Chen, Niu and MacDonald (Phys. Rev. Lett. 112, 017205 (2014)) predicted that L12-ordered Mn3Ir, a noncollinear antiferromagnet with nearly zero net magnetization, has a large intrinsic anomalous Hall conductivity, σ(111)≈218 Ω−1cm−1\sigma_{(111)}\approx 218\,\Omega^{-1}\mathrm{cm}^{-1}, carried by Berry curvature of spin-orbit-split bands, with opposite sign in the two time-reversed magnetic ground states (A and B phases). The paper left the experimental validation of this prediction open: no sample dominated by a single magnetic phase existed, the exchange-energy scale precludes field-based switching between phases, and the predicted value is highly sensitive to Fermi-level position, stoichiometry, and disorder, while intrinsic and extrinsic Hall contributions in real Mn3Ir were not disentangled. Later work confirmed anomalous Hall effects in related noncollinear antiferromagnets (Mn3Sn, Mn3Ge) and observed anomalous Hall signals in Mn3Ir thin films (about40 Ω−1cm−140\,\Omega^{-1}\mathrm{cm}^{-1}) and, most recently, in bulk Mn3Ir single crystals (about2 Ω−1cm−12\,\Omega^{-1}\mathrm{cm}^{-1}, attributed to mutually cancelling A and B domains), but no single-phase Mn3Ir sample, deterministic A/B domain selection, or quantitative intrinsic-versus-extrinsic accounting has been reported. The problem remains open.

Background

The anomalous Hall effect (AHE) is the appearance of a transverse voltage in a magnetized conductor in zero applied magnetic field; it is 'anomalous' because it cannot be attributed to the Lorentz force. Modern theory separates it into an intrinsic part, determined by the Berry curvature of the occupied Bloch states (Berry curvature is a momentum-space quantity that measures the phase structure of the electronic wavefunctions and enters the semiclassical velocity as an effective magnetic field in momentum space), and extrinsic parts arising from disorder scattering (skew scattering and side-jump mechanisms). In ordinary ferromagnets the AHE tracks the net magnetization, which is why antiferromagnets, whose sublattice moments cancel, were long expected to show no zero-field AHE.

Mn3Ir is an intermetallic compound crystallizing in the cubic L12 (Cu3Au-type) structure: Mn atoms occupy three of the four face-centered-cubic sublattices, so that (111) planes of Mn form a kagome lattice (a two-dimensional network of corner-sharing triangles) stacked along [111]. Its Mn moments form a coplanar three-sublattice triangular (T1) noncollinear antiferromagnetic order with a Néel temperature near 950 K, and the material is widely used as an exchange-bias reference layer in spin-valve devices (exchange bias is the pinning of an adjacent ferromagnet's magnetization by the antiferromagnet's order). In such a three-sublattice noncollinear antiferromagnet, neither time reversal TT alone nor any antiunitary operation combining TT with a lattice symmetry enforces Kramers-like band degeneracy, and combined with broken (111) mirror symmetry and the strong spin-orbit coupling of Ir, the Berry curvature integrates to a nonzero anomalous Hall conductivity even though the net magnetization is essentially zero.

Using symmetry analysis and first-principles (density-functional-theory) electronic-structure calculations with Wannier interpolation (a technique that builds localized Wannier orbitals from the calculated Bloch states in order to evaluate the band structure and Berry curvature on dense grids in momentum space), Chen, Niu and MacDonald found that in Mn3Ir the Mn moments tilt by only about0.1∘0.1^\circ out of the (111) planes (giving a tiny magnetization of about0.02 μB0.02\,\mu_\mathrm{B}per formula unit) and computed an intrinsic anomalous Hall conductivityσ(111)=218 Ω−1cm−1\sigma_{(111)}=218\,\Omega^{-1}\mathrm{cm}^{-1}for current and Hall voltage in the (111) kagome planes, comparable to elemental ferromagnets such as Fe, Co, and Ni. With spin-orbit coupling switched off the Hall conductivity vanishes, and constraining the moments to be exactly coplanar changes it by only1 Ω−1cm−11\,\Omega^{-1}\mathrm{cm}^{-1}, so the effect is a spin-orbit- plus mirror-symmetry-breaking phenomenon rather than a consequence of the small net moment. The same spin-orbit coupling produces a discrete two-fold ground-state degeneracy: the A phase and its time-reversal partner the B phase (and equivalents on other (111)-type planes), which have opposite small magnetizations and opposite anomalous Hall conductivities.

