Symmetry Reduction in the Quantum Kagome Antiferromagnet Herbertsmithite

Controlled Frustration Release on the Kagome Lattice by Uniaxial-Strain Tuning

It is predicted that strongly interacting spins on a frustrated lattice may lead to a quantum disordered ground state or even form a quantum spin liquid with exotic low-energy excitations. However, a controlled tuning of the frustration strength, separating its effects from those of disorder and other factors, is pending. Here, we perform comprehensive ^{1}H NMR measurements on Y_{3}Cu_{9}(OH)_{19}Cl_{8} single crystals revealing an unusual Q[over →]=(1/3×1/3) antiferromagnetic state below T_{N}=2.2  K. By applying in situ uniaxial stress, we break the symmetry of this disorder-free, frustrated kagome system in a controlled manner yielding a linear increase of T_{N} with strain, in line with theoretical predictions for a distorted kagome lattice. In-plane strain of ≈1% triggers a sizable enhancement ΔT_{N}/T_{N}≈10% due to a release of frustration, demonstrating its pivotal role for magnetic order.

Spin-flip-driven reversal of the angle-dependent magnetic torque in layered antiferromagnetic Ca0.9Sr0.1Co2As2

Spin-flip transition can occur in antiferromagnets with strong magnetocrystalline anisotropy, inducing a significant modification of the anisotropic magnetic properties through phase conversion. In contrast to ferromagnets, antiferromagnets have not been thoroughly examined in terms of their anisotropic characteristics. We investigated the magnetic-field and angle-dependent magnetic properties of Ising-type antiferromagnetic Ca_0.9Sr_0.1Co₂As₂ using magnetic torque measurements. An A-type antiferromagnetic order emerges below T_N = 97 K aligned along the magnetically easy c-axis. The reversal of the angle-dependent torque across the spin-flip transition was observed, revealing the strong influence of the magnetocrystalline anisotropy on the magnetic properties. Based on the easy-axis anisotropic spin model, we theoretically generated torque data and identified specific spin configurations associated with the magnetic torque variation in the presence of a rotating magnetic field. Our results enrich fundamental and applied research on diverse antiferromagnetic compounds by shedding new light on the distinct magnetic features of the Ising-type antiferromagnet.

Freezing of the Lattice in the Kagome Lattice Heisenberg Antiferromagnet Zn-Barlowite ZnCu_{3}(OD)_{6}FBr

We use ^{79}Br nuclear quadrupole resonance (NQR) to demonstrate that ultraslow lattice dynamics set in below the temperature scale set by the Cu-Cu superexchange interaction J (≃160  K) in the kagome lattice Heisenberg antiferromagnet Zn-barlowite. The lattice completely freezes below 50 K, and ^{79}Br NQR line shapes become twice broader due to increased lattice distortions. Moreover, the frozen lattice exhibits an oscillatory component in the transverse spin echo decay, a typical signature of pairing of nuclear spins by indirect nuclear spin-spin interaction. This indicates that some Br sites form structural dimers via a pair of kagome Cu sites prior to the gradual emergence of spin singlets below ∼30  K. Our findings underscore the significant roles played by subtle structural distortions in determining the nature of the disordered magnetic ground state of the kagome lattice.

The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate

Disordered magnetic states known as spin liquids are of paramount importance in both fundamental and applied science. A classical state of this kind was predicted for the Ising antiferromagnetic triangular model, while additional non-commuting exchange terms were proposed to induce its quantum version-a quantum spin liquid. However, these predictions have not yet been confirmed experimentally. Here, we report evidence for such a state in the triangular-lattice antiferromagnet NdTa₇O₁₉. We determine its magnetic ground state, which is characterized by effective spin-1/2 degrees of freedom with Ising-like nearest-neighbour correlations and gives rise to spin excitations persisting down to the lowest accessible temperature of 40 mK. Our study demonstrates the key role of strong spin-orbit coupling in stabilizing spin liquids that result from magnetic anisotropy and highlights the large family of rare-earth (RE) heptatantalates RETa₇O₁₉ as a framework for realization of these states, which represent a promising platform for quantum applications.

