Magnetic excitations and interactions in the Kitaev hyperhoneycomb iridate β−Li2IrO3

Abstract

We present a thorough experimental study of the three-dimensional hyperhoneycomb Kitaev magnet β-Li2IrO3, using a combination of inelastic neutron scattering (INS), time-domain THz spectroscopy, and heat capacity measurements. The main results include a massive low-temperature reorganization of the INS spectral weight that evolves into a broad peak centered around 12 meV, and a distinctive peak in the THz data at 2.8(1) meV. A detailed comparison to powder-averaged spin-wave theory calculations reveals that the positions of these two features are controlled by the anisotropic Γ coupling and the Heisenberg exchange J, respectively. The refined microscopic spin model places β-Li2IrO3 in close proximity to the Kitaev spin liquid phase.

Beyond Kitaev physics in strong spin-orbit coupled magnets

“…To give a rough idea of the typical energy scales and relative importance of the various microscopic couplings in Kitaev materials, we list in table 1 some representative numerical values for the most relevant microscopic couplings in four representative d 5 materials, α-RuCl 3 , Na 2 IrO 3 , α-Li 2 IrO 3 and β-Li 2 IrO 3 . These numbers have been extracted from ED computations of the Hubbard model on small clusters [6]), or ab initio quantum chemistry calculations [17], or fits of minimal models to experiments [47,49,101,115,124]. For a more complete overview of the numerical values extracted from various other methods see, e.g.…”

“…Fourth, other interactions are generally much weaker than K, but can nevertheless play a decisive role in the lowtemperature magnetic ordering because the K-Γ model is frustrated, as we discuss in more detail below. For example, the zigzag magnetic ordering in α-RuCl 3 [28,29,67] and Na 2 IrO 3 [21][22][23][24][25][26] is selected by the competition of K and Γ interactions with smaller Γ ′ , J and the longer-range Heisenberg coupling J 3 [6], while the incommensurate (IC) modulation [32] of the 3D hyperhoneycomb β-Li 2 IrO 3 , and many other experimental observations in this compound [96][97][98][99][100][101] can be well understood at the level of the J-K-Γ model, with dominant FM K, half-strong Γ and a much weaker J [46,47,49,51], see last row of table 1.…”

“…As was pointed by Maksimov Table 1. Numerical values (in units of meV) for the most relevant microscopic parameters of four representative d 5 materials, as extracted from: (i) exact diagonalization (ED) calculations of the Hubbard model on small clusters (first three materials [6]), (ii) ab initio quantum chemistry calculations [17], or (iii) fits to experiments based on minimal models of α-RuCl 3 [114] and β-Li 2 IrO 3 [47,49,101,115]. The values for the off-diagonal couplings Γ and Γ ′ correspond to the choice of the cubic frame shown in figure 2 for the layered materials (first three rows) and to the frame of equation ( 80) for β-Li 2 IrO 3 .…”

“…In the following we focus on the paradigm of β-Li 2 IrO 3 [32,35,96,101,115,242], which stands out among the three polymorphs for its quantitative level of description [46,47,49,51,242].…”

Soft-Chemical Synthesis, Structure Evolution, and Insulator-to-Metal Transition in Pyrochlore-like λ-RhO2

“…In the presence of strong spin–orbit coupling (SOC), as expected in 4d and 5d transition metals, a d 5 electronic configuration can give rise to an effective j = 1/2 ground state with enhanced correlations, paving the way for exotic long-range macroscopic quantum states such as in α-RuCl 3 , − Sr 2 IrO 4 , − Sr 3 Ir 2 O 7 , − and A 2 IrO 3 (A = Li and Na). − Compounds containing tetravalent rhodium (Rh 4+ , 4d 5 ), which is isoelectronic to Ru 3+ and is the 4d analogue of Ir 4+ , should possess electronic and magnetic properties similar to those observed in other d 5 compounds. However, studies of the chemistry and physics of Rh 4+ in the solid-state phase space remain rather limited due to the relatively greater stability of the trivalent state (Rh 3+ , 4d 6 ).…”