document: half - metallic ferromagnets with high ( room temperature and above ) curie temperatures @xmath1 are ideal for spintronics applications , and as such , much experimental and theoretical@xcite effort has been devoted in recent years to the designing of and search for such materials . among these , 
   cr - doped dilute magnetic semiconductors ( dms ) @xcite or cr - based alloys and in particular cras and crsb @xcite in zinc blende(zb ) structure have attracted particular attention , not only because of the possibility of complete spin polarization of the carriers at the fermi level , but also for their possible high @xmath1 . 
   akinaga @xcite were able to grow zb thin films of cras on gaas ( 001 ) substrates by molecular beam epitaxy , which showed ferromagnetic behavior at temperatures in excess of 400 k and magnetic moments of 3@xmath2 per cras unit . 
   theoretical calculations by akinaga @xcite and several other theoretical calculations since then @xcite have verified the half - metallic character of cras . 
   the high value of @xmath1 has also been supported by some of these studies@xcite . 
   thin films of crsb grown by solid - source molecular beam epitaxy on gaas , ( al , ga)sb , and gasb have been found to be of zb structure and ferromagnetic with @xmath1 higher than 400 k@xcite . 
   galanakis and mavropoulos@xcite , motivated by the successful fabrication of zb cras , crsb and mnas@xcite , have examined the possibility of half - metallic behavior in ordered zb compounds of transition metals v , cr and mn with the @xmath3 elements n , p , as , sb , s , se and te . 
   their theoretical study shows that the half - metallic ferromagnetic character of these compounds is preserved over a wide range of lattice parameters . 
   they also found that the half - metallic character is maintained for the transition element terminated ( 001 ) surfaces of these systems . 
   yamana @xcite have studied the effects of tetragonal distortion on zb cras and crsb and found the half - metallicity to survive large tetragonal distortions . 
   of course , the ground states of many of these compounds in the bulk are known to be different from the zb structure , the most common structure being the hexagonal nias - type . 
   zhao and zunger@xcite have argued that zb mnas , cras , crsb , and crte are epitaxially unstable against the nias structure , and zb crse is epitaxially stable only for lattice constants higher than 6.2  , remaining half - metallic at such volumes . 
   they also find that even though the ground state of crs is zb , it is antiferromagnetic at equilibrium lattice parameter , and thus not half - metallic . 
   these results reveal the challenge experimentalists face in synthesizing these compounds in zb structure . 
   however , the possibility remains open that such difficulties will be overcome with progress in techniques of film - growth and materials preparation in general . 
   recently , deng @xcite were successful in increasing the thickness of zb - crsb films to @xmath4 3 nm by molecular beam epitaxy using ( in , ga)as buffer layers , and li @xcite were able to grow @xmath4 4 nm thick zb - crsb films on nacl ( 100 ) substrates .    in view of the above situation regarding the state of experimental fabrication of these compounds and available theoretical results , it would be appropriate to study the variation of magnetic properties , particularly exchange interactions and the curie temperature , of cr - based pnictides and chalcogenides as a function of the lattice parameter . towards this goal , 
   we have carried out such calculations for the compounds crx ( x = as , sb , s , se and te ) and the mixed alloys cras@xmath0x@xmath0 with x = sb , s , se and te . 
   essentially we study the effect of anion doping by choosing elements of similar atomic sizes ( neighboring elements in the periodic table ) , one of which , namely sb , is isoelectronic to as , while the others ( s , se , te ) bring one more valence electron to the system . 
   the mixed pnictide - chalcogenide systems offer further opportunity to study the effects of anion doping . 
   the alloying with other 3d transition metals ( both magnetic , e.g. fe or mn , or non - magnetic , e.g. v ) on cation sublattice would also change the carrier concentration and bring about strong d - disorder which can additionally modify the shape of the fermi surface . 
   this , however , is not the subject of the present paper . 
   almost all theoretical studies on these alloys so far address aspects of electronic structure and stability of these alloys only . 
   although a few theoretical estimates of exchange interactions and the curie temperature for cras at equilibrium lattice parameter have appeared in the literature , a detailed study of the volume dependence of these quantities is missing . for the other alloys , crsb , 
   crs , crse and crte , no theoretical results for the exchange interaction , curie temperature and their volume dependence exist at present . 
   the mixed pnictide - chalcogenide systems offer the possibility of not only creating these alloys over a larger range of the lattice parameter , but also with a larger variation in the exchange interactions . 
   this is because at low values of the lattice parameter the dominant cr - cr exchange interactions in the chalcogenides can be antiferromagnetic , while for the pnictides they are ferromagnetic . 
   the pnictide - chalcogenide alloying is important from the experimental viewpoint of stabilizing the zb structure on a given substrate , via the matching of the lattice parameter of the film with that of the latter . 
   although the present study is confined to the zb structure only , we hope that it will provide some guidance to the experimentalists in their search and growth of materials suitable for spintronic devices . 
   electronic and magnetic properties of crx ( x = as , sb , s , se and te ) and cras@xmath0x@xmath0 ( x= sb , s , se and te ) were calculated for lattice parameters varying between 5.45 and 6.6  , appropriate for some typical ii - vi and iii - v semiconducting substrates . 
   calculations were performed using the tb - lmto - cpa method@xcite and the exchange - correlation potential given by vosko , wilk and nusair@xcite . in our lmto calculation 
   we optimize the asa ( atomic sphere approximation ) errors by including empty spheres in the unit cell . 
   we use the fcc unit cell , with cr and x ( as , sb , s , se and te ) atoms located at ( 0,0,0 ) and ( 0.25,0.25,0.25 ) , respectively , and empty spheres at locations ( 0.5,0.5,0.5 ) and ( -0.25,-0.25,-0.25 ) . for several cases , 
   we have checked the accuracy of the lmto - asa electronic structures against the full - potential lmto results@xcite and found them to be satisfactory . for the mixed alloys cras@xmath0x@xmath0 ( x= sb , 
   s , se and te ) , the as - sublattice of the zb cras structure is assumed to be randomly occupied by equal concentration of as and x atoms . 
   the disorder in this sublattice is treated under the coherent potential approximation ( cpa)@xcite . 
   our spin - polarized calculations assume a collinear magnetic model . in 
   the following we will present results referred to as fm and dlm . 
   the fm results follow from the usual spin - polarized calculations , where self - consistency of charge- and spin - density yields a nonzero magnetization per unit cell . 
   although we call this the fm result , our procedure does not guarantee that the true ground state of the system is ferromagnetic , with the magnetic moments of all the unit cells perfectly aligned . 
   this is because we have not explored non - collinear magnetic states , nor all antiferromagnetic ( afm ) states attainable within the collinear model . 
   indeed , our results for the exchange interactions in some cases do suggest the ground states being of afm or complex magnetic nature . for lack of a suitable label 
   , we refer to all spin - polarized calculations giving a nonzero local moment as fm state calculations . within the stoner model , a nonmagnetic state above the curie temperature @xmath1 
   would be characterized by the vanishing of the local moments in magnitude . 
   it is well - known and universally accepted that the neglect of the transversal spin fluctuations in the stoner model leads to an unphysical picture of the nonmagnetic state and a gross overestimate of @xmath1 . 
