Ab initio investigation of structural and magnetic properties of Fe|ZnSe(001)

0.74 MB·English

by  H. Dobler

Ab initio investigation of structural and magnetic properties of Fe|ZnSe(001)
H. Dobler and D. Strauch
Institut fu¨r Theoretische Physik, Universit¨at Regensburg, 93040 Regensburg, Germany
(Dated: February 2, 2008)
We investigate 1, 2, 3, and 4 monolayers of iron grown on the (001) surface of ZnSe using spin
densityfunctionaltheory,plane-waveexpansion,andultrasoft pseudopotentials. Anidealstructure
4
oftheinterfaceisplausibleduetotheverysmalllatticemismatchbetweenbothmaterials. However,
0
we observe dramatic deviations from this idealized configuration. The most distinctive variations
0
ariseinthecaseofasinglemonolayer. HereaterminatingZnlayerisbuoyingupwards. Thethicker
2
the Fe layer the weaker are the relaxations in the iron region. Nevertheless, in the case of the Se-

n terminated surface, thestructure changes significantly inside the semiconductor near the interface.
a The profiles of the electronic density and the magnetization perpendicular to the surface are quite
J sensitive to thechange from theideal to thereal structure.

1
2 PACSnumbers: 68.35.-p,75.50.Bb,75.70.Ak,81.05.Dz

]
r
e I. INTRODUCTION the deviations from the ideal behavior transcend small
h quantitative corrections even for the structural results.
ot Magnetoelectronics1andspintronics2arerapidlygrow- Because the orbital contribution can be shown6 to con-
tribute less than about 5% in the case of the ideal struc-
. ing fields in applied solid state physics. Since the
t
a proposal of a spin field-effect transistor by Datta and ture,weconsideronlythespinmagnetizationasthemain
m Das3 ferromagnet–semiconductor (FM–SC) heterostruc- contribution to the total magnetization. This quantity
is directly available from spin density functional theory
- tures have become very interesting candidates for the
d and thus easier to obtain. Furthermore, the small con-
realization of spin dependent injection of electrons in
n a semiconductive material. Therefore, theoretical4,5,6 tribution of the orbital moment can be neglected, if we
o
c and experimental7,8,9 effort has been made. Towards expect a sensitivity of the magnetic properties to struc-
turalchanges,whichshouldaffectthemagnetizationpro-
[ this goal, calculations were made for FM–SC–FM het-
files by more than a few percent.
erostructures, while thin Fe films epitaxially grown on
1
We choose Fe|ZnSe(001) as an example for the whole
semiconductorsurfaceswereinvestigatedexperimentally.
v
8 The first Fe|GaAs(001) systems7 had shown magnetic class of possible systems, because it is of experimen-
tal interest,8 and the pristine semiconductor surface
8 dead layers. This phenomenon of Fe layers at the in-
3 terface between the two materials with nearly vanishing shows much smaller reconstructions than any III-V
1 semiconductor.12,13 A II-VI material as ZnSe can satisfy
magneticmomentcanbepreventedbyloweringthetem-
0 the well established but not rigorous counting rules13,14
perature of the substrate to room temperature during
4 the film growth.10 Higher temperature leads to a mixing by building simple dimers at the (001) surface. Hence,
0
the often used GaAs(001) surface is much more compli-
/ of the materials at the interface which sensitively influ-
t cated.
a ences the magnetic properties. Thus, structure plays an
m important role.
- Nevertheless, the theoretical investigations of FM–SC
d heterostructures usually assume an ideal interface struc- II. METHOD
n
ture. Thisissuggestedbytheverysmallmismatchofthe
o
latticeconstantsbetweendiamond-structureelementalor Density functional theory (DFT)15,16 provides a reli-
c
: zincblende-structurecompoundsemiconductorsandofα- able ab initio method for computing the ground-state
v
Fe. Therefore, four Fe cubes excellently fit on a single energy and the associated one-particle density of an
i
X fcc cube of the semiconductor material. The advantage electronic many-particle system with given external po-
of these computations is the possibility of considering tential. Thus, it is possible to determine the ground-
r
a the contribution of orbital magnetic moments. This is state configuration of ions in a chemical system, such as
donewithintheLKKR-method11 whichprovidesthe op- molecules or crystals. Due to the ferromagnetic charac-
portunity to take into account the relativistic spin-orbit ter of iron we need to consider the spin degree of free-
coupling. However, the possibility of sensitive reactions dom. Thispossibilityisofferedbyspindensityfunctional
ofthe totalmagnetizationto minorstructuralchangesis theory (SDFT).17,18,19 Within this generalization of the
fully neglected. original DFT the ground-state energy is a functional of
In this article we show that these idealizing assump- the density as well as of the magnetization.
tionsarenotrealisticinmanycases. Therefore,wedeter- Inthiswork,weusetheabinitio packageVASP23,24,25
mine the equilibrium structure of the observed systems for the numerical implementation of DFT and SDFT.
