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among the most interesting new classes of materials under intense investigation in spintronics@xcite are the so - called multiferroics which combine several ferroic orders like ferromagnetism , ferroelectricity , ferroelasticity etc.@xcite the compounds combining the electric and magnetic order@xcite have several potential applications like magnetic - field sensors and electric - write magnetic - read random - access memories.@xcite magnetic order and ferroelectricity have different origins@xcite and thus the materials exhibiting the magnetoelectric effect are few and the coupling between the magnetic and electric properties is weak .
an alternative route to achieve a strong coupling could be the growth of thin film heterostructures and several advances have been made towards the magnetic control of ferroelectricity@xcite and the electric control of thin film magnetism.@xcite    bismuth ferrite is probably the most studied representative of magnetoelectric materials .
bulk bifeo@xmath0 crystallizes in a perovskite - like pseudocubic structure instead of a ferrite one and is classified as a ferroelectric g - type antiferromagnet.@xcite several first - principles calculations have been carried out to study the properties of bulk bifeo@xmath0@xcite and we refer readers to ref . for an overview of the literature on this compounds . since the single - component crystals like bifeo@xmath0 present only a weak magnetoelectric effect ,
an alternative route to achieve a more strong effect has been proposed to be the growth of heterostructures where epitaxial strain can enhance the phenomenon.@xcite thus first - principles calculations of such heterostructures involving alternating layers of bifeo@xmath0 and various spacers can serve as a test - ground to study the behavior of electric and magnetic properties of films .
the study of the latter in the case of ultrathin epitaxial films is the aim of the present manuscript .    in a recent publication ( ref . )
we have presented extended first - principles calculations , employing the quantum - espresso@xcite ab - initio electronic structure method in conjunction with the generalized - gradient approximation ( gga ) in the perdew - burke - erzenhof formulation,@xcite on the electronic and magnetic properties of bifeo@xmath0 alloy as a function of the lattice constant in the case of the cubic perovskite structure ( see figure 1 in ref . ) . in ref .
we have extended this study to cover also the case of mn substation for fe .
all compounds under study in these two references exhibited significant magnetic properties with spin magnetic moments at the fe and mn sites of the order of 3 @xmath1 .
in the present contribution we expand these two studies using the same ab - initio method with grids of the same density in the * k*-space to cover also the case of ultrathin epitaxial films .
although these films are ideal cases and can not be , with few exceptions , be realized experimentally , they can serve as starting point to understand the interplay between the interface structure and the magnetic properties of bifeo@xmath0 films with other spacers . for completeness we took into account three different spacers to cover different cases of electronic properties at the interface : inp semiconductor , metallic v and ferromagnetic fe .
in section ii we present the structure of the multilayers and the results for the case of the inp spacer , in section iii the cases of fe and v metallic spacers and finally in section iv we present the main conclusions of our work .
along the [ 001 ] direction bifeo@xmath0 can be considered to consist of alternating layers of bio and feo@xmath2 as shown in fig .
the in - plane unit cell is a square of the same lattice constant as the cubic unit cell of the bulk bifeo@xmath0 .
inp crystallizes in the zincblende structure , similar to gaas , as most of the iii - v semiconductors , and has an experimental lattice constants of 5.87  . along the [ 001 ] direction
, the zincblende structure can be viewed as consisting of alternating pure in and pure p atomic layers as shown in fig .
[ fig2 ] . to fully describe the zincblende structure we have to consider , except the in and p atoms , also the occurrence of vacant sites ( voids )
; there are exactly two no - equivalent voids within the zincblende unit cell . as shown in fig .
[ fig2 ] along the [ 001 ] direction there are not two but four alternating non - equivalent atomic layers .
the difference between the a(b ) and c(d ) layers is that the in(p ) atoms have exchanged sites with the voids .
this exchange of atomic positions is important since it lead to four non - equivalent interfaces between inp and bifeo@xmath0 in our study .
finally we have to mention that the lattice constant of inp coincides with the bifeo@xmath0 lattice constant multiplied by the square root of two : @xmath3 .
thus as shown in fig .
[ fig1 ] the diagonal of the bifeo@xmath0 two - dimensional square unit cell can be assumed to be the side of the corresponding unit cell of the inp ( denoted with red color in the figure ) and thus epitaxial growth between inp and bifeo@xmath0 can be assumed .
