Magnetic correlations in the quasi-two-dimensional semiconducting ferromagnet ${\text{CrSiTe}}_3$

Intrinsic, two-dimensional ferromagnetic semiconductors are an important class of materials for overcoming the limitations of dilute magnetic semiconductors for spintronics applications. ${\text{CrSiTe}}_3$ is a particularly interesting member of this class, since it can likely be exfoliated down to single layers, where $T_C$ is predicted to increase dramatically. Establishing the nature of the magnetism in the bulk is a necessary precursor to understanding the magnetic behavior in thin-film samples and the possible applications of this material. In this work, we use elastic and inelastic neutron scattering to measure the magnetic properties of single-crystalline ${\text{CrSiTe}}_3$. We find that there is a very small single ion anisotropy favoring magnetic ordering along the $c$ axis and that the measured spin waves fit well to a model where the moments are only weakly coupled along that direction. Finally, we find that both static and dynamic correlations persist within the $ab$ plane up to at least 300 K, strong evidence of this material's two-dimensional characteristics that are relevant for future studies on thin-film and monolayer samples.

Figure 1

(a) The crystal structure of ${\text{CrSiTe}}_3$. The ${\text{Cr}}^{3+}$ ions form hexagonal arrangements in the $ab$ plane, which are then stacked along the $c$ axis in an $ABC$-type stacking. This creates two magnetically inequivalent Cr sites, shown in red and blue. The Cr-I site (blue) has a Cr-II atom (red) above and a ${\text{Si}}_2$ pair (green) below, while it is reversed for the Cr-II site. Below $T_C=33.2$ K, the Cr $S=3/2$ spins align ferromagnetically along the $c$ axis, due to a single-ion anisotropy, $D_z$. The nearest-neighbor exchanges out to 8 Å are shown in the figure, which includes three in-plane exchanges, $J_{ab1}, J_{ab2}$, and $J_{ab3}$, and one out-of-plane exchange $J_c$. (b) The structure of a single layer is shown, highlighting the different exchange interactions in this plane.

Figure 2

(a) The temperature dependence of the measured intensity at the (1 0 1) Bragg peak. This peak is both nuclear and magnetic, but the magnetic intensity is larger by approximately a factor of 10. A fit to this curve gives a transition temperature of $T_C=33.2\left(1\right)$ K and a critical exponent $\beta =0.151\left(12\right)$. (inset) Scans through the (1 0 1) Bragg peak along $H$ at $T=10$ (black squares), 33 (red circles), and 50 K (blue triangles), plotted on a logarithmic scale. This shows the sharp increase in the intensity at (1 0 1), corresponding to the 3D order, while the diffuse scattering, corresponding to the 2D correlations, is most intense at the transition. (b) The temperature dependence of the in-plane correlation length, determined from the two-axis scans described in the text. The line is a guide to the eye. We note that the in-plane correlation length is greater than the nearest-neighbor Cr-Cr distance at all temperatures measured, suggesting that the in-plane magnetic correlations are important well above the bulk ordering temperature.

Figure 3

The panels on the left show the spin waves of ${\text{CrSiTe}}_3$ measured on the SEQUOIA spectrometer at $T=10$ K, while the panels on the right show the calculated spin wave dispersions, along the ($H$ 0 0) direction [(a) and (b)] and the (0 0 $L$) direction [(c) and (d)]. The calculated patterns use the model and exchange parameters described in the text, producing very good agreement with the experimental data.

Figure 4

(a) The constant-$E$ scans measured on the Cold Triple-Axis (CTAX) Spectrometer at 1.5 K along (0 0 L), which are offset along the $y$ axis for clarity. These scans focus on the region near the zone center (0 0 3), where a spin gap is expected in the spectrum. By assuming that the energy of the spin waves, $E\propto {\left|q\right|}^2$ in the long-wavelength limit, we can extract an approximate measure of the gap, despite it being within the resolution of the instrument. (b) The $q$ dependence of the spin waves near the zone center is plotted, showing $q^2$ dependence. A fit to these values gives a value for the gap $\mathrm{\Delta }=0.075\left(24\right)$ meV. (c) A constant-$\vec{Q}$ measurement at $\vec{Q}=\left(1.700\right)$ near the zone boundary, (0 0 1.5), allows for a determination of the value of the out-of-plane coupling, $J_c=-0.730\left(96\right)$ meV.

Figure 5

The temperature dependence of spin dynamics. (a) The inelastic neutron spectrum measured at $T=40$ K on the SEQUOIA spectrometer. We see that broadened spin wave features remain, even above the transition, while there are no such excitations along the $L$ direction. This is a clear signature of the two-dimensionality of this material. The feature at 20 meV is extrinsic to the sample, verified by performing an empty can measurement. (b) The in-plane spin dynamics along (H 0 3) at various temperatures, measured on CTAX and offset for clarity. Sharp spin waves are observed below the transition, but dynamic correlations exist at all temperatures measured. The high-temperature features are reminiscent of the spin waves seen below $T_C$, but significantly broadened. The lines are guides to the eye. (c) In contrast, there are no dynamic correlations along the $L$ direction above $T_C$ (also shown offset for clarity). This suggests that three-dimensional correlations only exist below the Curie temperature, while the in-plane dynamic correlations persist up to at least 300 K.