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magnetic phenomena at surfaces and interfaces have been studied extensively in recent years .
this interest in surface magnetism has been stimulated by the needs of technology ( magnetic storage media , spintronics ) as well as the development of tools for research in this field , both experimental ( e.g. the spin - polarized scanning tunneling microscope ) @xcite and computational ( increasing speed and memory capacity of computers ) .    reduced number of nearest neighbors at surfaces and lowering of crystal symmetry due to the presence of the surface are known to have a deep impact on magnetic properties .
the magnetic moments of atoms in the surface layer are often substantially enhanced as compared to corresponding local magnetic moments inside the bulk .
elements that are known to be nonmagnetic in their bulk form can be magnetic when placed on a surface .
an interesting example of how the chemical and geometrical properties of a surface may influence the magnetism of an adsorbate has been reported recently .
experiments indicated that iron monolayers on the ( 001 ) tungsten surface had zero net magnetization ( see @xcite and references therein ) , in contrast , e.g. , to iron monolayers on the w(110 ) surface that are known to be ferromagnetic @xcite .
the question whether they were really non - magnetic or rather antiferromagnetic was resolved by kubetzka @xcite using the spin - polarized scanning tunneling microscope . here , antiferromagnetic @xmath1 fe - monolayer on the w(001 ) was directly observed .
the subsequent theoretical study by ferriani @xcite showed that iron and cobalt monolayers tend to be antiferromagnetic on the w(001 ) surface while v , cr and mn monolayers tend to the ferromagnetic order .
it should be noted that just an opposite trend is observed on the w(110 ) surface , on which v , cr , and mn monolayers are @xmath2 antiferromagnets while fe and co order ferromagnetically .
the same or similar situation as on the w(110 ) surface occurs also on many other substrates , e.g. on cu , ag and pd ( 001 ) surfaces ( see references in @xcite ) .
our goal is to generalize the above study to the case of binary two - dimensional alloys on the w(001 ) surface .
the disorder in the surface layer and the interaction between chemically different surface atoms are expected to lead to new types of magnetic phases .
we have focused on the femn system in which alloy constituents exhibits antiferromagnetic ( fe ) and ferromagnetic ( mn ) order as pure overlayers .
the frustration that results from the competing interactions will play a key role in formation of more complex magnetic structures .
the electronic structure was described in the framework of the tight - binding linear muffin - tin orbital ( tb - lmto ) method with the atomic sphere approximation ( asa ) @xcite .
the spin - polarized local density approximation ( lda ) with the parametrization of vosko , wilk , and nusair @xcite for the exchange - correlation potential was used .
the spin - orbit interaction was neglected .
the surface green function formalism was used to describe the electronic structure of an overlayer on substrate with realistic boundary conditions .
the substitutional disorder was treated by means of the coherent potential approximation ( cpa ) , which neglects local environment effects .
in addition to the standard asa , a dipole surface barrier was included .
the geometry of the system is the body - centered cubic ( bcc ) lattice of tungsten with the experimental lattice constant .
the self - consistent electronic structure calculations were performed on an eight - layer slab : the slab consisted of four tungsten layers , one layer of @xmath0 transition - metal alloy , and three empty layers that mimicked the vacuum above the surface .
the slab was then matched to a semi - infinite vacuum region on one side and to a semi - infinite tungsten bulk on the other side .
the layers of the surface slab form an ideal continuation of the bulk structure and possible layer relaxations are neglected .
we have tested the stability of various magnetic phases of two - dimensional random overlayers on the w(001 ) substrate .
in addition to the ferromagnetic ( fm ) phase , we have also considered the dlm phase ( disordered local moments ) , the so - called apm phase ( antiparallel arrangement of moments ) , and the uncompensated dlm ( udlm ) phase .
the dlm phase is defined by randomly oriented local magnetic moments .
the distribution of directions is uniform in the whole space .
such a structure can be efficiently studied using the spin - polarized cpa : the infinite number of possible orientations of local moments can be replaced by two equally large groups of atoms with opposite orientations of local moments .
the dlm phase of a binary alloy x@xmath3y@xmath4 can be formally described as a four - component alloy x@xmath5x@xmath6y@xmath7y@xmath8 , where the superscripts denote the orientations of respective local moments .
the dlm structure has a zero total magnetization similarly as any antiferromagnetic structure .
in contrast to an ordered antiferromagnetic structure , however , the local moments in the dlm phase are distributed on the lattice randomly .
energetic preference of the dlm arrangement to the ferromagnetic one is an indication that the antiferromagnetic arrangement would be favored over ferromagnetism .
