Nontrivial triplet band-topology in the spin gap materials, KCuCl3 and TlCuCl3 (Part 2)

We investigate the spin gap system, XCuCl3 (X=K, Tl), where the magnetic copper ions form a 3D lattice of two inequivalent dimers. The dominant antiferromagnetic intra-dimer interaction leads to a dimer-singlet ground state. Inelastic neutron scattering[1] and electron spin resonance measurements[2] revealed dispersive triplet excitations. The spectrum has been studied using isotropic Heisenberg models, which include further neighbor exchange paths.

We extend this picture including symmetry allowed anisotropy terms and magnetic field and investigate their effects on the band-topology. Inversion symmetry excludes the intra-dimer antisymmetric exchange anisotropy preventing the mixing of singlets and triplets and limiting the variety of nontrivial band-topology. Nonetheless, inter-dimer anisotropies lead to nontrivial topology within the Sz subspaces. We find triplet bands analogous to nodal-line semimetals, Weyl semimetals, and Chern insulators depending on which anisotropy is finite. We perform detailed symmetry analysis to characterize the various band-topologies and determine corresponding topological invariants.

[1] T. Kato et al, J. Phys. Soc. Jpn. 67, pp. 752-754 (1998), N. Cavadini et al, Physica B 276-278, 540 542 (2000), N. Cavadini et al, Phys. Rev. B 63, 172414 (2001), A. Oosawa et al, Phys. Rev. B 65, 094426 (2002)

[2] H.Tanaka et al Physica B 246–247, 545(1998), M. Motokawa et al J. Phys. Soc. Jpn. 72, 1-11 (2003), S. Kimura et al Physica B 346–347, 15–18 (2004).