( b ) possible terminations of the bifeo@xmath0 alloy along the [ 001 ] direction . with the red lines we denote the limits of the two - dimensional unit cell of inp ( see fig . [ fig2 ] ) which has a lattice constant : @xmath4 . ]    for the inp / bifeo@xmath0 multilayers we studied four different cases with respect to the relative position of the atoms at the interface between the two spacers . along the growth axis we took into account eight atomics layers which are repeated in the [ 001 ] direction .
initially we studied the structure ... feo@xmath2//in / p / in / p / bio / feo@xmath2/bio / feo@xmath2//in ... , and thus in the first case we have two non - equivalent interface in our structure : a p / bi and an in / fe ones .
a close examination of figs . [ fig1 ] and [ fig2 ] reveals that , in the case just mentioned : ( a ) with respect to the p / bi interface p atoms are situated in the diagonal connecting bi atoms ( compare ( a ) in fig .
[ fig1 ] with the d layer in fig .
[ fig2 ] ) , and ( 2 ) with respect to the in / fe interface in atoms are situated in the midpoint between fe nearest neighbors ( take into account a layer in fig . [ fig2 ] and combine it with the ( b ) in fig .
[ fig1 ] ) .
direction taking into account also the vacant sites .
the structure is built using four alternating pure atomic layers a , b , c and d. the difference between a(b ) and c(d ) is that the in(p ) atoms and the voids have exchanged sites . ]    in the second case under study in and p atoms have exchanged sites with respect to the first case under study and thus now we have along the [ 001 ] direction a ... feo@xmath2//p / in / p / in / bio / feo@xmath2/bio / feo@xmath2//p ... structure , _
i.e. _ the inequivalent interfaces are now in / bi and fe / p .
notice that as in the fe / in interface in case 1 , also in the p / fe interface , which occurs in case 2 , the p atoms at the interface are located in the midpoints between the fe atoms ( if we examine only the in - plane projection of the multilayer ) just above the oxygen atoms and this results to vanishing magnetism in case 2 under study as will be discussed later in the next subsection .
as we mentioned above the structure of inp along the [ 001 ] direction should be viewed as consisting of four atomic layers ( see fig . [ fig2 ] ) since voids play a crucial role in interfaces . if in the two previous cases 1 and 2 we exchange layer a(b ) with layer c(d ) in fig .
[ fig2 ] we get two new cases 3 and 4 with different arrangement of the atoms at the interface . in case 3(4 ) , the succession of the atomic layers is similar to case 1(2 ) .
when we compare case 1(2 ) with case 3(4 ) , we conclude that the p(in)/bi interfaces are similar since the p(in ) atoms are now situated at the other diagonal connecting the bi atoms .
critical is the other in(p)/feo@xmath2 interface since now in case 3(4 ) the in(p ) atoms are located just above the fe atoms while in case 1(2 ) they were located above the oxygen atoms at the midpoints between neighboring fe atoms .      in all cases under study
our results converged to the ferromagnetic solution independently of the initial conditions and initial arrangement of the spin moments . as in - plane lattice
constant we have chosen the @xmath5   @xmath6   ( 11.1 a.u . ) which is the experimental lattice constant of inp and moreover for the lattice constant of 4.153   bifeo@xmath0 exhibits very pronounced magnetic properties.@xcite as a result of the epitaxial growth along the [ 001 ] axis the lattice constant was 14.182   ( 26.8 a.u . ) .
spacer ( fe@xmath7 at the middle of the spacer and fe@xmath8 at the feo@xmath2 interface for all four cases under study ( see text for explanation ) .
positive dos corresponds to the majority spin ( spin - up ) electrons and negative dos to the minority spin ( spin - down ) electrons .
the fermi level has been assigned to the zero energy . ]    in fig .
