First Principles Calculations of Fe on GaAs (100)

9 Pages·0.18 MB·English

by  S. Mirbt

First Principles Calculations of Fe on GaAs (100).
S. Mirbt, B. Sanyal, C. Isheden, and B. Johansson
Department of Physics, Uppsala University, Uppsala, Sweden
(Dated: February 2, 2008)
Wehavecalculatedfromfirstprinciplestheelectronicstructureof0.5monolayerupto5monolayer
3 thickFelayers on top of a GaAs (100) surface. WefindtheFemagnetic moment to bedetermined
0 by the Fe-As distance. As segregates to the top of the Fe film, whereas Ga most likely is found
0 withintheFefilm. Moreover,wefindanasymmetricin-planecontractionofourunit-cellalongwith
2 an expansion perpendicular to the surface. We predict the number of Fe 3d-holes to increase with

n increasing Fethickness on p-doped GaAs.
a
J PACSnumbers: 75.70.-i,82.65.+r,75.50.Bb,72.25.Mk

9
2
I. INTRODUCTION strate and 1 to 10 Fe atoms (0.5 monolayer to 5 mono-
] layers)on top of the GaAs substrate. A vacuum of 10 ˚A
ci Inthe contextofmagnetoelectronicsitisimportantto thicknessormorewaskepttoavoidinteractionsbetween
s understandthestructuralandelectronicpropertiesofthe neighboringunitcellsinthe(001)direction. Tosimulate
-
l interfacebetweenFeandGaAs[1,2]. Severalexperimen- a bulk semiconductor, the lowermost Ga/As layer was
tr tal investigations have been performed on this interface passivatedwithpseudohydrogenatoms[26]. Volumeand
m [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17]. Under shape relaxationswere allowedalongwith the relaxation
. As-rich conditions the Fe film growing on top of GaAs of the atoms. All atoms were relaxed except the 2 bulk
t
a is found to have a reduced magnetic moment, or even semiconducting atoms. It is worth mentioning that the
m a zero magnetic moment close to the interface [3, 4, 5]. bccFeisperfectlylatticematchedtotheGaAssubstrate
- Moreover,structuralinvestigationsofthe Fe film lead to (zinc-blende lattice). The GaAs lattice constant (5.65 ˚A
d the conclusion that between a bcc Fe film and the GaAs )isalmosttwice ofthe lattice constantofbcc Fe (2.87˚A
n
substratethereexistsanintermediatephase,Fe Ga As ). Thus the GaAs unit cell is equivalent to two bcc unit
o x y z
c [6, 7]. Under Ga-richconditions no traces of an interme- cells. We used a lattice constant of 5.735 ˚A which cor-
[ diatephasearefoundandthemagneticmomentisfound respondsto the calculatedGaAsbulk equilibriumlattice
to be bulk-like even close to the interface [8, 9]. constant within GGA. The lattice constant of bulk Fe is
1
Other theoretical investigations of the Fe/GaAs(100) calculated to be only 0.05% smaller. The energies were
v −4
3 interface [18, 19, 20, 21] have been performed. Except convergedwithanaccuracyof10 eV.ThePulaystress
6 of the calculations by Erwin et al [20], all other calcula- we find to be negligible, being of the order of 0.1 kB.
5 tions considered only an ideal Fe/GaAs interface. Erwin Local magnetic moments were obtained by projecting
1 focusedonFeadatomgrowthandmagneticpropertiesof wave functions onto spherical harmonics within spheres
0 the interface and allowed for ionic relaxations only per- centeredontheatoms[27]. Weused1.302˚A 1.402˚A and
3 pendicular to the surface (i.e along the z-direction). In 1.355˚AforFe,Ga,andAsspheres,respectively. Inorder
0
general their results agree with our calculations. In this tocompareenergiesofdifferentinterfacegeometrieswith
/
at paper wepresentaninvestigationofthe (completely)re- anon-equivalentnumberofatoms,weusedthe following
m laxedFe/GaAsinterfacestructure. WestudytheFemag- definition of the formation energy:
netic moment as a function of the Fe film thickness and
-
d therelaxedstructureoftheFefilm. Inadditionwestudy Eform =Etotal−XNiµi. (1)
n As and Ga segregation. We discuss the origin of the so i
o
called magnetically dead layers on top of GaAs and why
c N isthenumberofnonequivalentatomsofspeciesi,and
Fe growth differs on As terminated and Ga terminated i
:
v interfaces. µi is the chemical potential. We estimated the chemical
i potential by calculating the total energy of species i in
X
its bulk form.
