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Register a new userAnisotropic temperature-field phase diagram of single-crystalline $beta$-Li$_2$IrO$_3$: magnetization, specific heat, and $^7$Li NMR study
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Detailed magnetization, specific heat, and $^7$Li nuclear magnetic resonance (NMR) measurements on single crystals of the hyperhoneycomb Kitaev magnet $beta$-Li$_2$IrO$_3$ are reported. At high temperatures, {cred anisotropy of the magnetization is reflected by the different Curie-Weiss temperatures for different field directions}, in agreement with the combination of a ferromagnetic Kitaev interaction ($K$) and a negative off-diagonal anisotropy ($Gamma$) as two leading terms in the spin Hamiltonian. At low temperatures, magnetic fields applied along $a$ or $c$ have only a weak effect on the system and reduce the Neel temperature from 38 K at 0 T to about 35.5 K at 14 T, with no field-induced transitions observed up to 58 T on a powder sample. In contrast, the field applied along $b$ causes a drastic reduction in the $T_N$ that vanishes around $H_c=2.8$ T giving way to a crossover toward a quantum paramagnetic state. $^7$Li NMR measurements in this field-induced state reveal a gradual line broadening and a continuous evolution of the line shift with temperature, suggesting the development of local magnetic fields. The spin-lattice relaxation rate shows a peak around the crossover temperature 40 K and follows power-law behavior below this temperature.
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We present magnetization measurements on polycrystalline $beta$-Li$_2$IrO$_3$ under hydrostatic pressures up to 3 GPa and construct the temperature-pressure phase diagram of this material. The magnetically ordered phase with $T_{rm{N}}simeq 38$ K breaks down upon a pressure-induced first-order phase transition at $p_{rm{c}}$ $approx$ 1.4 GPa and gives way to a high-pressure phase, where a step-like feature in the magnetic susceptibility signals a structural dimerization with a loss of Ir$^{4+}$ magnetic moments. Nevertheless, magnetism manifests itself also above $p_{rm{c}}$ via the Curie-like susceptibility upturn with the effective moment of 0.7 $mu_B$. We suggest that a partially dimerized phase with a mixture of the magnetic and non-magnetic Ir$^{4+}$ sites develops above $p_{rm{c}}$. This phase is thermodynamically stable between 1.7 and 2.7 GPa according to our ab initio calculations. It confines the magnetic Ir$^{4+}$ sites to weakly coupled tetramers with the singlet ground state and no long-range magnetic order. Our results rule out the formation of a pressure-induced spin-liquid phase in $beta$-Li$_2$IrO$_3$ and reveal peculiarities of the magnetism collapse transition in a Kitaev material.
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.
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.
Recent scattering experiments in the 3D Kitaev magnet $beta$-Li$_2$IrO$_3$ have shown that a relatively weak magnetic field along the crystallographic ${bf b}$-axis drives the system from its incommensurate counter-rotating order to a correlated paramagnet, with a significant uniform `zigzag component superimposing the magnetization along the field. Here it is shown that the zigzag order is not emerging from its linear coupling to the field (via a staggered, off-diagonal element of the ${bf g}$-tensor), but from its intertwining with the incommensurate order and the longitudinal magnetization. The emerging picture explains all qualitative experimental findings at zero and finite fields, including the rapid decline of the incommensurate order with field and the so-called intensity sum rule. The latter are shown to be independent signatures of the smallness of the Heisenberg exchange $J$, compared to the Kitaev coupling $K$ and the off-diagonal anisotropy $Gamma$. Remarkably, in the regime of interest, the field $H^ast$ at which the incommensurate component vanishes, depends essentially only on $J$, which allows to extract an estimate of $J!simeq!4K$ from reported measurements of $H^ast$. We also comment on recent experiments in pressurized $beta$-Li$_2$IrO$_3$ and conclude that $J$ decreases with pressure.
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