Landau Theory of Altermagnetism

We formulate a Landau theory for altermagnets, a class of collinear compensated magnets with spin-split bands. Starting from the nonrelativistic limit, this Landau theory goes beyond a conventional analysis by including spin-space symmetries, providing a simple framework for understanding the key features of this family of materials. We find a set of multipolar secondary order parameters connecting existing ideas about the spin symmetries of these systems, their order parameters, and the effect of nonzero spin-orbit coupling. We account for several features of canonical altermagnets such as ${\mathrm{RuO}}_2$, MnTe, and ${\mathrm{CuF}}_2$ that go beyond symmetry alone, relating the order parameter to key observables such as magnetization, anomalous Hall conductivity, and magnetoelastic and magneto-optical probes. Finally, we comment on generalizations of our framework to a wider family of exotic magnetic systems derived from the zero spin-orbit coupled limit.

Figure 1

Illustration of the (a) crystal structure of ${\mathrm{RuO}}_2$ with magnetic Ru (orange) and oxygens (blue). (b) Fermi surface with $d$-wave spin splitting (up and down spins in blue and red, respectively) in the model of Eq. (2).

Figure 2

Illustration of the key features of altermagnetic MnTe including (a) the crystal structure with magnetic Mn ions on an $AA$ stacked triangular lattice, (b) the inequivalent bonds connecting neighboring magnetic layers along the $\mathit{c}$ direction that enter into the model of Eq. (2), and (c) the $g$-wave spin-split Fermi surface expected in weakly doped MnTe.