Low-energy Mott-Hubbard excitations in ${\text{LaMnO}}_3$ probed by optical ellipsometry

We present a comprehensive ellipsometric study of an untwinned, nearly stoichiometric ${\text{LaMnO}}_3$ crystal in the spectral range 1.2–6.0 eV at temperatures $20\le T\le 300\text{K}$. The complex dielectric response along $b$ and $c$ axes of the $Pbnm$ orthorhombic unit cell, ${\tilde{\epsilon }}^b\left(\nu \right)$ and ${\tilde{\epsilon }}^c\left(\nu \right)$, is highly anisotropic over the spectral range covered in the experiment. The difference between ${\tilde{\epsilon }}^b\left(\nu \right)$ and ${\tilde{\epsilon }}^c\left(\nu \right)$ increases with decreasing temperature, and the gradual evolution observed in the paramagnetic state is strongly enhanced by the onset of $A$-type antiferromagnetic long-range order at $T_N=139.6\text{K}$. In this study we focus on the analysis of excitations observed at high energy $\left(\sim 4–5\text{eV}\right)$ and show that the observed temperature changes of their spectral weight are opposite to those found for the lowest-energy gap excitation at $\sim 2\text{eV}$. We used a classical dispersion analysis to quantitatively determine the temperature-dependent optical spectral-weights shifts between low- and high-energy optical bands. Based on the observation of a pronounced spectral-weight transfer between both features upon magnetic ordering, they are assigned to high-spin and low-spin intersite $d^4{d}^4\rightleftharpoons d^3{d}^5$ transitions by Mn electrons. The anisotropy of the lowest-energy optical band and the spectral-weight shifts induced by antiferromagnetic spin correlations are quantitatively described by an effective spin-orbital superexchange model. An analysis of the multiplet structure of the intersite transitions by $\text{Mn}{e}_g$ electrons allowed us to estimate the effective intra-atomic Coulomb interaction, the Hund exchange coupling, and the Jahn-Teller splitting energy between $e_g$ orbitals in ${\text{LaMnO}}_3$, as well as to extract experimental information concerning the type of orbital order in ${\text{LaMnO}}_3$. This study identifies the lowest-energy optical transition at $\sim 2\text{eV}$ as an intersite $d\text{−}d$ transition whose energy is substantially reduced compared to that obtained from the bare intra-atomic Coulomb interaction.

Figure 1

(Color) (a) Pseudocubic perovskite structure of ${\text{LaMnO}}_3$ (space group $Pm\overline{3}m$) above $T_{OO}\simeq 780\text{K}$. Room-temperature-polarized optical images showing a part of the ${\text{LaMnO}}_3$ crystal (of $200\mu \text{m}$ length) (c) initially heavily twinned and (d) after detwinning; (b) Laue diagram demonstrating 95% detwinning at a particular surface location.

Figure 2

(Color online) Temperature variation of (a) real ${\epsilon }_1\left(\nu \right)$ and (b) imaginary ${\epsilon }_2\left(\nu \right)$ parts of the complex dielectric function spectra of the untwinned ${\text{LaMnO}}_3$ crystal in $b$-axis polarization. The representative spectra at the temperatures around $T_N\simeq 140\text{K}$ are indicated. The temperature evolution of the spectra (here and in the following figures) is shown in successive temperature intervals of 10 K between 20 and 200 K and of 25 K between 200 and 300 K.

Figure 3

(Color online) Temperature variation of (a) real ${\epsilon }_1\left(\nu \right)$ and (b) imaginary ${\epsilon }_2\left(\nu \right)$ parts of the complex dielectric function spectra of the untwinned ${\text{LaMnO}}_3$ crystal in $c$-axis polarization.

Figure 4

(Color online) Temperature variation of (a) real $\Delta {\epsilon }_1\left(20\text{K},T\right)={\epsilon }_1\left(\nu ,20\text{K}\right)-{\epsilon }_1\left(\nu ,T\right)$ and (b) imaginary $\Delta {\epsilon }_2\left(20\text{K},T\right)={\epsilon }_2\left(\nu ,20\text{K}\right)-{\epsilon }_2\left(\nu ,T\right)$ parts of the difference between the low-temperature complex dielectric function spectra measured at 20 K and the corresponding $T$-dependent spectra in the $b$-axis polarization.

Figure 5

(Color online) Temperature variation of the difference of (a) real part $\Delta {\epsilon }_1\left(20\text{K},T\right)={\epsilon }_1\left(\nu ,20\text{K}\right)-{\epsilon }_1\left(\nu ,T\right)$ and (b) imaginary part $\Delta {\epsilon }_2\left(20\text{K},T\right)={\epsilon }_2\left(\nu ,20\text{K}\right)-{\epsilon }_2\left(\nu ,T\right)$ of the dielectric response in the $c$-axis polarization.