andcomparetheidealandrealdensityprofilesofthe va- Due to the three-dimensional lattice symmetry of the
lenceelectronsandofthemagnetization. Wewillseethat bulk systems the wave functions of the valence electrons
2
a[˚A] K0 [GPa] K0′
crystal LDA GGA Exp LDA GGA Exp LDA GGA Exp
α-Fe 2.761 2.864 2.8662 232 152 167 5.04 5.06 5.97
γ-Fe 3.387 3.530 3.6468 282 155 — 6.00 5.33 —
ZnSe 5.578 5.741 5.6686 68.9 55.5 62.4 4.73 4.30 4.77
TABLE I: Cubic lattice constants of iron and zincselenide as results of LDA and GGA calculations, bulk moduli K0 and
the according pressure derivatives K0′. The experimental data is taken from Refs. 20,21,22. The lattice constant for γ-Fe is
◦
measured at a temperature of 916 C, theother data corresponds to room temperature.
are expanded in in terms of plane waves. The core iron. The dangling bonds at the uncovered side of ZnSe
states are accounted for by ultrasoft pseudopotentials26 are saturated with hydrogen atoms. The distance be-
similar to Vanderbilt’s potentials,27 which are no longer tween the slabs is about 8.5˚A. Tests showed that these
norm conserving. The exchange and correlation energy parameters are a good compromise between computa-
is treated within the local-density approximation(LDA) tional effort and accuracy. More details about the ge-
and the generalized-gradient approximation (GGA). In ometry of the used supercell can be taken from Sec. III
all LDA functionals the parameterizationof Perdew and and Fig. 1. In these computations we use a 6×6×1
Zunger28 to Monte-Carlo data of Ceperly and Alder29 is mesh of special points and an energy cut-off of 237.5eV.
used;intheGGAfunctionalstheproposalofPerdewand The ionic relaxation to the equilibrium structure is de-
Wang (1991)30 is adopted. termined using a conjugate-gradientalgorithm.40
Using these techniques we are able to determine the
minimal-energy lattice constants of zincblende ZnSe,
III. THE IDEAL INTERFACE
body-centered cubic (bcc) α-Fe, and face-centered cubic
(fcc) γ-Fe. Therefore, we compute the energy per unit
cell as a function of the cubic lattice constant. The cut- The lattice mismatch γ of α-Fe and ZnSe can be de-
off energies for the expansion in in terms of plane waves fined as follows:
are209.5eVforZnSeand297eVforFe. Themomentum- a −2a
ZnSe Fe
space integrations are done by summing over a grid of γ = . (1)
1(a +2a )
special points according to Monkhorst and Pack.31 Here 2 ZnSe Fe
we use a 10×10×10 mesh for ZnSe with two atoms per Comparison with Table I shows that this mismatch is
unit cell and 20×20×20 meshes for both modifications γ = 1.0% using LDA, γ = 0.2% using GGA, and
of iron each with one atom per cell. The results of the γ = −1.1% for the experimental values. Thus, the lat-
Murnaghan32 fitstotheresultsaregiveninTableI. The tice mismatch is very small, and the idea of an ideal
lattice constants agree very well with the experimental structure of the interface is suggestive. For many sys-
data and with the result of former calculations.33,34,35,36 tems of iron grown on the (001) surfaces of zincblende
Also the bulk moduli and their pressure derivatives, semiconductors the mismatch of the lattice constants is
which result from the Murnaghan fits, show good agree- quitesmall(experimentalvalues:20 e.g.,a =5.653˚A,
GaAs
ment with experiment and computation. Additionally, a =5.660˚A). Hence,manycalculations4,5,6arebased
AlAs
iron is ferromagnetic in the bcc structure. The sponta- on this idealization.
neous magnetic moment per atom is µ = 2.04 µB using Fig. 1 gives an intuitive picture of the ideal interface.
LDA and µ = 2.35 µB in a GGA computation. Thus, Regarding the pristine surface of ZnSe first, it is evident
the values µ = 2.12 µB using LDA and µ = 2.35 µB us- that (001) surfaces always are terminated by only one
ing GGA of a former calculation33 can be reproduced. sort of atom, thus we have to distinguish between the
These results soundly fit to the experimental37 value of Se- and Zn-terminated case. Due to the tiny lattice mis-
µ = 2.23 µB. However, using LDA γ-Fe turns out to match four iron cubes closely fit on a single ZnSe cube.
be stable in fcc and not the actual bcc structure. This Substitutionofthelowermostatomiclayerofironbythe
inconsistence with the experiment is an artifact of the first semiconductor layer results in the ideal structure
local-density approximation38 which can be repaired us- shown in the middle of Fig. 1. In this case the semicon-
ing generalized-gradientcorrections. ductor is Zn-terminated.