Heat Transport in Herbertsmithite: Can a Quantum Spin Liquid Survive Disorder?

One favorable situation for spins to enter the long-sought quantum spin liquid (QSL) state is when they sit on a kagome lattice. No consensus has been reached in theory regarding the true ground state of this promising platform. The experimental efforts, relying mostly on one archetypal material ZnCu_{3}(OH)_{6}Cl_{2}, have also led to diverse possibilities. Apart from subtle interactions in the Hamiltonian, there is the additional degree of complexity associated with disorder in the real material ZnCu_{3}(OH)_{6}Cl_{2} that haunts most experimental probes. Here we resort to heat transport measurement, a cleaner probe in which instead of contributing directly, the disorder only impacts the signal from the kagome spins. For ZnCu_{3}(OH)_{6}Cl_{2}, we observed no contribution by any spin excitation nor obvious field-induced change to the thermal conductivity. These results impose strong constraints on various scenarios about the ground state of this kagome compound: while certain quantum paramagnetic states other than a QSL may serve as natural candidates, a QSL state, gapless or gapped, must be dramatically modified by the disorder so that the kagome spin excitations are localized.

Crystal chemistry criteria of the existence of spin liquids on the kagome lattice

The structural-magnetic models of 25 antiferromagnetic kagome cuprates similar to herbertsmithite (ZnCu₃(OH)₆Cl₂)-a perspective spin liquid-have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii-Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is strengthened in all the kagome AFM, except herbertsmithite, by one more type of the anisotropy (duality) of the third in lengthJ3 magnetic couplings (strongJ3(J1₂) next-to-nearest-neighbor couplings in linear chains along the triangle edges and very weak FM or AFMJ3(J_d) couplings along the hexagon diagonals). The above couplings are crystallographically identical, but are divided to two types of different in strength magnetic interactions. The existence of duality ofJ3 couplings originated from the structure of the kagome lattice itself. Only combined contributions of dualJ3 couplings with anisotropic Dzyaloshinskii-Moriya interactions are capable to suppress frustration of kagome antiferromagnetics. It has been demonstrated that the possibility of elimination of such a duality in herbertsmithite, which made it a spin liquid, constitutes a rare lucky event in the kagome system. Three crystal chemistry criteria of the existence of spin liquids on the kagome lattice have been identified: first, the presence of frustrated kagome lattices with strong dominant antiferromagnetic nearest-neighborJ1 couplings competing only with each other in small triangles; second, magnetic isolation of these frustrated kagome lattices; and third, the absence of duality of the third in lengthJ3 magnetic couplings.

Dynamic fingerprint of fractionalized excitations in single-crystalline Cu3Zn(OH)6FBr

Beyond the absence of long-range magnetic orders, the most prominent feature of the elusive quantum spin liquid (QSL) state is the existence of fractionalized spin excitations, i.e., spinons. When the system orders, the spin-wave excitation appears as the bound state of the spinon-antispinon pair. Although scarcely reported, a direct comparison between similar compounds illustrates the evolution from spinon to magnon. Here, we perform the Raman scattering on single crystals of two quantum kagome antiferromagnets, of which one is the kagome QSL candidate Cu₃Zn(OH)₆FBr, and another is an antiferromagnetically ordered compound EuCu₃(OH)₆Cl₃. In Cu₃Zn(OH)₆FBr, we identify a unique one spinon-antispinon pair component in the E_2g magnetic Raman continuum, providing strong evidence for deconfined spinon excitations. In contrast, a sharp magnon peak emerges from the one-pair spinon continuum in the E_g magnetic Raman response once EuCu₃(OH)₆Cl₃ undergoes the antiferromagnetic order transition. From the comparative Raman studies, we can regard the magnon mode as the spinon-antispinon bound state, and the spinon confinement drives the magnetic ordering.

