Electron Correlations and the Minority-Spin Band Gap in Half-Metallic Heusler Alloys

0.2 MB·English

by  L. Chioncel

Electron Correlations and the Minority-Spin Band Gap in Half-Metallic Heusler
Alloys
1 1 2 3
L. Chioncel, E. Arrigoni, M.I. Katsnelson, and A.I. Lichtenstein
1Institute of Theoretical Physics, Graz University of Technology, A-8010 Graz Austria
2Radboud University Nijmegen, NL-6525 ED Nijmegen, The Netherlands
3Institute of Theoretical Physics, University of Hamburg, Germany
6
0 Electron-electron correlations affect the band gap of half-metallic ferromagnets by introducing
0 non-quasiparticle states just above the Fermi level. In contrast to the spin-orbit coupling, a large
2 asymmetric non-quasiparticle spectral weight is present in the minority-spin channel, leading to a
peculiar finite-temperature spin depolarization effects. Using recently developed first-principle dy-
n
namical mean field theory, we investigate these effects for the half-metallic ferrimagnetic Heusler
a
compound FeMnSb. We discuss depolarization effects in terms of strength of local Coulomb inter-
J
actionU andtemperatureinFeMnSb. WeproposeNi1−xFexMnSballoysasaperspectivematerials
7
to be used in spin-valve structures and for experimental search of non-quasiparticle states in half-
1
metallic materials.

]
l
e The realization of physical systems whose electronic and discussed the possible experimental investigation
-
r states can be easily manipulated by external actions is a (Bremsstrahlung isohromat spectroscopy, nuclear mag-
t
s verypromisingissue bothfromfundamentalandapplied netic resonance,scanningtunneling microscopy,andAn-
t. side. For example, spintronics materials in which charge dreev reflection) techniques to clarify the existence of
a
and spin degrees of freedom can be used simultaneously these states [13].
m
in order to produce devices with new functionality, have Here,weinvestigatethedistinctionbetweenstatic(i.e.
d- become subjects of growing interest. spin-orbit)anddynamic(correlation)effectsleadingtoa
n A family of extensively studied spintronics materials finite temperature depolarization. According to our re-
o are the half-metallic compounds (HM). First principle sults, for the class of Heusler HM, the strong depolar-
c
electronic structure calculations for HM showed unusual ization at finite temperatures is essentially due to cor-
[
properties in their spin-resolved band structure: while relation effects, while the spin-orbit interaction gives a

1 theelectronicstatesforonespinprojectionhaveametal- negligible effect. In addition, we identify characteristic
v
liccharacterwithanonzerodensityofstatesattheFermi features of the DOS spectrum that should help distin-
6
levelE ,thestateswiththeotherspinprojectiondemon- guishing between static and dynamic depolarization ef-
7 F
3 strate a band gap around EF[1, 2]. As a result, HM can fects.
1 in principle conduct a fully spin-polarized current, and Crystalimperfections[15],interfaces[16],andsurfaces
0 thereforeattractmuchattentionduetopotentialapplica- [17] constitute important examples of static perturba-
6
tions inthe fieldofspintronics[2,3]. Thesecalculations, tions of the ideal, periodic potential which affect the
0
basedonthedensity-functionaltheorywhithintheLocal states in the half-metallic gap. It was shown recently
/
t DensityApproximation(LDA)ortheGeneralizedGradi- [18], that due to finite temperatures, the static non-
a
m ent Approximation (GGA), are very successful in many collinear spin-configurations shows a mixture of spin-up
casestodescribeorpredictmaterialproperties. However, and spin-down density of states that destroy the half-
-
d they fail notably for the case of strongly-correlatedelec- metallic behavior. The non-collinearity could exist at
n
tron systems. For such systems the LDA+DMFT (Dy- zero temperature as well, in anisotropic structures, due
o
namical Mean-Field Theory) method has been designed to the spin-orbit coupling. In such cases static spin-flip
c
: [4,5,6]andcurrentlyisusedveryextensivelyforvarious scattering will introduce states in the half-metallic gap.
