Dynamic properties of spin-orbital correlation effects in the spinel ${\mathrm{MnV}}_2{\mathrm{O}}_4$

The spin-orbital-lattice coupling in spinel ${\mathrm{MnV}}_2{\mathrm{O}}_4$ single crystal has been investigated by static field magnetization (field sweep rate of 50 Oe/s), pulsed field magnetization (field sweep rate $\sim {10}^5$ kOe/s), dielectric permittivity, and magnetostriction. Experimental results show that the magnetization and magnetostriction are related to the field sweep rate. The analysis of the magnetization, dielectric permittivity and magnetostriction in static magnetic field shows that the collinear (CL) and non-CL (NCL) spin configurations coexist between $T_N\sim 56$ K and $T^{*}\sim 52$ K, and the NCL spin configuration can be induced by applied magnetic field. In particular, the magnetization and magnetostriction steps associated with CL and NCL transitions observed in the static magnetic field becomes smooth in the pulsed magnetic field, indicating the slow relaxation characteristic of these phase transitions. Based on the orbital state of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ and the Kugel-Khomskii model, we propose an quasiadiabatic spin-orbital correlation mechanism in which the interaction between the spin and the $t_{2g}$ orbital of ${\mathrm{V}}^{3+}$ ions is rather weak; this weak interaction results in the magnetic properties of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ is related to the field sweep rate.

Figure 1

(a) The magnetic susceptibility of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ under $H=0.01$ T in ZFC and FC. (b), (c) The temperature dependence of magnetic susceptibilities of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ under $H=0.1$ T and $H=1$ T with different magnetic directions, respectively.

Figure 2

(a), (b) The magnetic-field dependence of magnetization of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ measured by static magnetic field and pulsed magnetic field, respectively; the inset in (a) shows the local zoom of the hysteresis loop around $T^{*}$ and (b) gives the wave form of the pulsed magnetic field used. (c) The derivative signal of magnetization measured by pulsed magnetic field.

Figure 3

The temperature dependence of dielectric permittivity of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ under $H=1$ T with a 10 kHz AC electric field for $H\perp E$ and $H\parallel E$; the inset displays the temperature dependence of dielectric permittivity under zero field and $H=9$ T. (b), (c) The magnetic-field dependence of isothermal dielectric permittivity for $H\perp E$ and $H\parallel E$, respectively. The inset in (c) gives the isothermal magnetization for comparison. (d) The temperature dependence of dielectric permittivity of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ under different frequencies. The colored arrows represent the position of the plateaulike change.

Figure 4

(a) The temperature dependence of $\mathrm{\Delta }L/L$ under different magnetic fields. (b), (c) The magnetic-field dependence of $\mathrm{\Delta }L/L$ measured by the static magnetic field and pulsed field, respectively.

Figure 5

The phase diagram of the spin configuration of ${\mathrm{MnV}}_2{\mathrm{O}}_4$ by extracting the critical field ($H_c$) from the magnetization ($M$), dielectric permittivity (${\varepsilon }^{\prime }$), and magnetostriction ($\mathrm{\Delta }L/L$) measurements. The up (down) arrow represents the field-ascending (-descending) branch of the corresponding measurement, and the color lines represent the phase boundaries. Below $T^{*}$, the spin configuration is NCL, which is filled with purple color. The field-induced NCL phase is shown with lavender color. The CL and NCL spin configurations coexist in the striped shaded area. In the PM phase, which is filled with blue-green color, the spin is unpolarized. The inserted cartoons are for illustrating the different spin-orbital interaction strength; below $T^{*}$, the spin-orbital correlation effect is strong; above $T^{*}$, this correlation effect is weak.