  Mermin-Wagner theorem forbid spontaneous symmetry breaking of spins in
one/two-dimensional systems at finite temperature and rules out the
stabilization of this ordered state. However, it does not apply to all types of
phase transitions in low dimensions such as topologically ordered phase
rigorously shown by Berezinskii-Kosterlitz-Thouless (BKT) and experimentally
realized in very limited systems such as superfluids, superconducting thin
films. Quasi 2D van der Waals magnets provide an ideal platform to investigate
the fundamentals of low-dimensional magnetism. We explored the 2D honeycomb
antiferromagnetic single crystals of (NixFe1-x)2P2S6 with varying spins ( )
using in depth temperature dependent Raman measurements supported by
first-principles calculations of the phonon frequencies. As a function of
doping, a tunable transition from paramagnetic to antiferromagnetic ordering is
shown via phonons reflected in the strong renormalization of the self-energy
parameters of the Raman active phonon modes. An anomalously broad magnetic
continuum attributed to two-magnon excitations is observed and its coupling
with the phonons is revealed in the observation a Fano line asymmetry.
Interestingly, the two-magnon continuum is observed only for the finite doping
understood invoking underlying nature of insulator these materials belongs to,
i.e. exchange interaction between transition metals via surrounding ligands
(sulphur) and the resonance involving phonon modes associated with the (P2S6)
cage. Quite surprisingly, we also observed renormalization of the phonon modes
much below the long-range magnetic ordered temperature attributed to the
topological ordered state, namely the BKT phase, which is also found to change
as a function of doping. The extracted critical exponent of the order-parameter
evince the signature of topologically active state driven by vortex-antivortex
excitations.
