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modern technology uses extensively ferroic materials i.e . having a spontaneous and permanent order parameter of one kind or another with fairly exotic properties .
for example , commodity data - storage devices exploit ferromagnets with giant magnetoresistance in magnetic random - access memories , in a continued push toward increased information density and reduced dimensions and writing energy . besides their traditional use in sensors and actuators , ferroelectrics with their permanent and switchable electrical polarization are the building block of non - volatile , high speed , random - access memories which promise performances superior to semiconductor flash memories .    while their existence has been known since the 1960s , multiferroics , i.e. materials where polarization p and magnetization m coexist @xcite , have enjoyed a renaissance in recent years , because of great improvements in growth techniques and new theoretical approaches
. the coexistence of several order parameters and their mutual coupling may open the way to new device concepts , including the electrical addressing of magnetic memories without magnetic fields and their generating currents ; the creation of multi - layer multi - state logical devices , exploiting combinations of polarization and magnetization ; and magnetoelectric sensors .
however , most of the current multiferroics lack sufficiently strong polarization or magnetization , or sufficient magnetoelectric coupling , or the correct kind of magnetic order ( ferromagnets are desired , but antiferromagnets are much more common ) .    some of the difficulties of single - phase multiferroics are bypassed by `` metamultiferroics '' built of multilayer heterostructures of ferromagnets and ferroelectrics @xcite , as for example in multiferroic tunnel junctions ( mftj ) , where ferromagnetic electrodes are separated by a ferroelectric insulating barrier .
the resistance against tunneling across the junction depends on the relative orientation of magnetization of the two electrodes ( magnetoresistance ) and on the direction of ferroelectric polarization of the insulating layer ( electroresistance ) .
this enables in principle a 4-level switchable resistance using external electric and magnetic fields .
of course , a further magnetic degree of freedom in the insulating - barrier material could potentially duplicate the number of states , and any chance of locally tuning the magnetization would add further design leeway . following this line of thought , in this paper we report an _ ab initio _ investigation strongly suggesting that pbtio@xmath0 ( pto ) doped with v ( v : pto ) is a ferromagnetic small - gap insulator , hence a proper multiferroic .
this is particularly interesting in view of the giant electroresistance effect predicted in tunnel junctions with pto as ferroelectric tunnel layer @xcite .
here we report the first principles prediction of a multiferroic state of lead titanate doped with magnetic vanadium .
pto is a well - known tetragonal perovskite with a high spontaneous polarization ( 86 @xmath2c/@xmath3 ) of displacive origin .
pbvo@xmath0 also happens to be tetragonal , and with an even higher spontaneous polarization ( 152 @xmath2c/@xmath3 ) .
previous studies have shown its ground state to be an antiferromagnetic insulator ( c - type ) , making it not especially interesting as a multiferroic .
motivated by our previous study of v - doped ferroelectric titanates @xcite , we examine the magnetic properties of vanadium diluted within the robust pto ferroelectric .    _ ab initio _ calculations are performed within density functional theory in the generalized gradient approximation ( gga ) by perdew - wang using the paw method @xcite as implemented in the vasp code @xcite .
standard cutoff is used for the plane wave basis , and the k - point mesh for the bulk is 8@xmath48@xmath48 ( appropriately rescaled for defect super cells ) . the berry phase technique is used to calculate the polarization change upon v doping , using strings of 16 points in the polarization direction .
density of states for v : pto .
positive curve is majority spin , negative is minority spin .
fermi energy is at 0 ev .
inset shows a zoom of the gap peak .
the dotted line is a v @xmath5-up . ]    after studying pto and pvo in the respective ferroelectric phases , we substituted v for one ti in a 2@xmath42@xmath42 tetragonal supercell of ferroelectric pto , i.e. dopant concentration @xmath612.5% . a selection of structure parameters ( lattice constants , distance of v or ti from neighbouring o along the polar axis )
are collected in tab .
[ tab : table ] .
v has one excess electron compared to ti , so it is , as expected , spin - polarized with a moment of 1 @xmath1 .
orbital angular momentum is assumed to be quenched .
[ fig : dos ] displays the key result , i.e. the density of states ( dos ) of ferromagnetic v : pto .
as we can observe , a fully occupied peak appears in the gap of pto , placed so that a gap of about 0.2 ev survives . this dos feature is obviously related to the excess v electron occupying antibonding conduction states .
indeed , as shown in the inset , the main contribution to that peak is that of spin - up _ d _ orbitals of v. thus , pto doped with vanadium is a small - gap ferromagnetic insulator thanks to the unpaired electron of dopant vanadium .
the gap of pto is of course underestimated due to the known @xcite gap error of semi - local functionals ; it may well be that the small v - related gap be also somewhat larger than calculated due to the same effects ( self - interaction , xc discontinuity , etc . ) .
