Manipulating a stubborn magnet Spintronics is an alternative to conventional electronics, based on using the electron's spin rather than its charge. Spintronic devices, such as magnetic memory, have traditionally used ferromagnetic materials to encode the 1's and 0's of the binary code. A weakness of this approach—that strong magnetic fields can erase the encoded information—could be avoided by using antiferromagnets instead of ferromagnets. But manipulating the magnetic ordering of antiferromagnets is tricky. Now, Wadley et al. have found a way (see the Perspective by Marrows). Running currents along specific directions in the thin films of the antiferromagnetic compound CuMnAs reoriented the magnetic domains in the material. Science, this issue p. 587; see also p. 558 Transport and optical measurements are used to demonstrate the switching of domains in the antiferromagnetic compound CuMnAs. [Also see Perspective by Marrows] Antiferromagnets are hard to control by external magnetic fields because of the alternating directions of magnetic moments on individual atoms and the resulting zero net magnetization. However, relativistic quantum mechanics allows for generating current-induced internal fields whose sign alternates with the periodicity of the antiferromagnetic lattice. Using these fields, which couple strongly to the antiferromagnetic order, we demonstrate room-temperature electrical switching between stable configurations in antiferromagnetic CuMnAs thin-film devices by applied current with magnitudes of order 106 ampere per square centimeter. Electrical writing is combined in our solid-state memory with electrical readout and the stored magnetic state is insensitive to and produces no external magnetic field perturbations, which illustrates the unique merits of antiferromagnets for spintronics.

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Electrical switching of an antiferromagnet

Spin polarization due to spin–orbit coupling requires broken inversion symmetry. Now, calculations show that the effect arises from local site-asymmetry rather than global space-group asymmetry, and that a hitherto overlooked form of spin polarization should also exist in centrosymmetric structures.

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Hidden spin polarization in inversion-symmetric bulk crystals

We propose an efficient microscopic design procedure of electronic band structures having intrinsic spin and momentum dependences in spin-orbit-coupling free antiferromagnets. Our bottom-up design approach to creating desired spin-split and reshaped electronic band structures could result in further findings of practical spin-orbit-coupling free materials exhibiting a giant spin-dependent and/or nonreciprocal transport, magnetoelectric and elastic responses, and so on, as a consequence of such band structures. We establish a systematic guideline to construct symmetric/antisymmetric spin-split and antisymmetrically deformed spin-independent band structures in spin-orbit-coupling free systems by using two polar multipole degrees of freedom, i.e., electric and magnetic toroidal multipoles. The two polar multipoles constitute a complete set and describe arbitrary degrees of freedom in the hopping Hamiltonian, whose onsite and offsite degrees of freedom in a cluster are described as the so-called cluster and bond multipoles, respectively, and another degree of freedom connecting between clusters is expressed as momentum multipoles. By using these multipole descriptions, we elucidate simple microscopic conditions to realize intrinsic band deformations in magnetically ordered states: The symmetric spin splitting is realized in collinear magnets when cluster and bond multipoles contain the same symmetry of multipoles. The antisymmetric spin splitting occurs in noncollinear antiferromagnets when a bond-type magnetic toroidal multipole is present. Furthermore, the antisymmetric band deformation with spin degeneracy is realized in noncoplanar antiferromagnets. We exemplify three lattice systems formed by a triangle unit, triangular, kagome, and breathing kagome structures, to demonstrate the band deformations under the magnetic ordering. On the basis of the proposed procedure, we list up various candidate materials showing intrinsic band deformations in accordance with MAGNDATA, magnetic structures database.

Bottom-up design of spin-split and reshaped electronic band structures in antiferromagnets without spin-orbit coupling: Procedure on the basis of augmented multipoles

Antiferromagnetic order offers a non-relativistic route to create spin splitting and spin polarization effects that do not rely on heavy element compounds (with strong spin-orbit coupling, SOC), and could exist even in centrosymmetric crystals. Cases enabling such non-relativistic, SOC-unrelated spin polarization effect are classified as SST-4 (SST-4A and SST-4B) of all seven possible spin splitting prototypes derived in this paper based on magnetic symmetry analysis. The authors uncovered 422 magnetic space groups (160 centrosymmetric and 262 non-centrosymmetric) and 201 candidate antiferromagnets that belong to the SST-4 category. DFT calculations for collinear and noncollinear cases are provided as basis for guiding future experiments.

Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling

The Hall effect, in which a current flows perpendicular to an electrical bias, has been prominent in the history of condensed matter physics. Appearing variously in classical, relativistic and quantum guises, the Hall effect has — among other roles — contributed to the establishment of the band theory of solids, to research on new phases of interacting electrons and to the phenomenology of topological condensed matter. The dissipationless Hall current requires time-reversal symmetry breaking. When this symmetry breaking is due to an externally applied magnetic field, the effect is referred to as the ordinary Hall effect; when it is due to a non-zero internal magnetization (ferromagnetism), it is referred to as the anomalous Hall effect. The Hall effect has not usually been associated with antiferromagnetic order. More recently, however, theoretical predictions and experimental observations have identified large Hall effects in some compensated magnetic crystals, governed by neither of the global magnetic-dipole symmetry-breaking mechanisms mentioned above. The goal of this Review is to systematically organize the present understanding of anomalous antiferromagnetic materials that generate a Hall effect — which we call anomalous Hall antiferromagnets — and to discuss this class of materials in a broader fundamental and applied research context. Our motivation is twofold: first, because Hall effects that are not governed by magnetic-dipole symmetry breaking are at odds with the traditional understanding of the phenomenon, the topic deserves attention on its own. Second, this new incarnation of the Hall effect has placed it again in the middle of an emerging field in physics, at the intersection of multipole magnetism, topological condensed matter and spintronics. 

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Anomalous Hall antiferromagnets

The traditional bulk Rashba effect predicts spin-orbit coupling induced wave-vector-dependent spin splitting between energy bands in nonmagnetic solids that lack spatial inversion symmetry. The authors show here how the violation of magnetic symmetry leads instead to a few prototypes of momentum-dependent spin splitting of energy bands that are induced by antiferromagnetism. This discovery broadens the spintronics playing field to include centrosymmetric compounds, even made of light elements with low spin-orbit coupling. Atomistic density functional calculations show that giant splitting above 200 meV is possible between top two valence bands.

Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets

Crystallographic point group symmetry (CPGS) such as polar and nonpolar crystal classes have long been known to classify compounds that have spin-orbit-induced spin splitting. While taking a journey through the Brillouin zone (BZ) from one $k$-point to another for a fixed CPGS, it is expected that the wave vector point group symmetry (WPGS) can change, and consequently, a qualitative change in the texture of the spin polarization can occur [the expectation value of spin operator ${\stackrel{P\vec}{S}}_{n{k}_{0}}$ in Bloch state $u(n,k)$ and the wave vector ${k}_{0}$]. However, the nature of the spin texture (ST) change is generally unsuspected. In this paper, we determine a full classification of the linear-in-$k$ ST patterns based on the polarity and chirality reflected in the WPGS at ${k}_{0}$. The spin-polarization vector ${\stackrel{P\vec}{S}}_{n{k}_{0}}$ controlling the ST is bound to be parallel to the rotation axis and perpendicular to the mirror planes, and hence, symmetry operation types in WPGSs impose symmetry restriction to the ST. For instance, the ST is always parallel to the wave vector $k$ in nonpolar chiral WPGSs since they contain only rotational symmetries. Some consequences of the ST classification based on the symmetry operations in the WPGS include the observation of ST patterns that are unexpected according to the symmetry of the crystal. For example, it is usually established that spin-momentum locking effect (spin vector always perpendicular to the wave vector) requires the crystal inversion symmetry breaking by an asymmetric electric potential. However, we find that polar WPGS can have this effect even in compounds without electric dipoles or external electric fields. We use the determined relation between WPGS and ST as a design principle to select compounds with multiple STs near band edges at different $k$ valleys. Based on high-throughput calculations for 1481 compounds, we find 37 previously fabricated materials with different STs near band edges. The ST classification as well as the predicted compounds with multiple STs can be a platform for potential application for spin-valleytronics and the control of the ST by accessing different valleys.

Different shapes of spin textures as a journey through the Brillouin zone

Recent studies show the nonrelativistic antiferromagnetic ordering could generate momentum-dependent spin splitting analogous to the Rashba effect but free from the requirement of relativistic spin-orbit coupling. Whereas the classification of such compounds can be illustrated by different spin-splitting prototypes (SSTs) from symmetry analysis and density-functional-theory calculations, the huge variation in chemical bonding and structures of these diverse compounds possibly clouds the issue of how much of the variation in spin splitting can be traced back to the symmetry-defined characteristics, rather to the underlining chemical and structural diversity. The alternative model Hamiltonian approaches do not confront the issues of chemical and structural complexity but often consider only the magnetic sublattice, dealing with the all-important effects of the nonmagnetic ligands via renormalizing the interactions between the magnetic sites. To this end, we constructed a DFT model Hamiltonian that allows us to study SSTs at constant chemistry while retaining the realistic atomic-scale structure including ligands. This is accomplished by using a single, universal magnetic skeletal lattice (${\mathrm{Ni}}^{2+}$ ions in rocksalt NiO) and designing small displacements of the nonmagnetic (oxygen) sublattice which produce, by design, the different SST magnetic symmetries. We show that (i) even similar crystal structures having very similar band structures can lead to contrasting behavior of spin splitting vs momentum, and (ii) even subtle deformations of the nonmagnetic ligand sublattice could cause a giant spin splitting in AFM-induced SST. This is a paradigm shift relative to the convention of modeling magnets without considering the nonmagnetic ligand that mediates indirect magnetic interaction (e.g., superexchange).

Lin-Ding Yuan

Papers

Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets

Different shapes of spin textures as a journey through the Brillouin zone

Strong influence of nonmagnetic ligands on the momentum-dependent spin splitting in antiferromagnets