Spin-lattice coupling in a ferrimagnetic spinel: Exotic $H-T$ phase diagram of ${\mathrm{MnCr}}_2{\mathrm{S}}_4$ up to 110 T

In antiferromagnets, the interplay of spin frustration and spin-lattice coupling has been extensively studied as the source of complex spin patterns and exotic magnetism. Here, we demonstrate that, although neglected in the past, the spin-lattice coupling is essential to ferrimagnetic spinels as well. We performed ultrahigh-field magnetization measurements up to 110 T on a Yafet-Kittel ferrimagnetic spinel, ${\mathrm{MnCr}}_2{\mathrm{S}}_4$, which was complemented by measurements of magnetostriction and sound velocities up to 60 T. Classical Monte Carlo calculations were performed to identify the complex high-field spin structures. Our minimal model incorporating spin-lattice coupling accounts for the experimental results and corroborates the complete phase diagram, including two new high-field phase transitions at 75 and 85 T. Magnetoelastic coupling induces striking effects: An extremely robust magnetization plateau is embedded between two unconventional spin-asymmetric phases. Ferrimagnetic spinels provide a new platform to study asymmetric and multiferroic phases stabilized by spin-lattice coupling.

Figure 1

(a) Crystal structure of ${\mathrm{MnCr}}_2{\mathrm{S}}_4$ and the three main magnetic interactions, $J{}_{\text{Mn-Mn}}, J{}_{\text{Mn-Cr}}$, and $J{}_{\text{Cr-Cr}}$. (b) Magnetization and (c) its field derivative as a function of the magnetic field along the [110] direction. The curves at 4 K are shown on the original scale, while the curves at 7 and 14 K are vertically shifted for clarity. In (c), the arrows indicate the phase transitions, $H_1$–$H_5$, at which the steplike anomalies corresponding to the sudden changes in the slope in the magnetization were observed. The magnetization saturates in the fully polarized state above 85 T.

Figure 2

(a) Magnetization and (b) its field derivative as a function of the magnetic field applied along the [110] direction calculated from classical Monte Carlo simulations. The curves at 4 K are shown on the original scale, while the curves at 7 and 14 K are vertically shifted for clarity. The arrows ($H_1$–$H_5$) indicate transitions similar to those in Fig. 1. (c) Angles of the Cr, Mn1, and Mn2 spins with respect to the external-field direction. (d) Typical magnetic structures formed by Cr, Mn1, and Mn2 spins for each phase.

Figure 3

Magnetostriction and sound velocity obtained by experiment and theory. (a) Experimentally obtained magnetostriction along $\mathbf{H}\parallel \left[110\right]$. (b) Exchange-modification parameters $q_1$ and $q_2$, which are proportional to the Cr-Mn1 and Cr-Mn2 bond lengths, respectively. The magnetostriction measurement $\mathrm{\Delta }L/L$ should be proportional to $q=(q_1+q_2)/2$. In (b), $q_1$ and $q_2$ are identical below 20 T and above 60 T. (c) and (d) Relative changes of the sound velocity obtained in experiment and theory. The longitudinal acoustic mode $(c_{11}+2c_{12}+4c_{44})/3$ propagating along $\mathbf{H}\parallel \left[111\right]$ was measured. (e) Schematic illustration of antiferromagnetically ordered spins with $q_1$ and ferromagnetically ordered spins with $q_2$ in the plateau phase.

Figure 4

Magnetic-field-temperature phase diagram of ${\mathrm{MnCr}}_2{\mathrm{S}}_4$. The phase boundaries were obtained from the magnetization, ultrasound propagation, and magnetostriction experiments in pulsed fields. The solid circles with error bars of $\pm 2$ T and $\pm 1$ K were obtained in the present ultrahigh-field experiments. The open squares were taken from Ref. [15]. Typical magnetic structures revealed by the MC calculations are illustrated in each phase. The Cr spins (orange arrows) are almost perfectly aligned with the external field. The Mn spins (two blue arrows) show a complex, strongly field dependent order.

Figure 5

Inverse magnetic susceptibility ${\chi }^{-1}$ of ${\mathrm{MnCr}}_2{\mathrm{S}}_4$ obtained in the experiments [15] and the theory. An external magnetic field of 1 T is applied along the [111] direction. (a) and (b) show the data at high temperatures of 20–400 K. (c) and (d) show the data at low temperatures of 2.5–15 K.

Figure 6

Relative changes of sound velocity $\mathrm{\Delta }v/v$ of ${\mathrm{MnCr}}_2{\mathrm{S}}_4$ obtained in (a) the experiments [15] and (b) the theory.

Figure 7

Spin correlations of the Mn1 and Mn2 spins at (a) low temperatures and (b) high temperatures. (c) Schematic magnetic structures of the Yafet-Kittel triangular-structure phase ($T<T_{\text{YK}}$) and the ferrimagnetic phase with disordered transverse components of Mn spins ($T_{\text{YK}}<T<T_{\text{C}}$).