Surfacesaretreatedwithintheperiodic-slabmethod.39 But the presented cell is not elementary in a two-
TheprogrampackageVASPneedsthree-dimensionallat- dimensional sense parallel to the surface. However, an
tice symmetry, which is broken in the case of a surface. elementarycellcanbeobtainedbyrotatingthestructure
But it is possible to restore periodicity perpendicular to aroundanaxisperpendiculartothesurfacebyanangleof
◦
thesurfacebyperiodicallystackedslabsofmaterial. Here 45 andcutting off the corners. This is visualizedon the
we take into account nine atomic layers of the semicon- right side of Fig. 1 by showing the elementary cell used
ductor ZnSe coveredby one, two, three, or four layersof in the calculations for the Zn-terminated semiconductor
3
coveredbytwomonolayersofiron. Asalreadymentioned structure we show the profiles of the spin magnetization
in Sec. II we choose 9 atomic layers of ZnSe and 1, 2, 3, perpendicular to the interface. The term profile means
or 4 monolayers of iron. The separating vacuum slab of thatthecorrespondingmagnitudeisaveragedoverplanes
a thickness of about 8.5˚A is not displayed. A monolayer parallel to the surface. In bulk iron the orbital magne-
in ZnSe contains either one Zn or one Se atom in the tization is suppressed because of quenching by electric
cell, a single monolayer of Fe contains two inequivalent crystal fields.41 At the surface or interface the crystal
atoms. The dangling bonds at the bottom side are satu- symmetryisbroken;thus,the quenchingdoes notsuffice
ratedwithhydrogenatoms. ThepositionsoftheHatoms any more to disable completely the orbital contribution
and the lowermost atoms of ZnSe are fixed in the calcu- tothe magnetization. Nevertheless,incalculations6 con-
lations;thus,thebonddistancesbetweenHandSeorZn sidering the orbital contribution this appears to be not
are constant with d = 1.478˚A and d = 1.612˚A. more than a 6% effect. Thus, the mere spin polariza-
HSe HZn
These values are the equilibrium bond distances of the tion is a good indicator for the behavior of the magnetic
corresponding isolated dimers computed with VASP. propertieswhenstructuraldeviationsfromtheidealcase
Starting fromthe ideal structure it is possible to com- have to be expected.
pute the relaxation of the atoms in the elementary cell.
If restricted to the direction parallel to the surface nor-
mal the displacements turn out to be small, and thus A. A single monolayer of iron
the structure of the surface remains nearly ideal. How-
ever, this constraint may lead to possibly unstable equi- The most interesting results are obtained for only one
libriumpositions. Inordertoallowrelaxationintorecon- Fe monolayer on ZnSe(001). In particular, the relaxed
structed equilibrium positions we start from randomly structure deviates tremendously from the ideal case.
displaced positions of the peripheral Fe atoms. The re-
Fig.2showsthe peripheric regionofthe coveredSe- and
sultsofthesecomputationsmaydiffer dramaticallyfrom Zn-terminatedsurface. IntheSe-terminatedcasethetwo
the idealstructure. This is reportedinthe followingsec-
inequivalent Fe atoms obviously have very different ver-
tion. tical positions. One Fe atom is lowered, which enables a
bond to a Zn atom of the second atomic layer of ZnSe.
The other Fe atom is bonded to the uppermost Se and
IV. RESULTS
α d1 d2
In this section we present the results obtained for Se-
and Zn-terminated (001) surfaces of ZnSe covered by 1,
2, 3, and 4 monolayers of iron. In all cases the energy-
minimizing structure is determined first. For an esti-
mation of the dependence of magnetic properties on the
β
d3 d4
aFe
Se-terminated
γ
aZnSe d5 d6
≡ Fe ≡ Zn ≡ Se ≡ H
Zn-terminated
FIG. 1: Structure of the ideal interface. Here the semi-
conductorsurfaceisZn-terminated. 4Fecubesfitonasingle FIG.2: StructureoftheSe-terminated(upperpart)andZn-
ZnSecubeasdisplayedontheleft. Thus,thestructureshown terminated(lowerpart)ZnSe(001)surfacecoveredbyasingle
in the middle is plausible. The elementary cell used for the monolayer of iron. Only the crucial region near the interface
calculation is presented on theright. with interesting distances and angles is shown.
4
theotherFeatom. FeandSetogetherbuildupasurface
slabthatiscoupledtotheZnSesubstrateonlybyanFe–
Zn bond. So there is no bond between Se and Zn at the
two uppermost layers any more. In this slab, the the Fe
andSe ions formzigzagchains fromthe front backwards
0 5 10 15
(in Fig. 2) with bond lengths d1 = 2.30˚A, d2 = 2.42˚A, 0.8 ideal
and Se–Fe–Se bond angle α = 119◦. Similar chains run 3] relax.
