Microscopic NMR evidence for successive antiferroelectric and antiferromagnetic order in the van der Waals magnet CuCrP$_2$S$_6$

Abstract

We present a comprehensive $^{31}$P and $^{65}$Cu nuclear magnetic resonance (NMR) study of the layered van der Waals magnet CuCrP$_2$S$_6$. The compound exhibits a sequence of structural and magnetic phase transitions: a high-temperature paraelectric state, followed by a quasi-antiferroelectric (QAFE) state near 185 K, a long-range antiferroelectric (AFE) phase below 150 K, and finally, antiferromagnetic (AFM) order below $T_\mathrm{N}$ = 30 K. The evolution of the NMR spectra, NMR shift, and spin-lattice ($T_1^{-1}$) and spin-spin ($T_2^{-1}$) relaxation rates provide direct microscopic fingerprints of these transitions. The splitting of both the NMR line and $T_1^{-1}$ below the AFE transition demonstrates the emergence of two inequivalent P sites. From $K - \chi$ analysis, we extract nearly isotropic transferred hyperfine couplings and show that the NMR shift anisotropy originates primarily from the dipolar contribution, in contrast to Mn$_2$P$_2$S$_6$ and Ni$_2$P$_2$S$_6$. We determine the ferromagnetic intralayer exchange $J_{intra}\approx$ -4.9 K from the Curie Weiss temperature, consistent with ferromagnetic layers antiferromagnetically stacked along the $c$ axis, and evaluate the Moriya high temperature relaxation rate including cross correlation effects of the P P dimer. Critical divergence of $T_1^{-1}$ near $T_\mathrm{N}$ yields a critical exponent $\gamma\simeq$ 0.45(4), placing CuCrP$_2$S$_6$ in a three dimensional Heisenberg universality regime.