered.
8. Sparks shot from Destructor's muffler when he hit the ramp.
9. Fighter-Truck drove through the blazing ring.
10. Lugnut crossed the finish line on two wheels.
11. Toxic smoke poured from Lugnut's exhaust pipe.
12. Destructor drove through a car pile.
13. King Crush jumped over twelve buses.
14. King Crush rolled over Fighter-Truck while he was parked.
15. Lugnut couldn't finish the race without getting more gasoline.
16. King Crush is famous for his power jumps.
17. Drivers face big risks each time they get behind the wheel.
18. Lugnut's driver was racing for the glory.
19. Fear was in the air as King Crush revved his engine.
20. King Crush was still the champ after the race.
21. Truckavore has a claw on his roof.
22. King Crush was damaged during the big crash.
23. The seats were lined with Truckavore's fans.
24. Lugnut was buried under the wreck.
25. Truckavore swung his claw at King Crush but he missed.
26. Fighter-Truck drove through the brick wall and finished the race.
I. Rewrite each of the sentences below, and add one prepositional phrase.
1. The funny clowns jumped.
4. Shaurya threw the ball.
This is an excellent way to encourage students to make pp s by themselves. Add a few more sentences here (both parts).
II. Rewrite each of the sentences below, and add two prepositional phrases.
2. The small monkey climbed a tree.
3. The store sold toys.
The funny clowns jumped into the small car/on the trampoline.
The horse ran across the meadow/after the pony.
They ate dinner at the table/in silence.
Shaurya threw the ball to first base/at me.
The monster walked into the house on the corner.
The small monkey with his banana climbed a tree in the jungle.
The store across the street sold toys to the customers.
Mariam and Sara sang a pretty song for the audience at the show.
Make sentences using the following prepositional phrases.
About the book, on Tuesday, by the river, without electricity, for 13 years, for a change, at least a day, under my guidance, in place of Yash, apart from Physics, because of the rains, in case of an emergency, in spite of the rains, underneath the pillow, throughout the year, except for Myra, among the children, within a year.
Complete the following sentence using preposition phrases. Pointers have been given to help you. Each pointer MUST be introduced in the sentence with the help of a preposition phrase. In order to make logically and sequentially correct sentences, you may use the pointers in an order different from the one in which they appear in the brackets. One example has been done for you.
I wrote a letter to my friend in the morning to thank him for my gift.
Aarya put up the painting on the wall of her room to beautify it.
I won a scholarship to study art at the University of Pennsylvania for one year.
I play music on my phone while walking in the park with my dog.
I asked for directions to the City Hall from the Town Council.
Donald Trump is running (gerund) for/with the post of/in President of/for America. He is from/of Queens in/at New York. He is from/for the Republican party and is contesting against/with Hillary Clinton of/in the Democratic Party.
Britain recently exited from/to the European Union by/for voting against/for the Brexit motion. The pro exit camp won by/through a slim margin of/with 3.8%. After/Since the Brexit vote, UK will have to negotiate terms and come to agreements on/for important economic, political and other policy matters with/by the other members of/beside the Union. Currently, the world is sceptical about/for the consequences with/of this decision.
Fill in the blanks using the preposition phrases given below. For sentences 3 to 7 also identify and underline the second preposition phrase in the sentence.
1. Did you see Divya ________?
2. She was ______with the police.
5. She stopped talking ________and started to laugh.
6. A huge cargo ship sank ______ of Kerala.
Complete the following sentences using appropriate prepositional phrases. Each question is followed by three suggested answers. Choose the most appropriate one.
1. ……………………….. Nia, they all seemed pretty cordial.
2. ……………………………., cancer is curable.
3. The train was late. ………………………., I managed to get to the meeting in time.
4. ……………………… the starter, I thought the meal was excellent.
5. What is the …………………….. you?
6. My car is parked …………………………… the post office.
7. He acted ……………………….. my instructions.
8. He is ………………………… me.
9. I called him ………………………….. my voice.
10. His words are …………………………… the facts.
1. Except for Nia, they all seemed pretty cordial.
2. To a great extent, cancer is curable.
3. The train was late. In spite of this I managed to get to the meeting in time.
4. Apart from the starter, I thought the meal was excellent.
5. What is the matter with you? 6. My car is parked in front of the post office.
7. He acted according to my instructions.
8. He is at enmity with me.
9. I called him at the top of my voice.
10. His words are at variance with the facts.
Complete the sentences with a suitable verb or adjective plus a preposition. Choose from the following words. There are 5 words you do not need to use.
