Electronic structures of hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ ($R=\mathrm{Gd}$, Tb, Dy, and Ho) thin films: Optical spectroscopy and first-principles calculations

We investigated the electronic structure of multiferroic hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ ($R=\mathrm{Gd}$, Tb, Dy, and Ho) thin films using both optical spectroscopy and first-principles calculations. One of the difficulties in explaining the electronic structures of hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ is that they exist in nature with limited rare earth ions (i.e., $R=\mathrm{Sc}$, Y, and Ho-Lu), so a systematic study in terms of the different $R$ ions has been lacking. Recently, our group succeeded in fabricating hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ ($R=\mathrm{Gd}$, Tb, and Dy) using the epitaxial stabilization technique [Adv. Mater. (Weinheim Ger.) 18, 3125 (2006)]. Using artificially stabilized hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$, we extended the optical spectroscopic studies on the hexagonal multiferroic manganite system. We observed two optical transitions located near 1.7 and $2.3\mathrm{eV}$, in addition to the predominant absorption above $5\mathrm{eV}$. With the help of first-principles calculations, we attributed the low-lying optical absorption peaks to interband transitions from the oxygen states hybridized strongly with different Mn orbital symmetries to the $\mathrm{Mn}3d_{3z^2-r^2}$ state. As the ionic radius of the rare earth ion increased, we observed a systematic increase of the lowest peak position, which became more evident when compared with previously reported results. We explained this systematic change in terms of a flattening of the $\mathrm{Mn}{\mathrm{O}}_5$ triangular bipyramid.

Figure 1

(Color online) Optical spectra of YSZ(111) substrate (dashed lines) and hexagonal $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$ thin film (solid lines) artificially fabricated on YSZ(111) substrate using the epitaxial stabilization technique. Reflectance and transmittance spectra are shown as the thin red and thick blue lines, respectively.

Figure 2

Optical conductivity spectra of hexagonal $\mathrm{Ho}\mathrm{Mn}{\mathrm{O}}_3$, $\mathrm{Dy}\mathrm{Mn}{\mathrm{O}}_3$, $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$, and $\mathrm{Gd}\mathrm{Mn}{\mathrm{O}}_3$ thin films. For the sake of comparison, the reported spectrum of bulk $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ (Ref. 22) is also shown. For clarity, the spectra have been plotted with offsets of $1250{\Omega }^{-1}{\mathrm{cm}}^{-1}$ vertically between each curve, and the base line for each curve is shown by the horizontal dashed line. The arrows in the $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_3$ spectrum indicate the three peak positions where optical absorption occurs. The vertical dotted line indicates the first optical transition peak position of $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$.

Figure 3

(Color online) Orbital-resolved densities of states of $\mathrm{Mn}3d$ orbitals and the in-plane $\mathrm{O}2p$ orbital for $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$.

Figure 4

(a) Peak positions of the optical transition peak at $\sim 1.7\mathrm{eV}$ for numerous hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$. Empty squares denote the peak positions of the bulk hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ [$R=\mathrm{Lu}$ (Ref. 10), Er, and Y (Ref. 22)], whereas filled squares denote those of the thin film hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ ($R=\mathrm{Dy}$, Tb, and Gd). Filled circles denote the peak positions of the half-substituted hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ thin films [$R=\left({\mathrm{Dy}}_{0.5}{\mathrm{Ho}}_{0.5}\right)$ and $\left({\mathrm{Tb}}_{0.5}{\mathrm{Ho}}_{0.5}\right)$]. (b) The lattice constant ratio ($a∕c$, filled symbols) and the in-plane lattice constant ($a$, empty symbols) of bulk hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ [circles, $R=\mathrm{Lu}$, Yb, Tm, Er, Y, and Ho (Ref. 42)], and film hexagonal $R\mathrm{Mn}{\mathrm{O}}_3$ (squares, $R=\mathrm{Dy}$, Tb, and Gd). The thick gray lines in both (a) and (b) are included simply as visual aids.

Figure 5

(Color online) (a) Schematic representation of the crystal field splitting changes due to flattening of the $\mathrm{Mn}{\mathrm{O}}_5$ triangular bipyramid. The flattening occurs due to the increase of the rare-earth ionic radius with the fixed $c$-axis lattice constant. As the flattening occurs, due to the orbital symmetries, the $d_{3z^2-r^2}$ orbital will shift to higher energy, whereas the $d_{xy}$ and $d_{x^2-y^2}$ orbitals stay the same. (b) First-principles calculation results for the Mn orbital DOS of $\mathrm{Y}\mathrm{Mn}{\mathrm{O}}_3$ without and with flattening of the triangular bipyramid (results are shown only for up spins). The calculations took into account the hybridization between the in-plane $\mathrm{O}2p$ and associated $\mathrm{Mn}3d$ orbitals. When the spacing between the Mn and the apical oxygen ions is reduced by 2%, the DOS for the unoccupied Mn $d_{3z^2-r^2}$ orbital state shows an upward shift of $0.24\mathrm{eV}$, whereas the changes for other orbital states are relatively small.