Anisotropic magnons in a layered honeycomb ferromagnet

Abstract

Recent experimental and theoretical studies have suggested a possible Dirac magnon gap in the two-dimensional ferromagnetic semiconductor CrSiTe$_3$. Detailed neutron scattering measurements were performed to shed light on the existence of the magnon gap, and suggest that the gap is very small or non-existent, with previous measurements being complicated by experimental factors. During these measurements, it was found that the out-of-plane couplings could explain the usual property of the increase in the magnetic transition temperature when CrSiTe$_3$ is exfoliated to monolayers. Furthermore, the material was shown to have anisotropic magnons along the out-of-plane direction, through the proposed Dirac point. We speculate that this is due to an exchange anisotropy, though Kitaev-like interactions alone cannot explain the spectra.

Figures (3)

• Figure 1: (a) A line cut through the $K$-point by integrating ($\frac{1}{3}$$\pm$0.05 $\frac{1}{3}$$\pm$0.05 -6$\pm$0.1) and $\Delta E$ = 0.25 meV using the data collected on ARCS. The data was then fit to the Hamiltonian descibed in the text, including the DM term. The fit value for the DM term was 0.115(3) meV, in good agreement with Ref. Zhu_21 . (b) When the procedure done in the top panel was repeated for integrating different $Q$-volumes around the $K$-point, the fit value of the DM term was found to monotonically decrease with the integration range. The fits did not converge for volumes with $\delta <$ 0.025 r.l.u.
• Figure 2: A constant-$Q$ scan at the $K$-point on the HB3 thermal triple axis spectrometer. A background scan was also performed using the same configuration, but driving the analyzer flat. This removes coherent scattering from the analyzer, but preserves the incoherent signal that is a source of spurious scattering. The background-subtracted data is shown, where the solid line is a fit to the Hamiltonian with zero DM term, and convoluted with the instrumental resolution.
• Figure 3: (color online) (a) Spin waves measured along the ($\frac{1}{2}$$\frac{1}{2}$$L$) direction, where there is no contribution from a DM term. This data was used to constrain the fits to the out-of-plane excahnge constants. (b) Spin wave simulations of the ($\frac{1}{2}$$\frac{1}{2}$$L$) dispersion with the Kitaev interaction described in the text. (c) The data along ($\frac{1}{2}$$\frac{1}{2}$$L$) at the top of the band ($\Delta E$ = 10.5 meV) overlaid with simulations using a purely Heisenberg Hamiltonian and no DM interaction (solid line), and the same Hamiltionian, but with the nearest-neighbor in-plane interaction being a Kitaev interaction (dashed line). Both agree well with the data, as this reciprocal space direction is not sensitive to changes in these parameters. (d) Spin waves measured along the ($\frac{2}{3}$$\frac{2}{3}$$L$) direction, where the dispersion is seen to be anisotropic relative to $L$ = 0. (e) The simulations along the Fig. \ref{['spinw']}(a) direction including the Kitaev interaction. This distorts the spin wave spectrum and produces an anisotropy along the $L$ direction. (f) The data overlaid with the Heisenberg and Kitaev exchange simulations along the top of the band ($\Delta E$ = 10 meV). This shows that the anistropy produced by the Kitaev term does not change the band minima/maxima, fundamentally different from the spin wave anisotropy observed in the data.