r
a II. COMPUTATIONAL DETAILS
We have performed self-consistentfirst-principles den- III. GAAS SURFACE
sityfunctionalcalculationsemployingaplanewavepseu-
dopotential code (VASP ) [22]. PAW pseudopotentials The GaAs (100) surface structure depends on the
[23] with an energy cutoff of 24.61 Ryd were used. Ex- growthenvironment. UnderAsrichconditionstheGaAs
change correlation was treated within the generalized (100)surfaceshowsac(4x4)[28]reconstruction,whereas
gradient approximation (GGA) [24]. We used a (4x4x4) under Ga rich conditions the GaAs (100) surface shows
folding of special k-points [25]. We used a unit cell hav- an ǫ(4x2) [29] reconstruction. All these reconstructions
ing 6 semiconducting layers (3 Ga and 3 As) as the sub- differ from an ideally terminated surface -where either
2
−8
V A C U U M
−9 FeGa Fesideal Fes Fei Fes+Gai
V]
e
gy [ −10
er
n
e
e
esiv −11
h
o
C FeAs
−12 <001>
−13
2 2.2 2.4 2.6 2.8
D [Å]
BULK GaAs
FIG. 1: Cohesive energy as a function of the Fe-X distance
<1−10>
(X=As,Ga) for a bulk zincblende FeX structure. The up-
percurve(circles) correspondstozincblendeFeGa,thelower FIG. 2: Geometrical structure of 0.5ML Fe on top of
curve(squares) to zincblendeFeAs. GaAs(100). Circles (diamonds) represent As (Ga) and tri-
anglesrepresentFe. Thefourcolumnscorrespondtofourdif-
ferent interface configurations as discussed in the text. The
atomic positions are shown along the < 1¯10 > direction,
onlyGaoronlyAsexistsatthesurface-bytheexistence
bondsare indicated by thelines connecting theatoms.
of Ga-Ga and (or) As-As dimers.
In a first attempt to understandthe interface between
Fe and GaAs we neglect any surface reconstructions and
fore,ifitiskineticallypossible,FereplacesaGaatomin
assume an ideal Ga(As) terminated surface. In order
the interface region independent of the surface termina-
to justify this approximation, let us assume we would
tion. Inaddition,energyisgained,-independently ofthe
growFeontopofsomereconstructedGaAssurface. The
termination-, if As segregates to the surface (see section
interaction of Fe with the dangling bonds of As or Ga
VI). The experimentally observable physical properties
is already included in our calculation assuming an ideal
of the Fe on GaAs(100)system are thus governedby ex-
cut. The question is now what happens with the As-As
trinsic effects like growth conditions and in addition the
(Ga-Ga) dimers, when Fe is present at the surface? In
surfaceterminationgovernsthekineticconditionsforthe
a recent paper Erwin et al. [20] calculate that Ga and
Fe growth, i.e the height of involved barriers, diffusion
As surface dimers become unstable under Fe adsorption
probability, probability distribution of As atoms versus
and Fe-Ga resp. Fe-As bonds form instead. This implies
Ga atoms within the Fe film.
thatourcalculationassuminganidealcut surfacecovers
In this paper we discuss the physical properties of an
most of the physics at the Fe-GaAs interface. Moreover,
Fe filmonanAs-terminatedsurface,butourconclusions
experimental results by Kneedler et al. [16] warrant our
arevalidindependentofthetermination,sincewedonot
approximation to ignore the surface reconstruction de-
calculate any kinetic properties.
