Excitations in the field-induced quantum spin liquid state of α-RuCl3

Abstract

2 The Kitaev model on a honeycomb lattice predicts a paradigmatic quantum spin liquid (QSL) exhibiting Majorana Fermion excitations. The insight that Kitaev physics might be realized in practice has stimulated investigations of candidate materials, recently including α-RuCl3. In all the systems studied to date, significant non-Kitaev interactions induce magnetic order at low temperature. However, inplane magnetic fields of roughly 8 Tesla suppress the long-range magnetic order in α-RuCl3 raising the intriguing possibility of a field-induced QSL exhibiting non-Abelian quasiparticle excitations. Here we present inelastic neutron scattering in α-RuCl3 in an applied magnetic field. At a field of 8 Tesla the spin waves characteristic of the ordered state vanish throughout the Brillouin zone. The remaining single dominant feature of the response is a broad continuum centered at the Γ point, previously identified as a signature of fractionalized excitations. This provides compelling evidence that a field-induced QSL state has been achieved. 3 The Kitaev model on a honeycomb lattice [1] has been exactly solved to reveal a unique quantum spin liquid (QSL) exhibiting itinerant Majorana Fermion and gauge-flux excitations. The Kitaev candidate system α-RuCl3 is an insulating magnetic material comprised of van der Waals coupled honeycomb layers of 4d 5 Ru 3+ cations nearly centered in edge-sharing RuCl6 octahedra. A strong cubic crystal field combined with spin-orbit coupling leads to a Kramer's doublet, nearly perfect J = 1/2 ground state [2][3][4], thus satisfying the conditions necessary for producing Kitaev couplings in the low energy Hamiltonian [5]. Similar to the widely studied honeycomb [6] and hyper-honeycomb [7] Iridates, at low temperatures α-RuCl3 exhibits small-moment antiferromagnetic zigzag order [3,[8][9][10][11] with TN ≈ 7 K for crystals with minimal stacking faults. In the zigzag state the magnetic excitation spectrum shows well-defined low-energy spin waves with minima at the M points (See Supplementary Materials (SM) Fig. S1 for the Brillouin Zone (BZ) definition) as well as a broad continuum that extends to much higher energies centered at the Γ points [12,13]. Above TN the spin waves disappear but the continuum remains, essentially unchanged until high temperatures of the order of 100 K [3,12,13]. In analogy with the situation for coupled spin-½ antiferromagnetic Heisenberg chains [14], the high energy part of the continuum has been interpreted as a signature of fractionalized excitations [3,12,13]. The overall features of the inelastic neutron scattering (INS) response resemble those of the Kitaev QSL [15][16][17] and are consistent with an unusual response seen in Raman scattering [16,18,19], suggesting that the system is proximate to a QSL state exhibiting magnetic Majorana fermion excitations [3,12,13]. Magnetic field offers a clean quantum tuning parameter for Kitaev materials [7][8][9]20] and can be applied on large single crystals facilitating INS studies. It is known to suppress the magnetic ord...

Magnon bound states versus anyonic Majorana excitations in the Kitaev honeycomb magnet α-RuCl3

“…The M1 peak is ubiquitous in all measured fields. The excitation M2' (orange line; the notation "prime" is used to differentiate distinct modes in the high field regime B > B c ) is split off from the M1 peak above 12 T, while the higher-energy M3' excitation (red line) appears at the lower boundary of the gapped continuum above 10-14 T. In previous experimental field-dependent studies on α-RuCl 3 ranging from inelastic neutron scattering (INS) 21 , to THz absorption 22 , to ESR 23 similar sharp magnetic excitations were reported and interpreted in terms of onemagnon or magnon bound states. In consideration of the narrow spectral form and energy of the corresponding excitations observed in our data, we assign the M2' peak to a two-magnon bound state and the M3' peak to either a multimagnon excitation or a van Hove singularity of the gapped continuum.…”

“…As B c is approached and through 6.7 T, the spectral weight of the continuum is massively redistributed. A new lowenergy mode (MB) evolves from the low-field M2 mode with a shoulder structure (M3) and the continuum of Majorana excitations is gapped above 8.1 T. A recent INS study reported a similarly broad, emerging excitation in the intermediate field-induced phase 21 . It was tentatively discussed as a possible Majorana bound state, but an ultimate assignment was hindered by the lack of a detailed temperature study.…”

“…To resolve these opposing scenarios, one needs to clarify the nature of quasiparticle excitations emergent in the intermediate-to-high-field phase. So far, neutron scattering 21 , THz spectroscopy 22 , and electron spin resonance 23 have revealed a significant reconfiguration of the mag-netic response through B c . These methods generally probe ∆S = ±1 excitations.…”

Magnetic field-dependent low-energy magnon dynamics in α–RuCl3

“…1(b)] [23,24]. Nevertheless, spectroscopic probes, including inelastic neutron scattering (INS) [25][26][27][28], spontaneous Raman scattering [29,30], time-domain terahertz spectroscopy (TDTS) [31][32][33], and electron paramagnetic resonance (EPR) [34], have discovered signatures of a field-induced QSL state above 7.5 T in the form of a broad continuum at the 2D magnetic Brillouin zone center. Yet a complete understanding of the origin of these excitations as well as of the spin dynamics is still lacking.…”

Pressure-induced dimerization and valence bond crystal formation in the Kitaev-Heisenberg magnet α−RuCl3

“…While electronic-structure calculations indicate that K is ferromagnetic in α-RuCl 3 and indeed defines the largest exchange energy scale [7,8,14,15], the debate on the minimal effective spin model and precise magnitude of the different couplings is not fully settled yet. By applying a magnetic field in the basal plane, the magnetic zigzag ground state can be suppressed [6,16,17] and the phase above this transition was identified as a quantum spin liquid, by NMR [18], thermal conductivity [19][20][21], terahertz spectroscopy [22], and neutron scattering experiments [23].Further, it was very recently shown by specific heat, magnetization, and NMR measurements [24,25] that the Néel …”