Effect of hydrostatic pressure on ferromagnetism in two-dimensional ${\mathrm{CrI}}_3$

We have investigated the magnetic properties of the highly anisotropic layered ferromagnetic semiconductor ${\mathrm{CrI}}_3$ under hydrostatic pressure with the magnetic field along the easy axis of magnetization. At ambient pressure, ${\mathrm{CrI}}_3$ undergoes a second-order paramagnetic-to-ferromagnetic phase transition at $T_C=60.4$ K. $T_C$ is found to increase sublinearly from 60.4 to 64.9 K as pressure increases from 0 to 1.0 GPa. With the increase in pressure, the transition becomes sharper while magnetization at low field decreases monotonically due to a decrease in magnetocrystalline anisotropy. The weak low-field anomaly at around 48 K, resulting from two-step magnetic ordering, also shifts toward higher temperatures with increasing pressure. The observed increase in $T_C$ and the decrease in magnetization could originate from a change in coupling between the layers and the Cr-I-Cr bond angle with pressure.

Figure 1

(a) and (b) Field dependence of magnetization for a ${\mathrm{CrI}}_3$ crystal measured at different temperatures with applied field parallel to the $c$ axis and perpendicular to the $c$ axis, respectively. The insets show a hysteresis loop in the low-field regime. The observed behavior is qualitatively similar to what has been reported earlier [16, 19]. (c) and (d) Field-cooled magnetization for heating and cooling cycles with a magnetic field 500 Oe and 7 T, respectively, applied along the $c$ axis. A clear anomaly along with thermal hysteresis can be seen below $\sim 212$ K due to the first-order structural transition.

Figure 2

(a) Temperature dependence of field-cooled magnetization for a ${\mathrm{CrI}}_3$ crystal at different applied pressures with the magnetic field parallel to the $c$ axis. The inset shows $dM/dT$ as a function of $T$ for different pressures. Arrows indicate the direction of the increase in pressure. (b) $T_C$, determined from the position of the minimum in $dM/dT$ curves, along with the relative change in $T_C$ ($\mathrm{\Delta }{T}_C/T_C$), are plotted as a function of pressure.

Figure 3

(a) Field dependence of magnetization curves for a ${\mathrm{CrI}}_3$ crystal measured at ambient and 1 GPa pressure with the field parallel and perpendicular to the $c$ axis at a representative temperature of 5 K. (b) Temperature dependence of zero-field-cooled (ZFC) magnetization for ${\mathrm{CrI}}_3$ at different applied pressures with the magnetic field parallel to the $c$ axis. The inset shows the pressure dependence of the two-step transition temperature $T^{★}$, determined from the position of the weak anomaly in $M\left(T\right)$ curves as shown by the arrow in the main panel.