v
applications [7]. It is the purpose of the present paper to use a many-
i
X One of the dynamicalmany-electronfeatures of HMF, body approachto investigate dynamicalspin fluctuation
r the non-quasiparticle states [2, 8, 9], contribute signif- effects onthe electronic structure attemperatures below
a
icantly to the tunneling transport in heterostructures the Curie temperature, T < Tc, within the half-metallic
containing HMF [10, 11], even in the presence of arbi- state. In order to illustrate the specific differences be-
trary disorder [12]. The origin of these states is con- tweenthe many-bodyandthe staticnon-collineareffects
nected with “spin-polaron” processes: the spin-down we extend here our previous LDA+DMFT calculations
low-energy electron excitations, which are forbidden for [13, 14] to a different half-metallic Heusler alloy, that is,
HMF in the one-particle picture, turn out to be pos- ferrimagnetic FeMnSb. One of the motivations to study
sible as superpositions of spin-up electron excitations the hypothetical FeMnSb material is to explore the ef-
and virtual magnons [8, 9]. In previous publications, fects of Fe doping in the host NiMnSb compound.
we applied the LDA+DMFT approach to describe the In our approach, correlation effects are treated in
non-quasiparticle states in NiMnSb [13] and CrAs [14] the framework of dynamical mean field theory (DMFT)
2
[7], with a spin-polarized T-matrix Fluctuation Ex- electrons and holes. Contrary, the correlation effects re-
change (SPTF) type of the DMFT solver [6], the on- sult in an asymmetry in the gapfilling [2], namely, NQP
site Coulomb interaction being described by full four- states appear in spin-downchannel just above the Fermi
indices orbital matrix [5]. The essential quantity is the level[2,8,9,13,14],andinthespin-upchannelbelowthe
LDA+DMFT bath Green function Gσ , where 0 de- Fermi level [2, 9]. This asymmetry is a purely quantum
0,m,m′
notes the impurity site. The DMFT self-consistency effect connected with the Pauli principle and with the
equation G0−,m1m′ = G−LD1A,mm′ −Σ0,mm′ is used to com- quantumcharacterofspins; itdisappearsinthe classical
bine the LDA Green function with the solution of the limit [2]. For example, in the case under consideration
impurity model Σ0,mm′ =Σ0,mm′[G0,mm′]. Further com- (minority-spin gap) from a consequent quantum point
putational details are described in Refs. 13, 14, 19. of view, the conduction-electron spin projection is not a
In the simplest case of neglecting the dispersion of goodquantumnumberandrealelectronstatesaresuper-
the magnon frequency, ω ≈ ω , in comparison with positions of the minority-electron states and majority-
q m
the electronhoppingenergyt ,theelectronicself-energy electron states plus magnon, with the same projection
k
becomes local [2, 9]: For such a self-energy one can of the total spin of the crystal. However, the majority-
calculate the one-electron Green functions G (E) = electronstatesbelowtheFermienergycannotparticipate
k,↓
[E −t −Σloc(E)]−1, which allow us to evaluate the in this superposition since they are already completely
k,↓ ↓
additional contributions to the density of states. For il- occupied, therefore these quantum (spin-polaronic) ef-
lustrative purposes we write the lowest-order contribu- fects below the Fermi energy is totally suppressed at
tion: zerotemperature by the Pauliprinciple. As a result, the
statesintheminority-spingapatfinitetemperaturesare
1 ImΣ (E)
δN↓(E)=XReΣ↓(E)δ′(E−tk↓)− π X(E−↓tk↓)2 ftohremFeedrmfriomentehrgeysepslpuisn-tphoeladriosonrsdteart-essmeexairsetidngstoantelysafiblloinvge
k k
(1) the gap more or less uniformly.
