Magnetocaloric effect and spin-strain coupling in the spin-nematic state of ${\mathrm{LiCuVO}}_4$

We report on the magnetocaloric effect and ultrasound studies of the frustrated quasi-one-dimensional spin-1/2 compound ${\mathrm{LiCuVO}}_4$, evidencing a spin-nematic state. The magnetic Grüneisen parameter diverges at the transition to the spin-nematic phase, ${\mu }_0{H}_{\mathrm{c}3}\approx 40$ T, showing quantum criticality accompanied by entropy accumulation. The observed high-field anomalies in the acoustic properties clearly evidence a strong involvement of the lattice in the spin dynamics. The theoretical approach, based on exchange-striction coupling with dipolar and quadrupolar contributions, suggests that the spin-dipole-strain and quadrupole-strain interactions govern the spin-nematicity in ${\mathrm{LiCuVO}}_4$.

Figure 1

(a) Magnetocaloric effect in ${\mathrm{LiCuVO}}_4$ measured at various initial temperatures in pulsed magnetic fields $\left(H\parallel c\right)$. The inset shows an enlarged view near the saturation field. The symbols denote phase transitions extracted from previous studies (Refs. [8, 16, 36, 37]) and our ultrasound results. The dashed lines are guides to the eye and separate the paramagnetic (PM), the incommensurate planar spiral (PS), the collinear SDW, the spin-nematic (SN), and the fully polarized (FP) phases. Gray shadow shows the quantum-critical (QC) regime around ${\mu }_0{H}_{\mathrm{c}3}$ as evidenced by the minimum in the MCE. (b) Magnetic Grüneisen parameter, ${\mathrm{\Gamma }}_H$, obtained along the isentropic MCE curves for the down sweeps. The color of each curve corresponds to that of Fig. 1. (c) ${\mathrm{\Gamma }}_H$ versus magnetic field at several constant temperatures are plotted. The data follow the critical divergence ${\mathrm{\Gamma }}_H\propto {\mu }_0^{-1}{(H-H_{\mathrm{c}3})}^{-1}$ (dashed lines). (d) ${\mathrm{\Gamma }}_H$ versus temperature at some selected magnetic fields.

Figure 2

Sound-velocity and sound-attenuation change for the transverse acoustic (a), (b) $c_{\mathrm{t}}$ and (c), (d) $c_{{\mathrm{t}}^{\prime }}$ mode, respectively, measured in pulsed magnetic fields at 1.5, 2.3, and 4.2 K. Results for up and down field sweeps are shown. The ultrasound frequency was 110 MHz. The spin-nematic state is realized between $H_{\mathrm{c}3}$ and the saturation field, $H_{\mathrm{sat}}$. The cyan solid lines in (b) depict the calculated magnetic field dependence of the sound attenuation of the $c_{\mathrm{t}}$ mode of ${\mathrm{LiCuVO}}_4$ at $T=1.5$ and 4.2 K (see text for details).

Figure 3

Temperature dependence of the relative change of the sound velocity $\mathrm{\Delta }v/v$ for the acoustic $c_{\mathrm{t}}$ and $c_{33}$ modes in ${\mathrm{LiCuVO}}_4$. For the $c_{\mathrm{t}}$ mode the results obtained at 27 (blue line) and 182 MHz (orange line) are shown. In the case of the $c_{33}$ mode (black line) the ultrasound frequency was 52 MHz. The inset shows the sound velocity for the $c_{\mathrm{t}}$ mode in the vicinity of the AFM ordering.

Figure 4

Field dependence of the spin-quadrupolar contribution to the sound attenuation $\mathrm{\Delta }\alpha$ of the transverse $c_{\mathrm{t}}$ mode at $T=1.5$ K for the quasi-1D spin-1/2 chain model.

Figure 5

Temperature dependence of the sound velocity of the transverse $c_{\mathrm{t}}$ mode at zero magnetic field for the quasi-1D spin-1/2 chain model.