− 0.6
from the left to the right with the values d = 2.34˚A, ˚A
3 [
d4 =2.33˚A, and β =121◦. z) 0.4
(
n 0.2
The Zn-terminated surface provides the most amaz-
ing results. The uppermost Zn layer is buoying upwards 0
which canbe seenat the lowerpartof Fig. 2. We obtain −3] 0.3 ideal
˚A relax.
two layers in the perpheric region. The uppermost layer B
µ 0.2
consists of one Fe and one Zn atom in the elementary [
)
cell with nearly identical heights. The second layer is z( 0.1
z
made up of one Fe and one Se atom per cell. Similar to m
0
tshideewSea-rtdesr.miTnhaeterde tchaesebtohnedsedaisttoamncsebsuailrde zdigz=ag2c.4h4ai˚Ans, −3] 0.004 ideal
5 ˚A relax.
d =2.42˚A, andthe Se–Fe–Se angle is β =121◦. Again, B 0.002
6 µ
the uppermost Se atom is only bonded to iron, and the )[ 0
z
hole peripheric layer is coupled to the semiconductor by (z−0.002
m
an Fe–Zn bond. Both structural results can be inter-
−0.004
pretedinthewaythatnon-metallicSeformstightbonds
0 5 10 15
to Fe. This affinity is so distinctive that iron can even
displacetheoriginallyterminatingZnatomstowardsthe z[˚A]
outermost region.
An indicator for the stability of the surface structure
is the energy gain due to the relaxation in comparison
with the ideal structure. Also the results for DFT and
SDFT have to be differentiated. Because the relaxation
was done initially using usual DFT the result of which
was refined with SDFT afterwards, we have to distin-
guish between energies from DFT and SDFT. For the
Se-terminatedsurfacetheenergygainis∆E⊥ =0.638eV
fromthe smallrelaxationofthe peripheric atomperpen- FIG. 3: Structure and density profiles for one monolayer of
diculartotheinterface. CompleteDFTrelaxationcauses Fe (2 atoms per cell) on Se-terminated ZnSe(001). The ver-
an increase to ∆E = 1.663eV by more than 1eV. tical dotted lines mark the positions of the atomic layers in
DFT
ThisvalueismuchsmallerusingSDFTevenafterfurther the ideal case. At the top the elementary cell of the ideal
relaxations. Thesmallerenergygain∆E =0.346eV interface is presented. At the bottom the atoms are shown
SDFT
afterrelaxationintwodifferentperspectives. Theuppermost
can be interpreted in the following way: DFT only can
plot shows the density of the valence electrons, in the mid-
give the energy differences due to structural changes,
dlethemagnetization isdisplayed,andinthelowermost plot
whereas using SDFT this is corrected by the energy due
the magnetization is shown on an expanded scale. The solid
to the ordering of the spins. Thus, the ferromagnetic or-
(dashed) lines belong tothe relaxed (ideal) structure.
der in the ideal structure is energetically advantageous
in comparison with the relaxed structure. Nevertheless,
the structuralcontributionto ∆E outbalances the ferro-
magnetic one; thus, the energy gain is still much greater thisdramaticstructuralvariationreducestheenergygain
than the thermal energy k T ≈ 25meV corresponding due to ferromagnetism more than for the Se-terminated
B
to room temperature. surface. But still ∆ESDFT is much greater than typical
thermal energies at room temperature.
InthecaseoftheZn-terminatedsurfacetherespective
values are ∆E⊥ = 0.125eV, ∆EDFT = 2.767eV, and The density profiles measure the dependence of elec-
∆ESDFT = 0.577eV. ∆E⊥ is smaller than in the Se- tronic and magnetic properties on structural variations.
terminated case, because the reduction of the distance The profiles for the density of the valence electrons, the
betweenthemetalFeandthenonmetalSeyieldsahigher magnetization, and the magnetization on an expanded
energygainthanavariationoftheFe–Znbondlength. In scaleareshowninFigs.3and4. Additionally,theatomic
the DFT calculation, ∆E is much larger than in the positions in the elementary cells are presented for the
DFT
Se-terminatedcase. SotheenergeticadvantageoftheZn ideal and relaxed structure. The valence-charge density
atomsbuoyingupwardsisenormous. Ontheotherhand, has minima for Se layersand maxima for Zn and Fe lay-
5
the semiconductorevenhasthe directionoppositeto the
total moment. This antiferromagnetic ordering is obvi-
ously an effect of the structural changes,because for the
ideal interface the magnetization has the same direction
inside the semiconductive and the ferromagnetic region.
0 5 10 15
1 ideal Anappropriateinterpretationisgivenbythe Heisenberg
3] 0.8 relax. model.42 There, the coupling constants J are given by
− ij
˚A 0.6 the overlap of the wave functions of neighboring atoms.
[
z) 0.4 Because the comparativelystrongly localized d-electrons
(
n 0.2 dominate the ferromagnetism of Fe, a small change of
0 bond lengths or layer distances can invert the sign of
]
−3 0.3 ideal the coupling constants, which means a transition from
˚A relax.
ferro- to antiferromagnetism. Additionally, the relax-
B
µ 0.2 ation results in an Fe–Zn bond that does not exist in
[
z) the ideal case. In contrast to Fe–Se bonds, these bonds
( 0.1
mz lead to a flip of the magnetization, as can be seen for
0 the Zn-terminated interface. For the Zn-terminated sur-
−3] 0.002 ideal face (Fig. 3) a morecomplicated runof the curvesinside
˚A relax.
