Nonreciprocal linear dichroism observed in electron spin resonance spectra of the magnetoelectric multiferroic $\mathrm{Pb}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$

It is known that magnetic excitations in magnetoelectric multiferroics can be induced by the oscillation of electric polarization, called electromagnons, which often cause nonreciprocal optical phenomena. Energy diagrams of the excitations in the magnetoelectric multiferroic $\mathrm{Pb}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$ were obtained in wide ranges of magnetic fields up to 50 T and frequencies below 2 THz. Some of the observed resonance modes were reproduced qualitatively by a numerical analysis based on the generalized spin-wave theory. Moreover, we found that electron spin resonance (ESR) signals on some of the modes can be modulated by applying an electric field. This result implies the presence of nonreciprocal linear dichroism on the ESR signals in $\mathrm{Pb}\left(\mathrm{TiO}\right){\mathrm{Cu}}_4{\left({\mathrm{PO}}_4\right)}_4$.

Figure 1

Schematic of (a), (b) crystal and magnetic structures of ${\mathrm{Cu}}_4{\mathrm{O}}_{12}$ square cupolas and (c) crystal structure of PbTCPO. Green arrows represent ${\mathrm{Cu}}^{2+}$ spins in (a) Q1 and (b) Q2 domains. Solid lines in (c) represent a unit cell.

Figure 2

Pulsed high-field ESR absorption spectra of PbTCPO at 1.4 K for (a) $B\parallel \left[100\right]$ and (b) $B\parallel \left[001\right]$. Vertical dashed lines indicate the metamagnetic transition fields. Arrows denote the ESR signals of DPPH (2,2-diphenyl-1-picrylhydrazyl, ESR standard marker with $g=2.0036$) for the field calibration. Crosses at low fields denote artifact signals originating from the cryostat. Inverse triangles show the resonance fields of the main ESR signals of PbTCPO.

Figure 3

Frequency-magnetic field plots of the ESR resonance fields of PbTCPO for magnetic fields parallel to the (a) [100] and (b) [001] directions. Open circles are obtained from the static-field measurements at 1.6 K, and solid circles are obtained from the pulsed-field measurements at 1.4 K. The vertical dashed lines indicate the transition fields observed in the magnetization measurements. The gray shaded area represents an ESR-invisible region caused by phonon absorption. The solid lines are guides for the eye.

Figure 4

ESR absorption spectra $-[\mathrm{Im}{\chi }^{xx}\left(\omega \right)+\mathrm{Im}{\chi }^{yy}\left(\omega \right)]$ computed by the generalized spin-wave theory based on the cluster mean-field approach using the effective spin Hamiltonian [21] for (a) $B\parallel \left[100\right]$ and (b) $B\parallel \left[001\right]$. The labels (1), (2), $...$ in each panel indicate the modes corresponding to the experimentally observed ones (Fig. 3).

Figure 5

(a) ESR absorption spectra in ac electric fields at 4.1 K for $B\parallel E\parallel \left[100\right]$. $I_0$ is transmitted light intensity at zero magnetic field. The spectra are offset by 0.025 for clarity. (b), (c) Applied electric fields and enlarged views of the ESR absorption signal for $E=\pm 429$ kV/m. The inset of (b) shows a photograph of the sample used in this measurement and in the experimental setup. The inset of (c) shows the schematic diagram of the $P\text{−}E$ hysteresis curve.