Spin-lattice coupling in the frustrated antiferromagnet ZnCr${}_2$Se${}_4$ probed by ultrasound

Ultrasound and magnetization studies of the frustrated spinel ZnCr${}_2$Se${}_4$ are performed as a function of temperature and magnetic field up to 14 T. In zero field, the sound velocity and attenuation reveal significant anomalies at the antiferromagnetic transition at $T_N\approx$ 21 K indicating strong spin-lattice coupling. External magnetic fields shift these anomalies to lower temperatures concomitantly with the reduction of the Néel temperature. At 2 K, the sound velocity as a function of magnetic field manifests three pronounced anomalies: a deep minimum at 5.4 T related to an inflection point of the magnetization followed by two plateaus with distinct stiffness at fields above 7 and 10 T. The first plateau is ascribed to a transformation from a tetragonal to a cubic phase, while the second one corresponds to a state with fully polarized magnetization. The evolution of magnetic and structural states is discussed within a $H-T$ phase diagram and compared with related frustrated magnetic spinels with strong spin-lattice coupling.

Figure 1

Temperature dependencies of the magnetic susceptibility for ZnCr${}_2$Se${}_4$ measured in different static magnetic fields applied along the $\langle 001\rangle$ axis. The vertical arrow marks the magnetic phase transition at $T_N$ in a field of 0.01 T.

Figure 2

Temperature dependencies (a) of the relative change of the sound velocity, $\Delta v/v_0$, and (b) of the sound attenuation $\alpha$, for ZnCr${}_2$Se${}_4$ measured in different magnetic fields applied along the $\langle 001\rangle$ axis. v${}_0$ is the sound velocity at 2 K at a given magnetic field. The vertical arrow marks the magnetic phase transition at $T_N$ in zero field. The ultrasound frequency was set to 62 MHz.

Figure 3

Relative change of the (a) sound velocity $\Delta v/v_0$ and (b) attenuation $\alpha$ vs magnetic field at different temperatures in ZnCr${}_2$Se${}_4$. v${}_0$ is the sound velocity at 0 T at a given temperature. The vertical arrows mark the fields $H_{c2}$ and $H_{c3}$ of transitions to plateau states. The ultrasound frequency was set to 48.4 MHz. The inset shows the anomaly of attenuation $\alpha$ at $H_{c3}$ on an enlarged scale.

Figure 4

(a) Magnetization curves at different temperatures for ZnCr${}_2$Se${}_4$ measured along the $\langle 001\rangle$ axis. (b) Susceptibility $M/H$ for the same set of data. Arrows indicate the critical fields $H_{c1}$, $H_{c2}$, and $H_{c3}$ for 1.5 K. The dotted line presents the saturation dependence $\chi =M_s/H$, where $M_s$ is the saturation magnetization.

Figure 5

H-T phase diagram for ZnCr${}_2$Se${}_4$. Phase below $H_{c1}$ corresponds to a multidomain state. Phases PM and FM correspond, respectively, to the paramagnetic and magnetic field-induced ferromagnetic states. The boundary between the proposed spin nematic and PM phases at temperatures above 8 K is drawn arbitrarily.