B 0.001 ZnSe is obtained. Fe–Zn bonds at the interface instead
µ
)[ 0 of Fe–Se bonds for Se termination cause antiferromag-
z netic effects, even for the ideal structure. However, the
(
mz −0.001 magnetizationdeepinside the semiconductor hasflipped
−0.002 its direction after relaxation, too. The tiny peaks at the
0 5 10 15 position of the hydrogen atoms indicate too thin slabs
z [˚A] or vacuum layers. But incrementing those two parame-
ters would require a drastic increase of computing time.
Becausewejustwanttoestimatethedependenceofmag-
netic properties on the structure, the chosen accuracy is
sufficient.
B. Two, three, and four monolayers
Now we turn to the case of 2, 3, or 4 monolayersof Fe
FIG. 4: Same as Fig. 3, but for one monolayer of Fe on grown on ZnSe(001). The structure and the associated
Zn-terminated ZnSe(001). density profiles are presented in Figs. 5, 6, and 7 for the
Se-terminated surfaces and in Figs. 8, 9, and 10 for the
Zn-terminated case. Here, we omit the presentation of
ers. This is because Se is treated with a pseudopotential the structure like the one in Fig. 2 in a separate plot. In
for 6 valence electrons (4s24p4), whereas for Zn 12 elec- theresultsforagiventerminationclearsimilaritiesarise,
trons(3d104s2)aretakenintoaccount,althoughthetotal thus a common discussion is sensible.
number of electrons is larger for Se (Z = 34) than that
of Zn (Z = 30). All the changes of the electron den-
sity can be interpreted as a shift of the density along 1. Se termination
the direction of the corresponding relaxations. Also the
magnetization seems to follow the ionic relaxations, es- The structures of all three systems are very similar.
pecially for the Fe layers, although the total magnetic Those are presented beneath the plots of the profiles in
moment per cell decreases from 6.32µB for the ideal in- Figs.5(2monolayers),6(3monolayers),and7(4mono-
terface to 4.94µB after relaxation in the Se-terminated layers). The ironslabhasnearlyperfectbcc structureas
caseandfrom6.17µB to 5.34µB,ifthe ZnSe surfacewas known from bulk α-Fe. Relative relaxations paralleland
Zn-terminated. The exact run of the curves in Figs. 3 perpendicularto the interfacearenegligiblysmall. How-
and 4 according to the relaxed structure differs from the ever, the whole Fe region is relaxing towards the semi-
ideal case, which is clear because of the splitting of the conductor substrate by several 0.1˚A, which is an effect
Fe plane into two layers. of structural changes in ZnSe. The first atomic layer of
The lowermost graphics in both, Fig. 3 and 4, show ZnSedoesnotsolelyexistofSeanymore. TheZnatoms
drasticdifferencesbetweenthe magnetizationbeforeand of the originally second atomic layer together with the
after relaxationon an expanded scale. In the case of the terminatingSe atomsbuildaZnSelayeratthe interface.
Se-terminated surface (Fig. 3) the magnetization inside So it is possible that the uppermost Se atoms are not
6
bonded to Zn but to Fe, thus the whole surface slab is
coupled to the substrate by Fe–Zn bonds followed by a
Zn–Se bond. The distance of the second Se layer, which
canbe regardedas the uppermost layerof the substrate,
0 5 10 15 20
to the first layer of the peripheric part of the slab (the
ZnSe layer) is clearly greater than the layer distances in 3] 0.8 rideleaaxl.
−
the ideal structure. So the peripheric part of the slab ˚A 0.6
shouldbe coupledweaklyto the substrate,andit canbe )[ 0.4
z
displaced easily in the horizontal direction. This would (
n 0.2
implicate a very soft phonon mode. Measuring such a
0
minotdheecoseumldiccoonndfiurmctoorurthreessutlrtuscftourrtehebesctroumcetusrme.oDreeeapnedr −3˚A] 0.3 rideleaaxl.
more similar to that of zincblende. Beyond the fourth µB 0.2
[
atomic layer (second Zn layer) the structure can be re- )
garded as ideal. The energy gain per cell decreases with z(z 0.1
m
increasingnumber ofFe layersfrom0.451eV to 0.392eV 0
and 0.279eV due to the increasingly ideal character of −3] 0.004 ideal
the ionic configuration. ˚A relax.
B 0.003
Thealmostidealstructureoftheironisreflectedinthe µ
[ 0.002
nearly ideal profiles of the valence electron density and )
z( 0.001
the magnetization in the Fe region, too. The peaks cor- z
m 0
−0.001
0 5 10 15 20
z[˚A]
0 5 10 15
0.8 ideal
3] relax.
−
˚A 0.6
[
) 0.4
z
(
n 0.2
FIG. 6: Same as Fig. 3, but for three monolayers of Fe on
0
−3] 0.3 ideal Se-terminated ZnSe(001).
˚A relax.
B
µ 0.2
[
)
z
( 0.1
mz responding to iron are simply shifted along the direction
0 of the ionic relaxation. Only the peak nearest to the in-
]
−3 0.003 ideal terface is slightly decreased for the case of two and four
˚A relax.
