Half Metallic Ferromagnets
Jacques Pierre, Laurent Ranno
Laboratoire Louis Neel, CNRS,
The concept of half metallic
ferromagnets was introduced by de Groot et al., on the basis
of band structure calculations in NiMnSb and PtMnSb semi-Heusler
phases. Due to the ferromagnetic decoupling, one of the spin
subbands (generally the majority-spin or up-spin subband) is
metallic, whereas the Fermi level falls into a gap of the other
(down-spin) subband. Figure 1 gives the calculated density of
states for NiMnSb. Obvious conditions for the occurrence of this
new class of materials are the existence of narrow bands and
energy gaps in the energy spectrum, and of strong ferromagnetic
interactions. Half metals are the extreme case of strong
ferromagnets (or saturated Hubbard ferromagnets), where not only
3d electrons are fully polarized, but also other (sp) down-spin
bands do not cross the Fermi level.
Fig.1. Band structure for
These conditions can be met in manganese
compounds particularly, as the large intraatomic exchange results
in the full alignment of local spins and thus in the exclusion of
down-spin electrons from the 3d shell . Contrary to true
Heusler phases, semi-Heusler compounds have a vacant
crystallographic site, which gives rise to a smaller overlap
between 3d wavefunctions, and to the occurrence of gaps in the
energy spectrum. Besides the case of semi-Heusler compounds, half
metallic behaviour is found in CrO2 and in (La1-xSrx)MnO3
ferromagnetic manganites. However the high temperature
para-magnetic states of these materials are very different, and
will influence the thermal dependence of their properties. Fe3O4
is thought to be a ferrimagnetic half metal. Perhaps other types
of half metallic systems may arise from the magnetic decoupling
and band crossing in a paramagnetic semiconducting compound, as
for instance in EuO.
I. Low temperature properties
a. Spin polarization at EF
From the definition of half metals, the spin
polarization of electrons is 100% at the Fermi level, which may
be checked by spin-resolved photoemission studies. Figure 2 shows
resolved photoemission spectra
in La0.7Sr0.3MnO3 at 40K .
The majority spins have a large density of states (DOS) which
exhibits the metallic Fermi cutoff at EF, already seen
by classical photoemission , whereas the minority band
spectrum shows a vanishing DOS from about 0.4 eV below EF up
to the Fermi level . 0.4 eV is the gap between EF
and the top of the occupied valence band for the minority band.
Fig.2. Spin resolved
photoemission spectra for (La0.7 Sr0.3)MnO3
at 40K and 380K 
Another more important feature is the gap betwen EF and the bottom of the conduction band for the minority band, which measures the minimum energy for an individual electronic spin reversal. is smaller than the overall exchange splitting between the two subbands (fig.3), and will vanish when the magnetic splitting is reduced (see below). Only 50% polarization has been measured in NiMnSb  at low temperature, probably because the surface of this material is not so well ordered as the bulk. Early photoemission spectra for CrO2 failed to reveal a significant density of electrons at EF, but recent data show that EF actually lies near a minimum in the density of states, in accord with electronic structure calculations. The difficulties to prepare a clean surface of CrO2 should not be underestimated, as this compound decomposes at 200°C under vacuum.
For stoichiometric compounds, the last occupied down-spin band is filled and contains an integer number of electrons n. Hence the magnetization m /µB = (n - n) is integer (apart from a weak polarization of internal shells). For instance, the magnetization of NiMnSb and PtMnSb is 4.0 0.05 µB, that of CrO2 is 2.0 µB. Note that the magnetization may be shared between atoms, for instance 3.8 µB for Mn, 0.2µB for Ni respectively in NiMnSb. In CrO2, some of the spin polarization may be on the oxygen.
For solid solutions, like
intermediate-valent manganites, each electron added at the Fermi
level goes into the up-spin band, thus the magnetization
increases at the same rate as the number of electrons. For
ferromagnetic solutions around (La0.7Sr0.3)MnO3
, the magnetization increases with the slope (+1) as
function of La content. Some exceptions may arise when additional
electrons become localized in an internal magnetic shell (as for
instance in rare earths) rather than being added at the Fermi
Fig.3. Scheme of electronic excitations in half
The magnetization is fully saturated at low
temperature, i.e. the superposed high-field susceptibility is
vanishingly small, at least for a single crystal and a magnetic
field applied along the easy magnetization axis: the applied
field slightly increases the half metallic gap , but does not
modify the occupation of both subbands.