   an alternate description of the nonmagnetic state is provided by the disordered local moment ( dlm ) model , where the local moments remain nonzero in magnitude above @xmath1 , but disorder in magnitude as well as their direction above @xmath1 causes the global magnetic moment to vanish . 
   combining aspects of the stoner model and an itinerant heisenberg - like model , heine and co - workers@xcite have developed a suitable criterion for a dlm state to be a more appropriate description of the nonmagnetic state than what is given by the stoner model . within the collinear magnetic model , where all local axes of spin - quantization point in the same direction , dlm can be treated as a binary alloy problem and 
   thus described using the coherent potential approximation ( cpa)@xcite . we have carried out such dlm calculations , assuming the cr - sublattice to be randomly occupied by an equal number of cr atoms with oppositely directed magnetic moments . 
   the object for performing the dlm calculations is two - fold . 
   if the total energy in a dlm calculation is lower than the corresponding fm calculation , we can safely assume that the ground state ( for the given lattice parameter and structure ) is not fm , albeit of unknown magnetic structure . 
   the exchange interactions in the dlm state can also be used to compute estimates of @xmath1 , and such estimates of @xmath1 may be considered as estimates from above the magnetic - nonmagnetic transition . 
   @xmath1 computed from exchange interactions in the fm state are estimates from below the transition . 
   of course , if the ground state is known to be ferromagnetic , then estimates of @xmath1 based on exchange interactions in the fm reference state are the appropriate ones to consider .    in some cases where the fm results point to the possibility of the ground state magnetic structure being afm or of complex nature 
   , we have carried out a limited number of afm calculations to provide some insight into this problem ( see section [ subsec : stabilityjq ] ) . 
   we have computed the spin - resolved densities of states ( dos ) for all the alloys for varying lattice parameters , and for both the fm and dlm configurations . 
   the fm calculations show half - metallic character , due to the formation of bonding and antibonding states involving the @xmath5 orbitals of the cr - atoms and the @xmath3 orbitals of the neighboring pnictogen ( as , sb ) or chalcogen ( s , se , te ) . 
   the hybridization gap is different and takes place in different energy regions in the two spin channels . 
   the critical values of the lattice parameters above which the fm calculations show half - metallic character agree well with those reported by galanakis and mavropoulos@xcite . 
   the dos for the alloys of the type crx ( x = sb , s , se , te ) have been presented by several other authors@xcite and thus will not be shown here . in figs.[fig1 ] and [ fig2 ] we show the dos for the mixed alloys cras@xmath0sb@xmath0 and cras@xmath0se@xmath0 , for lattice parameters above and below the critical values for the half - metallic character . according to galanakis and mavropoulos@xcite , half - metallicity in zb cras appears between the lattice parameters of 5.45 and 5.65  . 
   the latter corresponds to the lattice parameter of the gaas substrate . for crsb 
   half - metallicity appears at a lattice parameter between 5.65 and 5.87  . 
   the mixed alloy cras@xmath0sb@xmath0 , as shown in fig.[fig1 ] , is not quite half - metallic at the lattice parameter of 5.65  , and fully half - metallic at the lattice parameter of 5.76  . 
   replacing sb with se in the above alloy , i.e. for cras@xmath0se@xmath0 , brings the critical lattice parameter down slightly . as shown in fig.[fig2 ] , at a lattice parameter of 5.65  , cras@xmath0se@xmath0 is half - metallic , although barely so . in our calculation 
   crs and crse are half - metallic at a lattice parameter of 5.65  , and not so at a lattice parameter of 5.55  . 
   crte is not half - metallic at a lattice parameter of 5.76  , but at a lattice parameter of 5.87  . 
   for both crs and crse the critical value should be close to 5.65  , and for crte it should be close to 5.87  .    note that in general the half - metallic gap is larger in the chalcogenides than in the pnictides . 
   this is due to larger cr - moment ( see section [ sec : mag.mom . 
   ] ) for the chalcogenides , which results in larger exchange splitting . 
   this explains the difference in the half - metallic gaps in figs . 
   [ fig1 ] and [ fig2 ] for similar lattice parameters .    fig . 
   [ fig3 ] compares the total dos of cras for the fm and dlm calculations for the equilibrium lattice parameter 5.65  . 
   higher dos at the fermi level for the dlm calculation , compared with the fm calculation , is an indication that the band energy is lower in the fm state . indeed , as indicated in table [ table1 ] , compared with the dlm state the total energy for zb cras is lower in the fm state for the lattice parameters from 5.44 to 5.98  . 
   in fact , this holds for lattice parameters up to 6.62  , showing the robustness of ferromagnetism in cras over a wide range of the lattice parameter . 
   this is also true for crsb . 
   sb@xmath0 for lattice parameters ( a ) 5.55  , ( b ) 5.65  , ( c ) 5.76 @xmath6 and ( d ) 5.87  , respectively . , 
   width=360 ]    se@xmath0 for lattice parameters ( a ) 5.55  , ( b ) 5.65  , ( c ) 5.76 @xmath6 and ( d ) 5.87  , respectively . , 
   width=360 ]     for the dlm and fm states.,width=360 ]    in table [ table1 ] we show the variation of total energies per atom in ry with the lattice parameter for crx ( x = as , sb , s , se and te ) in the dlm and fm states . 
   the purpose of tabulating these energies is not to determine the bulk equilibrium lattice parameters in the zb structure , as this has already been done by several authors@xcite . 
   our results for equilibrium zb phase lattice parameters agree with those found by galanakis and mavropoulos@xcite . 
   the important point is that for crs and crse at low values of lattice parameters the dlm energies are lower than the fm energies , showing clearly that the fm configuration is unstable . 
   the result for crs is in line with the observation by zhao and zunger@xcite , who find zb crs to be antiferromagnetic with an equilibrium lattice parameter of 5.37  . 
   as shown later ( section [ sec : exchange ] ) , the exchange coupling constants for the cr atoms in the fm calculations are negative , indicating the instability of the ferromagnetic spin alignment . the tendency to antiferromagnetism in crse at compressed lattice parameters 
   is also revealed in a study by sasaio@xmath7lu @xcite for crte at lower lattice parameters the fm energy is lower than the dlm energy , but the exchange constants for the cr - atoms in the fm calculations are still negative ( see discussion in section [ sec : exchange ] ) , signaling the possibility of the ground states in crte at low values of the lattice parameter being neither dlm nor fm . 
   note that in our discussion ground state implies the lowest energy state in zb structure . for crs , 
   crse and crte the ground states at low lattice parameters can be of an antiferromagnetic ( afm ) or complex magnetic structure . 
   a lower total energy may also mean a lower band energy , and in some cases , the latter may be reflected in a lower density of states at the fermi level . 
   this is shown in fig.[fig4 ] , where for crs at the lowest lattice parameter of 5.44 @xmath6 the dos at the fermi level is lower in the dlm state than in the fm state . 
   the deviation from ferromagnetism at low values of the lattice parameter for crs , crse and crte is also revealed by our study of the lattice fourier transform of the exchange interaction between the cr atoms in the fm state ( section [ sec : exchange ] ) . 
   the search for an antiferromagnetic state with lower energy is possible within our collinear magnetic model by enlarging the unit cell in various ways . 
   we have pursued this issue to a limited extent , by considering 001 , 111 afm configurations for crs , crse and crte at low values of the lattice parameter ( see discussion in section[sec : exchange ] ) . 
