University of Groningen
Half-metallic ferromagnets
Katsnelson, M. I.; Irkhin, V. Yu.; Chioncel, L.; Lichtenstein, A. I.; de Groot, R. A.
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10.1103/RevModPhys.80.315
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Katsnelson, M. I., Irkhin, V. Y., Chioncel, L., Lichtenstein, A. I., & de Groot, R. A. (2008). Half-metallic
ferromagnets: From band structure to many-body effects.
Reviews of Modern Physics
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Half-metallic ferromagnets: From band structure to many-body effects
M. I. Katsnelson
*
Institute for Molecules and Materials, Radboud University of Nijmegen, NL-6525 ED
Nijmegen, The Netherlands
V. Yu. Irkhin
Institute of Metal Physics, 620041 Ekaterinburg, Russia
L. Chioncel
Institute of Theoretical Physics, Graz University of Technology, A-8010 Graz, Austria
and Department of Physics, University of Oradea, 410087 Oradea, Romania
A. I. Lichtenstein
Institute of Theoretical Physics, University of Hamburg, 20355 Hamburg, Germany
R. A. de Groot
Institute for Molecules and Materials, Radboud University of Nijmegen, The Netherlands
and Zernicke Institute for Advanced Materials, NL-9747 AG Groningen, The
Netherlands
共Published 1 April 2008兲
A review of new developments in theoretical and experimental electronic-structure investigations of
half-metallic ferromagnets 共HMFs兲 is presented. Being semiconductors for one spin projection and
metals for another, these substances are promising magnetic materials for applications in spintronics
共i.e., spin-dependent electronics兲. Classification of HMFs by the peculiarities of their electronic
structure and chemical bonding is discussed. The effects of electron-magnon interaction in HMFs and
their manifestations in magnetic, spectral, thermodynamic, and transport properties are considered.
Special attention is paid to the appearance of nonquasiparticle states in the energy gap, which provide
an instructive example of essentially many-body features in the electronic structure. State-of-the-art
electronic calculations for correlated
d-systems are discussed, and results for specific HMFs 共Heusler
alloys, zinc-blende structure compounds,
CrO
2
, and Fe
3
O
4
兲 are reviewed.
DOI: 10.1103/RevModPhys.80.315 PACS number共s兲: 71.20.Be, 75.50.Cc, 71.10.Fd, 73.20.At
CONTENTS
I. Introduction 316
II. Classes of Half-Metallic Ferromagnets 318
A. Heusler alloys and zinc-blende structure compounds 318
1. Heusler C1
b
alloys 318
2. Half metals with zinc-blende structure 320
3. Heusler L2
1
alloys 321
B. Strongly magnetic half metals with minority-spin gap 322
1. Chromium dioxide 322
2. The colossal-magnetoresistance materials 323
C. Weakly magnetic half metals with majority-spin gap 323
1. The double perovskites 323
2. Magnetite 324
D. Strongly magnetic half metals with majority-spin gap 324
1. Anionogenic ferromagnets 324
E. Sulfides 324
1. Pyrites 325
2. Spinels 325
F. Miscellaneous 325
1. Ruthenates 325
2. Organic half metals 326
III. Model Theoretical Approaches 326
A. Electron spectrum and strong itinerant
ferromagnetism in the Hubbard model 326
B. Electron spectrum in the s-d exchange model:
The nonquasiparticle density of states 330
C. The problem of spin polarization 334
D. Tunneling conductance and spin-polarized STM 336
E. Spin waves 337
F. Magnetization and local moments 339
G. Nuclear magnetic relaxation 341
H. Thermodynamic properties 342
I. Transport properties 343
J. X-ray absorption and emission spectra. Resonant
x-ray scattering 346
IV. Modern First-Principles Calculations 347
A. Different functional schemes 347
B. LDA+DMFT: The quantum Monte Carlo solution
of the impurity problem 350
C. Spin-polarized T-matrix fluctuating exchange
approximation 352
V. Electronic Structure of Specific Half-Metallic
Compounds 354
*
M.Katsnelson@science.ru.nl
REVIEWS OF MODERN PHYSICS, VOLUME 80, APRIL–JUNE 2008
0034-6861/2008/80共2兲/315共64兲 ©2008 The American Physical Society315
A. Heusler alloys 354
1. NiMnSb: Electronic structure and
correlations 354
2. Impurities in HMF: Lanthanides in NiMnSb 360
3. FeMnSb: A ferrimagnetic half-metal 361
4. Co
2
MnSi: A full-Heusler ferromagnet 363
B. Half-metallic materials with zinc-blende structure 364
1. CrAs: Tunable spin transport 364
2. VAs: Correlation-induced half-metallic
ferromagnetism? 366
