Model for twin electromagnons and magnetically induced oscillatory polarization in multiferroic $R{\text{MnO}}_3$

We propose a model for the pair of electromagnon excitations observed in the class of multiferroic materials $R{\text{MnO}}_3$ ($R$ is a rare-earth ion). The model is based on a harmonic cycloid ground state interacting with a zone-edge magnon and its twin excitation separated in momentum space by two times the cycloid wave vector. The pair of electromagnons is activated by cross coupling between magnetostriction and spin-orbit interactions. Remarkably, the spectral weight of the twin electromagnon is directly related to the presence of a magnetically induced oscillatory polarization in the ground state. This leads to the surprising prediction that ${\text{TbMnO}}_3$ has an oscillatory polarization with amplitude 50 times larger than its uniform polarization.

Figure 1

(Color online) Coupled spin waves and optical phonons in the cycloid ground state. In-plane spin fluctuations are denoted by $\varphi$ while out-of-plane spin fluctuations are denoted by $\psi$.

Figure 2

(Color online) Typical dispersion curves along the cycloid direction $\widehat{b}$ for the cyclon (blue solid) and extra-cyclon (red dashed) modes in a $bc$ cycloid. Our theory gives rise to twin electromagnons depicted by a circle and a square. When the magnetoelectric interaction is rotationally invariant [$g_b=g_c$ in Eq. (4)], only the one denoted by a square is excited; in the absence of rotational invariance, both electromagnons are excited. Here $Q$ is the magnitude of the cyclon wave vector and $b$ the lattice constant along $\widehat{b}$ axis.

Figure 3

Diagrams for twin electromagnon excitation by light, involving momentum exchange with the cycloidal ground state. (a) Zone-edge electromagnon at $q=k_0$ and (b) its twin at $q=k_0-2Q$. The fact that momentum is not conserved by $k_0=2\pi /b$ reflects the underlying lattice symmetry, which produces spin-wave modes connected by $q\to q+k_0$.