Anomalous Hall effect and piezomagnetism in altermagnets

I define altermagnetism and introduce the two-dimensional Lieb lattice as the simplest realization of this novel magnetic phase. The anomalous Hall effect arising from altermagnetic order and spin–orbit interaction is illustrated with several examples. A comparison between the magnetic point-group and spin-space-group formulations is presented, demonstrating that the Berry-curvature singularity at nodal lines gives rise to a linear, non-analytic scaling of the intrinsic Hall conductivity with spin–orbit coupling. Extrinsic Hall is shown to be substantial in roughly half of altermagnets, namely featuring the Dzyaloshinskii-Moriya interaction.

The non-relativistic piezomagnetism is classified next as linear, quadratic and cubic in strain in g-, h- and i-wave altermagnets, respectively.

Finally I will discuss the odd-parity magnets as the zero spin-orbit realization of ising superconductors.