the apm arrangement in a binary alloy is defined as a magnetic phase in which all local moments of one component are aligned in one direction and all local moments of the other component are aligned in the opposite direction .
the apm phase can be described as x@xmath9y@xmath10 .
this arrangement resembles a ferrimagnetic one in a similar way as the dlm resembles antiferromagnetism .
it should be noted that both the antiferromagnet or ferrimagnet assume the existence of two different sublattices while the dlm or apm arrangement exist on one lattice .    a mixed magnetic state , which we denote as dlm(x)+fm(y ) ,
can be represented by a ternary compound x@xmath5x@xmath6y@xmath11 .
the most general phase is the uncompensated dlm state ( udlm ) .
it can be approximated as a four - component alloy x@xmath12x@xmath13y@xmath12y@xmath13 where all occupation probabilities ( concentrations ) , @xmath14 , @xmath15 , @xmath16 , @xmath17 , are arbitrary with the obvious constraints @xmath18 and @xmath19 .
all previously discussed phases can be viewed as special cases of the udlm .
the local magnetic moments of fm , dlm and apm phases of the femn / w(001 ) alloy are shown in fig .
1 and contrasted with behavior of the fev / w(001 ) system . magnetic moments of mn and also of fe are rigid , only weakly influenced by their environment .
total energies for the femn / w(001 ) alloys in different magnetic phases are presented in fig .  2 .
to analyze it , let us consider pairwise magnetic interactions only and suppose that the magnetic interaction between two atoms is determined by the atoms themselves independently of their environment .
we can then approximate the dependence of energy on magnetic configuration by a simple quadratic form @xmath20 specifically , we get : @xmath21 the parameters @xmath22 , @xmath23 , and @xmath24 have been chosen to fit the calculated total energies of the ferromagnetic fe / w(001 ) surface , the ferromagnetic mn / w(001 ) surface , and the fe@xmath25mn@xmath25/w(001 ) surface in the apm phase .    [ cols="^ " , ]     we have also investigated the udlm states to find the state with the lowest total energy .
good sampling of possible udlm configurations requires a large number of calculations .
we have therefore performed calculations for only three different compositions of femn ( see table  [ tabu ] ) . it should be noted that for all concentrations mn moments prefer ferromagnetic alignment ( @xmath26  =  0 ) .    for some surface alloy compositions ,
there are udlm states that have lower total energy than the special magnetic arrangements discussed so far .
we have verified that the formula ( [ eq1 ] ) describes fully self - consistent calculations for femn alloys with a good accuracy even in the udlm phase under the assumption that parameters @xmath22 , @xmath23 , and @xmath24 are determined from calculated total energies of the dlm , fm , apm , and dlm+fm phases .
the existence of udlm phases is a consequence of the interplay between the three basic trends discussed above .    for pure fe and mn monolayer
is the first interlayer distance reduced by 13.7% and 4.7% , respectively @xcite . to judge the impact of interlayer relaxation on our results , we have reduced distances between femn alloy addlayer and the first tungsten layer by 10% .
this relaxation has no remarkable influence on magnetic behavior of femn alloy film .
nevertheless , the surface relaxation suppress magnetic moments of iron and manganese atoms slightly because of @xmath27-band broadening due to stronger bonding with substrate .
we have investigated magnetic ground states of two - dimensional binary femn transition - metal alloys on w(001 ) . for pure monolayers
we have found that fe overlayer order antiferromagnetically while mn atoms prefer the ferromagnetic alignment . in alloy monolayers , fe and
mn tend to orient their local magnetic moments antiparallel to each other .
incompatible tendencies of magnetic moment alignments among fe and mn atoms lead to an uncompensated dlm phase , which becomes the calculated ground state for some alloy compositions .
this indicates tendency to a non - collinear ground state . to reach a more detailed understanding of the alloyed monolayers on w(001 ) , further sp - stm measurements as well as theoretical calculations
are needed . + * acknowledgments *
we investigate theoretically the ground state of the femn binary alloy monolayer on the w(001 ) surface , the stability of different magnetic configurations ( ferro / antiferromagnetic , disordered local moments , etc . ) and estimate concentrations at which a transition occurs between different magnetic orders . 
 the tight - binding linear muffin - tin orbital method combined with the coherent potential approximation is used to treat the surface alloy appropriately . 
 we discuss the role of disorder on the phase transitions in surface alloys composed from two different @xmath0 transition metals .    
 manganese ; iron ; alloy ; surface magnetism ; density functional calculations