Strong competition between orbital ordering and itinerancy in a frustrated spinel vanadate

The crossover from localized to itinerant electron regimes in the geometrically frustrated spinel system ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$ is explored by neutron-scattering measurements, first-principles calculations, and spin models. At low Co doping, the orbital ordering (OO) of the localized ${\mathrm{V}}^{3+}$ spins suppresses magnetic frustration by triggering a tetragonal distortion. At high Co doping levels, however, electronic itinerancy melts the OO and lessens the structural and magnetic anisotropies, thus increasing the amount of geometric frustration for the V-site pyrochlore lattice. Contrary to the predicted paramagentism induced by chemical pressure, the measured noncollinear spin states in the Co-rich region of the phase diagram provide a unique platform where localized spins and electronic itinerancy compete in a geometrically frustrated spinel.

Figure 1

Temperature dependence of the Bragg peaks, (002) (squares), (220) (circles), and (004) (triangles) in (a) ${\mathrm{Mn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{V}}_2{\mathrm{O}}_4$ and (b) ${\mathrm{Mn}}_{0.2}{\mathrm{Co}}_{0.8}{\mathrm{V}}_2{\mathrm{O}}_4$. The background has been subtracted. (c) The temperature versus Co-doping content ($x$) phase diagram. The para-to-CL magnetic transition temperature $T_{\text{CL}}$, the CL-NC ferrimagnetic phase transition temperature $T_{\text{NC}}$, and the cubic-to-tetragonal lattice transition temperature $T_S$ are determined from the magnetic susceptibility/heat capacity (solid lines) and neutron-scattering experiments (square, triangle, and circle for the transitions). (d) $A{\mathrm{O}}_4$ ($A={\mathrm{Mn}}^{2+}/{\mathrm{Co}}^{2+})$ tetrahedron and ${\mathrm{VO}}_6$ octahedron. (e) The $x$ dependence of the ${\mathrm{V}}^{3+}\text{−}{\mathrm{V}}^{3+}$ distance $R_{\text{V-V}}$ at 10 K (black dots).

Figure 2

(a)–(c) INS results for the magnetic excitations of ${\mathrm{Mn}}_{0.6}{\mathrm{Co}}_{0.4}{\mathrm{V}}_2{\mathrm{O}}_4$ at 8 K. (d)–(f) The calculated excitation spectra using the Hamiltonian, Eq. (1). The arrow line in (c) represents the position of the constant-$Q$ cut. (g) The constant-$Q$ cuts at (1.75 1.75 0) along [H H 0] direction in ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$ measured at 8 K, $x=0.4$, 0.6, and 0.8. The curves in (g) are Gaussian fits and guides to the eye. Note that the low-energy spin-wave branch hardens with increase of Co doping. (h) The spin-wave energy gap at the magnetic zone center (2 2 0) in ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$. The curves in (h) are power-law fits.

Figure 3

(a) and (b) Density-of-states for AFM ${\mathrm{MnV}}_2{\mathrm{O}}_4$ and ${\mathrm{CoV}}_2{\mathrm{O}}_4$, respectively. (c) NC state of ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$. $J_{AB}$, $J_{BB}^{ab}$, and $J_{BB}^c$ are the exchange interactions between nearest-neighbor sites. (d) and (e) Orbital energies estimated from DFT calculations. $|J_{A\text{−}\mathrm{V}}|$ is inversely proportional to the energy gap $\Delta$. Only up-spin energy levels are shown for ${\mathrm{V}}^{3+}$ for simplicity.

Figure 4

The hierarchical magnetic states with V-V and V-Mn/Co interactions and the distinct origins of isosymmetric phase transition with Co doping ($x)$.