Electronic structure of ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$

The electronic structure of ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ has been investigated using a combination of first-principles calculations, x-ray photoelectron spectroscopy (XPS), x-ray absorption spectroscopy (XAS), electron-energy loss spectroscopy (EELS), and optical absorption. The full range of compositions, $x=0,1/2,1$, and a variety of magnetic orders have been covered. Jahn-Teller as well as Zener polaron orders are considered. The free parameters of the local hybrid density functionals used in this study have been determined by comparison with measured XPS spectra. A model Hamiltonian, valid for the entire doping range, has been extracted. A simple local-orbital picture of the electronic structure for the interpretation of experimental spectra is provided. The comparison of theoretical calculations and different experimental spectra provide a detailed and consistent picture of the electronic structure. The large variations of measured optical absorption spectra are traced back to the co-existence of magnetic orders (respectively, to the occupation of local orbitals). A consistent treatment of the Coulomb interaction indicates a partial cancellation of Coulomb parameters and supports the dominance of the electron-phonon coupling.

Figure 1

DoS of ${\mathrm{CaMnO}}_3$ in the stable G-type magnetic order. The top figure shows the total DoS (black envelope) with the projected DoS for O-$p$ (red), $\mathrm{Mn}-t_{2g}$ (green), $\mathrm{Mn}-e_g$ (yellow), and Ca-$d$ (blue). Projected DoS are stacked on top of each other. The two spin densities are shown with opposite sign. The projected DoS is considered only for the Mn ions with one majority-spin direction. The graph in the middle shows the COOP between a $\mathrm{Mn}-t_{2g}$ orbital and an $\pi$-bonded O-$p$ state in green and the COOP between a $\mathrm{Mn}-e_g$ orbital and an $\sigma$-bonded $p$ state in yellow for the majority-spin direction. Unlike the DoS, the COOPs have positive and negative values, so that two spin direction cannot be combined into one graph. The two COOPs for $t_{2g}$ (green) and $e_g$ (yellow) states are stacked on top of each other. The bottom graph shows the same information for the minority-spin direction. The energy zero is aligned with the valence-band top. Empty states are drawn with a lighter color than filled states.

Figure 2

Spin-resolved DoS of ${\mathrm{PrMnO}}_3$ in the stable A-type magnetic order. The color coding in the upper graph is described in the text and in Fig. 1. The Pr-$f$ states are drawn in magenta and the Pr-$d$ states in orange. The graph at the bottom shows the DoS for the lower (orange) and upper (yellow) $e_g$ orbitals, which are split by the Jahn-Teller effect.

Figure 3

DoS for ${\mathrm{CaMnO}}_3$ (top) and ${\mathrm{PrMnO}}_3$ (bottom) for hybrid mixing factors from 0 to 0.25 in steps of 0.05 to bottom. The hybrid mixing factors are equal on all atoms. The energy zero has been set to the top of the O-$p$ band for $a_x=0.1$.

Figure 4

Mn-XPS (green), Pr-XPS (magenta), XANES (blue), and ELNES (orange), together with calculated ELNES spectra (shaded gray) and spin-resolved DoS (below). The results are shown for ${\mathrm{CaMnO}}_3$ (top) ($x=0.8$ for XANES and $x=0.95$ for ELNES), ${\mathrm{Pr}}_{1/2}{\mathrm{Ca}}_{1/2}{\mathrm{MnO}}_3$ (middle), and ${\mathrm{PrMnO}}_3$ (bottom). Projected DoS are color coded for $\mathrm{Mn}-e_g$ (yellow), $\mathrm{Mn}-t_{2g}$ (green), Pr-$f$ (magenta), Ca-$d$ (blue), Pr-$d$ (orange), and O-$p$ (red). The DoS of the two spin directions are shown with opposite sign. Only the majority-spin direction is shown for Mn and Pr.

Figure 5

Hopping parameters $t_{\text{hop}}$ extracted from the generalized DoS for ${\mathrm{PrMnO}}_3$ (red), ${\mathrm{Pr}}_{1/2}{\mathrm{Ca}}_{1/2}{\mathrm{MnO}}_3$ (black), and ${\mathrm{CaMnO}}_3$ (blue) as function of the mean orbital energies ${\epsilon }_1$ and ${\epsilon }_2$ in a bond. The straight lines are linear interpolations.

Figure 6

Schematic diagram of the energy levels in the for ${\mathrm{CaMnO}}_3$ (left) and ${\mathrm{PrMnO}}_3$ (right). The on-site model with parameters from Table 3 is used. The effect resulting from the individual terms of the model Hamiltonian on the energy levels is shown: Hund's-rule energy $E_{\text{e-S}}$ (e-S), Jahn-Teller $E_{\text{e-ph}}$ (e-ph), and the Coulomb energy $E_U$ separated into $E_H+E_{\text{SIC}}$ and $E_{\text{OR}}$ (e-e). The effect of the kinetic energy ($E_{\text{kin}}$) has been estimated using a second-order expression for the intersite hopping.