tails. They investigated the influence of the GaAs sur-
face reconstructions on the properties of the growing Fe
film. They compared two As-rich terminations, the 2x4
and the c(4x4). In summary they find, although the Fe IV. STRUCTURAL PROPERTIES
island morphology is different, the growth mode, inter-
facial structure, magnetic behaviour, and the uniaxial In GaAs bulk an Fe impurity is most likely found in a
anisotropy to be independent on the chosen As-rich sur- Ga-substitutionalposition,i.eFereplacesaGaatom. For
face reconstruction. 0.5 ML Fe on top of a (100) GaAs surface, we compare
The difference in Fe growth between a Ga-terminated herefourdifferentFeconfigurations(Fig.2). Weshowthe
andanAs-terminatedsurfacecanbeexplainedlargelyby fourdifferentFeconfigurationsintheorderofdecreasing
kinetic arguments. In Fig.1 we show the cohesive energy formation energy: Feideal corresponds to one Fe atom
s
asafunctionoftheFe-Ga(Fe-As)distanceforbulkFeGa (i.e. 0.5 ML) sitting on top of GaAs at the position of a
(FeAs) in a zincblende structure. (These artificial struc- Gaatom,thatisFesitssubstitutionally(s)followingthe
tures only serve as a tool to understand the FeAs and ideal stacking (no lattice relaxations). Fe corresponds
s
FeGa interaction.) The cohesive energy of zincblende to one Fe atom having replaced the Ga atom closest to
FeAs is about 4 eV lower than of FeGa. Thus the in- the surface, that is the Fe atom becomes buried under
teraction between Ga and Fe is much weaker than be- the surface. Fe corresponds to one Fe atom sitting in a
i
tween As and Fe, because As has three p-electrons and buried position but at an interstitial (i) position of the
Ga only one p-electron, which gives rise to a larger pd- ideal GaAs lattice. Fe +Ga finally corresponds to one
s i
hybridization between As and Fe. According to Eq.2, Fe atomsitting inasubstitutionally buriedposition, but
energy is gained, when Fe replaces a Ga atom. There- in addition a Ga atom is now sitting in an interstitial
3
2000 3 1000
Feideal 2.5
s
1500
2 500
meV] 1000 1.5µ]B meV]
E [form 1 M [Fe E [(Fe+Ga)si
500 Fes Fe 0.5 E−(Fe)i 0
i
Fe+Ga
s i
0 0
FIG.3: Formationenergy,Eform,of0.5MLFeconfigurations −500 1 2 3 4 5
Fe thickness [ML]
(see Fig.2) relative to the lowest configuration, Fes +Gai.
Alsoindicated is themagnetic moment of theFeatom (right
FIG. 4: Energy difference between an interface configuration
scale and diamonds).
whereFesitsinterstitial(Fei)andwhereFesitssubstitutional
together with an interstitial Ga (Fes+Gai) as a function of
theFe film thickness.
position.
In Fig.3 we show the formation energy relative to the
formation energy of the Fe +Ga configuration. Let us
s i
TABLE I: Calculated c/ < a > ratio and in-plane lattice
now discuss these results: The four configurations dif-
contraction of the unit cell along the < 1¯10 > and < 110 >
fer by the number of vacant neighbours that each Fe
direction for the lowest energy configuration of the specified
atom has: In the Feideal configuration, Fe has four va-
s Fefilm.
cant neighbours, in the Fe , Fe has three vacant neigh-
s c/<a> <1¯10> <110>
bours, and in the other two configurations, Fe has only
0.5 ML Fe 1.07 -1.15 % -6.92 %
two vacant neighbours. The more neighbours the Fe
1 ML Fe + 0.5 ML As 1.03 -0.51 % -3.66 %
atom has, the more energy is gained due to increased 1 ML Fe + 1ML As 1.02 +0.86 % -2.79 %
wavefunction overlap. Thus the Feisdeal configuration is 2 ML Fe + 0.5 ML As 1.10 -0.81 % -5.61 %
highest in energy, because the wavefunction overlap be- 2 ML Fe + 1 ML As 1.05 +0.86 % -2.79 %
tween Fe and its surrounding is minimal. Next we con- 5 ML Fe + 0.5 ML As 1.04 -1.15 % -2.74 %
sider the Fe configuration, which is already 1 eV lower 5 ML Fe + 1 ML As 1.03 +0.51 % -1.83 %
s
than Feideal. Besides having one more neighbour than
s
Feideal, in the Fe configuration two Fe-As bonds have
s s
formed. For this configuration the Fe magnetic moment
dilute (sub-monolayer)Fe filmon topofGaAs (100)will
is totally quenched. This will be further discussedin the
break the top GaAs bonds and create Fe-As bonds and
next section. The Fe and Fe +Ga configurations are
i s i Ga instead.
i
lowerthanFe becausetheyonlyhavetwovacantneigh-
s Even for thicker Fe films this is in principle still valid.
bours. These two configurations are similar except that
ButanFeinterfaceatomboundedtoanFefilmwillhave
thetopmostGaandFepositionshavebeeninterchanged.
