Half Metallic Ferromagnets

Jacques Pierre, Laurent Ranno

Laboratoire Louis Neel, CNRS, Grenoble

The concept of half metallic ferromagnets was introduced by de Groot et al.[1], 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 NiMnSb [1].

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 [2]. 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 (La_1-xSr_x)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 E_F

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 the spin-

resolved photoemission spectra in La_0.7Sr_0.3MnO₃ at 40K [3]. The majority spins have a large density of states (DOS) which exhibits the metallic Fermi cutoff at E_F, already seen by classical photoemission [4], whereas the minority band spectrum shows a vanishing DOS from about 0.4 eV below E_F up to the Fermi level . 0.4 eV is the gap between E_F and the top of the occupied valence band for the minority band.

Fig.2. Spin resolved photoemission spectra for (La_0.7 Sr_0.3)MnO₃ at 40K and 380K [3]

Another more important feature is the gap betwen E_F 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 [5] 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 E_F, but recent data show that E_F 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.

1. Saturation magnetization

For stoichiometric compounds, the last occupied down-spin band is filled and contains an integer number of electrons n. Hence the magnetization m /µ_B = (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 µ_B, that of CrO₂ is 2.0 µ_B. Note that the magnetization may be shared between atoms, for instance 3.8 µ_B for Mn, 0.2µ_B 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 (La_0.7Sr_0.3)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 level.

Fig.3. Scheme of electronic excitations in half

metals.

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.

1. Other experiments

Positron annihilation experiments have been performed for NiMnSb and brought, after some tedious analysis, the first experimental evidence for half metals [6].The possibility to check directly the absence of the down-spin Fermi surface by Compton scattering has been recently suggested [7], experiments are under way on Co₂MnSi. Another prediction from theory [8] is that there is no Korringa relaxation in a half-metal, as the relaxation rate 1/T₁ ~ k_BT. n(E_F).n(E_F) vanishes. Similarly, there can be no spin-flip scattering in the resistivity.

1. Behaviour at finite temperature. Excitations

Thermal excitations will destroy the half metallic character below the Curie temperature T_C, 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 [9] . 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) [10] 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-BT^3/2], 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 [8], following Moriya, have shown that other terms (T², T^4/3) occur due to spin fluctuations. Such a cross-over is observed near 80K for NiMnSb [11](fig.4) . Note that the magnetization is only slightly reduced at this temperature: M(80K) = 3.95 µ_B instead of M(0) = 4.02 µ_B.

Fig.4. Square of magnetization versus T² for a NiMnSb single crystal [11].

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 and magnetoresistance.

Fig.5. Variation of magnetization in CrO₂ at low temperature [10].

It is worth noting that the half metal gap has nothing in common with the spin wave gap G_a which may arise from the magnetocrystalline anisotropy. In the case of NiMnSb [11] as well as for ferromagnetic manganites [12], 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. G_a is of the order of 10 K in NiMnSb and no more than 15 K in (La_0.8 Sr_0.2)MnO₃ respectively , these values are much smaller than those estimated for (about 600K for NiMnSb at low temperatures). The magnetization for CrO₂ [10] follows a nice T^3/2 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 properties

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 [11] (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 (T^1.35). 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.7).

Fig.6. Resistivity of NiMnSb versus temperature [11].

A different behaviour has been observed in CrO₂ [10], where the resistivity follows the law = ₀ + AT² exp(-E/kT), with E= 80K. whereas the magnetization follows a T^3/2 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 order,…) gives rise to a huge scattering of conduction electrons related to the mixed-valent configuration and finite life time of electronic states. Measurements on La_1-x Sr_x MnO₃ single crystals [15] 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 T_C, for instance near 200K for (La₀₈Sr_0.2)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 [16] for PtMnSb ( _K = 2° for = 720 nm); the vanishing down-spin density at E_F 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 [17], 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 Sb orbitals.

b. GMR applications

As said above, the bulk magnetoresistance is low for half metals, and manganites present their intrinsic colossal MR close to T_C, 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 [18], 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 [21] 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 carriers

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. [22] have shown that the injection of a 100% polarized current in YBaCuO leads to a drastic decrease of the superconducting current I_c.

iii) Half metals can also be used to build a spin transistor, as described by M. Johnson [23], 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 [24].

1. Conclusions

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.

References

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[13] M. Otto, thesis, University of Gröningen, (1987).

[14] C. Hordequin, thesis, University of Grenoble (1997) .

[15] A. Urushibara et al., Phys. Rev. B 51(1995) 14103.

[16] P. G. van Engen et al., Appl. Phys. Lett. 42 (1983) 202.

[17] V. N. Antonov et al., Phys. Rev. B 56 (1997) 13012.

[18] C. Hordequin, Thesis, Grenoble (1997); J. Nozières et al., submitted.

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[22] T. Venkatesan et al., preprint.

[23] M. Johnson, J. Magn. Magn. Mater. 140 (1995) 21.

[24] H. van Leuken and R.A.de Groot, Phys. Rev. Lett. 74 (1995) 1171. Antiferromagnets cannot be half metallic, contrary to the title of this paper: only ferrimagnets can be!

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