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 $K - χ$ 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 $γ\simeq$ 0.45(4), placing CuCrP$_2$S$_6$ in a three dimensional Heisenberg universality regime.

Figures (12)

• Figure 1: Crystal structure of CuCrP$_2$S$_6$. (a )View along the $c^{*}$ direction showing the CuCrP$_2$S$_6$ layer with Cr$^{3+}$ ions forming a two-dimensional triangular magnetic lattice within a network of [P$_2$S$_6$]$^{4-}$ units. (b): Local bonding environment of the P--P dimer. Each P–P dimer is coordinated to the same three Cr$^{3+}$ ions within the layer. (c) & (d): Side view along the $a$ direction illustrating the stacking of quasi-2D layers separated by van der Waals gaps. (c): High-temperature ($T = 300$ K) configuration in the monoclinic $C2/c$ structure, where Cu ions occupy two (or four) partially occupied sites. (d): Low-temperature ($T = 64$ K) antiferroelectric structure, where Cu ions order into alternating up- and down-displacement positions, as indicated by the arrows, thereby lowering the crystal symmetry.
• Figure 2: Temperature dependence of $^{31}$P NMR frequency spectra of CuCrP$_2$S$_6$ measured at 2.5 T applied along $c^*$-axis (left panel) and $b$-axis (right panel).
• Figure 3: The measured $^{31}$P NMR shift $K_{\rm{raw}}$, contribution from bulk magnetic effects $K_{\rm{d}}$, and the intrinsic shift ($K = K_{\rm{raw}}-K_{\rm{d}}$) as a function of out-of-plane angle $\theta$, where $\theta$ = 0$^\circ$ represents ${\bf H}\parallel c^*$ and $\theta$ = 90$^\circ$ represents ${\bf H}\parallel b$ (b): K as a function of in-plane angle $\phi$, where $\phi$ = 0$^\circ$ represents ${\bf H}\parallel a$ and $\theta$ = 90$^\circ$ represents ${\bf H}\parallel b$. Solid lines represent the fit using Eq. \ref{['Angular1']} as described in the text.
• Figure 4: Temperature dependence of the $^{31}$P NMR linewidth and line splitting, both normalized by the bulk magnetic susceptibility, $\Delta \nu/\chi$, measured across the antiferroelectric (AFE) transitions. The linewidth is shown by filled symbols, while the line splitting is shown by open symbols.
• Figure 5: Temperature dependence of $^{31}$P NMR shift $K$. (a) NMR shift measured at 7 T applied along $c^*$-axis. $K_{\rm{HF}}$ and $K_{\rm{LF}}$ are the shifts corresponding to high frequency and low frequency lines and $K_{\mathrm{av}} = \frac{K_{\mathrm{HF}} + K_{\mathrm{LF}}}{2}$, represents the average shift. The inset shows the demagnetization correction of the shift, $K(T)= K_{\mathrm{av}}-K_{\mathrm{d}}$. (b): Corrected NMR shift $K(T)$ measured at 2.5 T and 7 T for ${\bf H}\parallel b$ and ${\bf H}\parallel c^*$.