a reduced mobility compared to an Fe adatom. This
We find from our calculation
might prevent Fe from dissolving GaAs. This kinetic is-
sue we have not studied any further. We calculate an
EGa−As+EFei >EFe−As+EGai, (2) Feideal IC to be preferred if As and Ga segregation is
s
where EGa−As (EFe−As) is the formation energy of a neglected. This result is in agreementwith a calculation
Ga-As (Fe-As) surface bond and E (E ) is the for- byErwinetal[20]. ButincludingAssurfacesegregation
Fei Gai
mation energy of an interstitial surface defect Fe (Ga ) (still neglecting Ga segregation) we find the Fe +Ga
i i s i
. IC to have the lowest energy almost independent of the
We compared the charge density and performed an Fe film thickness. InFig.4 we showthe energydifference
(unrelaxed)calculationwithouttherespectiveinterstitial between the Fe and Fe +Ga interface configurations
i s i
atom. Inbothconfigurations,the topGaatomformsto- (IC)for a varyingnumberofFe thickness. For 0.5,1and
getherwiththeFeatomametalliclayer. Thedifferenceis 5 ML of Fe we calculate the Fe +Ga IC to be lower in
s i
the bonding: For Fe we have mainly two Ga-As bonds energy. Ontheotherhand,for1.5and2MLofFewecal-
i
and one Ga-Fe metallic bond, whereas for Fe + Ga culatetheFe ICtobelowerinenergy. Itistheexchange
s i i
we have two Fe-As bonds and again one Ga-Fe metallic energy that stabilizes the Fe configuration, since in a
i
bond, but in addition the interstitial Ga atom bonds to non-spin polarized calculation we find again Fe +Ga
s i
it’s As neighbours. This Ga -As interaction reduces the to be lower. (This will be further discussed in the next
i
Fe-As interaction, whereby the Fe magnetic moment is section.) If both As and Ga segregation are included
closetoit’s bulkvalue. Itisthus theGa thatlowersthe (sectionVI), we find Fe to dissolve GaAs independent of
i
energy of the Fe +Ga configuration. In summary, a thickness.
s i
4
3
TABLE II: Total magnetic moment and atomic distances for
the respective closest topmost atoms for 1ML of Fe for the Fe interface
i
three interface configurations shown in Fig.6. Ga-As (h)
(GaAs (v)) indicates thehorizontal (vertical) distance. Bulk
2
Fei Fes+Gai Fes+Gai om]
start final µ/atB
Fe - As 2.61 ˚A 2.42 ˚A 2.32 ˚A > [
Fe - Ga 2.96 ˚A 2.42 ˚A 2.51 ˚A <MFe 1
Ga - As(h) - 2.87 ˚A 2.82 ˚A (Fes+Gai) interface
Ga - As(v) - 2.42 ˚A 3.61 ˚A
Ga - Ga - 2.44 ˚A 2.44 ˚A
Mcell 4.63 µB - 0.01 µB 0 1 2 3 4 5
Fe thickness [ML]
Inarecentx-rayabsorptionfinestructurespectroscopy FIG.5: AverageFemagnetization,<MFe >,asafunctionof
the Fe film thickness for two interface configurations. Solid
(XAFS) study Gordon et al [11] found the Fe film on
(dotted) line corresponds to the Fes +Gai (Fei) IC. The
GaAs(100) to be tetragonal distorted relative to bulk
solidhorizontallineindicatesthecalculatedFebulkmagnetic
bcc Fe. The measured distortion involved an in-plane moment.
contractionandanexpansionperpendiculartotheGaAs
V A C U U M
surface to give a c/a ratio of 1.03. In tab.1 we have col-
lected the calculated c/a ratio as a function of the Fe
Fe Fe+Ga Fe+Ga
film thickness and As coverage. Our results agree rather i s i s i
start final
goodwithexperiment. Wefindinagreementwithexper-
imentforourenergeticallylowestinterfaceconfigurations
an in-plane contraction and an expansion perpendicular
to the GaAs surface. In addition we find a rather large
asymmetry in the in-plane contraction. In general the >
1
contraction along the < 110 > direction is larger than 00
along the <1¯10> direction. We even find an expansion <
along the < 1¯10 > direction for all studied Fe coverages
which are covered by a complete As monolayer.
The expansion perpendicular to the GaAs surface is
connected to the Ga-content within the Fe-film, because
forourcalculationswithoutanyGaatomswithintheFe-
film we find instead a contraction perpendicular to the
BULK GaAs
GaAs surface. The in-plane asymmetry is caused by the
<1−10>
directional bonds of the GaAs substrate. On the As-
terminated surface, the As dangling bonds are oriented FIG. 6: Geometrical structure of 1 ML Fe on top of
along the <1¯10> direction. Because ofthe Fe-As inter- GaAs(100). Circles (diamonds) represent As (Ga) and tri-
angles represent Fe. The three columns correspond to three
action and the Fe +Ga IC, an expansion/contraction
s i
along the < 1¯10 > direction has to optimize the Fe- different configurations as discussed in the text.