C. Half-metallic transition-metal oxides 368
1. CrO
2
: A rutile structure half-metallic
ferromagnet 368
VI. Exchange Interactions and Critical Temperatures in
Half-Metallic Compounds 370
A. The Green’s function formalism 370
B. The frozen-magnon approach and DFT calculations
of spin spirals 371
C. First-principles calculations 371
1. Semi-Heusler C1
b
alloys 371
2. Full-Heusler L2
1
alloys 371
3. Zinc-blende half-metals 372
VII. Conclusions 372
Acknowledgments 373
References 373
I. INTRODUCTION
Twenty-five years ago the unusual magneto-optical
properties of several Heusler alloys motivated the study
of their electronic structure. This yielded an unexpected
result: Some of these alloys showed the properties of
metals as well as insulators at the same time in the same
material, depending on the spin direction. This property
was given the name of half-metallic magnetism 共de
Groot, Mueller, v. Engen, et al., 1983兲. Although it is not
exactly clear how many half metals are known to exist at
this moment, half-metallic magnetism as a phenomenon
has been generally accepted. Formally the expected
100% spin polarization of charge carriers in a half-
metallic ferromagnet 共HMF兲 is a hypothetical situation
that can be approached only in the limit of vanishing
temperature and by neglecting spin-orbital interactions.
However, at low temperatures 共as compared with the
Curie temperature, which exceeds 1000 K for some
HMFs兲 and minor spin-orbit interactions, a half metal
deviates so markedly from a normal material that the
treatment as a special category of materials is justified.
The confusion about the number of well-established half
metals originates from the fact that there is no “smoking
gun” experiment to prove or disprove half metallicity.
The most direct measurement is spin-resolved positron
annihilation 共Hanssen and Mijnarends, 1986兲, but this is
a tedious, expensive technique requiring dedicated
equipment. NiMnSb is the only proven HMF so far to
the precision of the experiment, which was better than
one-hundredth of an electron 共Hanssen et al., 1990兲. This
number also sets the scale for concerns about
temperature-induced depolarization and spin-orbit ef-
fects, detrimental for half metallicity.
The half metallicity in a specific compound should not
be confused with the ability to pick up 100% polarized
electrons from a HMF. The latter process involves elec-
trons crossing a surface or interface into some medium
where their degree of spin polarization is analyzed. This
is clearly not an intrinsic materials property. The rich-
ness but also the complications of surfaces and inter-
faces are still not fully appreciated.
Because of these experimental complications, it is not
surprising that electronic-structure calculations continue
to play an important role in the search for new HMFs, as
well as in the introduction of new concepts like half-
metallic antiferromagnetism. However, electronic-
structure calculations have weaknesses as well. Most of
the calculations are based on density-functional theory
共DFT兲 in the local-density or generalized gradient ap-
proximation. It is well known that these methods under-
estimate the band gap for many semiconductors and in-
sulators, typically by 30%. It has been assumed that
these problems do not occur in half metals since their
dielectric response is that of a metal. This assumption
was disproved recently. A calculation on the HMF
La
0.7
Sr
0.3
MnO
3
employing the GW approximation
共which gives a correct description of band gaps in many
semiconductors兲 leads to a half-metallic band gap 2 eV
in excess of the DFT value 共Kino et al., 2003兲. The con-
sequences of this result are potentially dramatic: If it
were valid in half-metallic magnetism in general, it
would imply that many of the materials showing band
gaps in DFT-based calculations of insufficient size to en-
compass the Fermi energy are actually true half metals.
Clearly more work is needed in this area.
The strength of a computational approach is that it
does not need samples: calculations can be performed
even for nonexistent materials. But, in such an endeavor,
a clear goal should be kept in mind. Certainly, computa-
tional studies can help in the design of new materials,
but the interest is not so much in finding exotic physics
in materials that have no chance of ever being realized.
