Nonlinear Anomalous Hall Effect for Néel Vector Detection

Antiferromagnetic (AFM) spintronics exploits the Néel vector as a state variable for novel spintronic devices. Recent studies have shown that the fieldlike and antidamping spin-orbit torques (SOTs) can be used to switch the Néel vector in antiferromagnets with proper symmetries. However, the precise detection of the Néel vector remains a challenging problem. In this Letter, we predict that the nonlinear anomalous Hall effect (AHE) can be used to detect the Néel vector in most compensated antiferromagnets supporting the antidamping SOT. We show that the magnetic crystal group symmetry of these antiferromagnets combined with spin-orbit coupling produce a sizable Berry curvature dipole and hence the nonlinear AHE. As a specific example, we consider the half-Heusler alloy CuMnSb, in which the Néel vector can be switched by the antidamping SOT. Based on density-functional theory calculations, we show that the nonlinear AHE in CuMnSb results in a measurable Hall voltage under conventional experimental conditions. The strong dependence of the Berry curvature dipole on the Néel vector orientation provides a new detection scheme of the Néel vector based on the nonlinear AHE. Our predictions enrich the material platform for studying nontrivial phenomena associated with the Berry curvature and broaden the range of materials useful for AFM spintronics.

Figure 1

(a) A noncollinear antiferromagnet with broken $\widehat{T}$ and absent $\widehat{T}\widehat{O}$ symmetry ($\widehat{O}$ is a crystal space group symmetry operation), such that $\widehat{T}\widehat{O}\mathbf{\Omega }({\mathit{k}}^{\prime })=-\mathbf{\Omega }(\mathit{k})$ (left), resulting in a linear AHE (right). (b) A collinear antiferromagnet with a specific arrangement of nonmagnetic atoms in the crystal lattice, in which both $\widehat{T}$ and $\widehat{T}\widehat{O}$ symmetries are absent (left), resulting in a linear AHE (right). (c) A collinear antiferromagnet with broken $\widehat{P}$ and $\widehat{T}$ symmetries but preserved $\widehat{T}{\widehat{t}}_{1/2}$ symmetry (left), resulting in a nonlinear AHE (right).

Figure 2

(a),(b) The collinear AFM magnetic structure of CuMnSb shown in a conventional cubic unit cell (a) and a rhombohedral primitive cell (b). Red arrows denote the magnetic moments of Mn. The light blue plane denotes the glide plane ${\widehat{g}}_{\overline{1}10}$. (c) The band structure of CuMnSb near $E_F$. (d) The band structures close to Weyl points $W_1$ with $k_2=0.054$ and $k_3=0.004{\AA }^{-1}$ (left) and $W_2$ with $k_2=0.115$ and $k_3=0.081{\AA }^{-1}$ (right). Here $k_1$, $k_2$, and $k_3$ are along the [$\overline{1}10$], [$\overline{1}\overline{1}2$], and [111] directions in the cubic lattice. The purple lines in (c),(d) denote the two bands forming Weyl points. The horizontal dashed line indicates the Fermi energy. (e) The Fermi surfaces at $k_3=0.004{\AA }^{-1}$ and $E=0.102\mathrm{eV}$ (left) and at $k_3=0.081{\AA }^{-1}$ and $E=-0.051\mathrm{eV}$ (right). The Weyl points are located at the intersection points of the Fermi surfaces.

Figure 3

(a),(b) The projections of the Berry curvature dipole on $k_1\text{−}{k}_2$ plane at (a) $E=0.102$ and (b) $E=-0.051\mathrm{eV}$. Black cross symbols denote position of the Weyl fermions. (c) The $D_{xz}$ as a function of energy for the AFM phase without (red line) and with (blue line) canting of the Néel vector. (Inset) Schematic showing the canting.

Figure 4

(a) The signs of the Hall voltages $V_y$ and $V_z$ for different AFM orders of CuMnSb. (b) A spin-orbit torque device where the AFM orders of CuMnSb are switched using the antidampinglike SOT generated by the writing current $J_w$.