As interaction. In contrast, an expansion/contraction
along the < 110 > direction is a reaction on the ex-
pansion/contraction along the other two directions in show the atomic
order to optimize the overall volume. Therefore, the configuration for Fe and Fe +Ga for the Fe thick-
i s i
< 1¯10 > and < 110 > direction are asymmetric. For a ness of 1 ML. It can be seen by comparing the starting
Ga-terminatedsurfacethesameisvalid,butthe<110> and final positions, that for Fe +Ga the Fe-As bond
s i
and<1¯10>directionsareinterchanged. Note,thatthis distance has decreased (tab.2). In addition the ’vertical’
in-plane asymmetry explains the in-plane uniaxial mag- Ga-Asbondsarebrokenandthethreetoplayersbecame
netocrystaline anisotropy [17, 30]. shifted along the < 1¯10 > direction. This suggests that
the three top layers now form a separate 2-dimensional
phase.
V. MAGNETIC PROPERTIES In order to understand the decreased magnetic mo-
ment, we plot in Fig.7 the Fe magnetic moment as a
In Fig.5 we show the average Fe magnetic moment as functionoftheFe-aniondistance,D,(i.e. theFe-Asdis-
a function of the Fe thickness for the Fe andFe +Ga tance) for all different configurations that we have cal-
i s i
IC. Surprisingly, we calculate for the thickness of 1 ML culated. It can be seen that for D = 2.36 ˚A, the Fe
of Fe the Fe magnetic moment to be zero. In Fig.6 we magnetic moment disappears. We interpret this to be
5
3 critical D. In contrast to Fe on GaAs, the Fe mag-
netic moment is not quenched on ZnSe [31]. In order
to understand the difference between GaAs and ZnSe
2 MBulk we also calculated zincblende FeSe and for comparison
zincblende FeTe. In all three cases, i.e. FeAs, FeSe, and
µM []FeB 1 iFoenT’se,pt-heeleFcterdo-nesl.ecTtrhoenrsefhoyrebrtihdeizreewexitishtsthaebreosnpdecdtiisvteanacne-
al
oc at which the Fe magnetic moment becomes quenched
L
(Fig.8). The exact value of the critical D depends on
0
the system in question. For a given lattice constant (set
by for example the semiconductor host), the anion will
occupya certainfractionofthe unit cellvolumethatde-
−1
2 2.2 2.4 2.6 2.8 3 pends on its atomic radius. GaAs and ZnSe have about
D [Å]
the same lattice constant. The As atomic radius (1.14
˚A) is larger than the Se radius (1.03 ˚A). The pd-overlap
FIG. 7: Local magnetic moment of Fe, MFe, as afunction of
between Fe and Se is therefore (for the same lattice con-
the Fe-As distance , D. Solid (dashed) horizontal line indi-
catesthebulkFemagneticmoment(zero-line)andthedashed stant) smaller than between Fe and As and the Fe mag-
vertical line at 2.37 ˚A indicates the Fe-As distance at which netic moment starts to become quenched for a smaller
theFe magnetic moment becomes zero. D. On the other hand the Te radius (1.23 ˚A) is larger
andthemagneticmomentbecomesquenchedalreadyfor
a larger D.
4
As clearly visible from Fig.8 there exist high-spin, low
spin, and zero moment phases as a function of D. The
3
energy difference between these phases becomes rather
small for a given D. This will be further investigated in
µ]B 2 MBULK the future. We concludethatthe magnetic configuration
M [Fe of Fe on GaAs will be determined by pd-hybridization,
cal 1 but that the specific magnetic phase of the Fe-As com-
o
L
plex depends on small variations of the Fe-As bonding.
0 For example, in earlier publications [19, 20] an antifer-
romagnetic (AFM) solution of the Fe film has been dis-
cussed and calculated. Especially for the 1 ML thick Fe
−1
2.1 2.3 2.5 2.7 film an AFM solution was found. We also investigated
D [Å]
the possibility of an AFM solution. For a 1 ML Fe film
coveredwithacomplete MLofAs wefindanAFMsolu-
FIG. 8: Bulk magnetic moment per Fe atom for zincblende
tionforaFe interfaceconfiguration(0.22µ ,−0.22µ ).
