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arXiv:2309.15153 · npj Quantum Materials

Kinetic ferromagnetism and topological magnons of the hole-doped Kitaev spin liquid

Hui-Ke Jin, Wilhelm Kadow, Michael Knap, Johannes Knolle

Published Sep 4, 2024• 9 citations
arXivHTMLPDF

Abstract

Abstract We study the effect of hole doping on the Kitaev spin liquid (KSL) and find that for ferromagnetic (FM) Kitaev exchange K the system is very susceptible to the formation of a FM spin polarization. Through density matrix renormalization group (DMRG) simulations on finite systems, we uncover that the introduction of a single hole with a hopping strength of just t~0.28K is enough to disrupt fractionalization and polarize the spins in the [001] direction due to an order-by-disorder mechanism. Taking into account a material relevant FM anisotropic spin exchange KΓK drives the polarization towards the [111] direction via a reorientation transition into a topological FM state with chiral magnon excitations. We develop a parton mean-field theory incorporating fermionic holons and bosonic spinons/magnons, which accounts for the doping induced FM phases and topological magnon excitations. We discuss experimental signatures and implications for Kitaev candidate materials.

DOI
10.1038/s41535-024-00678-8

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Abstract We study the effect of hole doping on the Kitaev spin liquid (KSL) and find that for ferromagnetic (FM) Kitaev exchange K the system is very susceptible to the formation of a FM spin polarization. Through density matrix renormalization group (DMRG) simulations on finite systems, we uncover that the introduction of a single hole with a hopping strength of just t~0.28K is enough to disrupt fractionalization and polarize the spins in the [001] direction due to an order-by-disorder mechanism. Taking into account a material relevant FM anisotropic spin exchange KΓK drives the polarization towards the [111] direction via a reorientation transition into a topological FM state with chiral magnon excitations. We develop a parton mean-field theory incorporating fermionic holons and bosonic spinons/magnons, which accounts for the doping induced FM phases and topological magnon excitations. We discuss experimental signatures and implications for Kitaev candidate materials.
Abstract The dynamical response of a quantum spin liquid upon injecting a hole is a pertinent open question. In experiments, the hole spectral function, measured momentum-resolved in angle-resolved photoemission spectroscopy (ARPES) or locally in scanning tunneling microscopy (STM), can be used to identify spin liquid materials. In this study, we employ tensor network methods to simulate the time evolution of a single hole doped into the Kitaev spin-liquid ground state. Focusing on the gapped spin liquid phase, we reveal two fundamentally different scenarios. For ferromagnetic spin couplings, the spin liquid is highly susceptible to hole doping: a Nagaoka ferromagnet forms dynamically around the doped hole, even at weak coupling. By contrast, in the case of antiferromagnetic spin couplings, the hole spectrum demonstrates an intricate interplay between charge, spin, and flux degrees of freedom, best described by a parton mean-field ansatz of fractionalized holons and spinons. Moreover, we find a good agreement of our numerical results to the analytically solvable case of slow holes. Our results demonstrate that dynamical hole spectral functions provide rich information on the structure of fractionalized quantum spin liquids.
Abstract Doped quantum magnets, especially spin liquids with fractionalized excitations, have long attracted attention as a promising path towards unconventional superconductivity. We investigate the hole-doped Kitaev-Heisenberg ( t – J – K ) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We consider the behavior of the antiferromagnetic Kitaev spin-liquid phase as a function of hopping strength t and doping level. This reveals intriguing pairing tendencies only for tK≲0.65\frac{t}{K}\lesssim 0.65Kt​≲0.65 t K ≲ 0.65 , consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between spatial profiles of the plaquette operator and the charge density. We also construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t = 1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Spin-density wave-like behavior is found in the Kitaev limits, and in the stripy phase.