.[tab : table]cell parameters for v doped pto , bulk pto and pvo .
theoretical values are calculated for this work in gga approximation .
experimental values are from ref . @xcite [ cols="^,^,^,^",options="header " , ]     in the cell just discussed , v is ferromagnetic by construction , being coupled to its periodic images . to study an antiferromagnetic configuration we consider two v s at the same concentration in a 2@xmath7@xmath42@xmath7@xmath42 tetragonal cell .
the two v are placed in that cell as far as possible from each other . while the ferromagnetic configuration is stable , the antiferromagnetic configuration is not .
the v moments disappear and the system converges to a metallic pauli paramagnet of zero moment , which is about 300 mev higher in energy than the ferromagnet .
of course , this prevents the evaluation of a coupling parameter for magnetic models , but the ferromagnet seems quite stable nevertheless .
@xmath8/@xmath9 ) .
the state is anti - bonding with first - neighbor o s , has @xmath10-like nodal structure , and propagates through @xmath10-like ti states . charge paths along the vertical axis are negligible . ]
inspection of the charge density of the impurity state ( fig .
2 ) suggests a @xmath10-like nodal structure and coupling of v s via v - o - ti - o- ... paths in the basal plane , whereas hardly any density is to be found along the vertical axis .
while the v - centered state is , as expected , anti - bonding with first neighbors , the bonding o - v states ( which mimic those of the substituted ti ) appear to make for a larger charge accumulation in the v - o bond region ( fig .
3 ) , matching the shorter v - o bond length compared to ti - o ( 1.71 vs 1.79  ) .        following ref.@xcite , the equilibrium concentration is @xmath11$]=@xmath12 , where @xmath13 is the density of ti sites and @xmath14 the growth temperature . assuming that the solubility limit for v in pto is pvo , i.e. that high v contents will eventually cause phase separation of pvo , the formation energy is e@xmath15(v)=e(v : pto)(@xmath161)e(pto)e(pvo)@xmath171.23 ev , involving the total energy of the doped supercell of v : pto comprising @xmath16 unit cells , and of the unit cells of pto and pvo .
since @xmath13=1.25@xmath1810@xmath19@xmath20 , at a typical @xmath14=650 k we find a logarithmic concentration @xmath21\approx$]13.4 , which may increase perhaps to about 16 due to vibrational entropy ( v is heavier than ti ) .
this thermodynamic solubility limit is relatively low , but it may well not apply whenever kinetics or non - equilibrium phenomena become dominant , as it happens in modern epitaxial growth techniques .    finally , we estimated the changes in polarization induced by v doping . at 12.5%
v we find a polarization increase of 8.3 @xmath2c/@xmath3 , which agrees nicely with 8.25 @xmath2c/@xmath3 obtained by linear interpolation between the bulk values of pto and pvo mentioned previously .
therefore , in terms of polarization , v does not seem detrimental , but in fact benign .
in summary , we presented an _ ab initio _ prediction of the proper multiferroicity of v - doped pto .
the gap is about 0.2 - 0.3 ev and the magnetization is 1 @xmath1/v , or 1.5@xmath410@xmath22 spins / cm@xmath9 at our chosen v density .
we predict the polarization to increase linearly with v concentration at the percentual rate of 0.7 @xmath2c/@xmath3 .
presumably this will only apply at relatively low concentrations , since the antiferromagnetic character of pvo will eventually take over .
+ _ note _  during review we have become aware of a very recent study @xcite of transition - metal doping in a perovskite ferroelectric ( batio@xmath0 ) , reporting results in general agreement with the ones just presented .
references                        see e.g. r. w. godby and p. garcia - gonzalez , in _ a primer in density functional theory _ , springer lecture notes in physics , c. fiolhais , f. nogueira , m. marques eds .
( springer , berlin 2003 ) , ch . 5 , p.185 .
we report _ ab initio _ predictions on the proper multiferroic ( ferromagnetic , insulating and ferroelectric ) character of pbtio@xmath0 doped with vanadium . 
 v impurities coupled ferromagnetically carry a magnetization of 1 @xmath1 each . 
 the coupling is expected to be strong , since the paramagnetic solution is higher by 150 mev / vanadium , and no stable antiferromagnetic solution was found . 
 the electronic gap in the doped system is about 0.2 - 0.3 ev in gga , hence the system is properly multiferroic . 
 v doping increases the spontaneous polarization in pbtio@xmath0 , with an approximate percentual rate of 0.7 @xmath2c/@xmath3 .