Strong uniaxial pressure dependencies evidencing spin-lattice coupling and spin fluctuations in ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$

Single crystals of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ were studied by high-resolution capacitance dilatometry to obtain in-plane ($B\parallel ab$) and out-of-plane ($B\parallel c$) thermal expansion and magnetostriction at temperatures between 2 and 300 K and in magnetic fields up to 15 T. The anomalies in both response functions lead to the “magnetoelastic” phase diagrams and separate the paramagnetic (PM), ferromagnetic low-temperature/low-field (LTF) and aligned ferromagnetic (FM) phases. Different signs of magnetostriction anomalies as well as the evolution of thermal expansion anomalies at small fields $B\parallel ab$ of different magnetic-field dependence clearly supports the scenario of an intermediate region separating PM and LTF phases in finite external in-plane magnetic fields and implies a triple point in the magnetic phase diagram. Simulations of the magnetostriction using the Stoner-Wohlfarth model for uniaxial anisotropy demonstrate that the observed quadratic-in-field behavior in the LTF phase is in line with a rotation of the spins from the preferred $c$ direction into the $ab$ plane. Both the LTF and the PM phase close to $T_{\mathrm{C}}$ exhibit very strong pressure dependencies of the magnetization, $\partial ln{M}_{\mathrm{ab}}/\partial p_{\mathrm{ab}}$, of several hundred %/GPa and the transition from the LTF to the FM phase strongly depends on $p_{\mathrm{ab}}$ ($\sim -280$%/GPa), indicating a strong decrease in the uniaxial anisotropy under applied in-plane pressure. Our data clearly demonstrate the relevance of critical fluctuations and magnetoelastic coupling in ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$.

Figure 1

Magnetic contributions to the thermal expansion coefficient in external fields between 0 and 15 T (a) and (b) and between 0 and 1 T (c) and (d) for $B\parallel c$ and $B\parallel ab$, respectively. Triangles in (b) and (c) mark the peak positions (see also Fig. S2 in the Supplemental Material [30]).

Figure 2

Relative length changes (a), magnetostriction coefficient (b), and magnetic susceptibility (c) at low fields for $B\parallel ab$ and temperatures from 2 to 70 K. Only up-sweep data are shown in (a) and (b), whereas up- and down-sweeps are shown in (c).

Figure 3

Comparison of experimental magnetostriction data (a) and (b) and magnetization data (c) for $H\parallel ab$ (solid lines) with calculations using the Stoner-Wohlfarth model (open circles). Only up-sweep data are shown in (b), whereas both up- and down-sweep data are shown in (a) and (c).

Figure 4

Pressure dependence of the magnetization for $B,p\parallel ab$ at (a) temperatures $T<T_C$ and (b) $T>T_C$.

Figure 5

Phase diagrams for (a) $B\parallel c$ and (b) $B\parallel ab$ with uniaxial pressure dependencies of the magnetization (see the text) as well as of the phase boundaries (red arrows) indicated. Color coding shows the magnetic thermal expansion coefficient (a) as well as the magnetostriction coefficient (b). Dashed lines indicate the crossover from the FM to the PM phase. The solid black line in (b) indicates the transition from the low temperature and field (LTF) phase to the phase where magnetic moments are fully aligned along the applied field. Red arrows show the effects of uniaxial pressure (see the text).