   a satisfactory resolution of such issues is possible only by going beyond the collinear model . 
   lcccccc lattice parameter (  ) & 5.44 & 5.55 & 5.65 & 5.76 & 5.87 & 5.98 + * cras * + dlm energy & -1653.4039 & -1653.4021 & -1653.3995 & -1653.3960 & -1653.3920 & -1653.3876 + fm energy & -1653.4068 & -1653.4055 & -1653.4034 & -1653.40026 & -1653.3966 & -1653.3922 + * crsb * + dlm energy & -3762.4738 & -3762.4781 & -3762.4807 & -3762.4821 & -3762.4822 & -3762.4814 + fm energy & -3762.4770 & -3762.4813 & -3762.4841 & -3762.4857 & -3762.4862 & -3762.4856 +   +   + * crs * + dlm energy & -723.4504 & -723.4468 & -723.4426 & -723.4381 & -723.4332 & -723.4280 + fm energy & -723.4491 & -723.4464 & -723.4434 & -723.4395 & -723.4351 & -723.4302 + * crse * + dlm energy & -1737.9146 & -1737.9139 & -1737.9123 & -1737.9100 & -1737.9071 & -1737.9036 + fm energy & -1737.9139 & -1737.9132 & -1737.9124 & -1737.9110 & -1737.9087 & -1737.9057 + * crte * + dlm energy & -3918.9074 & -3918.9124 & -3918.9158 & -3918.9179 & -3918.9189 & -3918.9188 + fm energy & -3918.9078 & -3918.9128 & -3918.9161 & -3918.9181 & -3918.9194 & -3918.9201 + 
   our spin - polarized calculations for the fm reference states lead to local moments not only on the cr atoms , but also on the other atoms ( as , sb , s , se , and te ) as well as the empty spheres . 
   sandratskii @xcite have discussed the problem associated with such induced moments in case of the heusler alloy nimnsb and the hexagonal phase of mnas . usually such systems can be divided into sublattices with robust magnetic moments and sublattices where moment is induced under the influence of the former . 
   these authors argue that the treatment of the induced moments as independent variables in a heisenberg hamiltonian may lead to artificial features in the spin - wave spectra , but these artificial features do not drastically affect the calculated curie temperatures of the two alloys , nimnsb and hexagonal mnas . clearly , in our case the sublattice with the robust magnetic moment is the cr - sublattice . among the three other sublattices , 
   the magnitudes of the induced moments decrease in the following order for the two robust ferromagnets cras and crsb : x - sublattice ( x = as , sb ) , sublattice es-1 ( the sublattice of empty spheres that is at the same distance with respect to the cr - sublattice as the x - sublattice ) , sublattice es-2 ( sublattice of empty spheres further away from the cr - sublattice ) . 
   this trend is particularly valid for low values of the lattice parameter . 
   the induced moments originate from the tails of the orbitals ( primarily @xmath8 ) on the nearby cr - atoms . 
   this is particularly true for the moments induced on the empty spheres . 
   the magnitudes of the induced moments on the two empty sphere sublattices decrease as the lattice parameter increases , and so do the differences in their magnitudes . 
   the signs of the moments on es-1 and es-2 may be the same for small lattice parameters , but are opposite for large lattice parameters . 
   the sign of the moment on the x - sublattice is opposite to that on the cr - sublattice and the magnitudes of the moments on the two sublattices increase with increasing lattice parameters , due to decreased hybridization between cr-@xmath8 and x-@xmath3 orbitals . above a critical value of the lattice parameter , the moment per formula unit ( f.u . ) 
   saturates at a value of 3.0 @xmath2 , as the half - metallic state is achieved , while the local moments on the cr- and x - sublattices increase in magnitude , remaining opposite in sign . 
   the maximum ratio between the induced moment on x ( x = as , sb ) and the moment on cr is 0.18 for cras and 0.15 for crsb , occurring at the highest lattice parameter of 6.62 @xmath6 studied . the maximum ratio between the induced moment on es-1 and that on cr is 0.06 , occurring at the lowest lattice parameter of 5.44 @xmath6 studied . 
   magnetic moments of cras and crsb per formula unit ( f.u . ) as well as the local moment at the cr site are shown in fig . 
   [ fig5 ] , where we compare the two compounds with each other for their magnetic moments in the fm and dlm states . 
   the same results are presented in fig . 
   [ fig6 ] , comparing the moment per f.u.in the fm state with the cr local moment in the fm and dlm states separately for each compound . 
   it is to be noted that there are no induced moments for the dlm reference states , i.e. the moments on the non - cr sublattices are several orders of magnitude smaller than the robust moment on the cr atoms . 
   the total moment per formula unit in the dlm state is zero by construction . 
   the local moment on the cr atom for the dlm reference state is usually less than the corresponding fm value for smaller lattice parameters , and larger for larger lattice parameters ( fig.[fig6 ] ) . 
   similar trends in the variation of the local moment on cr and the induced moments on the other sublattices for the fm reference states as a function of lattice parameter are revealed for crx ( x = s , se , te ) , except that the moments on es-1 are always an order of magnitude larger than those on es-2 . 
   i addition , the induced moments on es-2 are @xmath9 times larger than those on x sublattice for smaller values of the lattice parameter , with the two becoming comparable in magnitude for larger lattice parameters . 
   the induced moments on es-1 and x - sublattices are never larger than @xmath4 5% of the moment on the cr atoms . 
   the induced moments for the dlm reference states are several orders of magnitude smaller than the cr - moments , and can be safely assumed to be zero . 
   results for zb crs , crse and crte are presented in figs.[fig7 ] and [ fig8 ] . 
   the moment per f.u . reaches the saturation values of 4@xmath2 for crs , crse , and crte in the half - metallic state , as discussed in detail by galanakis and mavropoulos@xcite . 
   the saturation values of the moments for all these alloys ( crx , x = as , sb , s , se , and te ) satisfy the so - called `` rule of 8 '' : @xmath10 , where @xmath11 is the total number of valence electrons in the unit cell . 
   the number 8 accounts for the fact that in the half - metallic state the bonding @xmath12 bands are full , accommodating 6 electrons and so is the low - lying band formed of the @xmath13 electrons from the @xmath3 atom , accommodating 2 electrons . 
   the magnetic moment then comes from the remaining electrons filling the @xmath8 states , first the @xmath14 states and then the @xmath5 . 
   the saturation value of 3@xmath2/f.u . , or the half - metallic state , appears for a larger critical lattice constant in crsb than in cras . 
   similarly , the critical lattice constants for the saturation magnetic moment of 4@xmath2/f.u . 
   are in increasing order for crs , crse and crte . 
   the local moment on the cr atom can be less / more than the saturation value , depending on the moment induced on the non - cr atoms and empty spheres . 
