Microscopic model calculations for the magnetization process of layered triangular-lattice quantum antiferromagnets

Effects of third-neighbor interactions on the frustrated quantum Ising model

We investigate thermal and quantum phase transitions of the J_{1}-J_{2}-J_{3} transverse Ising model on the square lattice. The model is studied within a cluster mean-field decoupling, which allows us to describe phase diagrams and the free-energy landscape in the neighborhood of phase transitions. Our findings indicate that the third-neighbor coupling (J_{3}) can affect the nature of phase transitions of the model. In particular, ferromagnetic third-neighbor couplings favor the onset of continuous order-disorder phase transitions, eliminating the tricritical point of the superantiferromagnetic-paramagnetic (SAFM-PM) phase boundary. On the other hand, the enhancement of frustration introduced by weak antiferromagnetic J_{3} gives rise to the staggered dimer phase favoring the onset of discontinuous classical phase transitions. Moreover, we find that quantum annealed criticality (QAC), which takes place when the classical discontinuous phase transition becomes critical by the enhancement of quantum fluctuations introduced by the transverse magnetic field, is eliminated from the SAFM-PM phase boundary by a relatively weak ferromagnetic J_{3}. Nevertheless, this change in the nature of phase transitions can still be observed in the presence of antiferromagnetic third-neighbor couplings being also found in the staggered-dimer phase boundary. Therefore, our findings support that QAC persists under the presence of frustrated antiferromagnetic third-neighbor couplings and is suppressed when these couplings are ferromagnetic, suggesting that frustration plays a central role in the onset of QAC.

Giant magnetocaloric effect in spin supersolid candidate Na2BaCo(PO4)2

Supersolid, an exotic quantum state of matter that consists of particles forming an incompressible solid structure while simultaneously showing superfluidity of zero viscosity1, is one of the long-standing pursuits in fundamental research2,3. Although the initial report of 4He supersolid turned out to be an artefact4, this intriguing quantum matter has inspired enthusiastic investigations into ultracold quantum gases5-8. Nevertheless, the realization of supersolidity in condensed matter remains elusive. Here we find evidence for a quantum magnetic analogue of supersolid-the spin supersolid-in the recently synthesized triangular-lattice antiferromagnet Na2BaCo(PO4)2 (ref. 9). Notably, a giant magnetocaloric effect related to the spin supersolidity is observed in the demagnetization cooling process, manifesting itself as two prominent valley-like regimes, with the lowest temperature attaining below 100 mK. Not only is there an experimentally determined series of critical fields but the demagnetization cooling profile also shows excellent agreement with the theoretical simulations with an easy-axis Heisenberg model. Neutron diffractions also successfully locate the proposed spin supersolid phases by revealing the coexistence of three-sublattice spin solid order and interlayer incommensurability indicative of the spin superfluidity. Thus, our results reveal a strong entropic effect of the spin supersolid phase in a frustrated quantum magnet and open up a viable and promising avenue for applications in sub-kelvin refrigeration, especially in the context of persistent concerns about helium shortages10,11.

Spin Excitation Spectra of Anisotropic Spin-1/2 Triangular Lattice Heisenberg Antiferromagnets

Investigation of dynamical excitations is difficult but crucial to the understanding of many exotic quantum phenomena discovered in quantum materials. This is particularly true for highly frustrated quantum antiferromagnets whose dynamical properties deviate strongly from theoretical predictions made based on the spin-wave or other approximations. Here, we present a large-scale numerical calculation on the dynamical correlation functions of spin-1/2 triangular Heisenberg model using a state-of-the-art tensor network renormalization group method. The calculated results allow us to gain for the first time a comprehensive picture on the nature of spin excitation spectra in this highly frustrated quantum system. It provides a quantitative account for all the key features of the dynamical spectra disclosed by inelastic neutron scattering measurements for Ba_{3}CoSb_{2}O_{9}, revealing the importance of the interplay between low- and high-energy excitations and its renormalization effect to the low-energy magnon bands and high-energy continuums. We identify the longitudinal Higgs modes in the intermediate-energy scale and predict the energy and momentum dependence of spectral functions along the three principal axes that can be verified by polarized neutron scattering experiments. Furthermore, we find that the spin excitation spectra weakly depend on the anisotropic ratio of the antiferromagnetic interaction.

