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The $A$-site spinel NiRh$_2$O$_4$ is the only known realization of a spin-1 diamond lattice magnet and is predicted to host unconventional magnetic phenomena driven by frustrated nearest and next-nearest neighbor exchange as well as orbital degeneracy. Previous works found no sign of magnetic order but found a gapped dispersive magnetic excitation indicating a possible valence bond magnetic ground state. However, the presence of many competing low energy degrees of freedom and limited empirical microscopic constraints complicates further analysis. Here, we carry out resonant inelastic x-ray scattering (RIXS) and x-ray absorption spectroscopy (XAS) to characterize the local electronic structure of NiRh$_2$O$_4$. The RIXS data can be partly described by a single-ion model for tetrahedrally coordinated Ni$^{2+}$ and indicates a tetragonal distortion $\Delta t_2\!=\!70$ meV that splits the $t_2$ orbitals into a high energy orbital singlet and lower energy orbital doublet. We identify features of the RIXS spectra that are consistent with a Rh-Ni two-site excitation indicating strong metal-metal hybridization mediated by oxygen in NiRh$_2$O$_4$. We also identify signatures of electron-phonon coupling through the appearance of phonon sidebands that dress crystal field excitations. These results establish the key energy scales relevant to the magnetism in NiRh$_2$O$_4$ and further demonstrate that covalency and lattice dynamics play essential roles in controlling the magnetic ground states of $A$-site spinels.

Molecular magnets based on [Mo$_3$]$^{11+}$ units with one unpaired electron per trimer have attracted recent interest due to the identification of quantum spin liquid candidacy in some family members. Here, we present comprehensive measurements on polycrystalline samples of ZnScMo$_3$O$_8$, MgScMo$_3$O$_8$, and Na$_3$Sc$_2$Mo$_5$O$_{16}$ with the same Mo$_3$O$_{13}$ magnetic building blocks. The crystal structures are characterized with x-ray or neutron powder diffraction and the magnetic ground states are determined by performing ac and dc susceptibility, specific heat, neutron powder diffraction, and $μ$SR measurements. Our work indicates that ZnScMo$_3$O$_8$ and MgScMo$_3$O$_8$ have ferromagnetic Curie-Weiss temperatures of 18.5 K and 11.9 K, ordered ground states with net moments (low-moment ferromagnetism or canted antiferromagnetism), and zero field ordering temperatures of $T_c =$ 6 K and $, 13 pages, 9 figures, accepted for publication in Physical Review Materials

For materials near the phase boundary between weak and strong topological insulators (TIs), their band topology depends on the band alignment, with the inverted (normal) band corresponding to the strong (weak) TI phase. Here, taking the anisotropic transition-metal pentatelluride ZrTe$_5$ as an example, we show that the band inversion manifests itself as a second extremum (band gap) in the layer stacking direction, which can be probed experimentally via magneto-infrared spectroscopy. Specifically, we find that the band anisotropy of ZrTe$_5$ features a slow dispersion in the layer stacking direction, along with an additional set of optical transitions from a band gap away from the Brillouin zone center. Our work identifies ZrTe5 as a strong TI at liquid helium temperature and provides a new perspective in determining band inversion in layered topological materials., with supplemental materials

We successfully synthesized and characterized the triangular lattice anitferromagnet Ba$_8$MnNb$_6$O$_{24}$, which comprises equilateral spin-5/2 Mn$^{2+}$ triangular layers separated by six non-magnetic Nb$^{5+}$ layers. The detailed susceptibility, specific heat, elastic and inelastic neutron scattering measurements, and spin wave theory simulation on this system reveal that it has a 120 degree ordering ground state below T$_N$ = 1.45 K with in-plane nearest-neighbor exchange interaction ~0.11 meV. While the large separation 18.9 A between magnetic layers makes the inter-layer exchange interaction virtually zero, our results suggest that a weak easy-plane anisotropy is the driving force for the k$_m$ = (1/3 1/3 0) magnetic ordering. The magnetic properties of Ba$_8$MnNb$_6$O$_{24}$, along with its classical excitation spectra, contrast with the related triple perovskite Ba$_3$MnNb$_2$O$_9$, which shows easy-axis anisotropy, and the iso-structural compound Ba$_8$CoNb$_6$O$_{24}$, in which the effective spin-1/2 Co$^{2+}$ spins do not order down to 60 mK and in which the spin dynamics shows sign of strong quantum effects., Comment: Figures, sentences, and references are updated

