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Register a new userHidden spin-orbital order in the Kitaev hyperhoneycomb $beta$-Li$_2$IrO$_3$
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We report the existence of a phase transition at high temperature in the 3D Kitaev candidate material, $beta$-Li$_2$IrO$_3$. We show that the transition is bulk, intrinsic and orders a tiny magnetic moment with a spatially anisotropic saturation moment. We show that even though this transition is global, it does not freeze the local Ir moments, which order at much lower temperatures into an incommensurate state. Rather, the ordered moment has an orbital origin that is coupled to spin correlations, likely of a Kitaev origin. The separate ordering of spin-correlated orbital moments and of local Ir moments reveals a novel way in which magnetic frustration in Kitaev systems can lead to coexisting magnetic states.
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The family of edge-sharing tri-coordinated iridates and ruthenates has emerged in recent years as a major platform for Kitaev spin liquid physics, where spins fractionalize into emergent magnetic fluxes and Majorana fermions with Dirac-like dispersions. While such exotic states are usually pre-empted by long-range magnetic order at low temperatures, signatures of Majorana fermions with long coherent times have been predicted to manifest at intermediate and higher energy scales, similar to the observation of spinons in quasi-1D spin chains. Here we present a Resonant Inelastic X-ray Scattering study of the magnetic excitations of the hyperhoneycomb iridate $beta$-Li$_2$IrO$_3$ under a magnetic field with a record-high-resolution spectrometer. At low-temperatures, dispersing spin waves can be resolved around the predicted intertwined incommensurate spiral and field-induced zigzag orders, whose excitation energy reaches a maximum of 16meV. A 2T magnetic field softens the dispersion around ${bf Q}=0$. The behavior of the spin waves under magnetic field is consistent with our semiclassical calculations for the ground state and the dynamical spin structure factor, which further predicts that the ensued intertwined uniform states remain robust up to very high fields (100 T). Most saliently, the low-energy magnon-like mode is superimposed by a broad continuum of excitations, centered around 35meV and extending up to 100meV. This high-energy continuum survives up to at least 300K -- well above the ordering temperature of 38K -- and gives evidence for pairs of long-lived Majorana fermions of the proximate Kitaev spin liquid.
Hyperhoneycomb iridate $beta$-Li$_2$IrO$_3$ is a three-dimensional analogue of two-dimensional honeycomb iridates, such as $alpha$-Li$_2$IrO$_3$, which recently appeared as another playground for the physics of Kitaev-type spin liquid. $beta$-Li$_2$IrO$_3$ shows a non-collinear spiral ordering of spin-orbital-entangled $J_{rm eff}$ = 1/2 moments at low temperature, which is known to be suppressed under a pressure of $sim$2 GPa. With further increase of pressure, a structural transition is observed at $P_{rm S}$ $sim$ 4 GPa at room temperature. Using the neutron powder diffraction technique, the crystal structure in the high-pressure phase of $beta$-Li$_2$IrO$_3$ above $P_{rm S}$ was refined, which indicates the formation of Ir$_2$ dimers on the zig-zag chains, with the Ir-Ir distance even shorter than that of metallic Ir. We argue that the strong dimerization stabilizes the bonding molecular orbital state comprising the two local $d_{zx}$-orbitals on the Ir-O$_2$-Ir bond plane, which conflicts with the equal superposition of $d_{xy}$-, $d_{yz}$- and $d_{zx}$- orbitals in the $J_{rm eff}$ = 1/2 wave function produced by strong spin-orbit coupling. The results of resonant inelastic x-ray scattering (RIXS) measurements and the electronic structure calculations are fully consistent with the collapse of the $J_{rm eff}$ = 1/2 state. A subtle competition of various electronic phases is universal in honeycomb-based Kitaev materials.
Temperature-pressure phase diagram of the Kitaev hyperhoneycomb iridate $beta$-Li$_2$IrO$_3$ is explored using magnetization, thermal expansion, magnetostriction, and muon spin rotation ($mu$SR) measurements, as well as single-crystal x-ray diffraction under pressure and ab initio calculations. The Neel temperature of $beta$-Li$_2$IrO$_3$ increases with the slope of 0.9 K/GPa upon initial compression, but the reduction in the polarization field $H_c$ reflects a growing instability of the incommensurate order. At 1.4 GPa, the ordered state breaks down upon a first-order transition giving way to a new ground state marked by the coexistence of dynamically correlated and frozen spins. This partial freezing in the absence of any conspicuous structural defects may indicate classical nature of the resulting pressure-induced spin liquid, an observation paralleled to the increase in the nearest-neighbor off-diagonal exchange $Gamma$ under pressure.
$^7$Li nuclear magnetic resonance (NMR) and terahertz (THz) spectroscopies are used to probe magnetic excitations and their field dependence in the hyperhoneycomb Kitaev magnet $beta$-Li$_2$IrO$_3$. Spin-lattice relaxation rate ($1/T_1$) measured down to 100,mK indicates gapless nature of the excitations at low fields (below $H_csimeq 2.8$,T), in contrast to the gapped magnon excitations found in the honeycomb Kitaev magnet $alpha$-RuCl$_3$ at zero applied magnetic field. At higher temperatures in $beta$-Li$_2$IrO$_3$, $1/T_1$ passes through a broad maximum without any clear anomaly at the Neel temperature $T_Nsimeq 38$,K, suggesting the abundance of low-energy excitations that are indeed observed as two peaks in the THz spectra, both correspond to zone-center magnon excitations. At higher fields (above $H_c$), an excitation gap opens, and a re-distribution of the THz spectral weight is observed without any indication of an excitation continuum, in contrast to $alpha$-RuCl$_3$ where an excitation continuum was reported.
A pressure-induced collapse of magnetic ordering in $beta$-Li$_2$IrO$_3$ at $P_msim1.5- 2$ GPa has previously been interpreted as evidence for possible emergence of spin liquid states in this hyperhoneycomb iridate, raising prospects for experimental realizations of the Kitaev model. Based on structural data obtained at emph{room temperature}, this magnetic transition is believed to originate in small lattice perturbations that preserve crystal symmetry, and related changes in bond-directional anisotropic exchange interactions. Here we report on the evolution of the crystal structure of $beta$-Li$_2$IrO$_3$ under pressure at low temperatures ($Tleq50$ K) and show that the suppression of magnetism coincides with a change in lattice symmetry involving Ir-Ir dimerization. The critical pressure for dimerization shifts from 4.4(2) GPa at room temperature to $sim1.5-2$ GPa below 50 K. While a direct $Fddd rightarrow C2/c$ transition is observed at room temperature, the low temperature transitions involve new as well as coexisting dimerized phases. Further investigation of the Ir ($L_3$/$L_2$) isotropic branching ratio in x-ray absorption spectra indicates that the previously reported departure of the electronic ground state from a $J_{rm{eff}}=1/2$ state is closely related to the onset of dimerized phases. In essence, our results suggest that the predominant mechanism driving the collapse of magnetism in $beta$-Li$_2$IrO$_3$ is the pressure-induced formation of Ir$_2$ dimers in the hyperhoneycomb network. The results further confirm the instability of the $J_{rm{eff}}=1/2$ moments and related non-collinear spiral magnetic ordering against formation of dimers in the low-temperature phase of compressed $beta$-Li$_2$IrO$_3$.
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