Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Phonon Spectra and Phase Transitions in van der Waals Ferroics
  MM$'$P$_2$X$_6$   For CuInP$_2$S$_6$ layered ferrielectric crystal, that is most investigated
among wide family of van der Waals ferroics MM$'$P$_2$X$_6$ (M - Cu, Ag; M$'$ -
In, Bi, Cr, $\dots$; X - S, Se), by Brillouin spectroscopy the temperature
dependence of the longitudinal hypersound velocity was investigated for the
acoustic phonons propagated in the plane of crystal layers. Pronounced
softening of acoustic phonon branch is observed in the paraelectric phase below
$T^{*} \approx 330~$K at cooling to temperature $T_C \approx 312~$K of the
first order phase transition into ferrielectric phase. Below $T_C$ the
hypersound velocity growth in correlation with spontaneous polarization rise
and its temperature anomaly is similar to earlier observed temperature behavior
of longitudinal ultrasound velocity for acoustic wave propagated normally to
the structural layers. Determined anomalous part of the CuInP$_2$S$_6$ crystal
thermal conductivity in the vicinity of ferrielectric transition also
demonstrate lowering of the heat transferring phonons group velocity with
cooling from $T^{*}$ to $T_C$. Observed acoustic softening obviously is induced
by flexoelectric coupling of relaxational soft polar optic and acoustic
branches that is related to inhomogeneously polarized state appearing between
paraelectric and ferrielectric phases.

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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th