1. You should ___________________(say sorry) your friend ________your behaviour.
2. Kriti is __________________her friend because she has a nicer dress.
3. This city is _________________its beautiful churches.
4. What is the ______________ your delay? Was there a traffic jam?
5. We are ______________money. We need to go to the bank.
7. I was really ______________ the film yesterday. It was nothing like I expected.
8. Before Anya married Aarav she had been _______________him for 3 years.
9. Nowadays many people _______________depression because of stressful life.
10. Luckily I ________________ passing the test. I am so happy!
11. I am ________________ your behaviour. I've had enough of it!
12. The bus was ______________ passengers, so I could hardly move.
13. The factory ____________ the employees _________ proper safety equipment.
14. He is ______________the most famous scientist of the century.
15. There is a great ________________this performance. All the tickets have been sold out.
16. He isn't ___________________doing this exercise. It is too difficult.
17. The police were ________________him. They thought he was the murderer.
18. They could hardly ____________(stop) the prisoner __________escaping.
19. I ____________(like better) tea _________coffee.
20. Let me ______________you____________your exam results.


I completed the kickstarter video and I am quite proud of myself for doing so because initially I hated doing the lip sync animation. I don't know how some people do it, because only having 1 minute and 12 seconds was a lot. However, once I actually watched it back I was really satisfied with the outcome, and look forward to trying it again in the future.
I watched a really straightforward tutorial for how to create the lip sync. Initially I was going to attempt to use shapes and morph the mouth using different keyframes but this proved both problematic for creating the mouth shapes that had teeth and it didn't look right.
So watching the tutorial you simply create the layers of different phonemes in illustrator, bring them into after effects and make each layer one key frame. Each keyframe pays after the other and then you just cut the comp down to the correct time.
Once you add the slider, expression and control (watch the video for how) you simply slide the slider until you get the appropriate phoneme and key it.
However, I noticed (prior to receiving Danny's proper character versions)that I had forgotten to make the layer 3D so there was no shadow from them and also they don't blink. Another issue is, I designed the characters in photoshop and thought I turned off the white background layer but apparently hadn't, leading me to key out the white background and subsequently removing the whites of their eyes. Whoops.
Danny did the concept art for this, (which you can see in the background and the tow main characters at the front).
BloopAnimation. (2013). After Effects: How To Build a Mouth Rig For Lip Syncing (2D animation). Available: https://www.youtube.com/watch?v=lanbndDl1lg. Last accessed 1st Jul 2017.
Okay… This took a while. It wouldn't have been complete except for Jennie helping me. When I last met in person with Danny we had discussed the poster being similar to Christopher Nolan's film posters because I felt they were simple yet really effective at capturing the tone of the film.
As you can see, they are fairly straightforward. A silhouette in the foreground and a dramatic scene in the background.
I took it upon myself to design the poster, and created this initially after a few hours.
Jennie very graciously offered to help me and I sent her a version after that were I had added some trees to try and make the scene more interesting and add a sense of scale. Mainly thinking that all that needed fixed was the characters hair.
^^This was Jennie's quick version to help illustrate her advice. The clouds were much better than my attempt (using difference clouds) and i could see there was a difference in scale. I also liked how she blended the grass on the hill.
So I had another go.
I ended up producing this quick sketch to try and emphasise the height of the hill, and bringing back the trees to add a sense on scale.
This version features the font I designed called "BluQ" after the name of Danny's business. The white lines on the poster are there to help me remember where the two character's eye lines should be. I tried to make their poses more dynamic with Ari reaching for his sword and Ryne reaching out to him in fear.
By this point Jennie was actively collaborating with me on making the comic and I had shown Danny some of the earlier versions and he was pretty excited about it. I sent this version to Jennie and she came up with this quick doodle that I thought was more atmospheric than my 3 hour construction. This was to get the shape down right before she added in the two characters.
After all this, Jennie obviously had to focus on her own work, so I used her design to create the final poster (see below). Without Jennie's help I definitely would not have been able to get to this standard of poster. I would have handed in the first one, but I am pleased with what the outcome is. Chatting about it afterwards it seems that the turning point was with the character design, as the curved shapes (which Mike talked about in Life Drawing) really took away to stiffness on the characters and made the poster a more dynamic piece of work. (Also pleased to say I did the hair myself).
I've been learning quite a bit about after effects the past few months and when Danny and I discussed creating the logo for, the then, Faolen Studios it came in handy.
Danny liked the idea of a jumping wolf design and so I created this.
I firstly drew the shape of the wolf jumping in Illustrator then went into after effects. I made a black background, added a layer with triangular particles flying out and then brought in the wolf as a new layer and changed the alpha settings.
Then when I was satisfied with how the particles looked in the wolf and that there were no gaps, I rendered out a frame as a .jpeg.
However, after thinking about it, Danny thought it was too detailed so I bumped up the particle size and got this.
Now Danny has created this logo, (not the finished version). Also trying to think of a new name for the company at the minute it is now Blu Q Studios.
I watched a few kickstart videos but I have to say it seems to be an oddity for webcomics and there weren't that many examples that I could find. That being said maybe I just wasn't looking in the right place.
Danny wasn't in today but he let me know beforehand so I had this presentation all ready and made sure I knew what research he'd done on competitors etc.
I found this article quite helpful in breaking down the steps of building an audience on a web comic, because in all honestly social media and online communities are things that I'm just not that familiar with, so this was essential for walking through it.
I'll just write down the four main steps but I'd definitely recommend going and reading the article in full. Thats the four main phases but in each phase it breaks it down further into the various steps and questions you should be asking when working out your own webcomic.
Peterson, J.R.. (2012). Build a Strong Online Presence for Artists in Four Phases. Available: https://www.indiemade.com/resource/build-strong-online-presence-artists-four-phases. Last accessed 25th Apr 2017.