Linear Magnetoresistance as a Probe of the Neel Vector in Altermagnets with Vanishing Anomalous Hall Effect

Abstract

Despite time-reversal breaking in momentum space, several altermagnets remain electrically silent to the primary characterization tool anomalous Hall effect, due to crystalline symmetries, jeopardizing their experimental identification. Here, we show that time-reversal odd magnetoresistance exhibiting butterfly-like hysteresis with linear magnetic field dependence near the zero field provides a robust transport signature of altermagnetism even when the anomalous Hall effect vanishes. Using semiclassical theory and symmetry analysis, we demonstrate that this effect is generic across altermagnets and validate it through first-principles calculations in CrSb. Our results establish linear magnetoresistance as an alternative detection of the Berry curvature and Neel order in unconventional antiferromagnets.

Figures (2)

• Figure 1: (a) Typical anomalous Hall effect (AHE) and linear MR in butterfly-like hysteresis loop observed in ferromagnet and in some altermagnets (AMs). (b) When crystal symmetry forbids the AHE, the linear MR can still appear in the hysteresis loop, reflecting the Néel order orientation. (c) In the conventional AFMs with ${\mathcal{P}}{\mathcal{T}}$ and ${t} {\mathcal{T}}$ symmetry, the linear response measurement shows no hysteresis and hence can not detect Néel order. (d)-(g) The different linear MR measurements set up for the various AM candidates. (d) The longitudinal MR set up when all the fields are in the same direction. (e) The transverse MR set up when the magnetic field is perpendicular to the current. (f) The planar Hall set up, where the magnetic field is confined in the 2D plane of measurement. (g) The ordinary Hall set up where all the fields are perpendicular. The corresponding AM materials are indicated below each configuration. For Mn$_5$Si$_3$ and MnTe, spins in the hexagonal plane and along $2 \bar{1} \bar{1} 0$ axes are considered, respectively.
• Figure 2: Linear magnetoresistance (MR) in CrSb: (a) The in-plane crystal structure of CrSb with the ${\mathcal{M}}_x {\mathcal{T}}$, $\bar{\mathcal{M}}_y \equiv \{ {\mathcal{M}}_y | (0,0,\frac{1}{2})\}$ and ${\mathcal{C}}_{3z}$ symmetry highlighted. (b) The corresponding hexagonal Brillouin zone (BZ). (c) The expected angular variation of the longitudinal (cyan and orange) and perpendicular (magenta and turquoise) voltage with the magnetic field orientation. (d) The product of Berry curvature and velocity, ${\mathcal{K}}_y \equiv \Omega_y v_y v_y$, weighted band structure along the high symmetry line shown in (b). (e) The Berry curvature satisfies $\sum_{n \in \rm occ} \Omega^n_z(k_y) = -\sum_{n \in \rm occ} \Omega^n_z(-k_y)$ respecting the $\bar{\mathcal{M}}_y$ symmetry leading to vanishing AHE. (f) The product of Berry curvature and velocity in the BZ satisfies $\sum_n {\mathcal{K}}^n_y (k_y) \delta(\epsilon_n-\epsilon_F) = \sum_n {\mathcal{K}}^n_y (-k_y) \delta(\epsilon_n-\epsilon_F)$, resulting in a finite value of linear MR. (g) The MR percentage at $B=3T$ with the magnetic field along the $y$-axes.