Kramers degeneracy in a magnetic field and Zeeman spin-orbit coupling in antiferromagnetic conductors

Abstract

In this article, I analyze the symmetries and degeneracies of electron eigenstates in a commensurate collinear antiferromagnet. In a magnetic field transverse to the staggered magnetization, a hidden anti-unitary symmetry protects double degeneracy of the Bloch eigenstates at a special set of momenta. In addition to this 'Kramers degeneracy' subset, the manifold of momenta, labeling the doubly degenerate Bloch states in the Brillouin zone, may also contain an 'accidental degeneracy' subset, that is not protected by symmetry and that may change its shape under perturbation. These degeneracies give rise to a substantial momentum dependence of the transverse g-factor in the Zeeman coupling, turning the latter into a spin-orbit interaction.I discuss a number of materials, where Zeeman spin-orbit coupling is likely to be present, and outline the simplest properties and experimental consequences of this interaction, that may be relevant to systems from chromium to borocarbides, cuprates, hexaborides, iron pnictides, as well as organic and heavy fermion conductors.

Electric excitation of spin resonance in antiferromagnetic conductors

“…By symmetry, g ⊥ (p) in H ZSO (1) vanishes upon approaching the MBZ boundary, linearly in a generic case [9,10] -and can be recast as g ⊥ (p) = g pyξ with a constant ξ, for pyξ ≪ 1. Here, p y is the component of the momentum deviation from the band minimum, locally transverse to the MBZ boundary, as shown in Fig.…”

“…1(a). The length scale ξ is of the order of the antiferromagnetic coherence length v F /∆, and may be of the order of the lattice constant or much greater [9,10].…”

“…Numerous other antiferromagnets of different crystal symmetry and effective dimensionality are discussed in Ref. [10]. Magnetic field is assumed small on the scale of the electron excitation gap ∆ and of the reorientation threshold, and thus does not perturb antiferromagnetic order.…”

“…Being at least of the order of the lattice spacing, in a weaklycoupled spin density wave antiferromagnet ξ ∼ v F /∆ (see Refs. [9,10]) may reach a 10 nm scale [18]. At the same time, the ESR matrix elements are defined by the Compton length λ C = mc ≈ 0.4 pm.…”

“…While g is momentum-independent up to small relativistic corrections, g ⊥ (p) has a set of zeros in the Brillouin zone and thus substantially depends on the quasiparticle momentum momentum p. This remarkable fact is dictated by the symmetry of antiferromagnetic state [8,9,10], and gives rise to a number of interesting effects. One such effect amounts to excitation of spin resonance transitions by an AC electric field, with resonance absorption exceeding that of common electron spin resonance (ESR) by over four orders of magnitude.…”