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Register a new userField-induced intertwined orders in 3D Mott-Kitaev honeycomb $beta$-Li2IrO3
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Honeycomb iridates are thought to have strongly spin-anisotropic exchange interactions that could lead to an extraordinary state of matter known as the Kitaev quantum spin liquid. The realization of this state requires almost perfectly frustrated interactions between the magnetic Ir$^{4+}$ ions, but small imbalances in energy make other ordered states more favorable. Indeed, the closeness in energy of these ordered states is itself a signature of the intrinsic frustration in the system. In this work, we illustrate that small magnetic fields can be employed to drive the frustrated quantum magnet $beta-$Li$_2$IrO$_3$,between different broken symmetry states, but without causing a true thermodynamic phase transition. This field-induced broken symmetry phase has all the signatures of a thermodynamic order parameter, but it is never truly formed in zero field. Rather, it is summoned when the scales of frustration are appropriately tipped, intertwined with other nearby quantum states.
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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.
The realization of Kitaev spin liquid, where spins on a honeycomb lattice are coupled ferromagnetically by bond-dependent anisotropic interactions, has been a sought-after dream. 5d iridium oxides $alpha$-Li2IrO3 and $alpha$-Na2IrO3 with a honeycomb lattice of Jeff = 1/2 moments recently emerged as a possible materialization. Strong signature of Kitaev physics, however, was not captured. Here we report the discovery of a complex iridium oxide $beta$-Li2IrO3 with Jeff = 1/2 moments on hyper-honeycomb lattice, a three-dimensional analogue of honeycomb lattice. A positive Curie-Weiss temperature $theta_{CW}$ ~ 40 K indicated dominant ferromagnetic interactions among Jeff = 1/2 moments in $beta$-Li2IrO3. A magnetic ordering with a small entropy change was observed at Tc = 38 K, which, with the application of magnetic field of only 3 T, changed to a fully polarized state of Jeff = 1/2 moments. Those results imply that hyper-honeycomb beta-Li2IrO3 is located in the vicinity to a Kitaev spin liquid.
A family of insulating iridates with chemical formula Li$_2$IrO$_3$ has recently been discovered, featuring three distinct crystal structures $alpha,beta,gamma$ (honeycomb, hyperhoneycomb, stripyhoneycomb). Measurements on the three-dimensional polytypes, $beta$- and $gamma$-Li$_2$IrO$_3$, found that they magnetically order into remarkably similar spiral phases, exhibiting a non-coplanar counter-rotating spiral magnetic order with equivalent q=0.57 wavevectors. We examine magnetic Hamiltonians for this family and show that the same triplet of nearest-neighbor Kitaev-Heisenberg-Ising (KJI) interactions reproduces this spiral order on both $beta,gamma$-Li$_2$IrO$_3$ structures. We analyze the origin of this phenomenon by studying the model on a 1D zigzag chain, a structural unit common to the three polytypes. The zigzag-chain solution transparently shows how the Kitaev interaction stabilizes the counter-rotating spiral, which is shown to persist on restoring the inter-chain coupling. Our minimal model makes a concrete prediction for the magnetic order in $alpha$-Li$_2$IrO$_3$.
The recently-synthesized iridate $beta$-Li$_2$IrO$_3$ has been proposed as a candidate to display novel magnetic behavior stabilized by frustration effects from bond-dependent, anisotropic interactions (Kitaev model) on a three-dimensional hyperhoneycomb lattice. Here we report a combined study using neutron powder diffraction and magnetic resonant x-ray diffraction to solve the complete magnetic structure. We find a complex, incommensurate magnetic order with non-coplanar and counter-rotating Ir moments, which surprisingly shares many of its features with the related structural polytype stripyhoneycomb $gamma$-Li$_2$IrO$_3$, where dominant Kitaev interactions have been invoked to explain the stability of the observed magnetic structure. The similarities of behavior between those two structural polytypes, which have different global lattice topologies but the same local connectivity, is strongly suggestive that the same magnetic interactions and the same underlying mechanism governs the stability of the magnetic order in both materials, indicating that both $beta$- and $gamma$-Li$_2$IrO$_3$ are strong candidates to realize dominant Kitaev interactions in a solid state material.
The layered honeycomb iridate $alpha$-Li$_2$IrO$_3$ displays an incommensurate magnetic structure with counterrotating moments on nearest-neighbor sites, proposed to be stabilized by strongly-frustrated anisotropic Kitaev interactions between spin-orbit entangled Ir$^{4+}$ magnetic moments. Here we report powder inelastic neutron scattering measurements that observe sharply dispersive low-energy magnetic excitations centered at the magnetic ordering wavevector, attributed to Goldstone excitations of the incommensurate order, as well as an additional intense mode above a gap $Deltasimeq2.3$ meV. Zero-field muon-spin relaxation measurements show clear oscillations in the muon polarization below the N{e}el temperature $T_{rm N}simeq15$ K with a time-dependent profile consistent with bulk incommensurate long-range magnetism. Pulsed field magnetization measurements observe that only about half the saturation magnetization value is reached at the maximum field of 64 T. A clear anomaly near 25 T indicates a transition to a phase with reduced susceptibility. The transition field has a Zeeman energy comparable to the zero-field gapped mode, suggesting gap suppression as a possible mechanism for the field-induced transition.
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