“Unconventional magnetism” was proposed to describe the exotic states arising from Landau-Pomeranchuk instabilities in the spin channel nearly two decades ago. Its odd-partial-wave-channel (e.g., $p$-wave) states break parity giving rise to the dynamic generation of spin-orbit coupling, while its even-partial-wave-channel (e.g., $d$-wave) states break time-reversal symmetry. Both types of states can exhibit collinear and noncollinear spin configurations over Fermi surfaces with the former and latter termed as the $\alpha$ and $\beta$ phases, respectively. The collinear states in even partial-wave channels are in the same symmetry class of “altermagnetism”. In this work, we investigate unconventional magnetism in both $p$- and $d$-wave channels within spin-orbit coupled systems with parity and time-reversal symmetries maintained. Based on the Ginzburg-Landau free energy analysis, the $p$-wave channel yields the gyrotropic, Rashba, Dresselhaus-type spin-orbit couplings. They compete and mix evolving from the $\beta$ phase to the $\alpha$ phase with various types of spin-momentum lockings. Analyses are performed in parallel for the $d$-wave unconventional magnetism. We emphasize that the single-particle dispersion is not sufficient to justify the spin-group type symmetry of the full Hamiltonian. Furthermore, Goldstone manifolds and excitations are examined in each unconventional magnetic phase.

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• Magnetic order
• Spin-orbit coupling
• Strongly correlated systems