FeAs (circles), zincblende FeSe (diamonds), and zincblende s B B
FeTe (triangles) as a function of the Fe-anion distance, D. The involved magnetic moments are so small because of
The dashed vertical line is the same as in Fig. 7 shown here theFe-Aspd-hybridizationasdiscussedabove. Thetotal
for comparison. energy is 3 meV higher than a solution with a zero mag-
netic moment on both Fe sites, i.e the AFM solution is
almostdegeneratewiththezeromomentperFeatomso-
caused by pd-hybridization: The Fe spin-polarization is lution. FortheFes+Gaiinterfaceconfigurationweagain
drivenbytheon-siteexchangeinteraction. Thereforethe find an AFM solution (0.05µB, -0.05µB) being 10 meV
Fe magnetic moment decreases with increasing delocal- higher than a solution having a total magnetic moment
ization of the Fe d-states. Because, the delocalization of of0.5µB. Anotherexamplewefindfromourcalculations
the Fe d-states increases with increased overlapbetween is a ferrimagnetic solution. The structure consists of a 5
the Fed-statesandAs p-states,wefindthatthe Femag- MLthickFefilmontopofGaAscoveredwith0.5MLAs
neticmomentisquenchedforsmallFe-Asbonddistances. andanadditional0.5MLAswithinthe Fefilm. Thetop
Thespreadinmagneticmomentsforbondlengthsabove Fe atomhasamagneticmomentof−2.1µB, whereasthe
2.36˚A isduetotheotherfactorsinfluencingtheFemag- two Fe atoms/cellin the next layer beneath have a mag-
netic moment, likenumber ofFe neighboursandnumber netic moment of 0.95µB and 1.2µB, respectively. Below
of vacant neighbours. thislayertheadditional0.5MLAsislocated. Therestof
the Fe atoms have a magnetic moment close to or larger
Our interpretation is supported by the behaviour of
than the bulk value. The average magnetic moment for
theFemagneticmomentinthebulkFeAszincblendcom-
this ferrimagnetic solution is 1.55µ per Fe atom.
pound (circles in Fig.8). We show the Fe magnetic mo- B
ment as a function of the Fe-anion distance (D) in the Since the magnetic phase diagram of the Fe-As inter-
zincblend lattice. The same trend as before is observed, action is rather complex, it very much depends on small
namely the Fe magnetic moment becomes smaller at a details of the Fe film configuration which magnetic mo-
6
3 atoms per cell) on top of the Fe film. The Ga atom does
V Ga not influence the Fe magnetic moment, i.e the Ga-Fe in-
A As teraction is very weak. On the other hand, the Fe-As
C
atom] 2 UUM SUB ibnetfeorraec)t.ioFnorquthenec1hMesLthAesmcoavgenreatgice,mthome Fenetm(aasgndeistcicusmseod-
µ/B S mentofthetopFelayeristhusalmostzero(Fig.10). IfFe
M [Fe T is covered with only 0.5 ML As, the Fe-Fe interaction is
cal 1 RA strongerthan the Fe-As interactionandthe Fe magnetic
o
l T moment is not reduced (Fig.9).
E
From our calculations we can conclude:
0 Fe Fe Fe Fe Fe Fe > EFxce >EFe−As. (3)
As Fe Ga Fe Fe Fe As 10
−
<001> <1
FFeIG(.190:FLeoactaolmFse/cmelal)gnoentitcopmoofmGenatA,sMcoFvee,repdrowfiliethfo0r.56MMLL EFe−As >EFxce+EFe−Fe. (4)
As and 0.5 ML Ga within the Fe film. The horizontal line
indicatesthecalculatedbulkFemagneticmoment. Thefilled
(noeptiecnm)coimrcelnestocfortrheespreosnpdecttoivtehleayaevre.raOgnet(hinedxiv-aidxuisatl)heFaetmomagic- EFxce+EFe−Fe >EAs−Fe−As. (5)
structure is sketched along the < 001 > direction projected
on the<1¯10> direction. HereEFe−As istheFe-Assurfacebondformationenergy,
Exc istheenergygainduetothespin-polarizationofthe
Fe
Featom,EFe−Fe istheFe-Fesurfacebondformationen-
3 ergy, and EAs−Fe−As is the bond formation energy be-
Ga tweenaFe surfaceatombondedtotwoAsatoms. These
V As− As three equations explain the calculated magnetic proper-
A O S ties.
m] 2 C V U
ato U E B Equation 3:
µ/B U R S This equation states that the Fe magnetic moment will
cal M [Fe 1 M LAY TRA bFoerqeuxeanmchpelde,itfhFeeFoenmlyaghnaestoicnemoormmenotrebeAcosmneesigzhebrooufrosr.
Lo E T
R E 0.5 ML Fe with a Fes IC (Fig.3). Here the Fe atom has
no other Fe around it but an As atom.
Equation 4:
0
As Fe Fe Fe Fe Fe > ThisequationstatesthattheFemagneticmomentisnot
0
As Fe Ga Fe Fe Fe As 1
− quenched if the Fe atom is close to one As atom and at
<001> <1
leastoneFeatom. ThisisthecasefortheFe ICof1ML
i
FIG. 10: Same as Fig.9, but for 5ML Fe (9 Fe atoms/cell) Fe on top of GaAs (Fig.6 and tab.2).
covered with 1ML As.
