Nontrivial triplet band-topology in the spin gap materials, KCuCl3 and TlCuCl3

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 use symmetry arguments to extend the previously suggested Heisenberg model with possible anisotropies, such as the antisymmetric Dzyaloshinskii-Moriya (DM) interaction, and produce an effective triplet Hamiltonian to study the triplet spectra. Depending on the strength of the magnetic anisotropies and the direction of the external magnetic field, we find triplet analogs of Weyl semimetals and nodal line semimetals. We categorize the topological structure of the spectrum in all configurations of external fields and allowed symmetry terms. This result may indicate that the bands of the triplet excitation may carry finite Berry curvature and display nontrivial band-topology

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[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).