[ fig3 ] we present the density of states ( dos ) of the fe d - orbitals for all four cases under study .
we denote as fe@xmath7 the fe atoms within the bifeo@xmath0 spacer and with fe@xmath8 the fe atoms located at the interface .
we have also to note here that for the multilayer structures under study , we have a complete lift of the degeneracy of the fe d - orbitals and we can not refer anymore to the double - degenerated @xmath9 and triple degenerated @xmath10 orbitals as in bulk bifeo@xmath0 . in case 2 where we have
a p / bi interface our calculations have converged to a non - magnetic solution .
the loss of magnetism in this case should be attributed to the reduced hybridization between the neighboring fe and p atoms at the interface .
the latter have as valence 3p electrons which are less extended in space with respect to the in 5p valence states and do not hybridize with the fe d - orbitals at the interface . in case i ,
the d - band is shifted to higher energy values for the spin - down electrons with respect to the spin - up electrons .
this is more easy to visualize for the fe@xmath8 atoms since their hybridization with the p - orbitals of in leads to more pronounced electronic properties ( smaller bandwidth with respect to the fe@xmath7 atoms and thus more intense picks ) .
the latter is also reflected on the spin magnetic moments presented in table [ table1 ] where the spin magnetic moments are considerable larger for fe@xmath8 with respect to fe@xmath7 .
.fe spin magnetic moments in @xmath1 within the bifeo@xmath0 spacer for the inp / bifeo@xmath0 epitaxial ultrathin multilayers for all four cases under study ( see text for explanation of different cases ) .
the bifeo@xmath0 spacer contains two inequivalent atoms : fe@xmath7 at the middle of the bifeo@xmath0 spacer and fe@xmath8 at the interface . [
cols="<,^,^,^,^,^,^,^,^,^,^,^,^ " , ]     similar is the situation for the fe spacer where for the two smaller lattice constants we could not even converge our calculations .
as shown in table [ table3 ] only for the largest value of the lattice constant we got significant values of the fe spin magnetic moments , which even for this case , are considerable smaller than the spin magnetic moments of fe atoms of the bifeo@xmath0 spacer ( @xmath110.2 @xmath1 for fe spacer compared to @xmath11 0.8 @xmath1 for bifeo@xmath0 spacer ) and are about one order of magnitude smaller than in bulk fe .
we have also included in table [ table3 ] the results for the interface structure of fig .
[ fig6 ] , denoted as `` case 5-ii '' where we have changed the positions of the v(fe ) atoms at the interface .
overall also in this case the magnetic properties of the spacer are not significant . only in the case of the fe / bifeo@xmath0 multilayer half the fe atoms at layer 1 ( located at the interface with feo@xmath2 ) present a significant spin magnetic moment of about 0.5 @xmath1 which is still much lower than the bulk fe value .
we expand our study on the magnetic properties bifeo@xmath0 presented in refs . and to the case of ultrathin epitaxial multilayers using the quantum - espresso first - principles electronic structure
method.@xcite we have studied several cases of these ultrathin epitaxial bifeo@xmath0 multilayers using different types of spacers covering a wide range of electronic materials : inp semiconductor , ferromagnetic fe and metallic v. irrespectively of the spacer the magnetic properties of the multilayers were found to seriously degrade due to the low - symmetry of the film and in some cases magnetism vanished completely .
thus ultrathin multilayers of bifeo@xmath0 are not suitable for spintronic applications
. more extended calculations covering more thick multilayers and including quantum molecular dynamics are needed in the future to determine in more detail the properties of the interfaces of bifeo@xmath0 with other alloys .
y. h. chu , l. w. martin , m. b. holcomb , m. gajek , s .- j .
han , q. he , n. balke , c .- h .
yang , d. lee , w. hu , q. zhan , p .-
yang , a. fraile - rodriguez , a. scholl , s. x. wang , and r. ramesh , _ nature materials _ 7 , 478 ( 2008 ) .
preliminary first - principles calculations on the magnetic behavior of ultra - thin epitaxial multilayers between the bifeo@xmath0 magnetoelectric compound and various types of spacers are presented . as spacer we have considered i ) inp semiconductor , ii ) fe which is a ferromagnet , and iii ) metallic v. in all cases under study the growth axis of the multilayer was the [ 001 ] . 
 our results indicate that the magnetic properties are seriously downgraded for the ultrathin bifeo@xmath0 multilayers independent of the nature of the spacer and in some cases under study magnetism even vanishes . 
 more extensive calculations are needed to establish a more clear view of the physical properties of the interfaces involving the bifeo@xmath0 compound . 
 the present manuscript completes the study presented in two recent research articles [ k. koumpouras and i. galanakis , _ j. magn 
 . magn . 
 mater . 
 _ 323 , 2328 ( 2011 ) ; _ ibid _ , _ j. spintron . 
 magn . 
 nanomater . 
 _ 1 , in press ( 2012 ) ] . 
 + * keywords : * electronic structure calculations , magnetism , multiferroics , dft , ferrites