Axion-Higgs interplay and anomalous magnetic phase diagram in TlCuCl₃

TlCuCl₃ has been widely studied due to its peculiar magnetic phase diagram, observation of magnetic Higgs mode, BE condensation of the magnons etc. We study its peculiar magnetic phase, starting from the DFT band structure. (1) We discover that there exists a Su-Schrieffer-Heeger (SSH) like Cu-chain along the z-direction. We construct a 3D version of the SSH model. (2) As an AFM order sets in, we show that the system naturally transforms into a topological axion insulator. (3) Finally, we present a Chern-Simon-Ginzburg-Landau theory for the competition and coexistence of axion, Higgs and Goldstone modes, and present an anomalous magnetic phase diagram described in terms of topological axion angle.