Such studies can serve didactical purposes, in which case
they will be included in this review. However, the main
focus will be devoted to materials that either exist or are
共meta兲stable enough to have a fair chance of realization.
This review will cover half metals and will not discuss
the area of magnetic semiconductors. Some overlap ex-
ists, however. The older field of magnetic semiconduc-
tors started with semiconductors like the europium
monochalcogenides and cadmium-chromium chalco-
genides 共Nagaev, 1983兲. Later, the focus changed to the
so-called diluted magnetic semiconductors 共Delves and
Lewis, 1963兲. These are regular 共i.e., III-V or II-VI兲
semiconductors, where magnetism is introduced by par-
tial substitution of the cation by some 共magnetic兲 3d
transition element. The resulting Curie temperatures re-
mained unsatisfactory, however. The next step in the de-
velopment was the elimination of the nonmagnetic tran-
sition element altogether. HMFs could be realized in this
way, provided that the remaining transition-metal pnic-
tides could be stabilized in the zinc-blende or related
structures. The review will treat not the 共diluted兲 mag-
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Rev. Mod. Phys., Vol. 80, No. 2, April–June 2008
netic semiconductors as such, but some aspects of meta-
stable zinc-blende HMFs.
HMFs form quite a diverse collection of materials
with different chemical and physical properties, and
even the origins of the half metallicity can be quite dis-
tinct. For this reason, the origin of the band gap must be
discussed in terms of two ingredients that define a solid:
the crystal structure and the chemical composition. Two
aspects are of importance in this context. The first one is
“strong magnetism” versus “weak magnetism.” In a
strong magnet, the magnetic moment will not increase if
the exchange splitting is hypothetically increased. Thus
the size of the magnetic moment is not determined by
the strength of the exchange interaction, but is limited
instead by the availability of electron states. In practice,
this implies that either the minority-spin subshell共s兲 re-
sponsible for the magnetism is 共are兲 empty or the rel-
evant majority channel共s兲 is 共are兲 completely filled. In
the case of weak magnetism, the magnetic moment is
determined by a subtle compromise between the energy
gain of an increase in magnetic moment 共the exchange
energy兲 and the 共band兲 energy that the increase of the
magnetic moment costs. To avoid misunderstanding, we
emphasize that this definition of weak and strong mag-
nets differs from that used by Moriya 共1985兲 and most
theoretical work on itinerant-electron magnetism. Ac-
cording to Moriya, strong magnets are those with well-
defined magnetic moments, which means, for example,
Curie-Weiss behavior of the wave-vector-dependent
magnetic susceptibility
共q ,T兲 in the whole Brillouin
zone. In this sense, all HMFs containing Mn ions are
strong magnets. However, within this group of materials,
we may introduce a finer classification based on the sen-
sitivity of the magnetic moment to small variations of
parameters.
All combinations of weak or strong magnetism with
majority- or minority-spin band gaps are known today.
Thus weak magnets with minority-spin band gaps are
found in the Heusler alloys and artificial zinc blendes;
examples of weak magnets with majority-spin gaps are
the double perovskites and magnetite. The colossal-
magnetoresistance materials, as well as chromium diox-
ide, are examples of strongly magnetic half metals with
minority-spin band gaps, while the anionogenic ferro-
magnets such as rubidium sesquioxide are examples of
strongly magnetic half metals with a majority-spin band
gap.
An interesting and relatively new development is the
work on half-metallic sulfides. The HMF state in oxides
with the spinel structure is relatively rare. The prime
example, of course, is magnetite. However, any substitu-
tion into the transition-metal sublattice leads almost in-
variably to a Mott insulating state, like the one in mag-
netite itself below the Verwey transition at 120 K. On
the other hand, electrons in sulfides are substantially less
well correlated. Hence a wealth of substitutions is pos-
sible in order to optimize properties, design half-metallic
ferromagnets or antiferromagnets, and so on, without
the risk of losing the metallic properties for the second
spin direction as well. There is a price to be paid, how-
ever: Since the cation-cation distances are larger in sul-
fides, the Curie and Néel temperatures are lower than in
oxides. Nevertheless, the work on half-metallic sulfides
deserves much attention.
