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arXiv:1803.06100

Coexisting localized and itinerant gapless excitations in a quantum spin liquid candidate 1T-TaS$_2$

H. Murayama, Yuki Sato, Xiangzhuo Xing, Tomoya Taniguchi, S. Kasahara, Y. Kasahara, Masaro Yoshida, Yoshihiro Iwasa, Yuji Matsuda

Published Mar 16, 2018• 12 citations
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Abstract

To reveal the nature of elementary excitations in a quantum spin liquid (QSL), we measured low temperature thermal conductivity and specific heat of 1T-TaS$_2$, a QSL candidate material with frustrated triangular lattice of spin-1/2. The nonzero temperature linear specific heat coefficient $γ$ and the finite residual linear term of the thermal conductivity in the zero temperature limit $κ_0/T=κ/T(T\rightarrow 0)$ are clearly resolved. This demonstrates the presence of highly mobile gapless excitations, which is consistent with fractionalized spinon excitations that form a Fermi surface. Remarkably, an external magnetic field strongly suppresses $γ$, whereas it enhances $κ_0/T$. This unusual contrasting behavior in the field dependence of specific heat and thermal conductivity can be accounted for by the presence of two types of gapless excitations with itinerant and localized characters, as recently predicted theoretically (I. Kimchi et al., arXiv:1803.00013 (2018)). This unique feature of 1T-TaS$_2$ provides new insights into the influence of quenched disorder on the QSL.

DOI
10.48550/arxiv.1803.06100

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A quantum spin liquid (QSL) is an exotic state of matter characterized by quantum entanglement and the absence of any broken symmetry. A long-standing open problem, which is a key for fundamental understanding the mysterious QSL states, is how the quantum fluctuations respond to randomness due to quenched disorder. Transition metal dichalcogenide 1T-TaS$_2$ is a candidate material that hosts a QSL ground state with spin-1/2 on the two-dimensional perfect triangular lattice. Here, we performed systematic studies of low-temperature heat capacity and thermal conductivity on pure, Se-substituted and electron irradiated crystals of 1T-TaS$_2$. In pure 1T-TaS$_2$, the linear temperature term of the heat capacity $γT$ and the finite residual linear term of the thermal conductivity in the zero-temperature limit $κ_{0}/T\equivκ/T(T\rightarrow0)$ are clearly resolved, consistent with the presence of gapless spinons with a Fermi surface. Moreover, while the strong magnetic field slightly enhances $κ_0/T$, it strongly suppresses $γ$. These unusual contrasting responses to magnetic field imply the coexistence of two types of gapless excitations with itinerant and localized characters. Introduction of additional weak random exchange disorder in 1T-Ta(S$_{1-x}$Se$_x$)$_2$ leads to vanishing of $κ_0/T$, indicating that the itinerant gapless excitations are sensitive to the disorder. On the other hand, in both pure and Se-substituted systems, the magnetic contribution of the heat capacity obeys a universal scaling relation, which is consistent with a theory that assumes the presence of localized orphan spins forming random singlets. Electron irradiation in pure 1T-TaS$_2$ largely enhances $γ$ and changes the scaling function dramatically, suggesting a possible new state of spin liquid.

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Frustrated magnetism provides a rich platform for realizing exotic quantum phases in condensed matter systems. Among these, quantum spin liquids (QSLs) are a particularly intriguing class of states that exhibit no magnetic ordering and preserve all symmetries down to zero temperature. Just as conventional magnets can be thought of as spin crystals,QSLs represent their liquid analogs. This thesis explores two broad types of QSLs in two-dimensional magnets, with a focus on their dynamic properties and the nature of transitions from conventional magnetic states into QSL phases. QSLs are topological phases that host fractionalized excitations known as spinons. In these states, mobile spinons are coupled to an emergent gauge field, forming a highly entangled phase of matter. The first part of this thesis focuses on Dirac spin liquids (DSLs), a class of QSLs where spinons exhibit a gapless Dirac dispersion. To study the dynamicsof these spin liquids beyond leading-order mean-field theory, we develop a novel large-N fermionic limit of gapless spinons. In this limit, all gauge excitations are suppressed, and the leading-order corrections instead arise from order parameter fluctuations, which may condense and drive transitions into symmetry-broken phases from the parent DSL. Incorporating random phase approximation (RPA) corrections to the spin susceptibility, we find that sharp, spin-wave–like modes are recovered in the excitation spectrum. This methodology successfully captures characteristic features of the dynamics near phase transitions and in weakly symmetry-broken phases proximate to a DSL. We apply this approach to microscopic models, including the J1-J2 XXZ model on the triangular lattice and the J1-J3 XXZ model on the honeycomb lattice. These models closely represent a wide range of frustrated materials, such as triangular and honeycomb cobaltates and triangular ytterbium compounds. Our theoretical predictions show excellent agreement with experimentally measured inelastic neutron scattering spectra from these materials. Gapless spinons can also sometimes become gapped through chiral symmetry breaking, leading to the formation of a chiral spin liquid (CSL). The CSL is an archetypal bosonic realization of a fractional quantum Hall (FQH) state at half-filling, and has been proposed as a time-reversal–breaking ground state in a variety of frustrated spin models. The second part of this thesis addresses the intriguing possibility of realizing a CSL through the "melting" of a chiral spin crystal—a conventional magnet with non-coplanar ordering. Such a transition offers a physically appealing analogue to the melting of a Wigner crystal into a fermionic FQH liquid. Focusing on the kagome lattice, where chiral interactions are knownto stabilize a CSL ground state, we study the effects of additional long-range Heisenberg interactions and demonstrate a phase transition into a non-coplanar octahedral magnetic order. To describe the universal class of transition between a CSL and a non-coplanar anti-ferromagnetic order, we then develop a novel Chern-Simons–matter field theory framework, constrained by symmetry principles and symmetry fractionalization patterns. This thesis thus provides new insights into the dynamical signatures and phase transitions of quantum spin liquids, offering a bridge between theoretical models and experimental observations in frustrated magnetic systems.

