Session B24: Spin Frustration: Kitaev Systems

Anomalous Thermal Conductivity and Magnetic Torque Response in the Honeycomb Magnet α−RuCl3

We report on the unusual behavior of the in-plane thermal conductivity κ and torque τ response in the Kitaev-Heisenberg material α-RuCl3. κ shows a striking enhancement with linear growth beyond H ~ 7 T, where magnetic order disappears, while τ for both of the in-plane symmetry directions shows an anomaly at the same field. The temperature and field dependence of κ are far more complex than conventional phonon and magnon contributions, and require us to invoke the presence of unconventional spin excitations whose properties are characteristic of a field-induced spin-liquid phase related to the enigmatic physics of the Kitaev model in an applied magnetic field.   

Magnetic exchange interactions in alpha-RuCl3: ab initio study.

We study the magnetic exchange interactions in alpha-RuCl3, a promising candidate of the Kitaev quantum spin liquid, by density functional theory calculation based on the newly reported rhombohedral crystal structure (R-3). By precisely mapping the total energies of constrained non-collinear spin configurations into the Kitaev-Heisenberg Hamiltonian, we have obtained various isotropic and anisotropic interaction parameters of the zigzag magnetic order. Our calculation reveals the importance of further neighbor anisotropic and interlayer interactions to stabilize the zigzag-type antiferromagnetic order as a ground state of the system. Comparison with previous studies are also made.   

Magnetism of single crystal α-RuCl3 investigated by muon spin rotation

We have performed muon spin rotation measurements on single crystal α-RuCl₃, a honeycomb layered ruthenate that has been proposed to be close to a Kitaev quantum spin liquid ground state. Our investigation finds a single transition to long range magnetic order near $8$~K, in contrast to the two distinct transitions we previously observed in muon spin rotation measurements of a α-RuCl₃ powder sample [Lang et al, PRB 94 (2016) 020407(R)]. We interpret this in the light of a structural phase transition that has been recently discovered in high purity single crystals of this material. By employing density functional theory calculations we identify the likely muon stopping sites in this material and combine these with dipolar field calculations to investigate which previously reported zigzag antiferromagnetic structures are consistent with the two experimentally observed muon rotation frequencies.   

Correlations and Thermal Transport in α-RuCl3 at Finite Temperature

α-RuCl₃ has emerged as a candidate material for realising strongly anisotropic and frustrated interactions beyond the celebrated Kitaev model. Despite falling into an antiferromagnetically ordered state at low temperature, the combination of inelastic neutron scattering (INS) [1], electron spin resonance (ESR) [2] and Raman [3] measurements on α-RuCl₃ have revealed persistent magnetic correlations up to high temperatures. Such experiments also show a strong discrepancy between the low-energy response for the magnetically ordered phase (T < T_N) and paramagnetic phase (T > T_N). Here we discuss this phenomenology with reference to recent ab-initio derived magnetic models including terms beyond the Kitaev interaction. In particular, we will address [4]: (i) The evolution of the dynamical response (INS, ESR, Raman), (ii) the influence of local excitations on the static susceptibility, and (iii) the magnetic thermal transport in different temperature regimes.
[1] Do et. al, Nat. Phys. 13, 1079 (2017).
[2] Wang et. al, arXiv:1706.06157 (2017).
[3] Sandilands et. al, PRL 114, 147201 (2015).
[4] Riedl et. al, in preparation.   

Possible Proximity Effect in Graphene/$\alpha$-RuCl$_3$ Layered Heterostructure

Recently, the layered antiferromagnetic Mott insulator $\alpha$-RuCl$_3$ has been studied in bulk crystals and found to be proximate to a Kitaev quantum spin liquid. Since the QSL is primarily a two-dimensional phenomenon, it may be possible to stabilize the QSL phase in exfoliated single- or few-layer $\alpha$-RuCl$_3$. We performed DC transport measurement on exfoliated $\alpha$-RuCl$_3$ flakes of various thicknesses and found the resistance to freeze out above 30 K, well above the N\'eel temperature. To access the low temperature regime with transport, we fabricated van der Waals heterostructure consisting of graphene and $\alpha$-RuCl$_3$ layers in close proximity. The graphene resistance is found to show an unusually strong temperature dependence compared to graphene on SiO$_2$. More strikingly, a ``kink'' in the resistance centered at 20 K is observed, close to the onset of antiferromagnetic ordering in $\alpha$-RuCl$_3$.   

Magnetism in α-RuCl3 Under Pressure

Bond-dependent interactions between magnetic moments can lead to strong frustration and nontrivial ground states. In particular, the extended Kitaev model can host a spin liquid state or different frozen states depending on the strength of the additional Heisenberg interaction. In experiments, the relative interaction strengths in materials can be varied by applying pressure.

In this contribution I will present how the muon spin rotation technique can be used to study such materials and show examples of our recent high-pressure studies in Kitaev candidate materials based on iridium. I will then discuss the discovery of a new high-pressure phase in α-RuCl₃ and possible scenarios that can be responsible for it.   

