Intrinsic Coupling of Orbital Excitations to Spin Fluctuations in Mott Insulators

We show how the general and basic asymmetry between two fundamental degrees of freedom present in strongly correlated oxides, spin and orbital, has very profound repercussions on the elementary spin and orbital excitations. Whereas the magnons remain largely unaffected, orbitons become inherently coupled with spin fluctuations in spin-orbital models with antiferromagnetic and ferro-orbital ordered ground states. The composite orbiton-magnon modes that emerge fractionalize again in one dimension, giving rise to spin-orbital separation in the peculiar regime where spinons are faster than orbitons.

Figure 1

Two superexchange processes moving an electron in an excited orbital (indicated by oval) from site $j$ to its neighbor $j+1$. (a),(b) Orbiton motion when spins along the bond are antiparallel or parallel, respectively; see text. The states in the gray middle panels are not part of the low-energy Hilbert space corresponding to (1). These virtual excitations within the full two-orbital Hubbard model illustrate the origin of those superexchange interactions of Hamiltonian (1) that propagate the orbiton; note that the spin of the excited electron is conserved.

Figure 2

Spectral function $O(k,\omega )$ of orbital excitation obtained via the mapping onto the $t\mathrm{\text{−}}J$ model, Eq. (6), evaluated using Lanczos exact diagonalization on a 28 site chain. A broadening $\eta =0.03J$ and $E_z=10J$. The thick line shows orbital excitation in a mean-field (orbital-wave) approach, Eq. (3).

Figure 3

Schematic representation of the orbital motion and the induced spin fluctuations giving rise to spin-orbital separation in 1D. The first hop of the excited state [$(\mathrm{a})\to (\mathrm{b})$] creates a spinon (wavy line) that moves via spin exchange $\propto J$. The next hop [$(\mathrm{b})\to (\mathrm{c})$] does not produce any extra spinons: an “orbiton” freely propagating as a “holon” with an effective hopping $t\sim J/2$ is created.