Figure 7

Measured and calculated absorption coefficients of ${\mathrm{CaMnO}}_3$. Our room-temperature measured data for $x=0.95$ are shown as a gray-shaded area. Shown are also the results by Jung et al. [80] (solid symbols) and Asanuma et al. [81] (open symbols). The calculated spectra are not to scale. They are shown for G-type (orange), C-type (red), A-type (blue), and B-type (green) magnetic order. The inset illustrates the determination of the optical gap of 1.45 eV via linear extrapolation of the low energy tail of the spectrum.

Figure 8

Diagram of O-$p$ state (bottom) in the valence band and the $\mathrm{Mn}-e_g$ state (top) in the conduction band responsible for the charge-transfer transition in ${\mathrm{CaMnO}}_3$. The dashed line indicates the reflection plane defining the parity for the dipole selection rule. Each ${\mathrm{MnO}}_6$ octahedron has three such orbitals, each active for another polarization direction.

Figure 9

Measured room-temperature absorption spectra by Loshkareva et al. [79] for ${\mathrm{CaMnO}}_3$ (black) and calculated spectra for G-type ${\mathrm{CaMnO}}_3$. The calculated data (orange, gray) have been scaled independently to allow comparison of the spectral shapes.

Figure 10

Absorption coefficients of ${\mathrm{Pr}}_{1/2}{\mathrm{Ca}}_{1/2}{\mathrm{MnO}}_3$ (top) and ${\mathrm{PrMnO}}_3$ (bottom). Measured data are indicated by the black line and the shaded area. Calculated spectra for $d$ to $d$ transitions have been performed for the G-type (orange), C-type (red), A-type (blue), B-type (green), and CE-type (magenta) magnetic orders. Measurement for ${\mathrm{Pr}}_{1/2}{\mathrm{Ca}}_{1/2}{\mathrm{MnO}}_3$ have been performed at 300 K with (short-dashed line) and without (long-dashed line) reflection correction and at 80 K without (full line and shaded area) reflection correction. Spectra for ${\mathrm{PrMnO}}_3$ have been done at 300 K with reflection correction. Insets show the extrapolation used for the optical gap determination. For details, see text.

Figure 11

Orbitals involved in the optical transition in ${\mathrm{PrMnO}}_3$ from the filled (lower graph) to the empty Jahn-Teller split band (upper graph). Only the Mn-centered $e_g$ orbitals are shown. Orbitals are shown with the calculated orbital-mixing angle $\gamma ={55}^{\circ }$ of the occupied orbital. The octahedral tilt is ignored. The octahedron on the central site is expanded along the axis, while the octahedra on the terminal sites are expanded in the perpendicular direction.

Figure 12

Calculated absorption spectra (center) due to charge transfer excitations for ${\mathrm{CaMnO}}_3$ (red, gray) and ${\mathrm{PrMnO}}_3$ (black). Results are shown for different magnetic orders. The apparent right shift of the absorption edge from 2 to 4 eV is attributed the occupation of the $\mathrm{Mn}-e_g$ states, which disappear from the spectrum in ${\mathrm{PrMnO}}_3$, while they are empty and thus visible in the spectrum of ${\mathrm{CaMnO}}_3$. The top figure shows the integrated absorption spectra, which demonstrates the loss of absorption intensity due to occupation of $\mathrm{Mn}-e_g$ states. The bottom figure shows the experimental results for ${\mathrm{CaMnO}}_3$ (red, gray) and ${\mathrm{PrMnO}}_3$ (black), which demonstrate the lowering of the absorption intensity due to doping. The data by Asanuma [81] for oxidized (circles) and reduced (diamonds) ${\mathrm{CaMnO}}_3$ exhibit a similar lowering upon reduction, which partially occupies the $\mathrm{Mn}-e_g$ shell as in the ${\mathrm{Pr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ series.

Figure 13

Schematic drawing of the Zener-polaron arrangement in the E-type (left) and the CE-type (right) magnetic order of ${\mathrm{Pr}}_{1/2}{\mathrm{Ca}}_{1/2}{\mathrm{MnO}}_3$. Black and white spheres indicate the two spin orientations. Shown is the $ab$ plane. Different planes are antiferromagnetically coupled. The dimers are shown in the CE structure as conceptual units, while the symmetry breaking in the real structure is small.

Figure 14

Symmetry-adapted $e_g$ orbitals in the CE-type magnetic arrangement given in Eqs. (44) and (46) (left) and (right) the orbitals for a Zener polaron. For both, the optical transition takes the electron from the corresponding orbital $|w_1\rangle$ to $|w_2\rangle$.

Figure 15

DoS of ${\mathrm{Pr}}_{1/2}{\mathrm{Ca}}_{1/2}{\mathrm{MnO}}_3$ in the stable CE-type antiferromagnetic order (top). The projection on symmetry-adapted orbitals [see Fig. 14 and Eqs. (44) and (46)] is shown in the lower graph. The orbital $|w_1\rangle$ forming the occupied $e_g$ band is shown in yellow. The optically active excited orbital $|w_2\rangle$ is shown in blue. The fully antibonding orbital $|w_3\rangle$, shown in red, is optically inactive. The green area refers to the orbital $|w_4\rangle$ with $\delta$ symmetry on the central atom.