Field-induced phases in generalized Kitaev models and materials

By using a combination of exact diagonalization and semi-classical calculations we present a detailed analysis of possible field-induced phases obtained by adding to the Kitaev model further interaction terms. In particular we discuss the possibility of the appearance of topologically non-trivial field-induced spin liquid phases and the implications of these results in relation to the most studied α-RuCl₃ [1,2].
[1] Winter et al. arXiv:1707.08144
[2] Kaib et al. in preparation   

Effect of external magnetic field on Kitaev-Heisenberg model

Recent experiments on α-RuCl₃ have shown signatures of Kitaev quantum spin liquid when an external magnetic field larger than 7 T is applied. At zero field the system is known to order into a zigzag pattern that can be explained by several Kitaev-Heisenberg models. We explore the effects of the magnetic field on this ground state using classical Monte-Carlo simulations and spin wave analysis. We will show that the competition of the magnetic field with thermal fluctuations of the anisotropic Kitaev interaction leads to interesting new phases, including partially and fully incommensurate states.
  

Magnetic anisotropy due to pseudo-dipolar interactions in Kitaev-Heisenberg Model

Magnets with strong spin-orbit interactions often have large anisotropic interactions such as Kitaev (pseudo-dipolar) interactions. Such magnets show rich physics related to fluctuations such as spin liquid and order-by-disorder. On the other hand, later studies considering generalized effective models relevant to materials found that these models show rich ground state phase diagram due to the competition between different anisotropic interactions. Therefore, the understanding of the relative strength of anisotropic interactions is necessary for understanding the magnets, as well as to design a material with a desired property. However, there is no experimental method to estimate the strength of anisotropic interactions. In this work, we theoretically discuss the possibility of measuring the Kitaev interaction by magnetic-torque measurement. Focusing on Kitaev-Heisenberg model, we find that the pseudo-dipolar interactions give rise to a magnetic anisotropy with a unique temperature dependence [1]. Furthermore, we find that a linear combination of the magnetic-torque curve only depends on the Kitaev interactions. This allows an experimental observation of the pseudo-dipolar interactions. [1] H. Ishizuka, Phys. Rev. B 95, 184413 (2017).   

Cu2IrO3: a new honeycomb iridate material with an ideal lattice geometry for the Kitaev model

We present the first binary copper iridium oxide synthesized by a topotactic reaction from sodium iridate and copper chloride under mild conditions. Chemical analysis and crystallographic refinement reveal the composition Cu2IrO3 in a monoclinic C2/c space group with layered honeycomb structure. Magnetization measurements show a magnetic transition at low temperatures T = 2.75 K. The transition is subtle with weak hysteresis in the magnetization and without a clear signature in the heat capacity. The Curie-Weiss analysis reveals that the effective iridium magnetic moment and the exchange coupling strength in Cu2IrO3 are similar to its parent compound Na2IrO3. Resistivity measurements show insulator behavior with variable-range hopping. The frustration index f = 40 in Cu2IrO3 compared to 8 in Na2IrO3 brings copper iridate in closer proximity to a Kitaev spin liquid than its predecessors.   

Interplay between Kitaev Interaction and Single Ion Anisotropy in Ferromagnetic CrI3 and CrGeTe3 Monolayers

First-principles calculations are performed and analyzed to develop a rather simple Hamiltonian, in order to investigate the magnetic anisotropy of the recently discovered ferromagnetic monolayers made of CrI3 and CrGeTe3. The anisotropic exchange coupling in these two systems is surprisingly determined to be of Kitaev-type, which broadens the candidate materials that may realize quantum spin liquid states. Moreover, the interplay between this Kitaev interaction and single ion anisotropy (SIA) is found to naturally explain the Ising behavior of CrI3 versus the Heisenberg behavior of CrGeTe3, as well as other observed phenomena in other related 2D systems. Finally, both the Kitaev interaction and SIA are further found to be induced by the spin-orbit coupling of the heavy ligands (I of CrI3 or Te of CrGeTe3) rather than the 3d magnetic Cr ion.
  

Investigation of pressure driven transition in hyper-honeycomb iridates

Strong spin-orbit coupling in strongly correlated materials plays an important role in achieving quantum spin liquids. Among possible candidates, hyper-honeycomb iridates are particularly interesting as they may offer a three-dimensional spin liquid phase. We study the phase diagram of hyper-honeycomb iridate β-Li₂IrO₄ under pressure. Using ab initio densety functional theory results and experimental lattice parameters, we first derive a minimal spin model for low to high pressure regime. Exact diagonalization is used to determine the phase diagram as a function of pressure. Experimental implications, including branching ratio, are also discussed.   

Magnetic excitations in Z2 vortex crystals

Z₂ vortex crystals have been recently shown to be realized in triangular Kitaev-Heisenberg systems [1,2]. These Z₂ vortices are stablized by spin-orbit coupling introduced via the Kitaev term in the Hamiltonian. Here, we analyze the magnetic excitations of these Z₂ vortex crystals and investigate the spin wave spectrum, energy gap and dynamical spin structure factor in terms of the interplay between the Kitaev and isotropic Heisenberg interaction [3].
[1] I. Rousochatzakis et al., PRB 93, 104417 (2016).
[2] M. Becker et al., PRB 91, 155135 (2015)
[3] M. Li, I. Rousochatzakis, N. B. Perkins, in preparation