It is well established that in the low-temperature limit, the two-dimensional quantum Heisenberg antiferromagnet on a square lattice (2DQHAFSL) exhibits an anomaly in its spectrum at short-wavelengths on the zone-boundary. In the vicinity of the $(��,0)$ point the pole in the one-magnon response exhibits a downward dispersion, is heavily damped and attenuated, giving way to an isotropic continuum of excitations extending to high energies. The origin of the anomaly and the presence of the continuum are of current theoretical interest, with suggestions focused around the idea that the latter evidences the existence of spinons in a two-dimensional system. Here we present the results of neutron inelastic scattering experiments and Quantum Monte Carlo calculations on the metallo-organic compound Cu(DCOO)$_2\cdot 4$D$_2$O (CFTD), an excellent physical realisation of the 2DQHAFSL, designed to investigate how the anomaly at $(��,0)$ evolves up to finite temperatures $T/J\sim2/3$. Our data reveal that on warming the anomaly survives the loss of long-range, three-dimensional order, and is thus a robust feature of the two-dimensional system. With further increase of temperature the zone-boundary response gradually softens and broadens, washing out the $(��,0)$ anomaly. This is confirmed by a comparison of our data with the results of finite-temperature Quantum Monte Carlo simulations where the two are found to be in good accord. At lower energies, in the vicinity of the antiferromagnetic zone centre, there was no significant softening of the magnetic excitations over the range of temperatures investigated., Dedicated to the life and work of Professor Roger Cowley. 22 pages, 8 figures

One-dimensional (1D) magnetic insulators have attracted significant interest as a platform for studying emergent phenomena such as quasiparticle fractionalization and quantum criticality. The antiferromagnetic Heisenberg chain of spins-1/2 is an important reference system; its elementary excitations are spin-1/2 quasiparticles called spinons that are always created in pairs. However, while inelastic neutron scattering (INS) experiments routinely observe the excitation continuum associated with two-spinon states, the presence of more complex dynamics associated with four-spinon states has only been inferred from comparison with theory. Here, we show that resonant inelastic x-ray scattering (RIXS) is capable of accessing the four-spinon excitations directly, in a spectroscopic region separated from the two-spinon continuum. Our results provide the first direct measurement of four-spinon excitations, which is made possible by the fundamentally different correlation functions probed by RIXS compared to INS. This advance holds great promise as a tool in the search for novel quantum states, in particular quantum spin liquids.

We report a comprehensive inelastic neutron-scattering study of the frustrated pyrochlore antiferromagnet MgCr2O4 in its cooperative paramagnetic regime. Theoretical modeling yields a microscopic Heisenberg model with exchange interactions up to third-nearest neighbors, which quantitatively explains all the details of the dynamic magnetic response. Our work demonstrates that the magnetic excitations in paramagnetic MgCr2O4 are faithfully represented in the entire Brillouin zone by a theory of magnons propagating in a highly-correlated paramagnetic background. Our results also suggest that MgCr2O4 is proximate to a spiral spin-liquid phase distinct from the Coulomb phase, which has implications for the magneto-structural phase transition in MgCr2O4 ., Comment: 6 pages, 3 figures; supplementary material: 12 pages with figures

We report the discovery of a spin one diamond lattice in NiRh2O4. This spinel undergoes a cubic to tetragonal phase transition at T = 440 K that leaves all nearest neighbor interactions equivalent. In the tetragonal phase, magnetization measurements show a Ni2+ effective moment of p(eff) = 3.3(1) and dominant antiferromagnetic interactions with {\Theta}(CW) = -11.3(7) K. No phase transition to a long-range magnetically ordered state is observed by specific heat measurements down to T = 0.1 K. Inelastic neutron scattering measurements on sub-stoichiometric NiRh2O4 reveal possible valence-bond behavior and show no visible signs of magnetic ordering. NiRh2O4 provides a platform on which to explore the previously unknown and potentially rich physics of spin one interacting on the diamond lattice, including the realization of theoretically predicted quantum spin liquid and topological paramagnet states.

Antiferromagnetic insulators on the diamond lattice are candidate materials to host exotic magnetic phenomena ranging from spin-orbital entanglement to degenerate spiral ground-states and topological paramagnetism. Compared to other three-dimensional networks of magnetic ions, such as the geometrically frustrated pyrochlore lattice, the investigation of diamond-lattice magnetism in real materials is less mature. In this work, we characterize the magnetic properties of model A-site spinels CoRh2O4 (cobalt rhodite) and CuRh2O4 (copper rhodite) by means of thermo-magnetic and neutron scattering measurements and perform group theory analysis, Rietveld refinement, mean-field theory, and spin wave theory calculations to analyze the experimental results. Our investigation reveals that cubic CoRh2O4 is a canonical S=3/2 diamond-lattice Heisenberg antiferromagnet with a nearest neighbor exchange J = 0.63 meV and a Neel ordered ground-state below a temperature of 25 K. In tetragonally distorted CuRh2O4, competiting exchange interactions between up to third nearest-neighbor spins lead to the development of an incommensurate spin helix at 24 K with a magnetic propagation vector k = (0,0,0.79). Strong reduction of the ordered moment is observed for the S=1/2 spins in CuRh2O4 and captured by our 1/S corrections to the staggered magnetization. Our work identifies CoRh2O4 and CuRh2O4 as reference materials to guide future work searching for exotic quantum behavior in diamond-lattice antiferromagnets., Comment: 15 pages, 14 figures