In all metallic ferromagnets, the interaction between
conduction electrons and spin fluctuation is of crucial
importance for physical properties. In particular, the
scattering of charge carriers by magnetic excitations de-
termines the transport properties of itinerant magnets
共temperature dependences of resistivity, magnetoresis-
tivity, thermoelectric power, anomalous Hall effect, etc.兲.
From this point of view, HMFs, as well as ferromagnetic
semiconductors, differ from “normal” metallic ferro-
magnets by the absence of spin-flip 共one-magnon兲 scat-
tering processes. This difference is also important for
magnetic excitations since there is no Stoner damping,
and spin waves are well defined in the whole Brillouin
zone, as in magnetic insulators 共Auslender and Irkhin,
1984a; Irkhin and Katsnelson, 1994兲.
Electron-magnon interaction also modifies consider-
ably the electron energy spectrum in HMFs. These ef-
fects occur both in the usual ferromagnets and in HMFs.
However, the peculiar band structure of HMFs 共the en-
ergy gap for one spin projection兲 results in important
consequences. In generic itinerant ferromagnets, the
states near the Fermi level are quasiparticles for both
spin projections. In contrast, in HMFs, an important role
is played by incoherent 关nonquasiparticle 共NQP兲兴 states
that occur near the Fermi level in the energy gap 共Irkhin
and Katsnelson, 1994兲. The appearance of the NQP
states in the work of Edwards and Hertz 共1973兲 and
Irkhin and Katsnelson 共1983兲 is one of the most interest-
ing correlation effects typical of HMFs. The origin of
these states is connected with “spin-polaron” processes:
Spin-down low-energy electron excitations, which are
forbidden for HMFs in the one-particle picture, turn out
to be possible as a superposition of spin-up electron ex-
citations and virtual magnons. The density of the NQP
states vanishes at the Fermi level but increases greatly at
an energy scale of the order of the characteristic magnon
frequency
¯
. These states are important for spin-
polarized electron spectroscopy 共Irkhin and Katsnelson,
2005a, 2006兲, nuclear magnetic resonance 共NMR兲
共Irkhin and Katsnelson, 2001兲, and subgap transport in
ferromagnet-superconductor junctions 共Andreev reflec-
tion兲共Tkachov et al., 2001兲. The density of NQP states
was calculated from first principles for a prototype HMF,
NiMnSb 共Chioncel, Katsnelson, de Groot, et al., 2003兲,
as well as for other Heusler alloys 共Chioncel, Arrigoni,
Katsnelson, et al., 2006兲, zinc-blende structure com-
pounds 共Chioncel et al., 2005; Chioncel, Mavropoulos,
Lezaic, et al., 2006兲, and CrO
2
共Chioncel et al., 2007兲.
Figure 1 shows the NQP contribution to the density of
states.
Therefore, HMFs are interesting conceptually as a
class of materials which may be convenient to treat
many-body solid-state physics that cannot be described
by band theory. It is usually accepted that many-body
effects lead only to renormalization of the quasiparticle
parameters in the sense of Landau’s Fermi liquid 共FL兲
317
Katsnelson et al.: Half-metallic ferromagnets: From band …
Rev. Mod. Phys., Vol. 80, No. 2, April–June 2008
theory, the electronic liquid being qualitatively similar to
the electron gas 共see, e.g., Nozieres, 1964兲. On the other
hand, NQP states in HMFs are not described by the FL
theory. As an example of highly unusual properties of
the NQP states, we mention that they can contribute to
the T-linear term in the electron heat capacity 共Irkhin et
al., 1989, 1994; Irkhin and Katsnelson, 1990兲, even
though their density at E
F
is zero at temperature T
=0 K. Some developments concerning the physical ef-
fects of NQP states in HMFs are considered in this re-
view.
