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We study a Heisenberg-Dzyaloshinskii-Moriya Hamiltonian on AB-stacked kagome
bilayers at finite temperature. In a large portion of the parameter space, we
observe three transitions upon cooling the system: a crossover from Heisenberg
to the XY chiral paramagnet, Kosterlitz-Thouless transition to a chiral nematic
phase, and a fluctuation-induced first-order transition to an Ising-like phase.
We characterize the properties of phases numerically using Monte Carlo
finite-size analysis. To further explain the nature of the observed phase
transitions, we develop an analytical coarse-graining procedure that maps the
Hamiltonian onto a generalized XY model on a triangular lattice. To leading
order, this effective model includes both bilinear and biquadratic interactions
and is able to correctly predict the two phase transitions. Lastly, we study
the Ising fluctuations at low temperatures and establish that the origin of the
first-order transition stems from the quasi-degenerate ring manifold in the
momentum space.