B 0.002 monolayers of Fe. So the total magnetic moment per
µ
[ cell reduces from 11.14µB for the ideal structure with
) 0.001
z two Fe layersto 10.68µ after relaxation,from 16.79µ
( B B
mz 0 to 16.35µB for three monolayers and from 21.71µB to
20.49 µ for four monolayers. The ZnSe layer at the
−0.001 B
0 5 10 15 interfaceentailsanadditionalpeakintheelectronicden-
z [˚A] sity, because this layer is packed very densely. Towards
ZnSe this peak is followed by a dip, which clearly shows
the already assumed weakness of the expanded Zn–Se
bond. Inside the semiconductor the density corresponds
to a shift along the relaxationagain. The magnetization
insideZnSedeclinesveryfastinallthreecases. However,
the direction of the weak magnetization is flipped, simi-
lar to the case of a single monolayer of Fe (compare Fig.
3). Againdifferentlayerdistancesandchangingchemical
environmentsresultinantiferromagneticordering. Inall
FIG. 5: Same as Fig. 3, but for two monolayers of Fe on three cases the magnitude of the magnetization and the
Se-terminated ZnSe(001).
penetration depth slightly increase.
7
expect smaller energy gain due to relaxation. But sur-
prisingly the values 1.027eV, 0.814eV, and 0.610eV are
muchgreaterthanforSetermination. Changingtheionic
configuration in the Fe slab seems to reduce the energy
0 5 10 15 20
byagreateramountthantherelaxationsinthesemicon-
0.8 ideal
3] relax. ductor do. However, the energy gain decreases with the
−
˚A 0.6 number of Fe layers, which again shows the increasingly
[
) 0.4 ideal character of the system.
z
(
n 0.2 The density profiles of valence electrons do not ex-
0 hibitany astonishingeffects. Becausethere arenocloser
]
−3 0.3 ideal packedlayersor stronglyincreasing layerdistances, only
˚A relax.
B the outwards relaxation of the whole Fe region can be
µ[ 0.2 identified in a shift of the Fe peaks. However, the mag-
)
z( 0.1 netizationevenwithintheironregionextremelydeviates
z
m fromtheidealbehavior. Fortheidealstructurethemag-
0 netizationdue to the Fe layeratthe interface is strongly
]
−3 0.004 ideal suppressedinthecasesof2(Fig.8)and3(Fig.9)mono-
˚A relax.
B 0.003 layersofFe. Thisresultcouldbeinterpretedasmagnetic
µ
[ 0.002 dead layers claimed in older work.7 However, the effect
)
z( 0.001 of nearly vanishing magnetization at the interface turns
z
m
0
−0.001
0 5 10 15 20
z [˚A]
0 5 10 15
0.8 ideal
3] relax.
−
˚A 0.6
[
) 0.4
z
(
n 0.2
FIG. 7: Same as Fig. 3, but for four monolayers Fe on Se-
terminated ZnSe(001). −3] 0 ideal
˚A 0.3 relax.
B
µ 0.2
[
2. Zn termination )
z
( 0.1
z
m
For the Zn-terminated surfaces a different picture of 0
the structure is obtained. Here the deviationsfrom ideal −3] 0.003 ideal
˚A relax.
behavior preferentially appear in the Fe slab, whereas B
µ 0.002
ZnSe remainsin the almostperfectzincblende structure. [
)
InspectionofFigs.8,9,and10demonstratesthatthere- z( 0.001
z
laxations in the semiconductor region are nearly vanish- m
0
ing. Thereisnodrasticstructuralchangeattheinterface
like the formation of a ZnSe layer in the Se-terminated 0 5 10 15
case. However, relaxations in the Fe region are obvious.
z[˚A]
Here the Fe atoms are displaced in the direction paral-
lel to the interface; thus, the bond lengths change, but
the layer distances do not. For only two monolayers of
Fe these relaxations are most evident. Actually, the Fe
atoms at the interface are able to form additional bonds
within the layer. The deviations from the ideal struc-
ture seem to become weaker with an increasing number
ofmonolayers. IncontrasttotheSe-terminatedinterface
the Fe slab slightly relaxes outwards.
Because of the smaller extent of the structural mod- FIG. 8: Same as Fig. 3, but for two monolayers of Fe on
Zn-terminated ZnSe(001).
ification in comparison with the Se-terminated case we
8
0 5 10 15 20 0 5 10 15 20
−3˚A] 00..68 rideleaaxl. −3˚A] 00..68 rideleaaxl.
[ [
z) 0.4 z) 0.4
n( 0.2 n( 0.2
−3] 0.03 ideal −3] 0.03 ideal
˚A relax. ˚A relax.
B B
µ 0.2 µ 0.2
[ [
) )
z( 0.1 z( 0.1
mz mz
0 0
−3] 0.008 ideal −3] 0.003 ideal
˚A relax. ˚A relax.