Chemistry of Quantum Spin Liquids

Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection of solid-state chemistry, condensed matter physics, and materials science and engineering. In this review, we provide the current status of the crystal chemistry, synthetic techniques, physical properties, and research methods in the field of quantum spin liquids. We highlight a number of specific quantum spin liquid candidate materials and their structure-property relationships, elucidating their fascinating behavior and connecting it to the intricacies of their structures. Furthermore, we share our thoughts on defects and their inevitable presence in materials, of which quantum spin liquids are no exception, which can complicate the interpretation of characterization of these materials, and urge the community to extend their attention to materials preparation and data analysis, cognizant of the impact of defects. This review was written with the intention of providing guidance on improving the materials design and growth of quantum spin liquids, and to paint a picture of the beauty of the underlying chemistry of this exciting class of materials.

Origin of Magnetic Ordering in a Structurally Perfect Quantum Kagome Antiferromagnet

The ground state of the simple Heisenberg nearest-neighbor quantum kagome antiferromagnetic model is a magnetically disordered spin liquid, yet various perturbations may lead to fundamentally different states. Here we disclose the origin of magnetic ordering in the structurally perfect kagome material YCu_{3}(OH)_{6}Cl_{3}, which is free of the widespread impurity problem. Ab initio calculations and modeling of its magnetic susceptibility reveal that, similar to the archetypal case of herbertsmithite, the nearest-neighbor exchange is by far the dominant isotropic interaction. Dzyaloshinskii-Moriya (DM) anisotropy deduced from electron spin resonance, susceptibility, and specific-heat data is, however, significantly larger than in herbertsmithite. By enhancing spin correlations within kagome planes, this anisotropy is essential for magnetic ordering. Our study isolates the effect of DM anisotropy from other perturbations and unambiguously confirms the predicted phase diagram.

Spin-lattice Coupling and the Emergence of the Trimerized Phase in the S=1 Kagome Antiferromagnet Na_{2}Ti_{3}Cl_{8}

Spin-1 antiferromagnets are abundant in nature, but few theories exist to understand their properties and behavior when geometric frustration is present. Here we study the S=1 kagome compound Na_{2}Ti_{3}Cl_{8} using a combination of density functional theory, exact diagonalization, and density matrix renormalization group approaches to achieve a first principles supported explanation of its exotic magnetic phases. We find that the effective magnetic Hamiltonian includes essential non-Heisenberg terms that do not stem from spin-orbit coupling, and both trimerized and spin-nematic magnetic phases are relevant. The experimentally observed structural transition to a breathing kagome phase is driven by spin-lattice coupling, which favors the trimerized magnetic phase against the quadrupolar one. We thus show that lattice effects can be necessary to understand the magnetism in frustrated magnetic compounds and surmise that Na_{2}Ti_{3}Cl_{8} is a compound that cannot be understood from only electronic or only lattice Hamiltonians, very much like VO_{2}.

Site-Specific Structure at Multiple Length Scales in Kagome Quantum Spin Liquid Candidates

Realizing a quantum spin liquid (QSL) ground state in a real material is a leading issue in condensed matter physics research. In this pursuit, it is crucial to fully characterize the structure and influence of defects, as these can significantly affect the fragile QSL physics. Here, we perform a variety of cutting-edge synchrotron X-ray scattering and spectroscopy techniques, and we advance new methodologies for site-specific diffraction and L-edge Zn absorption spectroscopy. The experimental results along with our first-principles calculations address outstanding questions about the local and long-range structures of the two leading kagome QSL candidates, Zn-substituted barlowite (Cu₃Zn _x Cu_1-x (OH)₆FBr) and herbertsmithite (Cu₃Zn(OH)₆Cl₂). On all length scales probed, there is no evidence that Zn substitutes onto the kagome layers, thereby preserving the QSL physics of the kagome lattice. Our calculations show that antisite disorder is not energetically favorable and is even less favorable in Zn-barlowite compared to herbertsmithite. Site-specific X-ray diffraction measurements of Zn-barlowite reveal that Cu²⁺ and Zn²⁺ selectively occupy distinct interlayer sites, in contrast to herbertsmithite. Using the first measured Zn L-edge inelastic X-ray absorption spectra combined with calculations, we discover a systematic correlation between the loss of inversion symmetry from pseudo-octahedral (herbertsmithite) to trigonal prismatic coordination (Zn-barlowite) with the emergence of a new peak. Overall, our measurements suggest that Zn-barlowite has structural advantages over herbertsmithite that make its magnetic properties closer to an ideal QSL candidate: its kagome layers are highly resistant to nonmagnetic defects while the interlayers can accommodate a higher amount of Zn substitution.

