Orbital Disorder Induced by Charge Fluctuations in Vanadium Spinels

Motivated by recent experiments on vanadium spinels, $A{\mathrm{V}}_2{\mathrm{O}}_4$, that show an increasing degree of electronic delocalization for smaller cation sizes, we study the evolution of orbital ordering (OO) between the strong and intermediate-coupling regimes of a multiorbital Hubbard Hamiltonian. The underlying magnetic ordering of the Mott insulating state leads to a rapid suppression of OO due to enhanced charge fluctuations along ferromagnetic bonds. Orbital double occupancy is rather low at the transition point indicating that the system is in the crossover region between strong and intermediate-coupling regimes when the orbital degrees of freedom become disordered.

Figure 1

Pyrochlore lattice of ${\mathrm{V}}^{3+}$ ions in $A{\mathrm{V}}_2{\mathrm{O}}_4$. The solid diagonal lines are FM bonds along the $zx$ and $yz$ directions. These “strong” bonds form zigzag chains described by $\overline{H}$. The dashed lines are the “weak” AFM bonds that introduce interchain orbital coupling. The arrows indicate the spin ordering favored by a combination of the intrachain FM coupling and interchain AFM coupling induced by bonds oriented along the $xy$ direction. The letters $x$ (for $zx$) and $y$ (for $yz$) indicate the OO that is stable deep inside the Mott regime [7].

Figure 2

(a) Mapping between $H_{\lambda =0}$ and the QIM. The even and odd sublattices are indicated with blue and red circles, respectively. (b) and (c) show the projections of the pyrochlore lattice and the helicoid Ising chains (solid lines) on the $xy$ and $yz$ planes, respectively.

Figure 3

(a) Phase diagram of the three-dimensional quantum Ising model Eq. (10) for $\eta =0.229$. (b) $T=0$ ($\lambda$, $t$) phase diagram of the single helical chain Hamiltonian $H$ obtained with DMRG applied to chains of 48 unit cells. (c) Square of the staggered orbital order parameter as a function of $t$.