Electron spin resonance and ferromagnetic resonance spectroscopy in the high-field phase of the van der Waals magnet ${\mathrm{CrCl}}_3$

We report a comprehensive high-field/high-frequency electron spin resonance (ESR) study on single crystals of the van der Waals magnet ${\mathrm{CrCl}}_3$. This material, although being known for quite a while, has received recent significant attention in a context of the use of van der Waals magnets in novel spintronic devices. Temperature-dependent measurements of the resonance fields were performed between 4 and 175 K and with the external magnetic field applied parallel and perpendicular to the honeycomb planes of the crystal structure. These investigations reveal that the resonance line shifts from the paramagnetic resonance position already at temperatures well above the transition into a magnetically ordered state. Thereby the existence of ferromagnetic short-range correlations above the transition is established and the intrinsically two-dimensional nature of the magnetism in the title compound is proven. To study details of the magnetic anisotropies in the field-induced effectively ferromagnetic state at low temperatures, frequency-dependent ferromagnetic resonance (FMR) measurements were conducted at 4 K. The observed anisotropy between the two magnetic-field orientations is analyzed by means of numerical simulations based on a phenomenological theory of FMR. These simulations are in excellent agreement with measured data if the shape anisotropy of the studied crystal is taken into account, while the magnetocrystalline anisotropy is found to be negligible in ${\mathrm{CrCl}}_3$. The absence of a significant intrinsic anisotropy thus renders this material as a practically ideal isotropic Heisenberg magnet.

Figure 1

Crystal and magnetic structures of ${\mathrm{CrCl}}_3$ at low temperatures. (a) View along the $b$ axis of the unit cell (nonprimitive hexagonal) of the rhombohedral low-temperature structure (space group $R\overline{3}$ [9]). The magnetic ${\mathrm{Cr}}^{3+}$ ions (red spheres) are octahedrally coordinated by the Cl ligands (green spheres). (b) These ${\mathrm{CrCl}}_6$ octahedra build an edge-sharing network in the $ab$ plane which effectively leads to a honeycomb-like arrangement of the magnetic ions (illustrated by solid red lines). Each of these honeycomb layers in the $ab$ plane is well separated from its neighbors along the $c$ axis by the van der Waals gap, as shown in (a). At temperatures below the transition into a magnetically long-range ordered state, spins in the honeycomb layers are coupled ferromagnetically and oriented within the $ab$ plane, while spins in neighboring layers are coupled by a weaker antiferromagnetic interaction [10, 11]. The resulting spin structure in the magnetically ordered state at zero magnetic field [10, 11] is schematically illustrated by the arrows at the Cr sites. Crystallographic data are taken from Ref. [9].

Figure 2

Temperature dependence of the resonance shift $\delta H\left(T\right)=H_{\text{res}}\left(T\right)-H_{\text{res}}\left(100K\right)$ at microwave frequencies of about 9.6 and 90 GHz (open and filled symbols, respectively). In these measurements the external magnetic field was oriented parallel (red circles) as well as perpendicular (blue squares) to the $c$ axis. The dashed horizontal line represents the zero shift $\delta H=0$ expected for an uncorrelated paramagnet. Vertical dashed lines indicate the zero-field transition temperatures $T_c^{\text{2D}}$ and $T_N^{\text{3D}}$ of the transition into the 2D ferromagnetically ordered phase and the 3D antiferromagnetically ordered state [11], respectively.

Figure 3

Frequency dependence of the resonance field $H_{\text{res}}$ at (a) 100 and (b) 4 K, respectively. To quantitatively investigate the magnetic anisotropies in ${\mathrm{CrCl}}_3$, measurements were carried out with the external magnetic field applied parallel (red circles) and perpendicular (blue squares) to the crystallographic $c$ axis, respectively. Open symbols correspond to the resonance fields measured at $\nu =9.6\mathrm{GHz}$. Solid lines in (a) are linear fits to the $\nu \left(H_{\text{res}}\right)$ dependencies according to the standard resonance condition of a paramagnet given in Eq. (1) [32]. At 4 K, the measured frequency-field dependencies were simulated using Eq. (2) which describes the resonance frequency in the case of FMR. Corresponding simulations are shown in (b) as solid lines. Exemplary spectra recorded with $H\parallel c$ are presented for both temperatures in the respective insets. For comparison, all spectra shown were normalized (note the different breaks in the field axes). Arrows in the $\nu \left(H_{\text{res}}\right)$ denote the positions of the spectra given in the insets.

Figure 4

XRD powder pattern of a sample of ${\mathrm{CrCl}}_3$. Red ticks display the peak positions of the reference ${\mathrm{CrCl}}_3$ from the Inorganic Crystal Structure Database (22080-ICSD, SCXRD, 298 K). Note that only $\left(00l\right)$ peaks are visible due to the strong texturing of the powder sample.

Figure 5

SEM image of ${\mathrm{CrCl}}_3$ crystallites. Rectangles indicate the regions where EDX spectra were collected.