   -[fig8 ] ) , fm calculations produce induced moments on non - cr spheres representing the x - atoms ( x = as , sb , s , se , te ) , and one set of empty spheres . 
   the dlm calculations produce no such induced moments , i.e. , the moments reside on the cr - atoms only . 
   see text for discussion.,width=360 ]                fig.[fig9 ] shows the variation of the magnetic moment with the lattice parameter for the random alloys cras@xmath0x@xmath0 ( x = sb , s , se , te ) , where 50% of the as - sublattice is randomly occupied by x - atoms . 
   the saturation moment per f.u . 
   for cras@xmath0sb@xmath0 in the half - metallic state is 3@xmath2 , with the results falling between those for cras and crsb shown in fig.[fig6 ] . for cras@xmath0x@xmath0 ( x = s , se , te ) , the saturation moment per f.u . is 3.5@xmath2 . 
   the local cr - moment deviates from the saturation value in the half - metallic state , being higher than the saturation value for all lattice parameters above 6.1 .        from figs.[fig5]-[fig9 
   ] it is clear that the magnetic moment per formula unit is closer to the magnetic moment of the cr atoms in the fm calculations than in the dlm calculations . 
   local cr - moments in the dlm calculations are suppressed w.r.t . 
   the fm results for low lattice parameters and enhanced for larger lattice parameters . as shown in table [ table1 ] the total energy of the fm state is lower than that of the corresponding dlm state in almost all cases , except for some compressed lattice parameters for crs and crse . 
   however , the consideration of the dlm state does provide an advantage in that there are no associated induced moments , i.e. , the dlm calculations produce moments that reside on the robust magnetic sublattice only . 
   mapping of the total energy on to a heisenberg hamiltonian , therefore , does not result in exchange interactions involving atoms / spheres with induced moments and all associated artificial / non - physical features referred to by sandratskii @xcite 
   currently , most _ first - principles _ studies of the thermodynamic properties of itinerant magnetic systems proceed via mapping @xcite the system energy onto a classical heisenberg model : @xmath15 where @xmath16 are site indices , @xmath17 is the unit vector pointing along the direction of the local magnetic moment at site @xmath18 , and @xmath19 is the exchange interaction between the moments at sites @xmath18 and @xmath20 . 
   the validity of this procedure is justified on the basis of the adiabatic hypothesis- the assumption that the magnetic moment directions are slow variables on all the characteristic electronic time scales relevant to the problem , and thus can be treated as classical parameters . the energy of the system for a given set of magnetic moment directions is usually calculated via methods based on density functional theory ( dft ) . 
   one of the most widely used mapping procedures is due to liechtenstein @xcite it involves writing the change in the energy due to the deviation of a single spin from a reference state in an analytic form using the multiple scattering formalism and by appealing to the magnetic variant of the andersen force theorem@xcite . 
   the force theorem , derived originally for the change of total energy due to a deformation in a solid , dictates that the differences in the energies of various magnetic configurations can be approximated by the differences in the band energies alone@xcite . 
   the energy of a magnetic excitation related to the rotation of a local spin - quantization direction can be calculated from the spinor rotation of the ground state potential . 
   no self - consistent calculation for the excited state is necessary . 
   a second approach is based on the total energy calculations for a set of collinear magnetic structures , and extracting the exchange parameters by mapping the total energies to those coming from the heisenberg model given by eq.([e1 ] ) . 
   such calculations can be done using any of the standard dft methods . however , unlike the magnetic force theorem method , where the exchange interactions can be calculated directly for a given structure and between any two sites , several hypothetical magnetic configurations and sometimes large supercells need to be considered to obtain the values of a modest number of exchange interactions . in addition , some aspects of environment - dependence of exchange interactions are often simply ignored . 
   the difference between these two approaches is , in essence , the same as that between the generalized perturbation method ( gpm)@xcite and the connolly - williams method@xcite in determining the effective pair interactions in ordered and disordered alloys . 
   a third approach is a variant of the second approach , where the energies of the system in various magnetic configurations corresponding to spin - waves of different wave - vectors are calculated by employing the generalized bloch theorem for spin - spirals@xcite . 
   the inter - atomic exchange interactions can be calculated by equating these energies to the fourier transforms of the classical heisenberg - model energies . 
   this approach , known as the frozen magnon approach , is similar to the frozen phonon approach for the study of lattice vibrations in solids .    in this work , 
   we have used the method of liechtenstein , which was later implemented for random magnetic systems by turek , using cpa and the tb - lmto method@xcite . the exchange integral in eq.([e1 ] ) 
   is given by @xmath21 dz \ ; , \ ] ] where @xmath22 represents the complex energy variable , @xmath23 , and @xmath24 , representing the difference in the potential functions for the up and down spin electrons at site @xmath18. in the present work @xmath25 represents the matrix elements of the green s function of the medium for the up and down spin electrons . 
   for sublattices with disorder , this is a configurationally averaged green s function , obtained via using the prescription of cpa . 
   the integral in this work is performed in the complex energy plane , where the contour includes the fermi energy @xmath26 . 
   the quantity @xmath19 given by eq . 
   ( [ eq - jij ] ) includes direct- , indirect- , double - exchange and superexchange interactions , which are often treated separately in model calculations . the negative sign in eq.([e1 ] ) 
   implies that positive and negative values of @xmath19 are to be interpreted as representing ferromagnetic and antiferromagnetic interactions , respectively . 
   a problem with the mapping of the total energy to a classical heisenberg hamiltonian following the approach of liechtenstein @xcite is that it generates exchange interactions between sites , where one or both may carry induced moment(s ) . 
   of course this problematic scenario appears only for the fm reference states , as the dlm reference states do not generate induced moments . in the present work the liechtenstein mapping procedure , applied to fm reference sates , 
   generates exchange interactions between the cr atoms , between cr and other atoms x ( x = as , sb , s , se , te ) , and also between cr atoms and the nearest empty spheres es-1 . depending on the lattice parameter , this latter interaction is either stronger than or at least comparable to that for the cr - x pairs . the exchange interactions between cr atoms and the furthest empty spheres es-2 are always about one or two orders of magnitude smaller than the cr - es1 interactions and can be neglected . in cras , 
   the ratio of the nearest neighbor cr - es1 to cr - cr interaction varies from 0.2 - 0.25 at low lattice parameters to 0.06 - 0.07 at high values of the lattice parameter . in crsb , these ratios are smaller , varying between 0.14 and 0.05 . 
   the cr - es1 exchange interactions are also relatively strong in magnitude in crs , crse and crte . 
   one important point is that while these interactions are positive for nearest neighbors for all lattice parameters , cr - cr nearest neighbor interaction is negative for low values of lattice parameters in crs and crse . in crte 
   , this interaction changes sign from positive to negative and then back , as the lattice parameter is varied in the range 5.44 - 6.62  . 
   as mentioned earlier , the calculation for the dlm reference states do not produce induced moments , and thus no exchange interactions other than those between the cr atoms . 
   sandratskii@xcite have discussed the case when , in addition to the interaction between the strong moments , there is one secondary , but much weaker , interaction between the strong and one induced moment . in this case , the curie temperature , calculated under the mean - field approximation ( mfa ) , seems to be enhanced due to this secondary interaction , irrespective of the sign of the secondary interaction . in other words , the curie temperature would be somewhat higher than that calculated by considering only the interaction between the strong moments . 
   the corresponding results under the random phase approximation ( rpa ) have to be obtained by solving two equations simultaneously . 
