No Arabic abstract
We have used resonant inelastic x-ray scattering to reveal optical magnons in a honeycomb lattice iridate $alpha$-Li$_{2}$IrO$_{3}$. The spectrum in the energy region 20-25 meV exhibits momentum dependence, of which energy is highest at the location of the magnetic Bragg peak, ($textit{h}, textit{k}$) = ($pm$0.32, 0), and lowered toward (0, 0) and ($pm$1, 0). We compare our data with a linear spin-wave theory based on a generic nearest-neighbor spin model. We find that a dominant bond-directional Kitaev interaction of order 20 meV is required to explain the energy scale observed in our study. The observed excitations are understood as stemming from optical magnon modes whose intensity is modulated by a structure factor, resulting in the apparent momentum dependence. We also observed diffuse magnetic scattering arising from the short-range magnetic correlation well above $textit{T}_{N}$. In contrast to Na$_{2}$IrO$_{3}$, this diffuse scattering lacks the $C_3$ rotational symmetry of the honeycomb lattice, suggesting that the bond anisotropy is far from negligible in $alpha$-Li$_{2}$IrO$_{3}$.
Heisenberg interactions are ubiquitous in magnetic materials and have been prevailing in modeling and designing quantum magnets. Bond-directional interactions offer a novel alternative to Heisenberg exchange and provide the building blocks of the Kitaev model, which has a quantum spin liquid (QSL) as its exact ground state. Honeycomb iridates, A2IrO3 (A=Na,Li), offer potential realizations of the Kitaev model, and their reported magnetic behaviors may be interpreted within the Kitaev framework. However, the extent of their relevance to the Kitaev model remains unclear, as evidence for bond-directional interactions remains indirect or conjectural. Here, we present direct evidence for dominant bond-directional interactions in antiferromagnetic Na2IrO3 and show that they lead to strong magnetic frustration. Diffuse magnetic x-ray scattering reveals broken spin-rotational symmetry even above Neel temperature, with the three spin components exhibiting nano-scale correlations along distinct crystallographic directions. This spin-space and real-space entanglement directly manifests the bond-directional interactions, provides the missing link to Kitaev physics in honeycomb iridates, and establishes a new design strategy toward frustrated magnetism.
We studied the effect of external pressure on the electrodynamic properties of $alpha$-Li$_2$IrO$_3$ single crystals in the frequency range of the phonon modes and the Ir $d$-$d$ transitions. The abrupt hardening of several phonon modes under pressure supports the onset of the dimerized phase at the critical pressure $P_c$=3.8 GPa. With increasing pressure an overall decrease in spectral weight of the Ir $d$-$d$ transitions is found up to $P_c$. Above $P_c$, the local (on-site) $d$-$d$ excitations gain spectral weight with increasing pressure, which hints at a pressure-induced increase in the octahedral distortions. The non-local (intersite) Ir $d$-$d$ transitions show a monotonic blue-shift and decrease in spectral weight. The changes observed for the non-local excitations are most prominent well above $P_c$, namely for pressures $geq$12 GPa, and only small changes occur for pressures close to $P_c$. The profile of the optical conductivity at high pressures ($sim$20 GPa) appears to be indicative for the dimerized state in iridates.
We report equilibrium and nonequilibrium optical measurements on the recently synthesized harmonic honeycomb iridate gamma-Li$_2$IrO$_3$ (LIO), as well as the layered honeycomb iridate Na$_2$IrO$_3$ (NIO). Using Fourier transform infrared microscopy we performed reflectance measurements on LIO, from which we obtained the optical conductivity below 2 eV. In addition we measured the photoinduced changed in reflectance, Delta R, as a function of time, t, temperature, T, and probe field polarization in both LIO and NIO. In LIO, Delta R(t,T) is anisotropic and comprised of three T dependent components. Two of these components are related to the onset of magnetic order and the third is related to a photoinduced population of metastable electronic excited states. In NIO, Delta R(t,T) has a single T dependent component that is strikingly similar to the electronic excitation component of Delta R in LIO. Through analysis and comparison of Delta R(t,T) for two compounds, we extract information on the onset of magnetic correlations at and above the transition temperature in LIO, the bare spin-flip scattering rate in equilibrium, the lifetime of low-lying quasiparticle excitations, and the polarization dependence of optical transitions that are sensitive to magnetic order.
We explore the response of Ir $5d$ orbitals to pressure in $beta$-$mathrm{Li_2IrO_3}$, a hyperhoneycomb iridate in proximity to a Kitaev quantum spin liquid (QSL) ground state. X-ray absorption spectroscopy reveals a reconstruction of the electronic ground state below 2 GPa, the same pressure range where x-ray magnetic circular dichroism shows an apparent collapse of magnetic order. The electronic reconstruction, which manifests a reduction in the effective spin-orbit (SO) interaction in $5d$ orbitals, pushes $beta$-$mathrm{Li_2IrO_3}$ further away from the pure $J_{rm eff}=1/2$ limit. Although lattice symmetry is preserved across the electronic transition, x-ray diffraction shows a highly anisotropic compression of the hyperhoneycomb lattice which affects the balance of bond-directional Ir-Ir exchange interactions driven by spin-orbit coupling at Ir sites. An enhancement of symmetric anisotropic exchange over Kitaev and Heisenberg exchange interactions seen in theoretical calculations that use precisely this anisotropic Ir-Ir bond compression provides one possible route to realization of a QSL state in this hyperhoneycomb iridate at high pressures.
Single-crystal x-ray diffraction studies with synchrotron radiation on the honeycomb iridate $alpha$-Li$_{2}$IrO$_{3}$ reveal a pressure-induced structural phase transition with symmetry lowering from monoclinic to triclinic at a critical pressure of $P_{c}$ = 3.8 GPa. According to the evolution of the lattice parameters with pressure, the transition mainly affects the $ab$ plane and thereby the Ir hexagon network, leading to the formation of Ir--Ir dimers. These observations are independently predicted and corroborated by our textit{ab initio} density functional theory calculations where we find that the appearance of Ir--Ir dimers at finite pressure is a consequence of a subtle interplay between magnetism, correlation, spin-orbit coupling, and covalent bonding. Our results further suggest that at $P_{c}$ the system undergoes a magnetic collapse. Finally we provide a general picture of competing interactions for the honeycomb lattices $A_{2}$$M$O$_{3}$ with $A$= Li, Na and $M$ = Ir, Ru.