Quantum geometric planar magnetotransport: a probe for magnetic geometry in altermagnets

Abstract

Nonlinear and nonreciprocal transport phenomena provide a direct probe of band quantum geometry in noncentrosymmetric magnetic materials, such as the nonlinear Hall effect induced by the quantum metric dipole. In altermagnets, a recently discovered class of even-parity collinear magnets with $C_n\mathcal{T}$ symmetry, conventional second-order responses are prohibited by an emergent $C_{2z}$ symmetry. In this work, we demonstrate that an in-plane magnetic field lifts this prohibition, inducing a planar magnetotransport that directly probes the intrinsic quantum geometry and the distinctive $C_n\mathcal{T}$ nature of altermagnetic orders. We show that the field-dependent quantum geometric susceptibility generates versatile planar magnetotransport, including the planar Hall effects and nonreciprocal responses. Our work establishes distinctive signatures of altermagnetism in linear and nonlinear magnetotransport, providing a general framework for measuring quantum geometric responses and probing altermagnetic order.

Figures (6)

• Figure 1: The schematic picture of the planar magnetotransport of the altermagnets with $C_n \mathcal{T}$ symmetry. Coupled with the in-plane magnetic field, the $C_{2z}$ is broken, resulting in the linear planer Hall effect $J_\omega^{\perp}$, the nonlinear second-order planer Hall effect $J_{2 \omega}^{\perp}$, and nonreciprocal transport $J_{2 \omega}^{\|}$. $\theta$ and $\alpha$ label the angle between B field and E field, and the orientation of the sample with respected to E field.
• Figure 2: Comparison between the responses in different $C_nT$ symmetry of planar altermagnets coupled with planar magnetic field. The scaling behavior with respect to magnetic field depends on different altermagnetic order parameters.
• Figure 3: Band-normalized quantum metric component multiplied by group velocity $\tilde{g}_{xx}v_x$ of $d_{xy}$ planar altermagnet with different altermagnetic order magnitude: (a) $J=0.5 \mathrm{eV}\cdot nm^2$; (b) $J=0$. Other parameters are $v_R=1 \mathrm{eV}\cdot nm,\ g_s\mu_B B=0.2$ eV.
• Figure 4: The nonreciprocal longitudinal conductivity $\sigma^{x;xx}=\chi^{x;xx}|B|$ for d- ,g- , and i-wave altermagnets. (a), (b) and (c) are the angular dependence of $\sigma^{x;xx}$; (d) The Fermi energy $E_f$ dependence of $\sigma^{x;xx}$. Parameters: $J_d=J_g=J_i=1$, $v_R=1$, $T=0.1$ (on unit of $\mu$).
• Figure 5: The linear Hall conductivity of $d$-, $g$-, $i$-wave altermagnets. (a), (c) and (e) The angular dependence of Hall conductivity; (b), (d) and (f) The magnitude dependence of Hall conductivity at different directions. The parameters, in unit of $\mu$, are $J_d=J_g=J_i=1$, $v_R=1$, $T=0.1$.