B 0.006 B
µ µ 0.002
)[ 0.004 )[
mz(z 0.002 mz(z 0.001
0 0
0 5 10 15 20 0 5 10 15 20
z [˚A] z[˚A]
FIG. 10: Same as Fig. 3, but for four monolayers of Fe on
FIG. 9: Same as Fig. 3, but for three monolayers of Fe on
Zn-terminated ZnSe(001).
Zn-terminated ZnSe(001).
otherinthecaseoftwoandthreemonolayersofFe. This
out to be unrealistic: In the case of four monolayers of
isnosurprisebecauseofthedeadlayersintheidealstruc-
Feallmagneticmomentsarefullydevelopedevenforthe
ture. Sothedifferencesaredifficulttointerpret,themore
ideal structure, and in the case of two and three mono-
so as the lowermost profile in Fig. 10 for four monolay-
layers the dead layers disappear after the relaxation. So
ers shows only little difference between the two curves
we find in agreement with experiment10 and other theo-
correspondingto the ideal and relaxed structure. For all
reticalwork6thattherearenomagneticdeadlayersinall
Zn-terminated systems including a single monolayer of
realistic systems considered here. Due to the difficulties
Fe a tendency towards oscillations of the magnetization
in the treatment of the ideal interfaces the total mag-
is evident. This is in contrast to Se termination.
netic moment per cell increases for two monolayers from
7.83µ before relaxation to 11.09µ after and for three
B B
monolayersfrom 10.26µ to 16.64µ . The knowneffect
B B
of a slight decrease of the moment as seen for Se termi- V. SUMMARY AND CONCLUSIONS
nation is obtained again for four monolayersof Fe. Here
themomentreducesfrom21.62µBto21.52µBbythetiny In this work we have presented structural, electronic,
value of 0.1µB. The difference is obviously smaller than and magnetic results from spin density functional the-
for Se termination. Amazingly, the relaxations of the ory calculations for 1, 2, 3, and 4 monolayers of Fe on
Fe atoms parallel to the surface can stabilize the mag- Se- as well as Zn-terminated ZnSe(001). In spite of the
netic moment, whereas the decrease of the moment is tiny mismatch of the lattice constants of α-Fe and cu-
even less pronounced for Se-terminated surfaces, where bicZnSewefinddramaticstructuraldeviationsfromthe
the iron structure remains almost ideal. ideal interface. Especially for a single monolayer of iron
Inside the semiconductor the magnetizations for the thestructureischangedradically. Butalsoformorethan
idealandtherelaxedstructurestronglydeviatefromeach one monolayer we obtain amazing results, so we find a
9
separated ZnSe layer with Zn and Se at Fe positions at the sign might affect electronic and magnetic properties
theinterfaceinthecaseofSetermination. Otherwise,for near the interface. For example a reliable description
Znterminationthestructuralmodificationstakeplacein of the tunneling magneto resistance (TMR) requires an
the Fe region. accurate electronic density of states at the interface.5,6
Summarizing,wehavetopointoutthatthestructures However, this magnitude might be sensitive to small re-
become increasingly ideal with an increasing number of laxations due to changing bond conditions.
Femonolayers. WeseethetendencyoftightFe–Sebonds; Thus, the effect of relaxations should not be ne-
in every Se-terminated system the outermost Se atoms glected in more realistic calculations of electronic and
are bonded primarily to Fe. The raised Zn atoms are magnetic properties of ferromagnet–semiconductor het-
bonded to Fe and form a single weak bond to the sub- erostructures. The usage of the ideal interface in such
strate. In the Zn-terminated structures, too, the whole computationscanfoilambitiouseffortsusingcomplicated
surface layer is coupled to the substrate by an Fe–Zn methods.
bond.
We findacleardependence ofthe profilesofelectronic
density and magnetization on the relaxations. The elec-
Acknowledgments
tronicdensityandthemagnetizationduetotheFeatoms
canbe explainedby ashift of the curvesalongthe direc-
tionoftherelaxation. However,themagnetizationinside ThisworkwassupportedbytheDeutscheForschungs-
ZnSe often changes the directionin comparisonwith the gemeinschaft withastipendiumintheGraduiertenkolleg:
ideal structure or the total magnetic moment. Although Komplexita¨t in Festko¨rpern, Phononen, Elektronen und
the magnitude of this magnetization is small, the flip of Strukturen.
1 G. A. Prinz, Science 282, 1660 (1998). 19 A. K. Rajagopal and J. Callaway, Phys. Rev. B 7, 1912
2 S. A. Wolf, D. D. Awschalom, R. A. Buhrman, J. M. (1973).
Daughton,S.vonMoln´ar,M.L.Roukes,A.Y.Chtchelka- 20 K.-H. Hellwege and A. M. Hellwege, eds., Landolt-
nova, and D. M. Treger, Science 294, 1488 (2001). B¨ornstein, GroupIII:Crystal andSolidStatePhysics,vol.