II. CLASSES OF HALF-METALLIC FERROMAGNETS
A. Heusler alloys and zinc-blende structure compounds
In this section, we treat HMFs with the Heusler C1
b
and L2
1
structures. Although not Heusler alloys in the
strict sense, artificial half metals in the zinc-blende struc-
ture will also be discussed because of their close relation
with the Heusler C1
b
alloys. The zinc-blende structure
has a face-centered-cubic 共fcc兲 Bravais lattice with a ba-
sis of 共0,0,0兲 and 共 1/4,1/4,1/4兲, the two species coordi-
nating each other tetrahedrally. The Heusler C1
b
struc-
ture consists of the zinc-blende structure with additional
occupation of the 共1/2,1/2,1/2兲 site. Atoms at the latter
position, as well as those at the origin, are tetrahedrally
coordinated by the third constituent, which itself has a
cubic coordination consisting of two tetrahedra. The
Heusler L2
1
structure is obtained by additional occupa-
tion of the 共3/4,3/4,3/4兲 site by the same element al-
ready present at 共1/4,1/4,1/4兲. This results in the occur-
rence of an inversion center that is not present in the
zinc-blende and Heusler C 1
b
structures. This difference
has important consequences for the half-metallic band
gaps. The electronic structure of the Heusler alloys was
reviewed recently by Galanakis and Mavropoulos
共2007兲.
1. Heusler C1
b
alloys
Interest in fast, nonvolatile mass storage memory
sparked much activity in the area of magneto-optics in
general, and the magneto-optic Kerr effect 共MOKE兲
specifically, at the beginning of the 1980s. All existing
magnetic solids were investigated, leading to a record
MOKE rotation of 1.27° for PtMnSb 共van Engen et al.,
1983兲. The origin of these properties remained an un-
solved problem, however. This formed the motivation to
study the electronic structure of the isoelectronic Heu-
sler C1
b
compounds NiMnSb, PdMnSb, and PtMnSb,
and the subsequent discovery of half-metallic magne-
tism. Interestingly enough, there seems still to be no
consensus on the origin of the magneto-optical proper-
ties. The original simple and intuitive explanation
共de Groot, 1991兲 was complementary to the production
of spin-polarized electrons by optical excitation in III-V
semiconductors. In that case, the top of the valence band
is split by the spin-orbit coupling, and the photoexcita-
tion of electrons from the very top of the band by circu-
larly polarized light leads to 50% spin polarization. In
contrast, excitations from a valence band are possible
for only one of the two components of circular light, as
in the case of PtMnSb; this should result in a strong
difference of the refraction and absorption for the two
opposite polarizations. In PtMnSb, this difference is
maximal for visible light, and for NiMnSb the maximum
of off-diagonal optical conductivity is shifted to the ul-
traviolet region. The main contribution to this shift
comes from scalar relativistic interactions in the final
state 共Wijngaard et al., 1989兲, which are much weaker for
Ni than for Pt due to the difference in nuclear charge.
Further, the magneto-optical properties of the Heusler
alloys were calculated by Antonov et al. 共1997兲 in good
agreement with experimental data, but the physical ex-
planation was not provided. Recently, Chadov et al.
共2006兲 demonstrated that the agreement between the
calculated and experimental values for the Kerr rotation
and ellipticity in NiMnSb can be improved further by
taking into account correlation effects within the so-
called local-density approximation plus dynamical
mean-field theory 共LDA+DMFT兲 approach 共see Sec.
IV.A兲.
Since NiMnSb is the most studied HMF 共at least
within the Heusler C1
b
structures兲, we concentrate on it
here. The origin of its half-metallic properties has an
analogy with the electronic structure of III-V zinc-
blende semiconductors. Given the magnetic moment of
4
B
, manganese is trivalent for the minority-spin direc-
tion and antimony is pentavalent. The Heusler C1
b
structure is the zinc-blende one with an additional site
共1/2,1/2,1/2兲 being occupied. The role of nickel is both
to supply Mn and Sb with the essential tetrahedral coor-
dination and to stabilize MnSb in the cubic structure
共MnSb in the zinc-blende structure is half metallic, but
not stable兲. Thus a proper site occupancy is essential:
nickel has to occupy the double tetrahedrally coordi-
nated site 共Helmholdt et al., 1984; Orgassa et al., 1999兲.
The similarity in chemical bonding between NiMnSb
and zinc-blende semiconductors also explains why it is a
weak magnet, as discussed in the Introduction: the pres-
ence of occupied manganese minority d states is essen-
FIG. 1. 共Color online兲 Density of nonquasiparticle states for
half-metallic ferromagnets, possessing the gap in the minority
spin channel. NQP states are the dominant many-body feature
around E
F
in comparison with other mean-field effects, such as
spin-orbit or noncollinearity, as discussed.
318
Katsnelson et al.: Half-metallic ferromagnets: From band …
Rev. Mod. Phys., Vol. 80, No. 2, April–June 2008