   one can assume that the rpa results for the curie temperature follow the trends represented by the mfa results , being only somewhat smaller , as observed in the absence of induced moments . in our case 
   , since there are at least two secondary interactions ( cr - x and cr - es1 ) to consider in addition to the main cr - cr interaction , the influence of these secondary interactions is definitely more complex .    in view of the above - described situation involving secondary interactions between cr- and the induced moments for the fm reference states , we have adopted the following strategy . since no induced moments appear in calculations for the dlm reference states , the curie temperature @xmath1 for these can be calculated as usual from the exchange interaction between the cr - atoms , i.e. the strong moments . 
   for these cases the calculation of @xmath1 can proceed in a straightforward manner by making use of the mean - field approximation ( mfa ) or the more accurate random - phase approximation ( rpa)@xcite . 
   one can obtain the mfa estimate of the curie temperature from @xmath27 where the sum extends over all the neighboring shells . 
   an improved description of finite - temperature magnetism is provided by the rpa , with @xmath28 given by @xmath29^{-1 }   \ , .\ ] ] here @xmath30 denotes the order of the translational group applied and @xmath31 is the lattice fourier transform of the real - space exchange integrals @xmath32 . 
   it can be shown that @xmath33 is always smaller than @xmath34 @xcite . 
   it has been shown that the rpa curie temperatures are usually close to those obtained from monte - carlo simulations @xcite . 
   as shown by sandratskii @xcite the calculation of @xmath1 using rpa is considerably more involved even for the case where only one secondary interaction needs to be considered , in addition to the principal interaction between the strong moments . 
   the complexity of the problem increases even for mfa , if more than one secondary interaction is to be considered . 
   the same comment applies to stability analysis using the lattice fourier transform of the exchange interactions . 
   the deviation of the nature of the ground state from a collinear and parallel alignment of the cr moments in the fm reference states could be studied by examining the lattice fourier transform of the exchange interaction between the cr atoms : @xmath35 , if all the secondary interactions could be ignored . 
   this is definitely not possible for many of our fm results , where several pairs of interaction need to be considered , and @xmath36 is a matrix bearing a complicated relationship to the energy as a function of the wave - vector * q*. thus , in the following the results for @xmath1 will be presented mostly for the dlm reference states . for comparison , in a small number of cases we will present @xmath1 calculated for the fm reference states using only the cr - cr exchange interactions as the input . of course 
   , this will be done with caution only for cases where we have reason to believe that the results are at least qualitatively correct . 
   some fm results will also be included towards the stability analysis based on @xmath36 derived from cr - cr interactions only . again , this will be done with caution , only if the corresponding results can be shown to be meaningful via additional calculations .      the cr - cr exchange interactions for all the alloys studied and for both fm and dlm reference states become negligible as the inter - atomic distance reaches about three lattice parameters or , equivalently , thirty neighbor shells . 
   the same applies to the cr - x and cr - es interactions for the fm cases , these interactions in general being somewhat smaller . 
   the cr - cr interactions for the dlm reference states are more damped compared with the corresponding fm results , showing less fluctuations in both sign and magnitude . 
   the distance dependence of the exchange interactions between the cr atoms in cras is shown in fig.[fig10 ] for several lattice parameters . 
   although the nearest neighbor interaction is always positive ( i.e , of ferromagnetic nature ) , the interactions with more distant neighbors are sometimes antiferromagnetic . 
   such antiferromagnetic interactions are more common in cras for lower lattice parameters . 
   with increasing lattice parameter , interactions become predominantly ferromagnetic , and by the time the equilibrium lattice parameter of 5.52 @xmath6 is reached , antiferromagnetic interactions mostly disappear . 
   we have calculated such interactions up to the 405th neighbor shell , which amounts to a distance of roughly 8 lattice parameters . 
   although the interactions themselves are negligible around and after the 30@xmath37 neighbor shell , their influence on the lattice sums continues up to about 100 neighbor shells . by about the neighbor 110@xmath37 shell 
   ( a distance of @xmath4 5 lattice parameters ) the interactions fall to values small enough so as not to have any significant effect on the calculated lattice fourier transform of the exchange interaction and the curie temperature ( see below ) . 
   it is clear from fig.[fig10 ] that ferromagnetism in cras is robust and exists over a wide range of lattice parameters . 
   the distance dependence of the cr - cr exchange interactions in crsb is very similar to that in cras for both fm and dlm reference states . 
   for crs , crse , and crte the situation is somewhat different . for crs and crse , the fm reference states for some low lattice parameters 
   yield cr - cr interactions that are antiferromagnetic even at the nearest neighbor separation . for crte 
   , at the lowest lattice parameter studied ( 5.44  ) the nearest neighbor interaction for the fm reference state is ferromagnetic , but becomes antiferromagnetic with increasing lattice parameter , changing back to ferromagnetic at higher lattice parameters . 
   for all three compounds , the interactions are predominantly ferromagnetic at higher lattice parameters . 
   figs.[fig11 ] and [ fig12 ] show the distance dependence of the exchange interactions calculated for the fm reference states in crse and crte , respectively , for several lattice parameters . 
   predominant nearest neighbor antiferromagnetic interactions between the cr atoms result in negative values of the curie temperature , when calculated via eqs . 
   ( [ e2 ] ) or ( [ e3 ] ) . 
   these results for the curie temperature for the fm reference states can be discarded as being unphysical on two grounds : because of the neglect of the interactions involving the induced moments and also because they point to the possibility that the ground state is most probably antiferromagnetic or of complex magnetic structure . 
   the antiferromagnetic cr - cr interactions mostly disappear , when calculated for the dlm reference states . 
   this could be interpreted as being an indication that the actual magnetic structure of the ground states for these low lattice parameters in case of crs , crse and crte is closer to a dlm state than to an fm state . in fig.[fig13 ] we show the cr - cr exchange interactions for the dlm reference states in case of crse for the same lattice parameters as those considered for fig.[fig11 ] . 
   a comparison of the two figures shows that all interactions have moved towards becoming more ferromagnetic for the dlm reference states , the nearest neighbor interaction for the lowest lattice parameter staying marginally antiferromagnetic .     between the cr atoms in cras for various lattice parameters @xmath38 , calculated for the fm and dlm reference states . 
   the distance between the cr atoms is given in units of the lattice parameter @xmath38 ( the same applies to figs.[fig11]-[fig13 ] ) . 
   the main plot in fig.[fig10 ] shows the distance dependence up to 2.25@xmath38 , while the inset shows the values between 2.25@xmath38 and 5@xmath38 . 
   although the individual values of @xmath19 are small beyond about 2.25@xmath38 , their cumulative effects on the total exchange constant and the curie temerature can not be neglected ( see text for details ) . 
   comparison of the insets for the fm and dlm cases shows that the interactions are more damped for the dlm case , being at least an order of magnitude smaller for distances beyond @xmath42.25 - 2.5@xmath38 or 15 - 20 neighbor shells . 
   similar comments apply to the interactions presented in figs.[fig11]-[fig13].,width=379 ]    . 