3 D. Datta and B. Das, Appl. Phys.Lett. 56, 665 (1990). 6: Structure Data of Elements and Intermetallic Phases
4 W.H.Butler,X.-G.Zhang,X.Wang,J.vanEk,andJ.M. (Springer-Verlag, Berlin, 1971).
MacLaren, J. Appl.Phys.81, 5518 (1997). 21 K.-H. Hellwege and A. M. Hellwege, eds., Landolt-
5 J. M. MacLaren, W. H. Butler, and X.-G. Zhang, B¨ornstein, GroupIII:Crystal andSolidStatePhysics,vol.
J. Appl.Phys.83, 6521 (1998). 11: Elastic, Piezoelectric, Pyroelectric, Electrooptic Con-
6 M. Koˇsuth, J. Min´ar, I. Cabria, A. Y. Perlov, V. Crisan, stantsandNonlinearDielectricSusceptibilitiesofCrystals
H.Ebert,andH.Akai,inProceedings to the International (Springer-Verlag, Berlin, 1979).
symposium on structure and dynamics of heterogeneous 22 B. H. Lee, J. Appl. Phys. 41, 2988 (1973).
systems, Duisburg, August 28–29 (2000). 23 G. Kresse and J. Hafner, Phys. Rev.B 47, 558 (1993).
7 J. J. Krebs, B. T. Jonker, and G. A. Prinz, 24 G. Kresse and J. Furthmu¨ller, Phys. Rev. B 54, 11169
Appl.Phys. Lett. 61, 2526 (1987). (1996).
8 E. Reiger, E. Reinwald, G. Garreau, M. Ernst, M. Z¨olfl, 25 VASPhomepage: http://cms.mpi.univie.ac.at/vasp/.
F. Bensch, S. Bauer, H. Preis, and G. Bayreuther, 26 G. Kresse and J. Hafner, J. Phys.: Condens. Matter 6,
J. Appl.Phys.87, 5923 (2000). 8245 (1994).
9 F. Bensch, G. Garreau, R. Moosbu¨hler, E. Beaurepaire, 27 D. Vanderbilt,Phys.Rev.B 41, 7892 (1990).
and G. Bayreuther,J. Appl.Phys. 89, 7133 (2001). 28 J.P.PerdewandA.Zunger,Phys.Rev.B23,5048(1981).
10 M. Z¨olfl, M. Brockmann, M. K¨ohler, S. Kreuzer, 29 D. M. Ceperley and B. J. Alder, Phys. Rev.Lett. 45, 566
T. Schweinb¨ock, S. Miethaner, F. Bensch, and (1980).
G. Bayreuther, J. Magn. Magn. Mater. 175, 16 (1997). 30 J.P.PerdewandY.Wang,Phys.Rev.B45,13244(1992).
11 J. M. MacLaren, S. Crampin, D. D.Vvedensky,R. C. Al- 31 H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188
bers, and J. B. Pendry,Comput. Phys. Commun. 60, 365 (1976).
(1990). 32 F. D. Murnaghan, Proc. Natl. Acad. Sci. 30, 244 (1944).
12 A. Ohtake, T. Hanada, T. Yasuda, K. Arai, and T. Yao, 33 J. Zhu, X. W. Wang, and S. G. Louie, Phys. Rev. B 45,
Phys. Rev.B 60, 8326 (1999). 8887 (1992).
13 S. Mirbt, N. Moll, A. Kley, and J. D. Joannopulos, 34 J. H¨aglund, Phys. Rev.B 47, 566 (1993).
Surf. Sci. 422, L177 (1999). 35 G. Lee, M. H. Lee, and J. Ihm, Phys. Rev. B 52, 1459
14 W. A. Harrison, J. Vac.Sci. Technol. 16, 1492 (1979). (1995).
15 P.HohenbergandW.Kohn,Phys.Rev.136,B864(1964). 36 M.Asato,A.Settels,T.Hoshino,T.Asada,S.B.R.Zeller,
16 W. Kohn and L. J. Sham,Phys. Rev. 140, A1133 (1965). and P. H. Dederichs,Phys. Rev.B 60, 5202 (1999).
17 U. von Barth and L. Hedin,J. Phys.C 5, 1629 (1972). 37 H. P. J. Wijn, ed., Landolt-B¨ornstein, Group III: Crystal
18 M. M. Pant and A. K. Rajagopal, Solid State Commun. and Solid State Physics, vol. 19: Magnetic Properties of
10, 1157 (1972). Metals, Subvolume a: 3d, 4d, and 5d Elements, Alloys,
10
and Compounds(Springer-Verlag, Berlin, 1986). J. D. Joannopoulos, Rev.Mod. Phys. 64, 1045 (1992).
38 D. Bagayoko and J. Callaway, Phys. Rev. B 28, 5419 41 F. Brailsford, Physical Principles of Magnetism (D. van
(1983). Nostrand Company Ltd, London,1966).
39 J.R.ChelikowskyandM.L.Cohen,Phys.Rev.B13,826 42 O.Madelung,IntroductiontoSolid-StateTheory (Springer
(1976). Verlag, Berlin, 1978).
40 M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and