Altermagnetism classification

Altermagnets are magnetic states with fully compensated spins and broken PT (PT: parity times time reversal) symmetry (i.e., spin-split bands).We classify three kinds of altermagnets in terms of broken P and T. Furthermore, strong altermagnets have spin-split bands without spin-orbit coupling (SOC), and weak altermagnets has spin-split bands only with non-zero SOC.These strong vs. weak altermagnets can be identified from the total number of symmetric spin rotation operations.