   , width=336 ]    . , 
   width=336 ]    . , 
   width=336 ]      the deviation of the nature of the ground state from the reference state can be studied by examining the lattice fourier transform of the corresponding exchange interactions between the cr atoms : @xmath35 . as pointed out earlier , for the fm reference 
   states this procedure suffers from the drawback of neglecting the effects of all other interactions involving the induced moments . for the dlm reference states there are no induced moments , 
   so the relationship between the energy and @xmath36 is simpler , but a physical picture of the spin arrangement corresponding to a particular wave - vector @xmath39 is harder to visualize . for the fm reference states , if there were no moments other than those on the cr atoms , a maximum in @xmath36 at @xmath40 would imply that the ground state is ferromagnetic with collinear and parallel cr magnetic moments in all the unit cells . a maximum at symmetry points other than the @xmath41-point would imply the ground state being antiferromagnetic or a spin - spiral state . a maximum at a wave - vector @xmath39 that is not a symmetry point of 
   the bz would imply the ground state being an incommensurate spin spiral . 
   the presence of induced moments and the consequent interactions involving non - cr atoms and empty spheres spoil such interpretations based on @xmath36 derived from cr - cr interactions alone . 
   however , the tendencies they reveal might still be useful . 
   it is for this reason that we study the fourier transform @xmath36 , defined above , for both fm and dlm reference states .    in fig.[fig14 
   ] we have plotted this quantity for cras . 
   the results for crsb are quite similar . 
   the maximum in @xmath36 at the @xmath41-point for all lattice parameters and for both fm and dlm reference states can be taken as an indication that the ground state magnetic structure is ferromagnetic for cras for all the lattice parameters studied . 
   the same comment applies to crsb . 
   the apparent lack of smoothness in @xmath36 shown for the fm reference states is a consequence of the fact that there are other additional bands ( involving induced moments ) , which are supposed to cross the band shown , but have not been computed .                for crs , crse , and crte ( see figs.[fig15]-[fig16 ] ) , the deviation of the ground state for low lattice parameters from the parallel arrangement of cr moments is reflected in the result that the maximum moves away from the @xmath41-point for the fm reference states . at high values of the lattice parameter the maximum returns to the @xmath41-point . 
   the curves for crse are similar to those for crs and have therefore not been shown . 
   the fact that the maximum for the dlm reference sates lies at the @xmath41-point in most cases is again an indication that the ground state magnetic structure is closer to the dlm state than to the fm state . 
   the conclusions based on the fm reference state results in figs.[fig15 ] and[fig16 ] may be suspect on ground of neglecting the interactions involving the induced moments . 
   however , to explore whether they do carry any relevant information we have carried out additional calculations for the three compounds crs , crse and crte for two commonly occurring antiferromagnetic configurations : afm[001 ] , afm[111 ] . 
   note that another commonly occurring afm configuration afm[110 ] is not unique , i.e. there are several configurations that could be seen as an afm[110 ] arrangement ( see fig3 . of ref . 
   [ ] , table 2 of ref . 
   the simplest among these is actually equivalent to afm[100 ] . 
   the results for the total energy for the two afm calculations are shown in table [ table2 ] and compared with the corresponding fm and dlm total energies . 
   for crs , the lowest energy state for lattice parameters 5.44 and 5.55 @xmath6 is afm[111 ] , exactly as suggested by the maximum in @xmath36 appearing at the l - point in fig.[fig15 ] for the fm reference state and for these two lattice parameters . as the lattice parameter increases beyond 5.55  , 
   antiferromagnetic interactions diminish . for the next higher lattice parameter 5.66 @xmath6 in table [ table2 ] , 
   the lowest energy state is dlm . 
   this may suggest that the ground state has a complex magnetic structure , which remains to be explored . for higher lattice parameters the fm state has the lowest energy . for crse 
   , afm[111 ] state has the lowest energy up to the lattice parameter 5.66  , as is also supported by the maximum of @xmath36 at l - point . 
   the @xmath36 curves for crse are similar to those of crs , and have not been shown . 
   for crte , at the lowest lattice parameter of 5.44 @xmath6 the lowest energy state is fm , as is also indicated by the maximum of @xmath36 at the @xmath41-point . for higher lattice parameters 5.65 and 5.76 , 
   even though the @xmath36 curves point to the possibility of an afm[111 ] ground state , the fm state energy turns out to be the lowest among the configurations studied . 
   it could be concluded that in this case a proper relationship between the energy and @xmath36 , obtained without the neglect of the induced moments , would point to the ground state being fm . 
   for these three chalcogenides , for lattice parameters above 5.65 - 5.7 @xmath6the ground state should be fm .    [ 
   cols="<,^,^,^,^,^,^ " , ]      we determine the curie temperature using eqs . 
   ( [ e2 ] ) and ( [ e3 ] ) . for the dlm reference states , these produce estimates of @xmath1 from above the ferromagnetic@xmath42paramagnetic transition , and are free from errors due to induced moments 
   . however , these estimates are high compared with properly derived values of @xmath1 from below the transition . 
   the latter estimates would require the use of fm reference states ( where the ground states are known to be fm ) and thus a proper treatment of the induced moments . for cras and crsb 
   , the magnetic state is ferromagnetic for all the lattice parameters considered . 
   hence , for the sake of comparison we have calculated the @xmath1 for the fm reference states using eqs . 
   ( [ e2 ] ) and ( [ e3 ] ) as well . 
   according to the results of sandratskii @xcite the correctly calculated @xmath1 values , in the presence of interactions involving all the induced moments , would be higher . 
   thus , the correct estimates of @xmath1 should lie somewhere between the dlm results and the fm results obtained with the neglect of the induced moments . in fig . 
   [ fig17 ] we show these results for cras , crsb . 
   we have used up to 111 shells in the evaluation of eq . 
   ( [ e2 ] ) and for the lattice fourier transform of @xmath43 in eq . 
   ( [ e3 ] ) , after having tested the convergence with respect to the number of shells included . 
   the estimated computational error corresponding to the chosen number of shells used in these calculations is below @xmath44 . for comparison 
   we also include the results for the mixed alloy cras@xmath0sb@xmath0 , for which the calculated @xmath1 values fall , as expected , in between those of cras and crsb . 
   since rpa values are more accurate than mfa values , our best estimates of @xmath1 for cras range from somewhat higher than 500 k at low values of the lattice parameter , increasing to 1000 - 1100 k around the mid lattice parameter range ( 5.75 - 5.9  ) and then decreasing to around 600 k for higher lattice parameters ( 6.5 @xmath6 and above ) . for crsb 
   these estimates are consistently higher than those for cras : 1100 k , 1500 k and 1200 k , respectively . 
   the estimates for cras are similar to those provided by sasaiolglu @xcite    for crs , crse , the results obtained with the fm reference states would clearly be wrong , in particular , for the low values of the lattice parameters , for which we have shown the ground state to be antiferromagnetic within our limited search . 
   there is a possibility that the ground state for certain lattice parameters might have a complex magnetic structure . for crte 
   , even though the ground state appears to be ferromagnetic , there are considerable antiferromagnetic spin fluctuations , making the fm estimates unreliable . in fig . 
   [ fig18 ] we show the @xmath1 values for crs , crse and crte for the dlm reference states . 
   the values for lattice parameters for which the ground state has been shown to be antiferromagnetic in the preceding section should be discarded as being inapplicable . 
   similar results for the alloys cras@xmath0x@xmath0 ( x = s , se and te ) are shown in fig . 