Positron annihilation experiments have been
performed for NiMnSb and brought, after some tedious analysis,
the first experimental evidence for half metals .The
possibility to check directly the absence of the down-spin Fermi
surface by Compton scattering has been recently suggested ,
experiments are under way on Co2MnSi. Another
prediction from theory  is that there is no Korringa
relaxation in a half-metal, as the relaxation rate 1/T1
~ kBT. n(EF).n(EF) vanishes.
Similarly, there can be no spin-flip scattering in the
Thermal excitations will destroy the half metallic character below the Curie temperature TC, as the splitting between the two subbands decreases. The half metal gap is only a fraction of and can vanish well below Tc, before a substantial decrease of magnetization  . As said before, the high temperature paramagnetic states are different in semi-Heusler compounds which are normal metals with itinerant-type para-magnetism ((Tc) ~ 130 µW.cm), and in manganites which exhibit a semiconducting behaviour. CrO2 has a rather high resistivity at room temperature (about 500µW.cm)  and the conduction in the paramagnetic state may be of polaronic nature.
NiMnSb and PtMnSb turn to a normal metallic
behaviour, as soon as the Fermi level reaches the bottom of the
conduction band for the down-spin band (near 80K for NiMnSb).
Indeed low energy magnetic excitations in half metals can be only
transverse spin wave excitations ; the compounds then behave like
Heisenberg magnets, where the magnetization follows M(T) = M(0)
[1-BT3/2], neglecting any magneto-crystalline
anisotropy. resistivity and magnetoresistance. As soon as both
spin bands are occupied, individual spin reversals (Stoner-like
excitations) occur, and the temperature dependence of the
magnetization is modified. Irkhin and Katsnelson , following
Moriya, have shown that other terms (T2, T4/3)
occur due to spin fluctuations. Such a cross-over is observed
near 80K for NiMnSb (fig.4) . Note that the magnetization is
only slightly reduced at this temperature: M(80K) = 3.95 µB
instead of M(0) = 4.02 µB.
Fig.4. Square of
magnetization versus T2 for a NiMnSb single crystal
A question is whether
ferromagnetic manganites can turn directly from half metallic to
semiconducting behaviour or not. In the paramagnetic state,
atomic correlations still maintain a high local moment and expel
the local minority-spin density, but the behaviour of the
disordered magnetic system and the exact nature of the gap are
still not completely understood. The answer will be certainly
brought by temperature dependent spin-resolved photoemission
experiments, but also by the complete analysis of the resistivity
Fig.5. Variation of
magnetization in CrO2 at low temperature .
It is worth noting that the half metal gap has
nothing in common with the spin wave gap Ga which may
arise from the magnetocrystalline anisotropy. In the case of
NiMnSb  as well as for ferromagnetic manganites ,
inelastic neutron scattering experiments show classical magnon
excitations at low temperature, the analysis of which
demonstrates that these systems are 3D Heisenberg magnets rather
than 3D Ising systems. Ga is of the order of 10
K in NiMnSb and no more than 15 K in (La0.8 Sr0.2)MnO3
respectively , these values are much smaller than those
estimated for (about 600K for NiMnSb at low temperatures). The
magnetization for CrO2  follows a nice T3/2
law between 2 and 60K (fig.5), thus the anisotropy gap should be
small. Additional excitations (diffusive modes for manganites,
Stoner-like modes for NiMnSb) have been observed at high energies
and close to the Curie temperature. The analogy stops there, as
paramagnetic states are different for both systems.
III. Consequences for transport
As long as only one subband is occupied,
individual spin reversals are inelastic processes; the low
temperature magnetic resistivity is due to spin wave excitations
only and should behave as T2, if there is no large
magnetocrystalline anisotropy. A T2 behaviour has
indeed been observed in NiMnSb  (fig.6). The spin diffusion
length should then be large. For temperatures near the cross over
to a normal ferromagnet, the resistivity rapidly increases for
NiMnSb because a new spin-flip scattering channel is opened. It
follows above a different power law (T1.35). Another
manifestation of the long mean free path and large carrier
mobility in the half metallic state is the behaviour of the
normal Hall effect, which suddenly increases below 80K [13,14]
Fig.6. Resistivity of
NiMnSb versus temperature .
A different behaviour has been observed in CrO2
, where the resistivity follows the law = 0 + AT2
exp(-E/kT), with E= 80K. whereas the magnetization follows a T3/2
law ; the behaviour of the resistivity is still not understood.