Magnetic phase diagram of a 2-dimensional triangular lattice antiferromagnet Na2BaMn(PO4)2

We report the magnetic phase transitions of a spin-5/2, 2-dimensional triangular lattice antiferromagnet (AFM) Na₂BaMn(PO₄)₂. From specific heat measurements, we observe two magnetic transitions at temperatures 1.15 and 1.30 K at zero magnetic field. Detailed AC magnetic susceptibility measurements reveal multiple phases including the↑↑↓(up-up-down)-phase between 1.9 and 2.9 T at 47 mK when magnetic field is applied along thecaxis, implying that Na₂BaMn(PO₄)₂is a classical 2dTL Heisenberg AFM with easy-axis anisotropy. However, it deviates from an ideal model as evidenced by a hump region with hysteresis between the↑↑↓andV-phases and weak phase transitions. Our work provides another experimental example to study frustrated magnetism in 2dTL AFM which also serves as a reference to understand the possible quantum spin liquid behavior and anomalous phase diagrams observed in sibling systems Na₂BaM(PO₄)₂(M= Co, Ni).

Non-magnetic ion site disorder effects on the quantum magnetism of a spin-1/2 equilateral triangular lattice antiferromagnet

With the motivation to study how non-magnetic ion site disorder affects the quantum magnetism of Ba₃CoSb₂O₉, a spin-1/2 equilateral triangular lattice antiferromagnet, we performed DC and AC susceptibility, specific heat, elastic and inelastic neutron scattering measurements on single crystalline samples of Ba_2.87Sr_0.13CoSb₂O₉with Sr doping on non-magnetic Ba²⁺ion sites. The results show that Ba_2.87Sr_0.13CoSb₂O₉exhibits (i) a two-step magnetic transition at 2.7 K and 3.3 K, respectively; (ii) a possible canted 120 degree spin structure at zero field with reduced ordered moment as 1.24μ_B/Co; (iii) a series of spin state transitions for bothH∥ab-plane andH∥c-axis. ForH∥ab-plane, the magnetization plateau feature related to the up-up-down phase is significantly suppressed; (iv) an inelastic neutron scattering spectrum with only one gapped mode at zero field, which splits to one gapless and one gapped mode at 9 T. All these features are distinctly different from those observed for the parent compound Ba₃CoSb₂O₉, which demonstrates that the non-magnetic ion site disorder (the Sr doping) plays a complex role on the magnetic properties beyond the conventionally expected randomization of the exchange interactions. We propose the additional effects including the enhancement of quantum spin fluctuations and introduction of a possible spatial anisotropy through the local structural distortions.

Survival of itinerant excitations and quantum spin state transitions in YbMgGaO4 with chemical disorder

A recent focus of quantum spin liquid (QSL) studies is how disorder/randomness in a QSL candidate affects its true magnetic ground state. The ultimate question is whether the QSL survives disorder or the disorder leads to a “spin-liquid-like” state, such as the proposed random-singlet (RS) state. Since disorder is a standard feature of most QSL candidates, this question represents a major challenge for QSL candidates. YbMgGaO₄, a triangular lattice antiferromagnet with effective spin-1/2 Yb³⁺ions, is an ideal system to address this question, since it shows no long-range magnetic ordering with Mg/Ga site disorder. Despite the intensive study, it remains unresolved as to whether YbMgGaO₄ is a QSL or in the RS state. Here, through ultralow-temperature thermal conductivity and magnetic torque measurements, plus specific heat and DC magnetization data, we observed a residual κ₀/T term and series of quantum spin state transitions in the zero temperature limit for YbMgGaO₄. These observations strongly suggest that a QSL state with itinerant excitations and quantum spin fluctuations survives disorder in YbMgGaO₄.