The second term of Eq.(1) is formally connected with
thebranch-cutoftheGreenfunctionduetotheelectron-
0.08
magnon scattering processes [2, 9]. *
6 LSDA U
ptthulirmInonguglgeehffanneetcdrhtaeslt,shcocoeannlesanpsreihcnpotriunoslgddouttpchaetekrbeasetipontiwrtnsoe-.ueanpcTctaohhnueednast-tndsrgpeouniwnlgan-torhcrmbhoiaotfnmcntoehenuilss-- es)24 U=2eV Spectral weight FNeiMMnnSSbb 000...000246
interaction is proportional to the spatial derivatives of stat 0 1 2U(eV)3 4 50
tnhoenczreyrsotaolffp-doitaegnotniaall Vele(rm)e:ntVsSOVσ∝,σ′,gσra=dV↑,↓(l. ·Fso)rwHitMh OS(1/0 0
D-2 -2
withagapintheminority-spin(spindown)channel,one
could construct the wave function for spin-down elec- -4 -4
trons based on the general perturbation consideration
LSDA
so that the density of states (DOS) in the gap has a -6 UU==24eeVV -6
quadraticdependence ofthe spinorbitcouplingstrength -2 -1 0 1 2 -1 -0.5 0 0.5 1 1.5
E-E
[20]: δnSO(E) ∝ (V↓,↑)2 As one can see there is an F
↓
obvious qualitative distinctions between the many-body
FIG.1: Left: Densityofstatesofhalf-metallicFeMnSb,LSDA
(Eq.1) and the spin-orbit contribution in the minority (black line) and LSDA+DMFT (red line), for the efective
spin channel, in addition to the fact that the latter are CoulombinteractionU =2eVexchangeparameterJ =0.9eV
orders in magnitude smaller [20]. In the former case the andtemperatureT =300K. Lowerrightpanel: zoomaround
strong temperature dependence of the residues of the EF for different values of U. Upper right panel: Spectral
weight of the NQP states calculated as function of U. The
Green function and the “tail” of the NQP states give
valuesobtained for NiMnSb[13]areplotted for comparison.
rise to a strong temperature dependence of the spin po-
larization, while the spin-orbit term is very weakly tem-
perature dependent. Early theoretical studies showed that the gap of the
As a matter of fact, in the non-relativistic approxi- minorityspinchannelisstablewithrespecttodifferently
mation (without spin-orbit coupling) there are two es- chosen 3d atom X=Fe,Co,Ni in the XMnSb compounds
sentially different sources for states in the gap at finite [21, 22]. Notable difference between Ni- and Fe-based
temperatures. First, there is the simple classical effect Heusler alloys is that NiMnSb is a ferromagnetic half-
of band filling due to disorder, that is, due to scatter- metal, with a very small value of Ni magnetic moment
ing on static (classical) spin fluctuations. This kind of (0.2µ ), whereas in FeMnSb the ferrimagnetic coupling
B
the gap filling is symmetric with respect to the Fermi between Fe (−1µ ) and Mn (3µ ) moments stabilizes
B B
energy, that is, there is no essential difference between the gap and the half-metallic electronic structure[22].
3
In the calculations we considered the standard rep-
resentation of the C1 structure with a fcc unit cell
b
containing three atoms: Fe(0,0,0), Mn(1/4,1/4,1/4),
Sb(3/4,3/4,3/4) and a vacant site E(1/2,1/2,1/2),
respectively. Unfortunately the ternary compound
FeMnSb does not exist, however indications concerning
magnetic and crystallographic properties were obtained
byextrapolatingtheseriesofNi1−xFexMnSb[22],tohigh
Fe concentration. In this case we chose a lattice param-
eter ofa=5.882˚Afor FeMnSb the same as in the recent
LDA+SO calculation of Mavropoulos et.al. [20]. To il-
lustrate the differences between the static and dynamic
effectsweplottheDOSoftheLDA+DMFT calculations
which should be compared with recent results including
SO coupling [20, 22].