   [ fig19 ] for dlm reference states . 
   for these , the ground state is ferromagnetic for all lattice parameters . 
   however , because of the neglect of the induced moments related effects , our results for the curie temperatures for the fm reference states are lower than the properly calculated values . 
   thus in fig.[fig19 ] we show the dlm results only , which are devoid of the induced moment effects and provide us with estimates of @xmath1 from above the transition . 
   these are expected to be somewhat higher than the properly computed values for fm reference states . 
   thus , for these alloys the trend revealed in fig . [ fig19 ] for the variation of @xmath1 with lattice parameter is correct . 
   the estimates themselves are qualitatively correct , albeit somewhat higher than the correct values . 
   only the rpa values are plotted in fig . 
   [ fig19 ] , which are more reliable than the mfa values . for comparison 
   , we also show the results for the pnictides cras , crsb , and cras@xmath0sb@xmath0 , which are isoelectronic among themselves , but have half an electron per unit cell less than the mixed alloys cras@xmath0x@xmath0 ( x = s , se and te )    sb@xmath0 are also shown . 
   , width=360 ]        x@xmath0 alloys with x = s , se and te . for comparison , 
   the results for cras , crsb and cras@xmath0sb@xmath0 are also shown . 
   all results shown are for dlm reference states , and as such , should be considered as upper limits for @xmath1 . , width=336 ]    the differences between the results for the pnictides , chalcogenides and the mixed pnictide - chalcogenides can be summarized as follows . 
   the pnictides , cras , crsb , and cras@xmath0sb@xmath0 , are strong ferromagnets at all the lattice parameters studied ( 5.44 - 6.62  ) . in the dlm description , 
   their @xmath1 stays more or less constant ( apart from a minor increase ) as the lattice parameter increases from 5.4 /aa to 6.1  , and then decreases beyond ( figs . 
   [ fig17 ] and [ fig19 ] . 
   the chalcogenides are antiferromagnetic or have complex magnetic structure for low lattice parameters . in the dlm description , their @xmath1 in the ferromagnetic state increases and then becomes more or less constant as the lattice parameter increases ( fig . 
   [ fig18 ] ) . 
   the mixed alloys cras@xmath0x@xmath0 ( x = s , se , te ) are ferromagnetic at all the lattice parameters studied . in the dlm description , their @xmath1 rises and then falls as the lattice parameter is increased from 5.44 to 6.62  . 
   a comparison of the results presented in figs . 
   [ fig17]-[fig19 ] shows that large changes in @xmath1 take place by changing the number of carriers . 
   changes due to isoelectronic doping are small compared with changes brought about by changing carrier concentration . 
   our _ ab initio _ studies of the electronic structure , magnetic moments , exchange interactions and curie temperatures in zb crx ( x = as , sb , s , se and te ) and cras@xmath0x@xmath0 ( x = sb , s , se and te ) reveal that half - metallicity in these alloys is maintained over a wide range of lattice parameters . the results for the exchange interaction and the curie temperature show that these alloys have relatively high curie temperatures , i.e. room temperature and above . 
   the exceptions occur for the alloys involving s , se and te at some low values of lattice parameters , where significant inter - atomic antiferromagnetic exchange interactions indicate ground states to be either antiferromagnetic or of complex magnetic nature . 
   a comparison of total energies for the fm , dlm , and two zb antiferromagnetic configurations ( afm[001 ] and afm[111 ] ) show the lowest energy configuration to be afm[111 ] for crs and crse for compressed lattice parameters ( table[table2 ] ) . 
   the possibility of afm ground states for compressed lattice parameters for crs was noted by zhao and zunger@xcite and for crse by sasioglu @xcite . 
   our search for the antiferromagnetic ground states is more thorough than what was reported in these two studies . 
   an extensive study of several antiferromagnetic configurations as well as ferrimagnetic and more complex magnetic structures for crs , crse and crte is currently underway . 
   the mixed pnictide - chalcogenide alloys cras@xmath0x@xmath0 ( x= s , se , te ) do not show any tendency to antiferromagnetic spin fluctuations for the entire range of the lattice parameter studied . 
   presumably the pnictogens suppress antiferromagnetic tendencies . 
   such alloys may play an important role in fabricating stable zb half - metallic materials , as the concentration of the pnictogens and the chalcogens may be varied to achieve lattice - matching with a given substrate . as long as the concentration of as or sb is higher than the chalcogen concentration 
   , half - metallic ferromagnetic state can be achieved . 
   there is a large variation in the curie temperature of these alloys ( fig . 
   [ fig19 ] ) as the lattice parameter varies from the low ( @xmath4 5.4  ) to the mid ( @xmath4 6.1  ) range of the lattice parameters studied . 
   this variation is much smaller for the isoelectronic alloys cras , crsb and cras@xmath0sb@xmath0 ( fig . 
   [ fig17 ] ) over this range of lattice parameters . 
   note that most ii - vi and iii - v zb semiconductors have lattice parameters in this range . 
   large changes in @xmath1 can be brought about by changing the carrier concentrations . 
   the pnictides in general have a higher @xmath1 than the chalcogenides . 
   our results for the curie temperature , the lattice fourier transform of the exchange interactions , and the resulting stability analysis are based on the exchange interactions between the cr atoms only . for 
   the fm reference states this causes some errors due to the neglect of the effects of the induced moments . 
   the dlm results are free from such errors . 
   it is expected that the present study will provide both qualitative and quantitative guidance to experimentalists in the field . 
   99 k. sato and h. katayama - yoshida , semicond . 
   * 17 * , 367 ( 2002 ) . 
   see k. sato , t. fukushima and h. katayama - yoshida , j. phys . : 
   matter * 19 * , 365212 ( 2007 ) , and references therein . 
   see b. belhadji , l. bergqvist , r. zeller , p.h . 
   dederichs , k. sato and h. katayama - yoshida , j. phys . : condens . 
   matter * 19 * , 436227 ( 2007 ) , and references therein . 
   h. saito , v. zayets , s. yamagata , and k. ando , phys . 
   lett * 90 * , 207202 - 1 ( 2003 ) . 
   k. sato and h. katayama - yoshida , jpn . 
   . phys . * 40 * , l651 ( 2001 ) . h. akinaga , t. manago , and m. shirai , jpn . j. appl . 
   phys.*39 * , l1118 ( 2000 ) . 
   s. li , j - g duh , f. bao , k - x liu , c - l kuo , x. wu , liya l , z. huang , and y du , j. phys . 
   phys . * 41 * 175004 ( 2008 ) . 
   m. shirai , j. appl . phys . * 93 * , 6844 ( 2003 ) . h. akinaga , m. mizuguchi , k. nagao , y. miura , and m. shirai in _ 
   springer lecture notes in physics _ * 676 * , 293 - 311 ( springer - verlag , berlin 2005 ) . 
   k. yamana , m. geshi , h. tsukamoto , i. uchida , m. shirai , k. kusakabe , and n. suzuki , j. phys . : condens . 
   matter * 16 * , s5815 ( 2004 ) . 
   l. kahal , a. zaoul , m. ferhat , j. appl . phys . 
