Spectroscopic signatures of domain walls in hexagonal ${\mathrm{ErMnO}}_3$

We measured the spectroscopic response of stripe- and vortex-containing ${\mathrm{ErMnO}}_3$ in order to uncover the electronic properties of the domain walls. We quantify Born effective charge and polarization differences using the lattice behavior, analyze the local rare earth environment from the $f$-manifold excitations, and reveal how shifts in the charge transfer excitations impact the band gap. The increased Born charge, polarization, and band gap in the vortex-containing material are brought together with a discussion of hybridization and wall density effects. The domain wall optical constants are strongly frequency dependent.

Figure 1

(a, b) Atomic force microscope images of chemically etched ${\mathrm{ErMnO}}_3$ with stripe and vortex domain wall patterns [7]. (c, d) Real space microreflectance mapping of stripe- and vortex-containing ${\mathrm{ErMnO}}_3$ at 465 ${\mathrm{cm}}^{-1}$. The strong red and blue streaks are due to synchrotron injection cycles.

Figure 2

(a) Closeup view of the reflectance spectra of stripe- and vortex-containing ${\mathrm{ErMnO}}_3$ at 300 K. (b) Reflectance difference spectrum: $\Delta R=R_{\text{vortex}}-R_{\text{stripe}}$. (c) 300 K optical conductivity of stripe and vortex samples. Inset: Crystal structure of ${\mathrm{ErMnO}}_3$ [27]. The unit cell is hexagonal ($a=6.1121$ Å and $c/a=1.8684$ at 300 K), with 6 formula units and a $P{6}_{3}cm$ space group. ${\mathrm{O}}_A$ and ${\mathrm{O}}_B$ refer to the apical and basal plane oxygens of the triangular bipyramidal cages, respectively. (d) Optical conductivity difference spectrum: $\Delta {\sigma }_1={\sigma }_{1,\text{vortex}}-{\sigma }_{1,\text{stripe}}$. (e) Effective number of electrons involved in the excitations, $N_{\text{eff}}$, as a function of frequency.

Figure 3

(a) $ab$-plane absorption spectrum of stripe and vortex ${\mathrm{ErMnO}}_3$. Inset: Closeup of the ${}^4{I}_{15/2}\to {}^4{I}_{13/2}$ cluster, showing a 1:1 correspondence of peak positions but clear intensity differences. (b) Absorption difference spectrum, $\Delta \alpha ={\alpha }_{\text{vortex}}-{\alpha }_{\text{stripe}}={\alpha }_{\text{wall}}$, in the range of the $f$-manifold transitions and leading edge of the Mn on-site excitation.

Figure 4

(a) Optical conductivity of stripe and vortex ${\mathrm{ErMnO}}_3$ in the $ab$ plane at 300 K. Inset: A closeup view of 1.6 eV Mn $d\to d$ on-site excitation of stripe and vortex ${\mathrm{ErMnO}}_3$. (b) Optical conductivity difference spectrum: $\Delta {\sigma }_1={\sigma }_{1,\text{vortex}}-{\sigma }_{1,\text{stripe}}={\sigma }_{1,\text{wall}}$. (c) Effective number of electrons involved in the excitations, $N_{\text{eff}}$, as a function of energy.