Theory of Electromagnons in the Multiferroic Mn Perovskites: The Vital Role of Higher Harmonic Components of the Spiral Spin Order

We study theoretically the electromagnon and its optical spectrum (OS) of the terahertz-frequency regime in the magnetic-spiral-induced multiferroic phases of the rare-earth-metal ($R$) Mn perovskites, $R{\mathrm{MnO}}_3$, taking into account the spin-angle modulation or the higher harmonics of the spiral spin configuration, which has been missed so far. A realistic spin Hamiltonian, which gives phase diagrams in agreement with experiments, resolves a puzzle, i.e., the double-peak structure of the OS with a larger low-energy peak originating from magnon modes hybridized with the zone-edge state. We also predict the magnon branches associated with the electromagnon, which can be tested by neutron-scattering experiment.

Figure 1

(a) Superexchange interactions in $R{\mathrm{MnO}}_3$ described by the Hamiltonian Eq. (2). (b) Modulations of the in-plane nearest-neighbor ferromagnetic exchanges under $\mathit{E}\parallel a$. (c) Those under $\mathit{E}\parallel b$. Here FM and AFM denote ferromagnetic and antiferromagnetic exchanges, respectively.

Figure 2

Calculated electromagnon optical spectra for (a) $ab$-plane spiral state ($q_b=\pi /3$) with parameter set A, and (b) $bc$-plane spiral state ($q_b=2\pi /5$) with parameter set B. Values of ${\alpha }_G$ used in the calculations are 0.1 and 0.2 for (a) and (b), respectively. Insets show the experimental spectra of ${\mathrm{Eu}}_{0.55}{\mathrm{Y}}_{0.45}{\mathrm{MnO}}_3$ [17] and ${\mathrm{DyMnO}}_3$ [12], respectively.

Figure 3

Calculated intensity map of magnon (left panel) and electromagnon OS (right panel) for each Hamiltonian with successively adding the interactions. (a) ${\mathcal{H}}_{\mathrm{ex}}+{\mathcal{H}}_{\mathrm{sia}}^D$ giving a spin-spiral with uniform rotation angles. (b) Adding ${\mathcal{H}}_{\mathrm{DM}}$ induces negligibly small changes. (c) Incorporation of ${\mathcal{H}}_{\mathrm{sia}}^E$ causes the spin-angle modulation or higher harmonics of the spin-spiral, resulting in the magnon foldings and evolution of the lower-energy peak in the OS. (d) For full Hamiltonian including also ${\mathcal{H}}_{\mathrm{biq}}$, the lower-energy peak in the OS is further enhanced.

Figure 4

Calculated electromagnon spectra for various strength of (a) single-ion anisotropy $E$ and (b) biquadratic interaction $B_{\mathrm{biq}}$. Insets show calculated $\eta$ for the $ab$-plane spin spiral as functions of $E$ and $B_{\mathrm{biq}}$, respectively (see text). The value of $B_{\mathrm{biq}}$ [$E$] for (a) [(b)] is fixed at 0.025 [0.3].