Strong effects of uniaxial pressure and short-range correlations in ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$

${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ is a quasi-two-dimensional semiconducting van der Waals ferromagnet down to the bilayer with great potential for technological applications. Engineering the critical temperature to achieve room-temperature applications is one of the critical next steps on this path. Here, we report high-resolution capacitance dilatometry studies on ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ single crystals which directly prove significant magnetoelastic coupling and provide quantitative values of the large uniaxial pressure effects on long-range magnetic order ($\partial T_{\mathrm{C}}/\partial p_c=24.7$ K/GPa and $\partial T_{\mathrm{C}}/\partial p_{ab}=-15.6$ K/GPa) derived from thermodynamic relations. Moderate in-plane strain is thus sufficient to strongly enhance ferromagnetism in ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ up to room temperature. Moreover, unambiguous signs of short-range magnetic order up to 200 K are found.

Figure 1

Thermal expansion at 0 and 15 T with nonmagnetic background estimate. Relative length changes in zero field (black and blue circles) and at $B=15$ T (green and brown symbols) for $B\parallel ab$ and $B\parallel c$. Left and right ordinates have been shifted and scaled. The red curve shows the estimated phonon background (see the text). Vertical lines indicate the length changes between 0 and 15 T obtained from magnetostriction measurements at selected temperatures. The inset highlights the low-temperature behavior of $\mathrm{\Delta }{L}_{ab}(T$).

Figure 2

(a) Thermal expansion coefficients ${\alpha }_i, i=c,ab$, and (b) specific heat at $B=0$ T. The red curves show the background fits as explained in the text.

Figure 3

Grüneisen scaling of thermal expansion and specific heat. Comparison of ${\alpha }_{i,\mathrm{mag}}$ (red open symbols) and ${\mathrm{c}}_{p,\mathrm{mag}}$ (black closed symbols) at $B=0$ T for the in-plane direction (a) and the $c$ axis (b) yielding the magnetic Grüneisen parameters ${\gamma }_{ab,\mathrm{mag}}=4.2-7.8$ and ${\gamma }_{c,\mathrm{mag}}=11.3$ (see text).

Figure 4

Scaling of the specific heat and thermal expansion coefficients in order to obtain the uniaxial pressure dependence according to Ref. [38]. The thermal expansion coefficients were rescaled by (a) ${\eta }_{ab}=-10700$ J ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-1}$ and (b) ${\eta }_c=6750$ J ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-1}$. ${\eta }_{\mathrm{c}}{\alpha }_{\mathrm{c}}$T was shifted by $-0.8$ K so that its peak position overlaps with the peak position of $c_p^{*,c}$. Background subtractions with $a=48$ J ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-1}, b=1.42$ J ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-2}$ ($a=50$ J ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-1}, b=1.2$ J ${\mathrm{mol}}^{-1}$ ${\mathrm{K}}^{-2}$) were performed on $c_p$ to obtain $c_p^{*,ab}$ ($c_p^{*,c}$).