Three material facts frame the open experimental problem. First, the total energy rises by hundreds of meV per formula unit when the Mn moments are rotated away from their equilibrium orientation, so realistic laboratory fields can only produce minute moment rotations and cannot switch a sample between the A and B phases by directly rotating spins. Second, the calculatedσ(111)\sigma_{(111)}changes abruptly when spin-orbit-split band degeneracies near the Fermi energy cross the Fermi level, so the measurable Hall conductivity is sensitive to the exact Fermi-level position and hence to stoichiometry, chemical (L12) order, disorder, and doping; the collinear L10 phase of MnIr, for instance, should have no AHE at all. Third, in any multidomain sample the A and B phases contribute anomalous Hall conductivities of opposite sign that cancel. The original paper therefore proposed, without demonstration, that single-phase samples might be obtained by cooling in a field applied along a (111) direction, by crossing a collinear-to-noncollinear phase boundary under a field (as possible in the related compound Mn3Pt), or by controlling stoichiometry, and noted that a single-phase sample could be read out electrically via the AHE or optically via the associated gyrotropy (direction-dependent optical responses such as polarization rotation of reflected or transmitted light, permitted by the same broken mirror symmetry).

Problem Statement

Realize and quantitatively validate, in experiment, the intrinsic anomalous Hall effect that Chen, Niu and MacDonald predicted for L12-ordered noncollinear antiferromagnetic Mn3Ir. Concretely, the open problem is the following linked experimental program for this one material and prediction:

  1. Prepare Mn3Ir (bulk single crystal or epitaxial film, near-stoichiometric and with controlled L12 chemical order) that is dominated by a single magnetic phase — the A phase or its time-reversal partner the B phase — rather than a near-equal mixture of both, since the exchange energy of hundreds of meV per formula unit blocks switching by directly rotating the Mn moments with laboratory fields.

  2. Measure the anomalous Hall conductivity of such a sample quantitatively — its sign, magnitude, anisotropy with respect to the (111) kagome planes, and its temperature dependence — and establish how far it agrees with the predicted intrinsic valueσ(111)≈218 Ω−1cm−1\sigma_{(111)}\approx 218\,\Omega^{-1}\mathrm{cm}^{-1}, given that the prediction is sensitive to the Fermi-level position relative to spin-orbit-split band degeneracies and hence to stoichiometry, chemical order, disorder, and doping.

  3. Disentangle the intrinsic (Berry-curvature) contribution from extrinsic skew-scattering and side-jump contributions in the measured Hall response of real Mn3Ir samples, across temperature and disorder, and account for the observed suppression of the Hall conductivity relative to the single-phase prediction (domain averaging versus band-structure and Fermi-level effects).

  4. Demonstrate deterministic, reproducible selection and, where feasible, switching between the A and B phases (or their equivalents on other (111)-type planes) by non-field-rotation means, with the resulting antiferromagnetic state readable electrically through the anomalous Hall effect or optically through the associated gyrotropy (direction-dependent optical responses such as polarization rotation).

These four components jointly constitute the source paper's program of converting its prediction into an experimentally established, quantitatively understood property of Mn3Ir; the completion boundary — the experimental milestone at which the open problem would be resolved — is a single-phase (or domain-population-controlled) Mn3Ir sample whose measured Hall response is quantitatively accounted for by intrinsic Berry-curvature theory, together with a reproducible domain-selection protocol.

References

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