Equation 5:
The Fe magnetic momentbecomes quenched again,if Fe
is bonded to two As atoms (Fig.10, Fig.6), independent
ment will be measured. But the physical mechanism be-
on the number of Fe neighbours.
hind the reduction of the Fe magnetic moment on top of
For completeness, we show in Fig.11 the spin-
GaAs is without any doubt the Fe-As pd-hybridization.
polarization of the GaAs host. The Fe magnetic mo-
As canbe seenfromFig.5,the Fe magnetic momentis ment is not shown here (see Fig.10). The induced spin-
largerforFeithanforFes+Gai. IngeneraltheFes+Gai polarization is mostly antiparallel and rather small.
configuration has a smaller Fe-As bond distance than InarecentX-rayabsorptionstudy [12], the numberof
Fei,whichexplainsthesmallermagneticmomentforthe Fe 3d-holes was determined as a function of the Fe film
Fes+Gai configuration. For1.5and2MLofFe,theen- thicknessonn-dopedGaAs. Freelandetalfindthenum-
ergy gain due to increased Fe-As binding is smaller than berofholestoincreasewithdecreasingFefilmthickness.
the energy gain due to the increased spin-polarization They explain this due to charge transfer from Fe to As
of the Fe atoms. This explains why Fei is lower than which they also believe to be the cause for the reduced
Fes+Gai for 1.5 and 2 ML of Fe (see discussion above Fe magnetic moment.
and Fig.4) Our calculation describes the charge transfer between
In Figs.9 and 10 we show the structure and magnetic Fe and p-dopedGaAs, because due to numericalreasons
profile of a 5ML Fe film on top of GaAs(100) with one the Fermi energy of bulk GaAs is fixed at the top of the
Ga atom within the Fe film for two segregation profiles: valence band edge. From our calculations we directly
In Fig.9 for 0.5 ML As (i.e one As surface atomper cell) get the number of Fe 3d-holes as a function of the Fe
on top of the Fe film; in Fig.10 for 1 ML As (i.e two As film thickness (Fig.12). Our absoult number of the Fe
7
0.05 300
GaSurface + AsSurface
Ga
F e −
3000
V As GaInterface
µ/atom]B 0 ACUUM As f i l m Ga BULK energy [meV]200 12000000 GaiGn Fae Sfiulmrface
Local M [ −0.05 As As egrgation 100 0 1ML GaSurface
S
−
Ga Ga GaInterface + AsSurface
−0.1 Gain Fe Film + AsSurface
<001> 0
FIG.11: Localmagneticmoment,M,profileofGaandAsfor FIG.13: Gasegregation energyforfourdifferentGaconfigu-
thegeometrical structureof5MLFeontopofGaAscovered rations as discussed in the text for 5ML Feon top of GaAs.
with 1 ML As and 0.5 ML Ga within the Fe film. The Fe
magnetic moment is not shown here. 4000 AsInterface
4 V]
me 3000
bulk Fe y [
g
3.8 er
oles on en 2000
er of Fe 3d−h 33..46 As segregati 1000 AsSurface
mb Asin Film, AsSurface
u
N
1 ML AsSurface
3.2 0
FIG. 14: As segregation energy for four different As configu-
3 rations as discussed in the text for 5ML Feon top of GaAs.
0 2 4 6
Fe thickness [ML]
FIG.12: CalculatednumberofFe3d-holesasafunctionofthe servedchargetransferdiffersbetweenp-dopedGaAsand
Fe film thickness. The horizontal line indicates the number n-doped GaAs and that similar experiments performed
of Fe 3d-holes for Febulk. instead on p-doped GaAs should find an increase of the
3d-holeswith increasingthickness inagreementwith our
calculations.
3d-holes depends of course on the chosen Wigner-Seitz
radius for Fe, but the trend we find to be independent
on the chosenWigner-Seitz radius. In contrastto exper- VI. SURFACE SEGREGATION
iment we find anincrease of the holes with increasingFe
film thickness. It is well known that at metal-semiconductor inter-
Our explanation is the following: The Fe-As pd- faces the semiconductor constitutents segregate towards
hybridizationdeterminestheFemagneticmoment,nota thesurface. Forexample,forFeonGaAsitisknownthat
chargetransferbetweenFeandAs. Theelectrontransfer As segregatesto the surface, whereas Ga is not found at
between Fe and GaAs is different for n-type and p-type the surface but within the metal film [14, 15, 16]. It is
conditions, because for n-type (p-type) GaAs, the Fermi found that the segregation of As is independent of tem-
level of Fe has to align with the conduction (valence) perature,butthesegregationofGaisdependentontem-
band of GaAs. Under p-type conditions, a consequence perature. A quantitative understanding of segregationis
of the hybridization is that on average there are slightly obtained with a simple model put forward by Weaver et
more delocalized electrons on the Fe site, i.e. the num- al. [32]. The free energy of segregationis determined by
ber of 3d-holes decreases. The thicker the Fe film be- the strain energy and surface energy, the latter of which
comes,the moreFe atomsarewithoutanAs neighbour, they estimated with the cohesive energy. There model
whichis why the number ofd-electrons (holes)decreases predicts for Fe on GaAs both Ga and As to segregate
(increases) with increasing Fe thickness. Under n-type to the surface, whereas in experiment only As surface
conditionsitisplausibletoassumeviceversathatonav- segregation is observed. In the following we resolve this
erage there are slightly less delocalized electrons on the discrepancy.
