Magnetic anisotropy of the van der Waals ferromagnet ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ studied by angular-dependent x-ray magnetic circular dichroism

The van der Waals ferromagnet ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ (CGT) has a two-dimensional crystal structure where each layer is stacked through van der Waals force. We have investigated the nature of the ferromagnetism and the weak perpendicular magnetic anisotropy (PMA) of CGT by means of x-ray absorption spectroscopy and x-ray magnetic circular dichroism (XMCD) studies of CGT single crystals. The XMCD spectra at the Cr $L_{2,3}$ edge for different magnetic field directions were analyzed on the basis of the cluster-model multiplet calculation. The Cr valence is confirmed to be $3+$ and the orbital magnetic moment is found to be nearly quenched, as expected for the high-spin $t_{2g}^3$ configuration of the ${\mathrm{Cr}}^{3+}$ ion. A large ($\sim 0.2$ eV) trigonal crystal-field splitting of the $t_{2g}$ level caused by the distortion of the $\mathrm{Cr}{\mathrm{Te}}_6$ octahedron has been revealed, while the single-ion anisotropy (SIA) of the Cr atom is found to have a sign opposite to the observed PMA and too weak compared to the reported anisotropy energy. The present result suggests that anisotropic exchange coupling between the Cr atoms through the ligand Te $5p$ orbitals having strong spin-orbit coupling has to be invoked to explain the weak PMA of CGT, as in the case of the strong PMA of ${\mathrm{CrI}}_3$.

Figure 1

Crystal structure of ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$ (CGT). (a) Schematic drawing of the crystal structure. (b) $\mathrm{Cr}{\mathrm{Te}}_6$ octahedron which is elongated along the $c$ axis. (c) Crystal-field splitting of the Cr $3d$ orbital in the distorted octahedron to trigonal symmetry.

Figure 2

Cr $L_{2,3}$ XAS and XMCD spectra of CGT at ${\mu }_{0}H=3$ T and $T=20$ K. The red curve shows the average of XAS spectra obtained with left and right circularly polarized x rays. The green curve shows the XMCD spectrum, which is the intensity difference between the above two XAS spectra. The blue dotted curve shows the integral of the XMCD spectrum. Magnetic field is applied perpendicular to the sample surface ($H\parallel c$ axis), that is, along the easy magnetization axis.

Figure 3

Experimental and calculated Cr $L_{2,3}$ XMCD spectra of CGT. The experimental spectrum is the XMCD spectrum taken with magnetic field perpendicular to the $ab$ plane. The orange, green, light-blue, and blue curves show XMCD spectra calculated using the cluster model with parameters which yield the Cr valences of $3+$, $4+$, $2+$ high-spin (HS), and $2+$ low-spin (LS) states, respectively. The used parameter values are $(\mathrm{\Delta },U,10Dq)=(4.5,6,0.7)$, $(0,5.2,0.7)$, $(4.1,4.2,0.7)$, and $(4.1,4.2,2.1)$, respectively, in eV with $\left(pd\sigma \right)=2.6$ eV fixed. An unusually large $10Dq$ or $\left(pd\sigma \right)$ was necessary to stabilize the LS state.

Figure 4

Experimental Cr $L_{2,3}$ XAS and XMCD spectra of CGT obtained with different magnetic field directions. (a) Red and black curves show XAS spectra taken with the out-of-plane and in-plane magnetic fields, respectively. (b) XMCD spectra under out-of-plane and in-plane magnetic fields. Red and black spectra show the out-of-plane and in-plane XMCD spectra, respectively. The strength of the magnetic field was 1 T and the measurement temperature was 50 K.

Figure 5

Experimental and calculated Cr $L_{2,3}$ XMCD spectra of CGT for different magnetic field directions. The red and black curves show XMCD spectra taken under magnetic fields perpendicular (out of plane) and parallel (in plane) to the surface, respectively. Blue curves show the difference between the XMCD spectra measured with different magnetic field directions. (a) Experimental XMCD spectra. (b), (c) XMCD spectra obtained by cluster-model calculations with and without the trigonal crystal field. $Dt$ denotes the trigonal-field splitting. Clear differences in the line shapes between the different magnetic field directions are indicated by black arrows.