Figure 1

Temperature dependence of bulk susceptibility, elastic magnetic intensity, and lattice strain. (a) Zero field cooled bulk susceptibility $\chi$. (b) Elastic magnetic intensity (triangles) at $Q=1.67{Å}^{-1}$ that corresponds to the magnetic ($2,0,1$) reflection with a saturation moment of $\langle M\rangle =g\langle S\rangle =0.61(3){\mu }_B$ per $V$ ion ($g$-gyromagnetic ratio), and lattice strain (squares) along $a$ and $c$ measured by synchrotron x-ray diffraction on a single crystal with dimensions of ${10}^{-3}{\mathrm{m}\mathrm{m}}^3$ ($6\mu \mathrm{g}$). The x-ray measurements were carried out at the 33BM-C beam line at the Advanced Photon Source of Argonne National Laboratory.Reuse & Permissions

Figure 2

Neutron scattering intensity as a function of energy ($\hslash \omega$) and wave vector ($Q$) transfer obtained from a powder sample of $\mathrm{Z}\mathrm{n}{\mathrm{V}}_2{\mathrm{O}}_4$ at three different phases. (a) At 100 K, in the cubic and cooperative paramagnetic phase. (b) At 45 K, in the tetragonal phase without magnetic long-range order. (c) At 10 K, in the tetragonal and Néel phase.Reuse & Permissions

Figure 3

$Q$ dependence of inelastic magnetic neutron scattering intensity obtained by integrating the data shown in Fig. 1 over the range of energy that includes most of the excited spectral weight: (a) at 100, (b) 60, (c) 45, and (d) 10 K. The energy integration range is $3\mathrm{m}\mathrm{e}\mathrm{V}<\hslash \omega <10\mathrm{m}\mathrm{e}\mathrm{V}$ for (a), (b), and (c) and $9\mathrm{m}\mathrm{e}\mathrm{V}<\hslash \omega <13\mathrm{m}\mathrm{e}\mathrm{V}$ for (d). Lines are fits to the models explained in the text.Reuse & Permissions

Figure 4

(a),(b) Illustrations of the orbital states of $\mathrm{Z}\mathrm{n}{\mathrm{V}}_2{\mathrm{O}}_4$ in one cubic unit cell. Balloons represent the $t_{2g}$ orbitals of the $V^{3+}(3d^2)$ ions: $d_{xy}$ (blue), $d_{yz}$ (red), and $d_{zx}$ (yellow) orbitals located at the vanadium site. The four different sizes of the balloons represent four different $ab$ planes with different $z$ coordinates. (a) The cubic phase above 50 K. The three orbitals are randomly distributed. The blue rods connect possible dynamic magnetic interactions at a snap shot due to direct overlap of the neighboring orbitals. (b) Antiferro-orbital model for the tetragonal phase. $J$, $J^{\prime }$, and $J_3$ represent coupling constants for the nearest neighbor intrachain, the nearest neighbor interchain (interplane), and the second nearest neighbor intrachain interactions, respectively. In this model, $J^{\prime }$ is negligible because $d_{yz}$ and $d_{zx}$ orbitals do not overlap.Reuse & Permissions