Figure 6

(Color online) Spectral and temperature dependencies of the SW shifts $\Delta N_{\text{eff}}\left(\Delta T\right)=N_{\text{eff}}\left(20\text{K}\right)-N_{\text{eff}}\left(T\right)$ in the (a) $b$ axis $\Delta N_{\text{eff}}^{\left(b\right)}\left(\Delta T\right)=\frac{2m}{\pi e^{2}N}{\int }_{1.2\text{eV}}^{\nu }\Delta {\sigma }_1\left({\nu }^{\prime },\Delta T\right)d{\nu }^{\prime }$ and (b) $c$ axis $\Delta N_{\text{eff}}^{\left(c\right)}\left(\Delta T\right)=\frac{2m}{\pi e^{2}N}{\int }_{1.7\text{eV}}^{\nu }\Delta {\sigma }_1\left({\nu }^{\prime },\Delta T\right)d{\nu }^{\prime }$.

Figure 7

(Color online) Partial SW gain or loss of low- and high-energy optical bands in (a) $b$ axis $\Delta N_{\text{eff},\text{HS}}^{\left(b\right)}=\frac{2m}{\pi e^{2}N}{\int }_{1.2\text{eV}}^{2.7\text{eV}}\Delta {\sigma }_1\left({\nu }^{\prime },\Delta T\right)d{\nu }^{\prime }$ and $\Delta N_{\text{eff},\text{LS}}^{\left(b\right)}=-\frac{2m}{\pi e^{2}N}{\int }_{2.7\text{eV}}^{5.6\text{eV}}\Delta {\sigma }_1\left({\nu }^{\prime },\Delta T\right)d{\nu }^{\prime }$ and (b) $c$ axis $\Delta N_{\text{eff},\text{HS}}^{\left(c\right)}=-\frac{2m}{\pi e^{2}N}{\int }_{1.7\text{eV}}^{3.8\text{eV}}\Delta {\sigma }_1\left({\nu }^{\prime },\Delta T\right)d{\nu }^{\prime }$ and $\Delta N_{\text{eff},\text{LS}}^{\left(c\right)}=\frac{2m}{\pi e^{2}N}{\int }_{3.8\text{eV}}^{5.0\text{eV}}\Delta {\sigma }_1\left({\nu }^{\prime },\Delta T\right)d{\nu }^{\prime }$.

Figure 8

(Color online) Real and imaginary parts of $b$-axis complex dielectric response ${\tilde{\epsilon }}^b\left(\nu \right)$ at (a) 20 K and (b) 300 K, represented by the total contribution of the separate Lorenzian bands determined by the dispersion analysis, as described in the text.

Figure 9

(Color online) Real and imaginary parts of $c$-axis complex dielectric response ${\tilde{\epsilon }}^c\left(\nu \right)$ at (a) 20 K and (b) 300 K, represented by the total contribution of the separate Lorentzian bands determined by the dispersion analysis.

Figure 10

(Color online) Temperature dependencies of the peak energies ${\nu }_j$ in the spectral ranges of low- and high-energy optical bands, as determined by the dispersion analysis, in (a) and (b) $b$-axis and (c) and (d) $c$-axis polarization. The filled symbols show the results of the fit from 20 to 300 K, the open symbols show the results of the fit from 300 to 20 K.

Figure 11

(Color online) Temperature and polarization dependencies of the total SW $N_{\text{eff}}$ of the low-energy optical band, represented by a summary contribution from the three Lorentzian subbands (the temperature dependencies of the subbands are detailed in Ref. 19).

Figure 12

(Color online) Comparison between the experimental (a) partial and (b) total (filled symbols) and the calculated (total) (empty symbols) SWs for HS and LS optical bands in the $b$-axis polarization.

Figure 13

(Color online) Comparison between the experimental (a) partial and (b) total (filled symbols) and the calculated (total) (empty symbols) SWs for HS and LS optical bands in the $c$-axis polarization.

Figure 14

(Color online) Magnetic exchange constants, $J_{ab}$ and $J_c$, as obtained for the varying orbital angle $\theta$ from Eqs. (12, 13). Parameters: $U=3.1\text{eV}$, $J_H=0.6\text{eV}$, ${\Delta }_{\text{JT}}=0.7\text{eV}$, $t=0.41\text{eV}$, and $J_t=1.67\text{meV}$. Dashed lines indicate the experimental values of $J_{ab}$ and $J_c$ determined by neutron scattering (Ref. 39) in ${\text{LaMnO}}_3$.