Destabilization of Magnetic Order in a Dilute Kitaev Spin Liquid Candidate

P. Lampen-Kelley, A. Banerjee, A. A. Aczel, H. B. Cao, M. B. Stone, C. A. Bridges, J.-Q. Yan, S. E. Nagler, and D. Mandrus

Phys. Rev. Lett. 119, 237203 – Published 6 December 2017

Abstract

The insulating honeycomb magnet $α − {RuCl}_{3}$ exhibits fractionalized excitations that signal its proximity to a Kitaev quantum spin liquid state; however, at $T = 0$ , fragile long-range magnetic order arises from non-Kitaev terms in the Hamiltonian. Spin vacancies in the form of ${Ir}^{3 +}$ substituted for Ru are found to destabilize this long-range order. Neutron diffraction and bulk characterization of ${Ru}_{1 - x} {Ir}_{x} {Cl}_{3}$ show that the magnetic ordering temperature is suppressed with increasing $x$ , and evidence of zizag magnetic order is absent for $x > 0.3$ . Inelastic neutron scattering demonstrates that the signature of fractionalized excitations is maintained over the full range of $x$ investigated. The depleted lattice without magnetic order thus hosts a spin-liquid-like ground state that may indicate the relevance of Kitaev physics in the magnetically dilute limit of ${RuCl}_{3}$ .

Received 21 December 2016

DOI:https://doi.org/10.1103/PhysRevLett.119.237203

Physics Subject Headings (PhySH)

Magnetic phase transitions Magnetic susceptibility Quantum spin liquid

Crystal growth Neutron diffraction SQUID

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

P. Lampen-Kelley^1,2, A. Banerjee³, A. A. Aczel³, H. B. Cao³, M. B. Stone³, C. A. Bridges⁴, J.-Q. Yan², S. E. Nagler³, and D. Mandrus^1,2

¹Department of Materials Science and Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA
²Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
³Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
⁴Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

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Vol. 119, Iss. 23 — 8 December 2017

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Figure 1
(a) Magnetic susceptibility curves of ${Ru}_{1 - x} {Ir}_{x} {Cl}_{3}$ single crystals ( $x$ values indicated in legend) with a magnetic field of $B = 1$ T applied in the $a b$ plane. Inset: magnification of low-temperature range. Red arrow and black/grey arrows mark the evolution of $T_{N 1}$ and $T_{N 2}$ , respectively. (b) Field-dependent magnetization at 2 K. The data of (a) and (b) with normalization to Ru content are shown in Supplemental Material [68], Fig. S7. (c) Heat capacity curves of crystals with small Ir concentration. Solid lines are an estimate of the lattice contribution. Dotted lines are a guide to the eye.
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Figure 2
(a) Scan at 1.5 K collected at HB-1A along [1/2 0 L] through characteristic magnetic reflections $Q_{1} = (1 / 2 0 1)$ and $Q_{2} = (1 / 2 0 3 / 2)$ for a 50-mg single crystal with $x = 0.035$ . 20 K ( $T > T_{N}$ ) data are subtracted as a background. (b) Temperature scans of the scattering intensity at $Q_{1}$ and $Q_{2}$ . Scans along [1/2 0 L] at (c) 4 K and (d) 0.3 K in a 20-mg single crystal with $x = 0.06$ . 50 K data are subtracted as a background.
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Figure 3
Phase diagram of ${Ru}_{1 - x} {Ir}_{x} {Cl}_{3}$ . Transition temperatures $T_{N 1}$ (red symbols) and $T_{N 2}$ (blue symbols) determined from magnetic susceptibility, heat capacity, and neutron diffraction mark the boundaries of the ABC-stacked (ZZ1) and ABAB-stacked (ZZ2) zigzag phases in multiphase single crystals. Linear fitting to $T_{N} (x)$ (dotted lines) gives a critical dilution level for $T_{N 1} \to 0$ of $x \sim 0.11$ . The cusp at $T_{N 2}$ is driven below the experimental base temperature of 2 K (indicated by hashmarks) by $x ≃ 0.2$ ; at larger $x$ , $T_{N 2}$ is estimated by extrapolation to $d χ / d T = 0$ (grey symbols).
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Figure 4
Powder inelastic scattering of ${Ru}_{1 - x} {Ir}_{x} {Cl}_{3}$ measured at SEQUOIA with $Ei = 25 meV$ . The background from Al sample cans is subtracted from all data, and a correction for the increasing absorption cross section with Ir content is applied to allow direct comparison of intensities. (a)–(c) 2D spectra at 5 K ( $x$ values indicated). Constant- $Q$ cuts integrated over $Q = [0.5, 1] Å^{- 1}$ are shown at (d) 5 K and (e) 15 K. Solid lines are a guide to the eye. The data in (d),(e) are normalized by sample mass; see Supplemental Material [68], Sec. V for a discussion of the data normalized per Ru ion. (f) Constant- $Q$ cuts at 5 K for $x = 0$ and $x = 0.35$ after subtraction of a linear background. The $x = 0.35$ data have been scaled by a factor of 1.6 to match the height of the $x = 0$ data. Solid blue and red lines represent the calculated scattering of the upper mode of the Kitaev model convoluted with experimental resolution (grey bar) for $x = 0$ and $x = 0.35$ , respectively. At low energies, the scattering in the magnetically ordered parent compound departs from the model (open symbols, dashed line). (g) Constant-energy cuts at the $M 2$ peak position of [6,7] meV for $x = 0.35$ normalized by $n (ω) + 1$ to account for the temperature dependence of phonon contamination at low $Q$ . Solid lines are a guide to the eye.
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