Fesite. Wethereforepredictthattheexperimentallyob- InFigs.13and14,weshowtheGa(respectiveAs)seg-
8
regationenergyrelativetotheenergeticallylowestconfig- model), if no As has segregated. If As has segregated,
uration. ForGawehavetoconsidertwocasesseparately: Ga will stay within the Fe-film ( in agreement with ex-
(i) no As has segregated to the surface and (ii) As has periment).
segregated to the surface. In case (i) (insert of Fig.13),
Ga prefers to segregate to the surface (1ML GaSurface).
Thesegregationenergyof1MLGaamountsto2.4eV.In
VII. DISCUSSION AND SUMMARY
case (ii) where As already has segregated to the surface
(Fig.13), Ga prefers to leave the interface (GaInterface)
andstaysomewherewithintheFefilm(GainFe−film). It WefindAstosegregatetothe surfaceontopoftheFe
is more costly (280 meV) for the Ga to be in the surface film independent of termination, which is in agreement
layer together with an As atom (GaSurface). Therefore, with experiments. The Fe/GaAs interface is not stable
if As has segregated to the surface, no Ga will be found against further segregation. An As atom within the Fe
at the surface. film has a lower energy than at the interface. In an ex-
The As segregation energy (Fig.14) shows the same perimentonewillthus alwaysfind Aswithin the Fe film,
trend as the Ga segregationenergy(inset ofFig.13), but wheretheFe-Aspd-hybridizationwillquenchtheFemag-
the segregation energy of one As atom to the surface is netic moment. Since Ga also has a lower energy within
1.5eVlargerthanforoneGaatom. Notice,thatbothGa theFefilmthanattheinterface,onewillalsoalwaysfind
andAs prefertobe withinthe Fe film ratherthanatthe Ga within the Fe film. Ga itself does not influence the
interface. In summary, this suggests the following: On magneticmoment(Fig.9),butprobablyGaintheFefilm
topoftheFefilmalwaysAswillbefoundindependentof will prevent further As segregation. This would explain
the GaAs surface termination. The segregation profiles themuchlowerthicknessofthemagneticallyquenchedFe
should more or less be independent on the GaAs sur- layers for Ga terminated samples. The thickness of the
face termination, because the Fe-As interaction is much magnetically quenched Fe layers is then determined by
stronger than the Fe-Ga interaction. the probability of finding As and Ga within the Fe film.
TheAssegregationpathisaresultofthelatticerelax- This probability depends on the termination and the Fe
ationduetothechemicalinteractionbetweentheFeand growth conditions. Our results presented here for Fe on
As, which implies that As segregates already at T = 0 GaAs are most likely also valid for other semiconductor
K. The segregation is thus not diffusion controlled, but substrates. For example, we find more or less the same
only controlled by chemical bonding, which is in agree- structures for Fe on ZnSe [31] and the segregation be-
mentwithexperiment. WefindGatoleavetheinterface, haviouris the same, but the Fe-Se hybridizationis much
but onlyto segregatetothe surface,if noAs alreadyhas weaker.
segregated. IncontrasttoAs,thesegregationofGa,does
nottakeplaceatT =0K.Thereexistsanactivationbar-
rier for the segregation, i.e. the segregation is diffusion
Acknowledgments
controlled. The amount of Ga on top of or within the
Fe film is therefore strongly dependent on temperature,
whereas the amount of As on top of the Fe film is only We are grateful to the Swedish foundation for strate-
weakly dependent on temperature. This is in agreement gic research (SFS), the Swedish Research Council (VR),
with an experimentalstudy of the Fe/GaAs interface in- the G¨oran Gustafsson foundation, and the European
terdiffusion [6]. RTN network on ”computational spintronics” for finan-
Regarding the Weaver model, we find that Ga seg- cial support. We thank the Swedish supercomputer cen-
regates to the surface (in agreement with the Weaver ter (SNAC) for providing us with supercomputer time.
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