One-Dimensional Orbital Excitations in Vanadium Oxides

The $d$ electron orbital is a hidden but important degree of freedom controlling novel properties of transition-metal oxides. A one-dimensional orbital system is especially intriguing due to its enhanced quantum fluctuation. We present a combined experimental and theoretical study on the Raman scattering spectra in perovskite oxides ${\mathrm{N}\mathrm{d}\mathrm{V}\mathrm{O}}_3$ and ${\mathrm{L}\mathrm{a}\mathrm{V}\mathrm{O}}_3$ to prove that the quasi-one-dimensional orbital chain described by fermionic pseudospinons bears orbital excitations exchanging occupied orbital states on the neighboring sites, termed a two-orbiton in analogy with two-magnon.

Figure 1

(a) Structure of $C$-type SO and $G$-type OO in $R{\mathrm{V}\mathrm{O}}_3$. Arrows and lobes indicate spins, and occupied $d_{yz}$ or $d_{zx}$ orbitals on ${\mathrm{V}}^{3+}$, respectively. (b) Spin-orbital phase diagram of $R{\mathrm{V}\mathrm{O}}_3$. Closed and open circles indicate transition temperatures, $T_{\mathrm{O}\mathrm{O}}$ and $T_{\mathrm{S}\mathrm{O}}$, respectively. (c) $T$ dependence of the integrated Raman intensity of the peak around 87 meV in $y(xx)\overline{y}$ polarization (open circles) and that around 62 meV in $y(zz)\overline{y}$ (closed circles) for ${\mathrm{N}\mathrm{d}\mathrm{V}\mathrm{O}}_3$. Closed triangles indicate the $T$-dependent linewidth of the 62 meV band, which was estimated by the Fano model [14]. (d) Raman spectra for $y(zz)\overline{y}$ and $y(xx)\overline{y}$ configurations at various $T$ in ${\mathrm{N}\mathrm{d}\mathrm{V}\mathrm{O}}_3$ with the exciting photon energy of 1.96 eV. The 43 and 62 meV peaks in $y(zz)\overline{y}$, indicated by filled triangles, are assigned to the two-orbiton excitation, while the 87 meV one in $y(xx)\overline{y}$, by an open triangle, to the phonon mode activated by the OO.

Figure 2

(a) Optical conductivity spectra for $\mathbf{E}\parallel c$ at 10 K in ${\mathrm{N}\mathrm{d}\mathrm{V}\mathrm{O}}_3$ and ${\mathrm{L}\mathrm{a}\mathrm{V}\mathrm{O}}_3$. (b) Two-orbiton Raman process in staggered orbital chain with ferromagnetic spin order. (c) Raman spectra at 4.2 K in ${\mathrm{N}\mathrm{d}\mathrm{V}\mathrm{O}}_3$ and ${\mathrm{L}\mathrm{a}\mathrm{V}\mathrm{O}}_3$ with the exciting photon energies of 1.96 and 2.41 eV (from He-Ne and ${\mathrm{A}\mathrm{r}}^{+}$ lasers). The triangles indicate the peaks due to two-orbiton.

Figure 3

Comparison between the experimental and theoretical Raman spectra in $R{\mathrm{V}\mathrm{O}}_3$. (a) Theoretical results for the Raman spectra in static ($A$, $E_{\mathrm{C}\mathrm{J}\mathrm{T}}/J=0.15$, $E_{\mathrm{D}\mathrm{J}\mathrm{T}}/J=0$) and dynamical Jahn-Teller case ($B$, $E_{\mathrm{C}\mathrm{J}\mathrm{T}}/J=0.15$, $E_{\mathrm{D}\mathrm{J}\mathrm{T}}/J=0.01$), and for simple particle-hole excitation spectra of pseudospinons ($C$). The inset is a density plot for the pseudospinon excitation spectra, where the red density represents the intensity of the spectra. For comparison, a pseudospinon dispersion in the case of $E_{\mathrm{C}\mathrm{J}\mathrm{T}}=0$ is shown by a black curve. For the definition of $J$, $E_{\mathrm{C}\mathrm{J}\mathrm{T}}$ and $E_{\mathrm{D}\mathrm{J}\mathrm{T}}$, see Eq. (1) in text. (b) Experimental spectra in $y(zz)\overline{y}$ polarization for ${\mathrm{N}\mathrm{d}\mathrm{V}\mathrm{O}}_3$ and ${\mathrm{L}\mathrm{a}\mathrm{V}\mathrm{O}}_3$ at 4.2 K between 38 and 70 meV to be compared with the red curve $B$ in the (a).