Spin Waves and Revised Crystal Structure of Honeycomb IridateNa2IrO3

Abstract

We report inelastic neutron scattering measurements on Na2IrO3, a candidate for the Kitaev spin model on the honeycomb lattice. We observe spin-wave excitations below 5 meV with a dispersion that can be accounted for by including substantial further-neighbor exchanges that stabilize zig-zag magnetic order. The onset of long-range magnetic order below TN = 15.3 K is confirmed via the observation of oscillations in zero-field muon-spin rotation experiments. Combining single-crystal diffraction and density functional calculations we propose a revised crystal structure model with significant departures from the ideal 90• Ir-O-Ir bonds required for dominant Kitaev exchange. [6,7], in which edge-sharing IrO 6 octahedra form a honeycomb lattice [see Fig. 1b)], have been predicted to display novel magnetic states for composite spin-orbital moments coupled via frustrated exchanges. The exchange between neighboring Ir moments (called S i,j , S=1/2) is proposed to be [2]where J K > 0 is an Ising ferromagnetic (FM) term arising from superexchange via the Ir-O-Ir bond, and J 1 > 0 is the antiferromagnetic (AFM) Heisenberg exchange via direct Ir-Ir 5d overlap. Due to the strong spin-orbital admixture the Kitaev term J K couples only the components in the direction γ, normal to the plane of the Ir-O-Ir bond [8,9]. Because of the orthogonal geometry, different spin components along the cubic axes (γ = x, y, z) of the IrO 6 octahedron are coupled for the three bonds emerging out of each site in the honeycomb lattice. This leads to the strongly-frustrated Kitaev-Heisenberg (KH) model [2], which has conventional Néel order [see Fig. 3a)] for large J 1 , a stripy collinear AFM phase [see Fig. 3c)] for 0.4 α 0.8, where α = J K / (J K + 2J 1 ) (exact ground state at α = 1/2), and a quantum spin liquid with Majorana fermion excitations [10] at large J K (α 0.8). Measurements of the spin excitations are very important to determine the overall energy scale and the relevant magnetic interactions, however because Ir is a strong neutron absorber inelastic neutron scattering (INS) experiments are very challenging. Using an optimized setup we here report the first observation of dispersive spin wave excitations of Ir moments via INS. We show that the dispersion can be quantitatively accounted for by including substantial further-neighbor in-plane exchanges, which in turn stabilize zig-zag order. To inform future ab initio studies of microscopic models of the interactions we combine single-crystal xray diffraction with density functional calculations to determine precisely the oxygen positions, which are key in mediating the exchange and controlling the spin-orbital admixture via crystal field effects. We propose a revised crystal structure with much more symmetric IrO 6 octahedra, but with substantial departures from the ideal 90• Ir-O-Ir bonds required for dominant Kitaev exchange [9], and with frequent structural stacking faults. This differs from the currentlyadopted model, used by several band-structure calculations [14,15], with asymme...

Tuning into the Kitaev spin liquid phase: A spin model on the honeycomb lattice with two types of Heisenberg exchange couplings

“…The zigzag AFM order was found in experiments for the iridates [6][7][8][9]. This zig-zag order phase in the phase diagram appears in the third quarter of Fig.…”

“…A phase transition from a stripy antiferromagnetic(AFM) order to the Kitaev SL phase was predicted. Experiments for the iridates, however, found a zig-zag AFM order [6][7][8][9]. These progresses drive a number of further researches [10][11][12][13][14][15][16][17][18].…”

Finite-temperature phase diagram of the classical Kitaev-Heisenberg model

“…Using MC simulations, we investigate the finite temperature properties of this extended model (11) and present the finite temperature phase diagram in Fig.10. In its full parameter space, the extended KH model accommodates four different classical phases.…”

“…Recently, Jackeli and Khaliullin 1 suggested that the Kitaev model could actually be realized within the honeycomb iridates with general formula A 2 IrO 3 , since the anisotropic part of the interactions among Ir-ions has the same form as the Kitaev coupling. This suggestion has triggered a lot of experimental [7][8][9][10][11] and theoretical [12][13][14][15][16][17][18] activity in the study of Na 2 IrO 3 and Li 2 IrO 3 compounds.…”

Zigzag Magnetic Order in the Iridium OxideNa2IrO3

“…Magnetic susceptibility, spin wave spectra, and zigzag order parameter are calculated and compared to the experimental data, obtaining thereby the spin coupling constants in Na2IrO3 and Li2IrO3. In the quest for the materials with novel electronic phases, iridium oxide Na 2 IrO 3 came into focus recently [1][2][3][4][5][6][7] due to theoretical predictions [8,9] that this system may host Kitaev model physics and quantum spin Hall effect. Na 2 IrO 3 is an insulator with sizable and temperature independent optical gap ≃ 0.35 eV [7], and shows CurieWeiss type susceptibility [1,6] with moments corresponding to effective spin one-half of Ir 4+ ion with t 5 2g configuration [10].…”