The magnetoresistance (MR) of half metals at low temperatures is
due only to the cyclotron effect and should be positive, as
observed in NiMnSb below 100K. Conversely spin disorder terms
prevail at higher temperatures and lead to a negative MR.
Fig.7. Normal and anomalous Hall effect in NiMnSb
Again manganites may not exhibit a simple
behaviour: first the magnetic field gives rise to significant
modifications of the band structure, second, any perturbation of
the ferromagnetic state (spin waves, canting, charge
) gives rise to a huge scattering of conduction
electrons related to the mixed-valent configuration and finite
life time of electronic states. Measurements on La1-x
Srx MnO3 single crystals  show that the
resistivity and MR become very small at low temperatures and
their magnitudes are compatible with the half metallic state.
This state should be destroyed below TC, for instance
near 200K for (La08Sr0.2)MnO3
(Tc ~ 301K), when the resistivity and MR steeply increase.
IV. Applications of half metals
a. Magnetooptical effects
A very large Kerr rotation has been observed
 for PtMnSb ( K = 2° for = 720 nm); the vanishing
down-spin density at EF leads to a non-cancellation of
the optical transitions arising from up- and down-bands. The half
metallic properties also lead to a small plasma frequency ,
enhancing the Kerr effect. The other quantities which play a role
are the large spin-orbit coupling strength of Pt, the large
magnetic moment on Mn and the strong hybridization of Mn, Pt and
b. GMR applications
As said above, the bulk magnetoresistance is low for half metals, and manganites present their intrinsic colossal MR close to TC, when they are no longer half metals. However, the main property of half metals, the vanishing down-spin density, will be most useful in multilayer spin valve systems. Important factors in the GMR of multilayer systems are the spin diffusion length and the resistivity of magnetic layers for both types of spin, the ratio of the spin-dependent scattering probabilities at the interfaces, which are related to the ratio (n / n) of the DOS at the Fermi level. The largest effects are expected for spin valve systems with the CPP (conduction perpendicular to plane) geometry, where there is no short-circuit by the non magnetic spacer, and a complete switch-off of the current for the antiparallel configuration of magnetic layers is possible. Some experiments have already been performed with metallic non magnetic spacers , but are still not very satisfactory due to lattice imperfections of thin films, diffusion at the interfaces and depolarisation of carriers, or due to the resistance of the hard ferromagnetic layer used as pinning layer.
A much better result has been obtained in spin tunneling experiments with manganite/ insulator / manganite trilayers [19,20]. Up to now, an important increase in conductance has been achieved only at low temperatures. The lowering of the spin polarization with increasing temperatures and the reduction in the spin diffusion length may be the reasons for the important drop in efficiency of spin-polarized tunneling.
The same reasoning may explain the rapid decrease of the low-field MR (extrinsic contribution arising from intergrain resistivity or tunneling) in sintered manganites. Besides the work on powder magnetoresistance (PMR), a recent study  has shown that high MR also occurs in partially decomposed CrO2 films, where grains are coated by a Cr2O3 layer, allowing spin-dependent tunneling between half metallic grains.
c. Spin electronics. Injection of polarized
The current tunneling out of a ferromagnetic material is spin polarized. The largest polarization will of course be obtained with half metals. This can be used in different ways:
i) The spin injection in a normal metal can give information on the spin diffusion length in this metal.
ii) Spin injection may act as a pair-breaking agent in a superconductor, T.Ventakesan et al.  have shown that the injection of a 100% polarized current in YBaCuO leads to a drastic decrease of the superconducting current Ic.
iii) Half metals can also be used to build a
spin transistor, as described by M. Johnson , where they can
act as the polarized current source as well as the analyzing
filter. iiii). Another possible application is as polarized tips
in STM, in order to vizualize the orientation of magnetic
domains. A problem is the presence of stray fields from the tip
which may modify the domain patterns. This may be solved by
finding a half metallic ferrimagnet with vanishing magnetization
The technical impact of half metals will
increase if the spin polarization can be maintained to a high
value up to room temperature. Thus we must search for
ferromagnets with a higher Curie temperature and a wider gap. It
could also be interesting to find uniaxial half metals with a
higher anisotropy than CrO2: in a cubic, or worse in a
distorted and twinned perovskite crystal, the magnetization
domains in zero field are aligned along different equivalent easy
axes, giving for instance 90° domain walls. These walls do not
build as large barriers as those occurring between 180° domains
in uniaxial materials.
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