Note that depending on the character of chemical
bonding, the value of U for all 3d metals is predicted FIG. 2: Contour plots of polarization as function of energy
to vary between 2 and 6-7 eV [7] A relatively weak de- andtemperaturefordifferentvaluesoflocalCoulombinterac-
tionU.LeftU =2eV,rightU =4eV. TheLSDApolarization
pendence of the non-quasiparticle spectral weight, on
isplottedastheT =0K temperatureresult. Theasymmetry
the U value, (Fig. 1) is evidenced for both NiMnSb
of the NQPstates, is clearly visible for U =4eV.
and FeMnSb compounds. A “saturation” of the spec-
tral weight of FeMnSb takes place for almost the same
value, U∗ ≈ 1eV as in the case of NiMnSb. This effect NQP.WhenthetailofthesestatescrossestheFermilevel
is understood in terms of the T-matrix renormalization a drastic depolarization at Fermi level takes place. One
ofthe Coulombinteractions[6]. Thespectralweightval- can notice that for the case of U = 4eV, the NQP is
ues for FeMnSb are larger in comparison with the ones pinned at the Fermi level, and has a large contribution
obtained for NiMnSb [13], which can be attributed to also due to a large value of DOS in the spin up channel.
the fact that at the Fermi level a larger DOS is present
in the ferrimagnetic FeMnSb than in the ferromagnetic
NiMnSb.
The spin-orbit coupling produce a peak close to the
Fermilevel[20]inthe minority-spinchannel,whichis an
order of magnitude smaller than the spectral weight of
the NQP states. According to the SO results [20], the
polarization at the Fermi level for NiMnSb and FeMnSb
are almost the same. In contrast, our calculation shows
that the spectral weight of NQP states in FeMnSb is
almosttwiceaslargeasthevaluecalculatedforNiMnSb.
Inordertodiscusstheinfluenceoftemperatureandlo-
calCoulombinteractions,onthepolarizationinFeMnSb
compound, we present results of LDA+DMFT calcula-
tions for T ≤ 400K, and different U’s. Fig 2 presents
the contour plot of polarization P(E) = (N (E) −
↑
N (E))/(N (E)+N (E)) as a function of temperature
↓ ↑ ↓
T for U = 2 and 4eV. The LDA value, plotted for con- FIG. 3: Temperature dependent polarization at the Fermi
venience as the T = 0 result shows a gap of magnitude level, P(E = EF,T) (solid line) and magnetization (dashed
0.8eV in agreement with previous calculations [20]. line) for different values of local Coulomb interaction U.
One can see a peculiar temperature dependence of the
spin polarization. The NQP features appears for E − In Fig. 3 one can see a clear distinction between the
E ≥ 0, and is visible in Fig. 1, for U = 2eV and the finite-temperaturebehaviorofthepolarizationandmag-
F
temperature T = 300K. A strong depolarization effect netization, for different values of U. It is interesting
is evidenced for the larger value of U = 4eV. Already to note that the reduced magnetization M(T)/M(0) de-
at 100K, there is a strong depolarization of about 25%. creases slowly in the temperature range studied in Fig.
