Mott-Hubbard versus charge-transfer behavior in $\mathrm{La}\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_4$ studied via optical conductivity

Using spectroscopic ellipsometry, we study the optical conductivity $\sigma \left(\omega \right)$ of insulating $\mathrm{La}\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_4$ in the energy range of $0.75–5.8\mathrm{eV}$ from $15\text{to}330\mathrm{K}$. The layered structure gives rise to a pronounced anisotropy. A multipeak structure is observed in ${\sigma }_1^a\left(\omega \right)$ ($\sim 2$, 3.5, 4.5, 4.9, and $5.5\mathrm{eV}$), while only one peak is present at $5.6\mathrm{eV}$ in ${\sigma }_1^c\left(\omega \right)$. We employ a local multiplet calculation and obtain (i) an excellent description of the optical data, (ii) a detailed peak assignment in terms of the multiplet splitting of Mott-Hubbard and charge-transfer absorption bands, and (iii) effective parameters of the electronic structure, e.g., the on-site Coulomb repulsion $U_{\mathrm{eff}}=2.2\mathrm{eV}$, the in-plane charge-transfer energy ${\Delta }_a=4.5\mathrm{eV}$, and the crystal-field parameters for the $d^4$ configuration ($10Dq=1.2\mathrm{eV}$, ${\Delta }_{eg}=1.4\mathrm{eV}$, and ${\Delta }_{t2g}=0.2\mathrm{eV}$). The spectral weight of the lowest absorption feature (at $1–2\mathrm{eV}$) changes by a factor of 2 as a function of temperature, which can be attributed to the change of the nearest-neighbor spin-spin correlation function across the Néel temperature $T_N=133\mathrm{K}$. Interpreting $\mathrm{La}\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_4$ effectively as a Mott-Hubbard insulator naturally explains this strong temperature dependence, the relative weight of the different absorption peaks, and the pronounced anisotropy. By means of transmittance measurements, we determine the onset of the optical gap ${\Delta }_{\mathrm{opt}}^a=0.4–0.45\mathrm{eV}$ at $15\mathrm{K}$ and $0.1–0.2\mathrm{eV}$ at $300\mathrm{K}$. Our data show that the crystal-field splitting is too large to explain the anomalous temperature dependence of the $c$-axis lattice parameter by thermal occupation of excited crystal-field levels. Alternatively, we propose that a thermal population of the upper Hubbard band gives rise to the shrinkage of the $c$-axis lattice parameter.

Figure 1

Sketch of the density of states [photoemission (PES) and inverse photoemission (IPES) spectra] for a single, half-filled $3d$ orbital and degenerate, full $\mathrm{O}2p$ orbitals. The on-site Coulomb repulsion $U$ increases from top to bottom, whereas the charge-transfer energy $\Delta$ is assumed to be constant. $E_F$ denotes the Fermi level. Top: Mott-Hubbard insulator for $U⪡\Delta$. Bottom: charge-transfer insulator for $U⪢\Delta$. In the absence of hybridization, the bands follow the straight lines with increasing $U$. With hybridization, one has to distinguish bonding (B), antibonding (AB, both black), and nonbonding bands (NB, gray).

Figure 2

(Color online) [(a) and (b)] Dielectric constant and optical conductivity of $\mathrm{La}\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_4$ for the $a$ and $c$ directions between 0.75 and $5.80\mathrm{eV}$ for different temperatures. (c) Change of the optical conductivity: ${\sigma }_1\left(330\mathrm{K}\right)-{\sigma }_1\left(230\mathrm{K}\right)$, ${\sigma }_1\left(230\mathrm{K}\right)-{\sigma }_1\left(120\mathrm{K}\right)$, and ${\sigma }_1\left(120\mathrm{K}\right)-{\sigma }_1\left(15\mathrm{K}\right)$.

Figure 3

(Color online) Top: effective carrier concentration $N_{\mathrm{eff}}({\omega }_1,{\omega }_2)$ for the $a$ and $c$ directions with ${\omega }_1=0.75\mathrm{eV}$ and ${\omega }_2=5.5\mathrm{eV}$. Middle and bottom: $N_{\mathrm{eff}}$ for the $a$ direction for different energy ranges.

Figure 4

(Color online) (a) Lorentzian fit of ${ϵ}_1^a$ (top panel) and ${ϵ}_2^a$ (middle and bottom) for $T=15$ and $330\mathrm{K}$. (b) $N_{\mathrm{eff}}$ of peaks (1)–(3) as obtained from the Drude-Lorentz fit. The horizontal lines indicate theoretical estimates of $N_{\mathrm{eff}}$ for $T⪡T_N$ and $T⪢T_N$ as derived from the kinetic energy for an effective Mn-Mn hopping amplitude $t=0.55–0.65\mathrm{eV}$ (see Sec. 5C).

Figure 5

(Color online) (a) Transmittance $T$ (top panel) of a thin $\mathrm{La}\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_4$ sample $(d\sim 70\mu \mathrm{m})$ and $-\ln \left(T\right)\propto \alpha$ for 5 and $150\mathrm{K}$. (b) Evolution of the onset of the optical gap as determined from $-\ln \left(T\right)=\mathrm{const}$.

Figure 6

(Color online) Comparison between $ϵ$ as obtained from the multiplet calculation and the measured data at $15\mathrm{K}$.

Figure 7

(Color online) Energy level diagrams from the multiplet calculation for the $d^3$, $d^4$, and $d^5$ configurations as a function of $10Dq$ in $O_h$ and as a function of $x$ in $D_{4h}$ for a fixed value of $10Dq$. The control parameter $x$ denotes the strength of ${\Delta }_{eg}$ and ${\Delta }_{t2g}$; $x=1$ represents the full strength used for the spectra shown in Fig. 6. The low-lying multiplets are labeled by their irreducible representations in $D_{4h}$; those being not relevant for the optical transitions are shown in brackets. The electronic fit parameters can be found in Ref. 33 and are summarized in Table (for more details, see the Appendix and Ref. 33).

Figure 8

(Color online) Sketch of the lowest Mott-Hubbard excitation in $\mathrm{La}\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_4$ in the strong crystal-field limit, i.e., configuration mixing is neglected. In the final state, the $d^5$ site is in a high-spin $S=5∕2$ configuration. This excitation is assigned to the feature observed around $2\mathrm{eV}$ in ${\sigma }_1^a\left(\omega \right)$. The spectral weight is largest for parallel alignment of neighboring spins.

Figure 9

(Color online) Sketch of Mott-Hubbard excitations to final states with $S\left(d^5\right)=3∕2$. These excitations are degenerate in the strong crystal-field limit and are assigned to the peak at $3.5\mathrm{eV}$ in ${\sigma }_1^a\left(\omega \right)$. The spectral weight is largest for an antiferromagnetic arrangement of neighboring spins.

Figure 10

Estimate of the thermally activated population of the UHB using ${\Delta }_{\mathrm{act}}=(1∕2){\Delta }_{\mathrm{opt}}^a$ and the temperature dependence of ${\Delta }_{\mathrm{opt}}^a$ depicted in Fig. 5b.