Thermodynamic, Dynamic, and Transport Properties of Quantum Spin Liquid in Herbertsmithite from an Experimental and Theoretical Point of View

In our review, we focus on the quantum spin liquid (QSL), defining the thermodynamic, transport, and relaxation properties of geometrically frustrated magnet (insulators) represented by herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 . The review mostly deals with an historical perspective of our theoretical contributions on this subject, based on the theory of fermion condensation closely related to the emergence (due to geometrical frustration) of dispersionless parts in the fermionic quasiparticle spectrum, so-called flat bands. QSL is a quantum state of matter having neither magnetic order nor gapped excitations even at zero temperature. QSL along with heavy fermion metals can form a new state of matter induced by the topological fermion condensation quantum phase transition. The observation of QSL in actual materials such as herbertsmithite is of fundamental significance both theoretically and technologically, as it could open a path to the creation of topologically protected states for quantum information processing and quantum computation. It is therefore of great importance to establish the presence of a gapless QSL state in one of the most prospective materials, herbertsmithite. In this respect, the interpretation of current theoretical and experimental studies of herbertsmithite are controversial in their implications. Based on published experimental data augmented by our theoretical analysis, we present evidence for the the existence of a QSL in the geometrically frustrated insulator herbertsmithite ZnCu 3 ( OH ) 6 Cl 2 , providing a strategy for unambiguous identification of such a state in other materials. To clarify the nature of QSL in herbertsmithite, we recommend measurements of heat transport, low-energy inelastic neutron scattering, and optical conductivity σ ¯ in ZnCu 3 ( OH ) 6 Cl 2 crystals subject to an external magnetic field at low temperatures. Our analysis of the behavior of σ ¯ in herbertsmithite justifies this set of measurements, which can provide a conclusive experimental demonstration of the nature of its spinon-composed quantum spin liquid. Theoretical study of the optical conductivity of herbertsmithite allows us to expose the physical mechanisms responsible for its temperature and magnetic field dependence. We also suggest that artificially or spontaneously introducing inhomogeneity at nanoscale into ZnCu 3 ( OH ) 6 Cl 2 can both stabilize its QSL and simplify its chemical preparation, and can provide for tests that elucidate the role of impurities. We make predictions of the results of specified measurements related to the dynamical, thermodynamic, and transport properties in the case of a gapless QSL.

Chiral Spin Liquid on a Kagome Antiferromagnet Induced by the Dzyaloshinskii-Moriya Interaction

The quantum spin liquid material herbertsmithite is described by an antiferromagnetic Heisenberg model on the kagome lattice with a non-negligible Dzyaloshinskii-Moriya interaction (DMI). A well-established phase transition to the q=0 long-range order occurs in this model when the DMI strength increases, but the precise nature of a small-DMI phase remains controversial. Here, we describe a new phase obtained from Schwinger-boson mean-field theory that is stable at small DMI, and which can explain the dispersionless spectrum seen in the inelastic neutron scattering experiment by Han et al. [Nature (London) 492, 406 (2012)NATUAS0028-083610.1038/nature11659]. It is a time-reversal symmetry breaking Z_{2} spin liquid, with the unique property of a small and constant spin gap in an extended region of the Brillouin zone. The phase diagram as a function of DMI and spin size is given, and dynamical spin structure factors are presented.