Increasing the value of U, form 2eV to 4eV, the non- 2. This reduction is a consequence of the finite temper-
quasiparticle contribution is more significant, therefore ature excitations, i.e spin-flip processes, affecting both
thepredominantfactorindepolarizationisplayedbythe spin channels. In the minority spin channel, NQP states
4
areformed,andinthemajoritychannelaspectralweight duced [25]. The associated GMR exhibits a clear spin-
redistributionaroundthe Fermi level(Fig.1) contributes valve contribution of around ∆R/R ≈ 1% [25]. One of
to the depolarization. The corresponding depolarisation the limiting factor for such a small value is the large re-
increaseswiththestrengthofcorrelations. Thedensityof sistivity of the Mo layer which determines limited flow
NQP states displays a rather strong temperature depen- of active electrons exchanged between the two ferromag-
dence[9,10],resultingintheasymmetrythatisvisiblein netic layers without being scattered. To improve on the
Figs. 1 and 2. Recently Dowben et. al. [18] showed that GMRvaluetheusealow-resistivitystandardspacersuch
non-collinearityresultsinaspinmixingwhichultimately as Au or Cu was suggested [25]. On the other hand,
leads to a nonvanishing but symmetric DOS around the having a larger value of DOS at the Fermi level which
Fermi level in the gap of the insulating spin channel. occurs in the majority spin channel (Fig. 1), the ferri-
Therefore,wesuggestthatthe asymmetryintheDOSof magnetic FeMnSb or Ni1−xFexMnSb could increase the
the minority channel is the key feature that should help number of active electrons in such a spin valve configu-
distinguishing whethercorrelationeffects areresponsible ration. In addition, due to its ferrimagnetic properties,
for the finite-temperature depolarisation or not. thespin-valvedemagnetizationfieldcanbereduced. The
Our results show that at finite temperatures the NQP reduced demagnetization is extensively exploited in syn-
states appear in the gap of the minority spin channel, thetic ferrimagnet spin valves heads and are known to
reducing the polarization significantly. In such a situa- have advantages over conventionalspin-valve heads [26].
tion, the half-metallic state is depleted. On the other It is interesting to note that, due to its larger DOS in
hand, recently, Wang [23] suggested that states in the the majority spin channel, FeMnSb is expected on the
minority-spin gap of a half-metallic ferromagnet are lo- one hand to provide a better performance in Half-metal
calized due to disorder (Anderson localization). In such based spin-valves in comparison with NiMnSb. On the
case, the material behaves like a fully polarized HFM. otherhand,ourcalculationshowsthatsuchalargerDOS
The question whether NQP states are conducting or not is accompanied by an equally larger DOS of NQP that,
hasnotbeenstudiedinthepresentwork,andwillbethe on the other hand, suppresses polarisation. The conclu-
subject of our future research. sion, thus, is that correlation effects are important and
Our work suggests that depolarisation in this class of should not be neglected precisely in putatively ”good”
Heusler compounds is dominated by NQP states, while HM materials,i. e. in materialswith a largeDOS in the
spin-orbit contributions are much smaller. In addition, majority spin channel.
many-bodyeffectsaremorepronouncedinFeMnSbthan Acknowledgement We thank Dr. R.A. de Groot for
in NiMnSb. This is tightly connected to the larger DOS helpfuldiscussions,andacknowledgeDr. Ph. Mavropou-
in the majority spin channel in the former material. los for providing his LDA+SO results. We acknowledge
Therefore, doping of NiMnSb by Fe could be an inter- financial support by the KFA Juelich (LC) and by the
esting issue to investigate the interplay between alloying FWF project P18505-N16(LC and EA).
and many body effects. In this respect, we have car-
ried out preliminary LDA+DMFT calculations [24] on
NiMnSbsupercellcontaining25%Feimpurities,i. e. for
(Ni3Fe)Mn4Sb4. Our results show a half-metallic char-
[1] R.A. de Groot, F.M. Mueller, P.G. van Engen, and
acter at the LDA level, with similar strong correlation-
K.H.J. Buschow, Phys. Rev.Lett. 50, 2024 (1983).
induceddepolarizationeffectsasinpureFeMnSb. There-
[2] V.Yu.IrkhinandM.I.Katsnelson,Usp.Fiz.Nauk164,
fore, for this material, many body effects are of primary
705 (1994) [Physics Uspekhi37, 659 (1994)].
importance even in the presence of disorder. Correla- [3] I. Zˇuti`c, J. Fabian, and S. Das Sarma, Rev. Mod. Phys.
tion effects on surfaces of half-metals were dicussed re- 76, 323 (2004).
centy and it was shown that these states can be probed [4] V. I. Anisimov, A. I. Poteryaev, M. A. Korotin, A. O.
both directly and via their effect on surface states [12]. Anokhin, and G. Kotliar, J. Phys.: Condens. Matter 9,
7359 (1997).
