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We present the results of a combined $^{7}\mathrm{Li}$-NMR and diffraction study on ${\mathrm{LiGa}}_{0.95}{\mathrm{In}}_{0.05}{\mathrm{Cr}}_{4}{\mathrm{O}}_{8}$, a member of the ${\mathrm{LiGa}}_{1\ensuremath{-}x}{\mathrm{In}}_{x}{\mathrm{Cr}}_{4}{\mathrm{O}}_{8}$ ``breathing'' pyrochlore family. Via specific heat and NMR measurements, we find that the complex sequence of first-order transitions observed for ${\mathrm{LiGaCr}}_{4}{\mathrm{O}}_{8}$ is replaced by a single second-order transition at ${T}_{f}=11\text{ }\text{ }\mathrm{K}$. Neutron and x-ray diffraction rule out both structural symmetry lowering and magnetic long-range order as the origin of this transition. Instead, reverse Monte Carlo fitting of the magnetic diffuse scattering indicates that the low-temperature phase may be described as a collinear spin nematic state, characterized by a quadrupolar order parameter. This state also shows signs of short-range order between collinear spin arrangements on tetrahedra, revealed by mapping the reverse Monte Carlo spin configurations onto a three-state color model.

We present new magnetic heat capacity and neutron scattering results for two magnetically frustrated molybdate pyrochlores: $S=1$ oxide Lu$_2$Mo$_2$O$_7$ and $S={\frac{1}{2}}$ oxynitride Lu$_2$Mo$_2$O$_5$N$_2$. Lu$_2$Mo$_2$O$_7$ undergoes a transition to an unconventional spin glass ground state at $T_f {\sim} 16$ K. However, the preparation of the corresponding oxynitride tunes the nature of the ground state from spin glass to quantum spin liquid. The comparison of the static and dynamic spin correlations within the oxide and oxynitride phases presented here reveals the crucial role played by quantum fluctuations in the selection of a ground state. Furthermore, we estimate an upper limit for a gap in the spin excitation spectrum of the quantum spin liquid state of the oxynitride of ${\Delta} {\sim} 0.05$ meV or ${\frac{\Delta}{|\theta|}}\sim0.004$, in units of its antiferromagnetic Weiss constant ${\theta} {\sim}-121$ K., Comment: 8 pages, 9 figures

A unique type of frustrated lattice is found in two $A$-site ordered spinel oxides, ${\mathrm{LiGaCr}}_{4}{\mathrm{O}}_{8}$ and ${\mathrm{LiInCr}}_{4}{\mathrm{O}}_{8}$. Because of the large size mismatch between ${\mathrm{Li}}^{+}$ and ${\mathrm{Ga}}^{3+}/{\mathrm{In}}^{3+}$ ions at the $A$ site, the pyrochlore lattice, made up of ${\mathrm{Cr}}^{3+}$ ions carrying spin $3/2$, becomes an alternating array of small and large tetrahedra, i.e., a ``breathing'' pyrochlore lattice. We introduce a parameter, the breathing factor ${B}_{f}$, which quantifies the degree of frustration in the pyrochlore lattice: ${B}_{f}$ is defined as ${J}^{\ensuremath{'}}/J$, where ${J}^{\ensuremath{'}}$ and $J$ are nearest-neighbor magnetic interactions in the large and small tetrahedra, respectively. ${\mathrm{LiGaCr}}_{4}{\mathrm{O}}_{8}$ with ${B}_{f}\ensuremath{\sim}0.6$ shows magnetic susceptibility similar to that of conventional Cr spinel oxides such as ${\mathrm{ZnCr}}_{2}{\mathrm{O}}_{4}$. In contrast, ${\mathrm{LiInCr}}_{4}{\mathrm{O}}_{8}$ with a small ${B}_{f}\ensuremath{\sim}0.1$ exhibits a spin-gap behavior in its magnetic susceptibility, suggesting a proximity to an exotic singlet ground state. Magnetic long-range order occurs at 13.8 and 15.9 K for ${\mathrm{LiGaCr}}_{4}{\mathrm{O}}_{8}$ and ${\mathrm{LiInCr}}_{4}{\mathrm{O}}_{8}$, respectively, in both cases likely owing to the coupling to structural distortions.

A unique type of frustrated lattice is found in two A-site ordered spinel oxides, LiGaCr(4)O(8) and LiInCr(4)O(8). Because of the large size mismatch between Li(+) and Ga(3+)/In(3+) ions at the A site, the pyrochlore lattice, made up of Cr(3+) ions carrying spin 3/2, becomes an alternating array of small and large tetrahedra, i.e., a "breathing" pyrochlore lattice. We introduce a parameter, the breathing factor B(f), which quantifies the degree of frustration in the pyrochlore lattice: B(f) is defined as J'/J, where J' and J are nearest-neighbor magnetic interactions in the large and small tetrahedra, respectively. LiGaCr(4)O(8) with B(f)~0.6 shows magnetic susceptibility similar to that of conventional Cr spinel oxides such as ZnCr(2)O(4). In contrast, LiInCr(4)O(8) with a small B(f)~0.1 exhibits a spin-gap behavior in its magnetic susceptibility, suggesting a proximity to an exotic singlet ground state. Magnetic long-range order occurs at 13.8 and 15.9 K for LiGaCr(4)O(8) and LiInCr(4)O(8), respectively, in both cases likely owing to the coupling to structural distortions.

Neutron spectroscopy and diffuse neutron scattering on herbertsmithite [ZnCu3(OH)(6)Cl-2], a near-ideal realization of the s=1/2 kagome antiferromagnet, reveal the hallmark property of a quantum spin liquid: instantaneous short-ranged antiferromagnetic correlations in the absence of a time-averaged ordered moment. These dynamic antiferromagnetic correlations are weakly dependent of neutron-energy transfer and temperature, and persist up to 25 meV and 120 K. At low energy transfers a shift of the magnetic scattering to low Q is observed with increasing temperature, providing evidence of gapless spinons. It is argued that these observations provide important evidence in favor of resonating-valence-bond theories of (doped) Mott insulators.