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Coexisting localized and itinerant gapless excitations in a quantum spin liquid candidate 1T-TaS2_22​
To reveal the nature of elementary excitations in a quantum spin liquid (QSL), we measured low temperature thermal conductivity and specific heat of 1T-TaS2_22​, a QSL candidate material with frustrated triangular lattice of spin-1/2. The nonzero temperature linear specific heat coefficient γγγ and the finite residual linear term of the thermal conductivity in the zero temperature limit κ0/T=κ/T(T→0)κ_0/T=κ/T(T\rightarrow 0)κ0​/T=κ/T(T→0) are clearly resolved. This demonstrates the presence of highly mobile gapless excitations, which is consistent with fractionalized spinon excitations that form a Fermi surface. Remarkably, an external magnetic field strongly suppresses γγγ, whereas it enhances κ0/Tκ_0/Tκ0​/T. This unusual contrasting behavior in the field dependence of specific heat and thermal conductivity can be accounted for by the presence of two types of gapless excitations with itinerant and localized characters, as recently predicted theoretically (I. Kimchi et al., arXiv:1803.00013 (2018)). This unique feature of 1T-TaS2_22​ provides new insights into the influence of quenched disorder on the QSL.
Effect of quenched disorder on a quantum spin liquid state of triangular-lattice antiferromagnet 1T-TaS2_22​
A quantum spin liquid (QSL) is an exotic state of matter characterized by quantum entanglement and the absence of any broken symmetry. A long-standing open problem, which is a key for fundamental understanding the mysterious QSL states, is how the quantum fluctuations respond to randomness due to quenched disorder. Transition metal dichalcogenide 1T-TaS2_22​ is a candidate material that hosts a QSL ground state with spin-1/2 on the two-dimensional perfect triangular lattice. Here, we performed systematic studies of low-temperature heat capacity and thermal conductivity on pure, Se-substituted and electron irradiated crystals of 1T-TaS2_22​. In pure 1T-TaS2_22​, the linear temperature term of the heat capacity γTγTγT and the finite residual linear term of the thermal conductivity in the zero-temperature limit κ0/T≡κ/T(T→0)κ_{0}/T\equivκ/T(T\rightarrow0)κ0​/T≡κ/T(T→0) are clearly resolved, consistent with the presence of gapless spinons with a Fermi surface. Moreover, while the strong magnetic field slightly enhances κ0/Tκ_0/Tκ0​/T, it strongly suppresses γγγ. These unusual contrasting responses to magnetic field imply the coexistence of two types of gapless excitations with itinerant and localized characters. Introduction of additional weak random exchange disorder in 1T-Ta(S1−x_{1-x}1−x​Sex_xx​)2_22​ leads to vanishing of κ0/Tκ_0/Tκ0​/T, indicating that the itinerant gapless excitations are sensitive to the disorder. On the other hand, in both pure and Se-substituted systems, the magnetic contribution of the heat capacity obeys a universal scaling relation, which is consistent with a theory that assumes the presence of localized orphan spins forming random singlets. Electron irradiation in pure 1T-TaS2_22​ largely enhances γγγ and changes the scaling function dramatically, suggesting a possible new state of spin liquid.
This paper reports the effect of randomness on a quantum spin liquid state of 1T-TaS2{}_{2}2​ with a two-dimensional perfect triangular lattice. Systematic measurements of heat capacity and thermal conductivity in pure, Se-substituted, and electron-irradiated crystals reveal the microscopic coexistence of localized orphan spins that form random valence bonds and itinerant spinons that appear to form a Fermi surface.
Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations.Several quasi-two-dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacking.In this paper, we show that the interplane thermal conductivity in layered QSLs carries a unique signature of fractionalization.We examine several types of gapless QSL phases-a Z 2 QSL with either a Dirac spectrum or a spinon Fermi surface, and a Uð1Þ QSL with a Fermi surface-and consider both clean and disordered systems.In all cases, the in-plane and c-axis thermal conductivities have a different power-law dependence on temperature because of the different mechanisms of transport in the two directions: In the planes, the thermal current is carried by fractionalized excitations, whereas the interplane current is carried by integer (nonfractional) excitations.In layered Z 2 and Uð1Þ QSLs with a Fermi surface, and in the disordered Z 2 QSL with a Dirac dispersion, the c-axis thermal conductivity is parametrically smaller than the in-plane one but parametrically larger than the phonon contribution at low temperatures.
Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations. Several quasi-two-dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacking. In this paper, we show that the interplane thermal conductivity in layered QSLs carries a unique signature of fractionalization. We examine several types of gapless QSL phases - a Z2 QSL with either a Dirac spectrum or a spinon Fermi surface, and a U(1) QSL with a Fermi surface - and consider both clean and disordered systems. In all cases, the in-plane and c-axis thermal conductivities have a different power-law dependence on temperature because of the different mechanisms of transport in the two directions: In the planes, the thermal current is carried by fractionalized excitations, whereas the interplane current is carried by integer (nonfractional) excitations. In layered Z2 and U(1) QSLs with a Fermi surface, and in the disordered Z2 QSL with a Dirac dispersion, the c-axis thermal conductivity is parametrically smaller than the in-plane one but parametrically larger than the phonon contribution at low temperatures.
Quantum spin liquids (QSLs) host exotic fractionalized magnetic and gauge-field excitations whose microscopic origins and experimental verification remain frustratingly elusive. In the absence of static magnetic order, the spin excitation spectrum constitutes the crucial probe of QSL behavior, but its theoretical computation is a serious challenge. Here we employ state-of-the-art tensor-network methods to obtain the full dynamical spectral function of the J1J_1J1​-J2J_2J2​ kagome Heisenberg model and benchmark our results by tracking their evolution across the magnetically ordered and QSL phases. Reducing ∣J2∣/J1|J_2|/J_1∣J2​∣/J1​ causes increasingly strong spin-wave renormalization, flattening these modes then merging them into a continuum characteristic of deconfined spinons at all finite energies in the QSL. The low-energy continuum and the occurrence of gap closure at multiple high-symmetry points identify this gapless QSL as the U(1) Dirac spin liquid. These results establish a unified understanding of spin excitations in highly frustrated quantum magnets and provide clear spectral fingerprints for experimental detection in candidate kagome QSL materials.
Frustrated magnetism provides a rich platform for realizing exotic quantum phases in condensed matter systems. Among these, quantum spin liquids (QSLs) are a particularly intriguing class of states that exhibit no magnetic ordering and preserve all symmetries down to zero temperature. Just as conventional magnets can be thought of as spin crystals,QSLs represent their liquid analogs. This thesis explores two broad types of QSLs in two-dimensional magnets, with a focus on their dynamic properties and the nature of transitions from conventional magnetic states into QSL phases. QSLs are topological phases that host fractionalized excitations known as spinons. In these states, mobile spinons are coupled to an emergent gauge field, forming a highly entangled phase of matter. The first part of this thesis focuses on Dirac spin liquids (DSLs), a class of QSLs where spinons exhibit a gapless Dirac dispersion. To study the dynamicsof these spin liquids beyond leading-order mean-field theory, we develop a novel large-N fermionic limit of gapless spinons. In this limit, all gauge excitations are suppressed, and the leading-order corrections instead arise from order parameter fluctuations, which may condense and drive transitions into symmetry-broken phases from the parent DSL. Incorporating random phase approximation (RPA) corrections to the spin susceptibility, we find that sharp, spin-wave–like modes are recovered in the excitation spectrum. This methodology successfully captures characteristic features of the dynamics near phase transitions and in weakly symmetry-broken phases proximate to a DSL. We apply this approach to microscopic models, including the J1-J2 XXZ model on the triangular lattice and the J1-J3 XXZ model on the honeycomb lattice. These models closely represent a wide range of frustrated materials, such as triangular and honeycomb cobaltates and triangular ytterbium compounds. Our theoretical predictions show excellent agreement with experimentally measured inelastic neutron scattering spectra from these materials. Gapless spinons can also sometimes become gapped through chiral symmetry breaking, leading to the formation of a chiral spin liquid (CSL). The CSL is an archetypal bosonic realization of a fractional quantum Hall (FQH) state at half-filling, and has been proposed as a time-reversal–breaking ground state in a variety of frustrated spin models. The second part of this thesis addresses the intriguing possibility of realizing a CSL through the "melting" of a chiral spin crystal—a conventional magnet with non-coplanar ordering. Such a transition offers a physically appealing analogue to the melting of a Wigner crystal into a fermionic FQH liquid. Focusing on the kagome lattice, where chiral interactions are knownto stabilize a CSL ground state, we study the effects of additional long-range Heisenberg interactions and demonstrate a phase transition into a non-coplanar octahedral magnetic order. To describe the universal class of transition between a CSL and a non-coplanar anti-ferromagnetic order, we then develop a novel Chern-Simons–matter field theory framework, constrained by symmetry principles and symmetry fractionalization patterns. This thesis thus provides new insights into the dynamical signatures and phase transitions of quantum spin liquids, offering a bridge between theoretical models and experimental observations in frustrated magnetic systems.