Coupling of phonons and electromagnons in ${\mathrm{GdMnO}}_3$

The infrared and terahertz properties of ${\mathrm{GdMnO}}_3$ have been investigated as functions of temperature and magnetic field, with special emphasis on the phase boundary between the incommensurate and the canted antiferromagnetic structures. The heterogeneous incommensurate phase reveals strong magnetodielectric effects, characterized by significant magnetoelectric contributions to the static dielectric permittivity and by the existence of electrically excited magnons (electromagnons). In the commensurate canted antiferromagnetic phase the magnetoelectric contributions to the dielectric constant and electromagnons are suppressed. The corresponding spectral weight is transferred to the lowest lattice vibration, demonstrating the strong coupling of phonons with electromagnons.

Figure 1

(Color online) Upper panel: Magnetic phase diagram of ${\mathrm{GdMnO}}_3$ for $H\parallel c$ for zero-field cooling. Circles and stars, results of magnetization measurements; triangles, data from dielectric experiments (Ref. 14). Lines are drawn to guide the eye. PM, paramagnetic; IC-AFM, incommensurate antiferromagnetic [probably sinusoidally modulated (Ref. 6)]; CA-AFM, canted antiferromagnetic structure. The hatched region indicates the ordering of the Gd sublattice. Lower panel: Reflectance of ${\mathrm{GdMnO}}_3$ with polarization along the $a$ axis and at phonon frequencies. Symbols, experiment; solid line, model calculation assuming a sum of 15 Lorentzians (see text).

Figure 2

(Color online) Magnetic-field dependence of the parameters of the phonon at $119{\mathrm{cm}}^{-1}$ crossing the boundary between IC-AFM and CA-AFM phases. Upper panel: dielectric contribution $\left(\mathrm{\Delta }\epsilon \right)$. Lower panel: eigenfrequency $\left({\nu }_0\right)$. The lower inset shows the reflectance spectra at typical magnetic fields. The upper inset shows the changes in dielectric permittivity at a frequency close to the electromagnon, which demonstrates a direct connection of the two effects.

Figure 3

(Color online) Spectra of the $a$-axis dielectric permittivity of ${\mathrm{GdMnO}}_3$ in the frequency range between the electromagnon at $25{\mathrm{cm}}^{-1}$ and the phonon at $119{\mathrm{cm}}^{-1}$ at $0\mathrm{T}$ (incommensurate state) and $2\mathrm{T}$ (canted state). Upper panel: real part of the dielectric permittivity. Lower panel: imaginary part. Triangles represent the results from the terahertz transmittance. Circles are spectra obtained via Kramers-Kronig analysis of the reflectance. Solid line corresponds to a sum of Lorentzians as described in the text.

Figure 4

(Color online) Schematic presentation of magnetic structures, showing different magneto-electric behavior. (a) Homogeneously modulated structure: no static electric polarization $(\mathrm{\Delta }{P}_{\mathrm{ME}}=0)$, no ME contribution to the dielectric permittivity $(\mathrm{\Delta }\epsilon =0)$. (b) Inhomogeneously modulated collinear structure: no electric polarization, but nonzero contribution to the dielectric permittivity. (c) Cycloidally modulated structure: finite electric polarization and ME contribution to the dielectric permittivity.