We investigate the hole-doped Kitaev-Heisenberg (ttt-JJJ-KKK) model on a two-leg ladder geometry using the density-matrix renormalization group (DMRG). We first consider the behavior of the antiferromagnetic Kitaev (AFK) spin-liquid phase as a function of hopping strength ttt and doping level. This reveals intriguing pairing tendencies only for tK≲0.65\frac{t}{K} \lesssim 0.65Kt​≲0.65, consistent with prior results on three-leg ladders, and firmly supports the emerging picture that the physics of doped Kitaev spin liquids strongly depends on the kinetic energy of the doped holes. Analysis of one- and two-hole doping uncovers close links between the spatial profiles of the plaquette operator and the charge density. We construct a doping-dependent phase diagram for antiferromagnetic Heisenberg interactions and intermediate hopping t=1t=1t=1. Upon doping, the rung-singlet region develops dominant superconducting correlations. Charge-density-wave correlations dominate at weak doping near the transition to the stripy phase. Spin-density wave-like behavior is found in the AFK and ferromagnetic Kitaev limits, and in the stripy phase.
We study the dynamics of fractionalized excitations in a Kitaev spin liquid (KSL) induced by a local magnetic field perpendicular to the Kitaev honeycomb lattice. The local magnetic field induces a dynamic excitation of a pair of fluxes described by a generally particle-hole asymmetric interacting resonant level model and the dynamics resembles that of a Kondo problem. The p-h asymmetry competes with the magnetic field and results in a rich phase diagram. Moreover, the magnetic field breaks the gauge equivalence of the ferromagnetic (FM) and anti-ferromagnetic (AFM) Kitaev couplings of the ground state and leads to dramatically different behaviors for the two cases. The latter experiences a first order phase transition during magnetization whereas the former does not. By studying the response of the KSL to the magnetic field in different regimes, we obtain the RG flow and phase diagram of the system in the whole space. This study can be generalized to the KSL in a uniform magnetic field and help resolve issues in recent experiments on KSL candidates.
We investigate magnetic-field-induced transitions in the dynamical spin correlation functions of the Kitaev spin liquid (KSL). Using time-dependent Majorana mean-field theory, we show that in the ferromagnetic KSL, the real-space propagation of spin correlations evolves from isotropic to highly anisotropic with increasing field strength. Notably, the anisotropy emerges as a unidirectional propagation of spin correlations, whose direction is dictated by the orientation of the magnetic field relative to the underlying Kitaev bond geometry. We analyze this phase transition through both a Majorana mean-field framework and perturbative approach, and propose some experimental signatures and possible detection schemes. We further demonstrate that a similar transition occurs in the antiferromagnetic KSL, and discuss why previous studies focusing on the [111] field direction have overlooked this phenomenon, which further suggests the possibility to identify such anisotropic dynamics in candidate Kitaev materials.
There has been great interest in identifying a Kitaev quantum spin liquid state in frustrated magnets with bond-dependent interactions. In particular, the experimental report of a half-quantized thermal Hall conductivity in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ in the presence of a magnetic field has generated excitement as it could be strong evidence for a field-induced chiral spin liquid. More recent experiments, however, provide a conflicting interpretation advocating for topological magnons in the field-polarized state as the origin of the nonquantized thermal Hall conductivity observed in their experiments. An inherent difficulty in distinguishing between the two scenarios is that the phase transition between a putative two-dimensional spin liquid and the field-polarized state exists only at zero temperature, while the behavior at finite temperature is mostly crossover phenomena. In this work, we provide insights into the finite-temperature crossover behavior between the spin excitation continuum in a quantum spin liquid and topological magnons in the field-polarized state in three different theoretical models with large Kitaev interactions. These models allow for a field-induced phase transition from a spin liquid (or an intermediate field-induced spin liquid) to the field-polarized state in the quantum model. We obtain the dynamical spin structure factor as a function of magnetic field using molecular dynamics simulations and compute thermal Hall conductivity in the field-polarized regime. We demonstrate the gradual evolution of the dynamical spin structure factor exhibiting crossover behavior near magnetic fields where zero-temperature phase transitions occur in the quantum model. We also examine nonlinear effects on topological magnons and the validity of thermal Hall conductivity computed using linear spin wave theory. We discuss the implications of our results for existing and future experiments.