Altermagnetism and generalised tensorial properties in the exchange multiplet framework

Abstract

A representation-theoretic framework for the calculation of time-reversal-odd tensorial properties of magnetic materials based on the Bertaut--Izyumov exchange-multiplet formalism is developed. In contrast to approaches based on distinct magnetic point groups or spin groups for different orientations of the magnetic order parameter, the exchange-multiplet framework permits the order parameter to be treated as a continuous variable. It is shown that, for constant-moment collinear structures, covariance imposes a simple set of symmetry constraints on the tensor intertwiners appearing in a Landau--Lifshitz expansion. This leads to canonical intertwiner forms that factorise the magnetic and crystallographic parts of the tensor construction. Tensor fields can be built to retain a Cartesian representation in the physical variables while acquiring a systematic dependence on the order-parameter direction through symmetry-adapted polynomial bases. Magnetic-point-group selection rules are recovered automatically for arbitrary order-parameter directions, while the framework also provides a natural separation of co-rotating (SOC-free) and non-co-rotating contributions. The approach is applicable to altermagnets and conventional antiferromagnets alike and is particularly suited to experiments and first-principles calculations in which the magnetic order parameter can be continuously varied.