Engineering altermagnetic symmetry to enable anomalous Hall response in Cr$_{1-x}$Mn$_x$Sb

TL;DR

Altermagnetism seeks an anomalous Hall effect (AHE) in materials with specific symmetry and good metallic conductivity at high ordering temperatures, which is hard to achieve. The authors demonstrate that partial Cr→Mn substitution in CrSb(100) tunes magnetocrystalline anisotropy and the magnetic-space symmetry, enabling an AHE in Cr$_{0.75}$Mn$_{0.25}$Sb(100); this AHE is observed as a nonlinear, hysteretic Hall signal under a small out-of-plane field tilt. A Landau-theory framework is developed, introducing an altermagnetic order parameter $Q_{ m AM}$ and modeling the field-driven Néel-vector orientation to reproduce the qualitative AHE behavior via the relation $ ho_ ext{AHE}= ho_ ext{AHE}=\\alpha_ ext{AHE}Q_{ m AM} n_z+eta_ ext{AHE} \\hat{m}_y(f n)$. The energy landscape of the Néel vector, including Dzyaloshinskii–Moriya interactions and strain-induced terms, yields multiple low-energy configurations whose field evolution accounts for the observed hysteresis and sign changes, illustrating a path to electrical read-out of the Néel vector for spintronic applications.

Abstract

Altermagnets are a promising class of materials for spintronic applications. However, compounds that simultaneously combine the symmetry required to support an anomalous Hall effect with good metallic conductivity and magnetic ordering temperatures well above room temperature remain elusive. Here, we demonstrate that partial substitution of Cr by Mn in epitaxial CrSb(100) thin films provides a viable route to engineer the combined structural and magnetic symmetry necessary to enable an otherwise symmetry-forbidden anomalous Hall effect. By systematically exploring the magnetic phase diagram Cr$_{1-x}$Mn$_{x}$Sb thin films, we identify a pronounced anomalous Hall effect in Cr$_{0.75}$Mn$_{0.25}$Sb. Guided by Landau theory, we model the field-driven reorientation of the Néel vector and the resulting anomalous Hall response, achieving good qualitative agreement with the experimental observations.

Figures (7)

• Figure 1: Magnetic orientation of Cr$_{1-x}$Mn$_{x}$Sb samples. a Magnetic phase diagram of Cr$_{1-x}$Mn$_{x}$Sb. The arrows represent the direction of the magnetic moments, where upwards and downwards allign with the crystallographic c-axis and left and right correspond towards ab-plane. b Temperature-dependant phase transition of Cr$_{0.62}$Mn$_{0.38}$Sb. c Temperature-dependant phase transition of Cr$_{0.75}$Mn$_{0.25}$Sb. d Spin-flop transition of CrSb (red) and Cr$_{0.87}$Mn$_{0.13}$Sb. e CrSb and Cr$_{0.87}$Mn$_{0.13}$Sb sample orientation during the spin-flop transition measurement.
• Figure 2: Hall-resistivity of Cr$_{0.75}$Mn$_{0.25}$Sb(100). Magnetic field dependence of the Hall-resistivity at 300 K for field directions close to the in-plane [1000]-direction. The inset shows a schematic representation of the sample geometry indicating the angle $\phi$ by which the magnetic field direction is tilted with respect to the in-plane [1000]-direction.
• Figure 3: Longitudinal magnetoresistance (AMR) of Cr$_{0.75}$Mn$_{0.25}$Sb(100). Dependence of the longitudinal resistance on the orientation of magnetic fields with different magnitude (at 300 K). The inset shows a schematic representation of the sample geometry indicating the angle $\phi$ by which the magnetic field direction is tilted with respect to the in-plane [1000]-direction.
• Figure 4: Altermagnetic order parameter. Schematic representation of the two altermagnetic sublattices with the Cr atom in the center and the surrounding Sb atoms. The red and blue lobes represent the spherical harmonics whose difference represents the altermagntic order parameter.
• Figure 5: Néel vector orientation and free energy.a Color scale representation of the dependence of the free energy on the Néel vector orientation. $\theta$ represents the polar angle with respect to the z-direction and $\varphi$ the azimuthal angle of the Néel vector. b Corresponding coordinate system illustrating the orientation of the unit cell relative to the substrate.