We report the magnetic excitation spectrum as measured by inelastic neutron scattering for a polycrystalline sample of Sr$_3$CuPtO$_6$. Modeling the data by the 2+4 spinon contributions to the dynamical susceptibility within the chains, and with interchain coupling treated in the random phase approximation, accounts for the major features of the powder-averaged structure factor. The magnetic excitations broaden considerably as temperature is raised, persisting up to above 100 K and displaying a broad transition as previously seen in the susceptibility data. No spin gap is observed in the dispersive spin excitations at low momentum transfer, which is consistent with the gapless spinon continuum expected from the coordinate Bethe ansatz. However, the temperature dependence of the excitation spectrum gives evidence of some very weak interchain coupling., Comment: 9 pages, 5 figures

The perovskite Ba8CoNb6O24 comprises equilateral effective spin-1/2 Co2+ triangular layers separated by six non-magnetic layers. Susceptibility, specific heat and neutron scattering measurements combined with high-temperature series expansions and spin-wave calculations confirm that Ba8CoNb6O24 is basically a twodimensional (2D) magnet with no detectable spin anisotropy and no long-range magnetic ordering down to 0.06 K. In other words, Ba8CoNb6O24 is very close to be a realization of the paradigmatic spin-1/2 triangular Heisenberg model, which is not expected to exhibit symmetry breaking at finite temperature according to the Mermin and Wagner theorem., Comment: 8 pages, 5 figures with SI

Specific heat, elastic neutron scattering, and muon spin rotation ($\mu$SR) experiments have been carried out on a well-characterized sample of "stuffed" (Pr-rich) Pr$_{2+x}$Ir$_{2-x}$O$_{7-\delta}$. Elastic neutron scattering shows the onset of long-range spin-ice "2-in/2-out" magnetic order at $T_M = 0.93$ K, with an ordered moment of 1.7(1)$\mu_\mathrm{B}$/Pr ion at low temperatures. Approximate lower bounds on the correlation length and correlation time in the ordered state are 170 \AA\ and 0.7 ns, respectively. $\mu$SR experiments yield an upper bound 2.6(7) mT on the local field $B_\mathrm{loc}^{4f}$ at the muon site, which is nearly two orders of magnitude smaller than the expected dipolar field for long-range spin-ice ordering of 1.7$\mu_B$ moments (120--270 mT, depending on muon site). This shortfall is due in part to splitting of the non-Kramers crystal-field ground-state doublets of near-neighbor Pr$^{3+}$ ions by the $\mu^+$-induced lattice distortion. For this to be the only effect, however, $\sim$160 Pr moments out to a distance of $\sim$14 \AA\ must be suppressed. An alternative scenario, which is consistent with the observed reduced nuclear hyperfine Schottky anomaly in the specific heat, invokes slow correlated Pr-moment fluctuations in the ordered state that average $B_\mathrm{loc}^{4f}$ on the $\mu$SR time scale (${\sim}10^{-7}$ s), but are static on the time scale of the elastic neutron scattering experiments (${\sim}10^{-9}$ s). In this picture the dynamic muon relaxation suggests a Pr$^{3+}$ $4f$ correlation time of a few nanoseconds, which should be observable in a neutron spin echo experiment., Comment: 14 pages, 9 figures. To appear in Phys. Rev. B