   * 101 * , 093912 ( 2007 ) . 
   i. galanakis and p. mavropoulos , , 104417 ( 2003 ) ; see also i. galanakis , , 012406 ( 2002 ) . 
   pask , l.h . 
   yang , c.y . 
   fong , w.e . 
   pickett , and s. dag , , 224420 ( 2003 ) . 
   t. ito , h. ido , and k. motizuki , j. mag . mag . mat . * 310 * , e558 ( 2007 ) . 
   l - j shi and b - g liu , j. phys . : condens . 
   matter * 17 * , 1209 ( 2005 ) . 
   m. zhang , j. phys . : 
   matter * 15 * , 5017 ( 2003 ) . 
   j. kbler , , 220403(r ) ( 2003 ) . 
   b. sanyal , l. bergqvist , and o. eriksson , , 054417 ( 2003 ) . 
   xie , y - q . 
   xu , b - g . 
   liu , and d.g . 
   pettifor , 037204 ( 2003 ) . 
   zhao , f. matsukura , k. takamura , e. abe , d. chiba , and h. ohno , appl . 
   lett . * 79 * , 2776 ( 2001 ) . 
   k. ono , j. okabayashi , m. mizuguchi , m. oshima , a. fujimori , and h. akinaga , j. appl . 
   phys . * 91 * , 8088 ( 2001 ) . 
   zhao and a. zunger , , 132403 ( 2005 ) . 
   deng , j.h . 
   zhao , j.f . 
   niu , f.h . 
   yang , x.g . 
   wu , and h.z . 
   zheng , j. appl . phys . * 99 * , 093902 ( 2006 ) . j. kudrnovsk and v. drchal , , 7515 ( 1990 ) . 
   i. turek , v. drchal , j. kudrnovsk , m. ob , and p. weinberger , _ electronic structure of disordered alloys , surfaces and interfaces _ 
   ( kluwer , boston - london - dordrecht , 1997 ) . 
   vosko , l. wilk , and m. nusair , can . j. phys . * 58 * , 1200 ( 1980 ) . 
   savrasov , and d.yu . 
   savrasov , , 12181 ( 1992 ) . v. heine , j.h . 
   samson , and c.m.m . 
   nex , j. phys . 
   phys . * 11 * , 2645 ( 1981 ) . v. heine and j.h . 
   samson , j. phys . 
   * 13 * , 2155 ( 1983 ) . 
   h. hasegawa , j. phys . 
   jpn . * 46 * , 1504 ( 1979 ) . 
   pettifor , j. magn . 
   mater * 15 - 18 * , 847 ( 1980 ) . 
   staunton , b.l . 
   gyorffy , a.j . 
   pindor , g.m . 
   stocks , and h. winter , j. phys . 
   f * 15 * , 1387 ( 1985 ) . 
   pindor , j. staunton , g.m . 
   stocks , h. winter , j. phys . 
   f * 13 * , 979 ( 1983 ) . 
   e. sasaio@xmath7lu , i. galanakis , l.m . 
   sandratskii , and p. bruno , j. phys : condens . 
   matter * 17 * 3915 ( 2005 ) . 
   sandratskii , r. singer , and e. sasiolu , , 184406 ( 2007 ) . 
   m. pajda , j. kudrnovsk , i. turek , v. drchal , and p. bruno , phys . 
   b * 64 * , 174402 ( 2001 ) . 
   liechtenstein , m.i . 
   katsnelson and v.a . 
   gubanov , j. phys.f : met.phys . 
   * 14 * , l125 ( 1984 ) . 
   a. i. liechtenstein , m. i. katsnelson , v. p. antropov , v. a. gubanov , j. magn . 
   magn . mater . * 
   67 * , 65 ( 1987 ) . 
   liechtenstein , m.i . 
   katsnelson and v.a . 
   gubanov , solid.state.commun . * 
   51 * , 1232 ( 1984 ) . 
   a.i . liechtenstein , m.i . 
   katsnelson , v.p . 
   antropov and v.a . 
   gubanov , j.magn.magn.mater . 
   * 21 * , 35 ( 1988 ) . 
   gubanov , a.i . 
   liechtenstein , a.v . 
   postnikov _ magnetism and the electronic structure of crystals _ , edited by m. cardona , p. fulde , k. von klitzing , h .- j . 
   queisser ( springer , berlin , 1992 ) . 
   see , e.g. , o.k . 
   andersen , o. jepsen , and d. gltzel , in _ highlights of condensed matter theory _ , edited by f. bassani ( north - holland , amsterdam , 1985 ) , p.59 . v. heine , _ solid state physics _ * 35 * ( academic press , new york ) , 1 ( 1980 ) . a. oswald , j. phys . 
   f * 15 * , 193 ( 1985 ) . 
   f. ducastelle , `` order and phase stability in alloys '' ( north - holland , amsterdam , 1991 ) . 
   m. sluiter , and p.e . 
   a. turchi , phys . 
   b * 40 * , 11215 ( 1989 ) . 
   connolly and a.r . 
   williams , phys . 
   b * 27 * , 5169 ( 1983 ) . 
   z.w . lu , s .- h . 
   wei , a. zunger , s. frota - pessoa , and l.g . 
   ferreira , phys . 
   b * 44 * , 512 ( 1991 ) . l.m . 
   sandratski , j. phys . : condens . 
   matter 3 , 8565 ( 1991 ) . 
   i. turek , j. kudrnovsk , v. drchal , and p. bruno , philos . mag . * 86 * , 1713 ( 2006 ) . 
   wang , r.e . 
   prange , and v. korenman , phys . 
   b * 25 * , 5766 ( 1982 ) . 
   j. rusz , l. bergqvist , j. kudrnovsk , and i. turek , phys . 
   b * 73 * , 214412 ( 2006 ) . 
   l. jiang , q. feng , y. yang , z. chen , and z. huang , sol . 
   . comm . * 139 * , 40 ( 2006 ) . 
   s. curtarolo , d. morgan and g. ceder , comp . 
   phase diagrams and thermochemistry * 29 * , 163 ( 2005 ) .
summary: we present calculations of the exchange interactions and curie temperatures in cr - based pnictides and chalcogenides of the form crx with x = as , sb , s , se and te , and the mixed alloys cras@xmath0x@xmath0 with x = sb , s , se , and te . 
   the calculations are performed for zinc blende ( zb ) structure for 12 values of the lattice parameter between 5.44 and 6.62  , appropriate for some typical ii - vi and iii - v semiconducting substrates . 
   electronic structure is calculated via the linear muffin - tin - orbitals ( lmto ) method in the atomic sphere approximation ( asa ) , using empty spheres to optimize asa - related errors . whenever necessary 
   , the results have been verified using the full - potential version of the method , fp - lmto . 
   the disorder effect in the as - sublattice for cras@xmath0x@xmath0 ( x = sb , s , se , te ) alloys is taken into account via the coherent potential approximation ( cpa ) . 
   exchange interactions are calculated using the linear response method for the ferromagnetic ( fm ) reference states of the alloys , as well as the disordered local moments ( dlm ) states . 
   these results are then used to estimate the curie temperature from the low and high temperature side of the ferromagnetic / paramagnetic transition . 
   estimates of the curie temperature are provided , based on the mean field and the more accurate random phase approximations . 
   dominant antiferromagnetic exchange interactions for some low values of the lattice parameter for the fm reference states in crs , crse and crte prompted us to look for antiferromagnetic ( afm ) configurations for these systems with energies lower than the corresponding fm and dlm values . 
   results for a limited number of such afm calculations are discussed , identifying the afm[111 ] state as a likely candidate for the ground state for these cases .