  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.
