Magnetoelectric Raman Force on Shear Phonons in a Frustrated van der Waals Bilayer Magnet

Abstract

We show that the concept of coherent phonon generation by second order response to incident electric laser fields, which is a hallmark of pump-probe spectroscopy on conventional solids, can be expanded to include frustrated quantum magnets. For that purpose, we analyze the Raman force on the shear phonons of a frustrated magnetoelectric bilayer spin system. The bilayer is a stacked triangular magnet, motivated by recently emerging type-II van der Waals multiferroic transition metal dihalides and comprises a spin system which allows for incommensurate spiral order. The magnon excitations are treated by linear spin wave theory. In the spiral state, a finite electric polarization is obtained from the spin-current interaction which induces a coupling of the magnons to the electric field. Scattering of the bilayer shear phonons from the magnons is derived from a magnetoelastic energy. In this scenario, a mixed three-point response function for the Raman force is evaluated. We find it to be strongly anisotropic and very sensitive to the magnon lifetime.

Figures (9)

• Figure 1: Top view of the triangular bilayer: black(green) bonds refer to bottom(top) layer. Layers are vertically separated by $d$. Each layer has NN and 3NN exchange, $J_{1}<0$ and $J_{3}>0$, respectively. Beige: interlayer bonds with NN exchange $J_{\perp}>0$.
• Figure 2: Contour plot of the pitch angle, tantamount to the classical phases of the bilayer. FM (dark green), critical line (white), and ICS (green to yellow gradient). Inset: Representative cut, displaying the pitch at $j_{\perp}=0$.
• Figure 3: Magnon dispersion. (a) 3D plot in first BZ. (b) Blow up of (a) in center of BZ. (c) Bottom-up view of (b). (d) Cut along straight line through $K$-point. Parameters: $j=0.6$, $j_{\perp}=0.5$, and $\nu=0$. For these $j$, $j_{\perp}$ the pitch is $q{\simeq}1.3217$
• Figure 4: Representative plots of the classical polarization versus exchange for (a) $\gamma=0.4$, $\gamma_{\perp}=0.2$ and (b) $\gamma=-0.3$, $\gamma_{\perp}=0.2$. White line: classical critical line, as in Fig. (\ref{['fig:classph']}).
• Figure 5: Planar phonon dispersions for $c_{1,2}=1$ and for two representative directions in the BZ, (a) $\Gamma-M$, (b) $\Gamma-K$.