Berry curvature-induced transport signature for altermagnetic order

Altermagnetism has been detected in several materials using spin-sensitive probes. These measurements require rather complex setups that make it challenging to track variations in altermagnetic order, e.g., to identify a temperature-tuned altermagnetic phase transition. We propose a simple transport measurement that can probe the order parameter for $d$-wave altermagnetism. We suggest magnetoconductivity anisotropy -- the difference between the two principal values of the magnetoconductivity tensor. This quantity can be easily measured as a function of temperature, without any spin-selective apparatus. It acquires a nonzero value in a $C_4K$ phase, where $C_4$ rotations and time reversal $K$ are not symmetries but their combination is. This effect can be traced to the modification of phase space density due to Berry curvature, which we demonstrate using semiclassical equations of motion for band electrons. As an illustration, we build a minimal tight-binding model with altermagnetic order that breaks $C_4$ and $K$ symmetries while preserving $C_4K$.