Pressure control of the magnetic anisotropy of the quasi-two-dimensional van der Waals ferromagnet ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$

We report the results of the pressure-dependent measurements of the static magnetization and of the ferromagnetic resonance (FMR) of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ to address the properties of the ferromagnetic phase of this quasi-two-dimensional van der Waals magnet. The static magnetic data at hydrostatic pressures up to 3.4 GPa reveal a gradual suppression of ferromagnetism in terms of a reduction of the critical transition temperature, a broadening of the transition width, and an increase of the field necessary to fully saturate the magnetization $M_{\mathrm{s}}$. The value of $M_{\mathrm{s}}\simeq 3{\mu }_{\mathrm{B}}/\mathrm{Cr}$ remains constant within the error bars up to a pressure of 2.8 GPa. The anisotropy of the FMR signal continuously diminishes in the studied hydrostatic pressure range up to 2.39 GPa, suggesting a reduction of the easy-axis-type magnetocrystalline anisotropy energy (MAE). A quantitative analysis of the FMR data gives evidence that up to this pressure the MAE constant $K_{\mathrm{U}}$, although getting significantly smaller, still remains finite and positive, i.e., of the easy-axis type. Therefore, a recently discussed possibility of switching the sign of the magnetocrystalline anisotropy in ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ could only be expected at still higher pressures, if possible at all, due to the observed weakening of the ferromagnetism under pressure. This circumstance may be of relevance for the design of strain-engineered functional heterostructures containing layers of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$.

Figure 1

Temperature dependence of the magnetization $M\left(T\right)$ of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ measured in the FC mode at ${\mu }_{0}H=0.1\mathrm{T}$ parallel to the $c$ axis for pressures up to 3.4 GPa. The inset shows the corresponding $dM\left(T\right)/dT$ curves.

Figure 2

Magnetization $M$ as a function of applied field $\mathbf{H}\parallel c$ at $T=15\mathrm{K}$ for pressures up to 3.4 GPa. The solid lines are guides to the eye. A demagnetization correction has been applied [23].

Figure 3

Saturation magnetization $M_{\mathrm{s}}$ and the FM transition temperature $T_{\mathrm{c}}$ as a function of the applied pressure (symbols). $M_{\mathrm{s}}$ was calculated as the average magnetization value for applied fields ${\mu }_{0}H\ge 2\mathrm{T}$, with $2\mathrm{T}$ determined as the lower limit of the applied field at which $dM/dH=0$ for all the curves within the experimental error bar. The solid lines are guides to the eye.

Figure 4

Representative FMR spectra of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ at zero and the maximum applied pressure for the applied magnetic field (a) parallel and (b) perpendicular to the $c$ axis. The sharp spike is a signal from the paramagnetic reference DPPH with a $g$ factor of $g\simeq 2$. Some distortions of the line shape can be ascribed to the interference effects of the microwaves in the pressure cell [24, 25]. (c) The frequency-field diagram obtained from FMR measurements at various pressures up to 2.39 GPa for $\mathbf{H}\parallel c$. Solid lines are fits according to Eq. (2), while the dashed blue line indicates the paramagnetic $\nu \left(H_{\text{res}}\right)$ dependence of the DPPH reference sample with $g\simeq 2$. Details of the frequency-field diagram for intermediate fields are shown in the inset in order to emphasize the systematic shift of the resonance line with increasing pressure.

Figure 5

Examples of simulations (solid lines) of the measured frequency-field dependences (symbols) at (a) 0 GPa and (b) 2.01 GPa. In these simulations experimental data sets obtained for $\mathbf{H}\parallel c$ (circles) and $\mathbf{H}\perp c$ (squares) were taken into account simultaneously in order to determine the value of $K_{\mathrm{U}}$.

Figure 6

Pressure dependence of the uniaxial magnetocrystalline anisotropy constant $K_{\mathrm{U}}$ of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$. Red circles denote the results obtained from fitting the different $\nu \left(H_{\text{res}}\right)$ curves according to Eq. (2) for $\mathbf{H}\parallel c$. Blue squares are the $K_{\mathrm{U}}$ values determined from simulations according to Eq. (5) considering the experimental data sets for $\mathbf{H}\parallel c$ and $\mathbf{H}\perp c$ simultaneously. The horizontal dashed line shows the absolute value of the negative shape anisotropy constant $K_{\mathrm{shape}}\approx -2.54\times {10}^5\mathrm{erg}/{\mathrm{cm}}^3$. It compensates the decreasing positive value of $K_{\mathrm{U}}$ at $p\gtrsim 2\mathrm{GPa}$, yielding a seemingly isotropic behavior.