As a consequence in addition to the previously dis-
[5] A. I. Lichtenstein and M. I. Katsnelson, Phys. Rev. B
cussed experimental techniques [13], we propose the use
57, 6884 (1998).
of Ni1−xFexMnSb alloys both in spin-valve structures, [6] M. I. Katsnelson and A. I. Lichtenstein, J. Phys.: Con-
and to investigate the existence of NQP states in half- dens. Matter 11, 1037 (1999); M. I. Katsnelson and A.
mettalic materials. I. Lichtenstein, Eur. Phys.J. B 30, 9 (2002).
The discovery of giant magneto-resistance (GMR) [7] G. Kotliar and D. Vollhardt, Phys. Today 57 (3),
has led to tremendous amount of activity to under- 53 (2004); G. Kotliar, S. Y. Savrasov, K. Haule,
V. S. Oudovenko, O. Parcollet, C.A. Marianetti,
stand and develop technology based on high-density
cond-mat/0511085.
magnetic recording. The dominant mechanism lead-
[8] D. M. Edwards and J. A. Hertz, J. Phys. F 3, 2191
ing to GMR is the spin-dependent s-d scattering.
(1973).
NiMnSb-basedspin-valvestructuresusingMospacerlay- [9] V.Yu.IrkhinandM.I.Katsnelson,FizikaTverdogoTela
ers NiMnSb/Mo/NiMnSb/SmCo2 were successfully pro- 25,3383(1983)[Sov.Phys.-SolidState25,1947(1983)];
5
J. Phys. : Condens. Matter 2, 7151 (1990). 93, 7948 (2003).
[10] V.Yu.Irkhinand M. I.Katsnelson, Eur. Phys.J. B 30, [19] L. Chioncel, L.Vitos, I. A. Abrikosov, J. Kollar, M. I.
481 (2002). Katsnelson, and A. I. Lichtenstein, Phys. Rev. B 67,
[11] G. Tkachov, E. McCann and V. I. Fal’ko, Phys. Rev. B 235106 (2003).
65, 024519 (2001); E. McCann and V. I. Fal’ko, Phys. [20] Ph. Mavropoulos, I. Galanakis, V. Popescu and P. H.
Rev.B 68, 172404 (2003). Dederichs J. Phys.: Condens. Matter 16, S5759 (2004).
[12] V.Yu.Irkhin and M. I. Katsnelson, cond-mat/0512245. [21] J. Kubler,Physica 127 B,257 (1984).
[13] L.Chioncel, M. I.Katsnelson, R.A.deGroot, and A.I. [22] R.A. de Groot, A.M. van der Kraan, and K.H.J.
Lichtenstein,Phys. Rev.B 68, 144425 (2003). Buschow, Journal of Mag. Mag. Matt. 61, 330 (1986).
[14] L. Chioncel, M. I. Katsnelson, G. A. de Wijs, R. A. de [23] X. Wang and X.-G. Zhang, Phys. Rev. Lett. 82, 4276
Groot, and A. I. Lichtenstein, Phys. Rev. B 71, 085111 (1999).
(2005). [24] L. Chioncel et. al. in preparation.
[15] H.Ebert andG.Schu¨tz,J.Appl.Phys.69,4627 (1991). [25] C. Hordequin, J.P. Nozieres and J. Pierre, Journal of
[16] G.A. de Wijs and R.A. de Groot, Phys. Rev. B 64, Mag. Mag. Matter. 183, 225 (1998).
020402(R) (2001). [26] H. Kanai, K. Noma and J. Hong, Fujitsu Sci. Tech. J.,
[17] I.Galanakis, J. Phys.: Cond. Matter. 14, 6329 (2003). 37, 174 (2001).
[18] R. Skomski and P. A. Dowben, Europhys. Lett. 58, 544
(2002); P. A. Dowben and R. Skomski, J. Appl. Phys.