Magnetic excitations in the Kitaev material Na$_2$IrO$_3$ studied by neutron scattering

TL;DR

This paper probes magnetic excitations in Na2IrO3, a Kitaev-material candidate, using inelastic neutron scattering on co-aligned crystals to map the low-energy spin dynamics. The authors observe a magnon gap of $Δ = 1.7(1)$ meV and a largely two-dimensional dispersion dominated by zone-boundary zigzag-domain modes, with no detectable low-energy ferromagnetic fluctuations. Linear spin-wave theory applied to the $HK\Gamma\Gamma'$ Hamiltonian (model A3 from Kim 2020) accurately describes both the low-energy and high-energy features seen in RIXS, indicating a strong but non-dominant Kitaev exchange and highlighting the role of $J_1$, $\Gamma$, and $\Gamma'$ in Na2IrO3. Compared to α-RuCl3, Na2IrO3 displays a qualitative absence of a ferromagnetic instability, attributable to the different signs of NN interactions, underscoring distinct realizations of Kitaev physics in these materials. The work thus provides a consistent microscopic picture bridging high- and low-energy spectroscopies for Na2IrO3 and informs the broader understanding of Kitaev materials.

Abstract

Inelastic neutron scattering experiments with a large set of comounted Na$_2$IrO$_3$ crystals reveal the low-energy magnon dispersion in this candidate material for Kitaev physics. The magnon gap amounts to 1.7(1) meV and can be interpreted similarly to the sister compound $α$-RuCl$_{3}$ to stem from the zone boundaries in the antiferromagnetic zigzag structure. The neutron experiments find no evidence for low-energy excitations with ferromagnetic character, which contrasts to the findings in $α$-RuCl$_{3}$. Our results are consistent with a recently proposed microscopic model that involves an antiferromagnetic Heisenberg nearest-neighbor exchange in Na$_2$IrO$_3$ in contrast to the ferromagnetic one considered for $α$-RuCl$_{3}$. Although the magnetic response shows the signatures of bond-directional anisotropy in both materials the different relative signs of Kitaev and Heisenberg interaction result in different deviations from the initial Kitaev model. Low-energy ferromagnetic fluctuations cannot be considered as a fingerprint of ferromagnetic Kitaev interaction.

Figures (6)

• Figure 1: Rocking scans on the nuclear reflections (0, 0, 1) (a) and (0, 6, 0) (b) measured on IN8(2). The inset presents a photo of the 63 co-aligned Na$_2$IrO$_3$ single crystals glued on an Aluminum plate with 30 mm diameter.
• Figure 2: (a) Scheme of the zigzag magnetic order in Na$_2$IrO$_{3}$ : Ir sites (spheres) and ordered moments (arrows) are indicated in gray for a single honeycomb layer. The red, green and blue thick lines indicate the $X$, $Y$ and $Z$ bonds, respectively, with the colored double arrows denoting the component ferromagnetically coupled by the Kitaev interaction acting on this bond. The monoclinic in-plane lattice parameters are shown by the black rectangle with $\boldsymbol{a}$ perpendicular and $\boldsymbol{b}$ parallel to an Ir-Ir bond. On $Thales$, we scanned the (0, 1, $\frac{1}{2}$) magnetic Bragg peak along the $k$ (b) and $l$ (c) directions; some data were shifted vertically for clarity vertical_shifts. Temperature dependence of the (0, 1, $\frac{1}{2}$) magnetic Bragg peak amplitude (d) and background (e), for both scan directions. The vertical dashed line indicates $T_{\rm N}$. The dashed-dotted line in panel (d) is a guide to the eye, see main text. The horizontal dotted line in panel (e) indicates the paramagnetic background, averaged for both scan directions.
• Figure 3: INS results obtained on the cold TAS $Thales$: Constant-$\boldsymbol Q$ scans at the AFM zone center $(0, 1, 0.5)$ at various temperatures, (a), and at $(0,\,1,\,l)$ for selected $l$ values at $T$ = 1.5 K, (b). Background scans measured after rotating the sample by $\pm 45^{\circ}$ are subtracted from the data. (c) Constant-$E$ scans across the AFM zone center at $T$ = 1.5 K. A background scan measured after rotating the sample by $45^{\circ}$ has been subtracted from the data collected at $E$ = 2.25 meV, and the magenta dotted line indicates zero intensity. In panels (a-c), the monitor was set to $4\cdot10^6$ counts and solid lines are Gaussian fits to the data, see main text. From these fits the magnon dispersion along the $l$ (d) and the $k$ (e) directions is drawn. Black dashed-dotted lines in panels (d,e) are guides to the eye, while the blue dashed-dotted lines in (e) indicate the calculated spin-wave dispersion. The square blue symbol refers to the data point collected at $E=1.5$ meV.
• Figure 4: Data obtained on $IN8(1)$ normalized to $2\cdot10^5$ monitor counts. Constant-$E$ scans across AFM zone centers at (0, 1, 0.5) (a), (0, 1, 1) (b) and (0, 1, 1.5) (c) at $T$ = 1.5 K (some data are vertically shifted vertical_shifts). In (a) background scans (collected after rotation of the sample by 45$^{\circ}$) have been subtracted from the data sets with $E$ = 2, 3 and 4 meV. Panel (d) compares the $E=2$ meV data for different temperatures. Panel (e) shows energy scans at the AFM zone centers (0, 1, 0.5) and (0, 1, 1) after subtraction of the background measured by rotating the sample by 50$^{\circ}$.
• Figure 5: Constant-$E$ scans along $k$ direction obtained on $IN8(2)$ normalized to $2\cdot10^5$ monitor counts: across the AFM zone centers (0, 1, $l$) with $l=0.5$ (a) and $l=1.5$ (b), some data are shifted vertically vertical_shifts. Panel (c) shows constant-$E$ scans across (0, 1, 1.5) measured with a larger final energy, $k_f$ = 4.1 Å$^{-1}$. Because of the high background, intensity of the 6 meV scan has been divided by a factor 2. Panels (d-f) show constant-$E$ scans (with $k_f=2.662$ Å$^{-1}$) for different temperatures. In all panels solid lines represent fits with Gaussian functions.