Specific heat, elastic neutron scattering, and muon spin rotation ($��$SR) experiments have been carried out on a well-characterized sample of "stuffed" (Pr-rich) Pr$_{2+x}$Ir$_{2-x}$O$_{7-��}$. Elastic neutron scattering shows the onset of long-range spin-ice "2-in/2-out" magnetic order at $T_M = 0.93$ K, with an ordered moment of 1.7(1)$��_\mathrm{B}$/Pr ion at low temperatures. Approximate lower bounds on the correlation length and correlation time in the ordered state are 170 �� and 0.7 ns, respectively. $��$SR experiments yield an upper bound 2.6(7) mT on the local field $B_\mathrm{loc}^{4f}$ at the muon site, which is nearly two orders of magnitude smaller than the expected dipolar field for long-range spin-ice ordering of 1.7$��_B$ moments (120--270 mT, depending on muon site). This shortfall is due in part to splitting of the non-Kramers crystal-field ground-state doublets of near-neighbor Pr$^{3+}$ ions by the $��^+$-induced lattice distortion. For this to be the only effect, however, $\sim$160 Pr moments out to a distance of $\sim$14 �� must be suppressed. An alternative scenario, which is consistent with the observed reduced nuclear hyperfine Schottky anomaly in the specific heat, invokes slow correlated Pr-moment fluctuations in the ordered state that average $B_\mathrm{loc}^{4f}$ on the $��$SR time scale (${\sim}10^{-7}$ s), but are static on the time scale of the elastic neutron scattering experiments (${\sim}10^{-9}$ s). In this picture the dynamic muon relaxation suggests a Pr$^{3+}$ $4f$ correlation time of a few nanoseconds, which should be observable in a neutron spin echo experiment., 14 pages, 9 figures. To appear in Phys. Rev. B

Inelastic neutron scattering for temperatures below 30 K from a powder of LiZn2Mo3O8 demonstrates this triangular-lattice antiferromagnet hosts collective magnetic excitations from spin 1/2 Mo3O13 molecules. Apparently gapless (\Delta < 0.2 meV) and extending at least up to 2.5 meV, the low energy magnetic scattering cross section is surprisingly broad in momentum space and involves one third of the spins present above 100 K. The data are compatible with the presence of valence-bonds involving nearest-neighbor and next-nearest-neighbor spins forming a disordered or dynamic state., Comment: Main text: 5 pages, 4 figures. Supplementary materials: 4 pages, 4 figures, 2 tables. Accepted to PRL

As an elementary particle the electron carries spin \hbar/2 and charge e. When binding to the atomic nucleus it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies (e.g., s, p or d). Even if electrons in solids form bands and delocalize from the nuclei, in Mott insulators they retain their three fundamental quantum numbers: spin, charge and orbital[1]. The hallmark of one-dimensional (1D) physics is a breaking up of the elementary electron into its separate degrees of freedom[2]. The separation of the electron into independent quasi-particles that carry either spin (spinons) or charge (holons) was first observed fifteen years ago[3]. Using Resonant Inelastic X-ray Scattering on the 1D Mott-insulator Sr2CuO3 we now observe also the orbital degree of freedom separating. We resolve an orbiton liberating itself from spinons and propagating through the lattice as a distinct quasi-particle with a substantial dispersion of ~0.2 eV., 35 pages, 8 figures

We study high-field magnon dynamics and examine the dynamical structure factor in the quasi-2D tetragonal Heisenberg antiferromagnet with interlayer coupling corresponding to realistic materials. Within spin-wave theory, we show that a non-zero interlayer coupling mitigates singular corrections to the excitation spectrum occurring in the high-field regime that would otherwise require a self-consistent approach beyond the 1/S approximation. For the fields between the threshold for decays and saturation field we observe widening of the two-magnon sidebands with significant shifting of the spectral weight away from the quasiparticle peak. We find spectrum broadening throughout large regions of the Brillouin zone, dramatic redistributions of spectral weight to the two-magnon continuum, two-peak structures and other features clearly unlike conventional single-particle peaks., 12 pages, 7 figures. Accepted to PRB

It is well established that in the low-temperature limit, the two-dimensional quantum Heisenberg antiferromagnet on a square lattice (2DQHAFSL) exhibits an anomaly in its spectrum at short-wavelengths on the zone-boundary. In the vicinity of the (pi, 0) point the pole in the one-magnon response exhibits a downward dispersion, is heavily damped and attenuated, giving way to an isotropic continuum of excitations extending to high energies. The origin of the anomaly and the presence of the continuum are of current theoretical interest, with suggestions focused around the idea that the latter evidences the existence of spinons in a two-dimensional system. Here we present the results of neutron inelastic scattering experiments and Quantum Monte Carlo calculations on the metallo-organic compound Cu(DCOO)(2) center dot 4D(2)O (CFTD), an excellent physical realisation of the 2DQHAFSL, designed to investigate how the anomaly at (pi, 0) evolves up to finite temperatures T/J similar to 2/3. Our data reveal that on warming the anomaly survives the loss of long-range, three-dimensional order, and that it is thus a robust feature of the two-dimensional system. With further increase of temperature the zone-boundary response gradually softens and broadens, washing out the (pi, 0) anomaly. This is confirmed by a comparison of our data with the results of finite-temperature Quantum Monte Carlo simulations where the two are found to be in good accord. In the vicinity of the antiferromagnetic zone centre, there was no significant softening of the magnetic excitations over the range of temperatures investigated.