What is so unique in TlCuCl3 which drives so many unique magnetic features in this compound? To study these properties, here we employ a combination of ab-initio band structure, tight-binding model, and an effective quantum field theory. Within a density-functional theory (DFT) calculation, we find an unexpected bulk Dirac cone without spin-orbit coupling (SOC). Tracing back to its origin, we identify, for the first time, the presence of a Su-Schrieffer-Heeger (SSH) like dimerized Cu chain lying in the 3D crystal structure. The SSH chain, combined with SOC, stipulates an anisotropic 3D Dirac cone where chiral and helical states are intertwined. As a Heisenberg interaction is introduced, we show that the dimerized Cu sublattices of the SSH chain condensate into spin-singlet, dimerized magnets. In the magnetic ground state, we also find a topological phase, distinguished by the axion angle. Finally, to study how the topological axion term couples to magnetic excitations, we derive a Chern-Simons-Ginzburg-Landau action from the 3D SSH Hamiltonian. We find that axion term provides an additional mass term to the Higgs mode, and a lifetime to paramagnons, which are independent of the quantum critical physics. The axion-Higgs interplay can be probed with electric and magnetic field applied parallel or anti-parallel to each other.
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