It remains an open question as to whether the quantum spin liquid state survives material disorder, or is replaced by some spin-liquid like state. Here, Rao et al succeed in resolving a resolving a κ₀/T residual in the thermal conductivity of YbMgGaO₄ strongly suggesting the survival of the quantum spin liquid state.

Continuous control of classical-quantum crossover by external high pressure in the coupled chain compound CsCuCl3

In solid materials, the parameters relevant to quantum effects, such as the spin quantum number, are basically determined and fixed at the chemical synthesis, which makes it challenging to control the amount of quantum correlations. We propose and demonstrate a method for active control of the classical-quantum crossover in magnetic insulators by applying external pressure. As a concrete example, we perform high-field, high-pressure measurements on CsCuCl₃, which has the structure of weakly-coupled spin chains. The magnetization process experiences a continuous evolution from the semi-classical realm to the highly-quantum regime with increasing pressure. Based on the idea of "squashing” the spin chains onto a plane, we characterize the change in the quantum correlations by the change in the value of the local spin quantum number of an effective two-dimensional model. This opens a way to access the tunable classical-quantum crossover of two-dimensional spin systems by using alternative systems of coupled-chain compounds.

In real materials, a spin quantum number assumes a fixed value, which makes it challenging to realize a crossover between quantum and classical spin regimes. Here the authors demonstrate such a crossover in a weakly coupled chain compound by controlling the amount of quantum correlations, in the form of the inverse spin quantum number, with external pressure.

Thermally driven state in a spin-1 model with competing interactions

We study a recently proposed spin-1 model with competing antiferromagnetic first-neighbor interaction and a third-neighbor coupling mediated by nonmagnetic states, which reproduces topological features of the phase diagrams of high-T_{c} superconductors [S. A. Cannas and D. A. Stariolo, Phys. Rev. E 99, 042137 (2019)2470-004510.1103/PhysRevE.99.042137]. We employ a cluster mean-field approach to investigate effects of crystal field anisotropy on the phase transitions hosted by this model. At low temperatures, the temperature-crystal field phase diagram exhibits superantiferromagnetic (SAF), antiferromagnetic (AF), and paramagnetic (PM) phases. In addition, we found a thermally driven state between SAF and PM phases. This thermally driven state and the SAF phase appears in the phase diagram as a domelike structure. Our calculations indicate that only second-order phase transitions occur in the PM-AF phase boundary, as suggested by previous Monte Carlo simulations.

Transverse field effects on the competition between antiferromagnetic and cluster spin-glass phases

We investigate a disordered cluster Ising antiferromagnet in the presence of a transverse field. By adopting a replica cluster mean-field framework, we analyze the role of quantum fluctuations in a model with competing short-range antiferromagnetic and intercluster disordered interactions. The model exhibits paramagnetic (PM), antiferromagnetic (AF), and cluster spin-glass (CSG) phases, which are separated by thermal and quantum phase transitions. A scenario of strong competition between AF and CSG unveils a number of interesting phenomena induced by quantum fluctuations, including a quantum PM state and quantum driven criticality. The latter occurs when the thermally driven PM-AF discontinuous phase transition becomes continuous at strong transverse fields. Analogous phenomena have been reported in a number of systems, but a description of underlying mechanisms is still required. Our results indicate that quantum driven criticality can be found in a highly competitive regime of disordered antiferromagnets, which is in consonance with recent findings in spin models with competing interactions.

Effects of interlayer and bi-quadratic exchange coupling on layered triangular lattice antiferromagnets

The magnetic field evolution of ground spin states of the stacked planar triangular antiferromagnet with antiferromagnetic interlayer interaction J _c is explored using a minimal 3D classical Heisenberg model. A bi-quadratic coupling is also used to mimic the effect of spin fluctuations (Zhitomirsky 2015 J. Phys.: Conf. Ser. 592 012110) which are known to stabilize the magnetization plateau. A single ion anisotropy is included and states with a magnetic field applied in the ab plane and along the c axis are determined. For [Formula: see text]-plane, an additional new state, in contrast to 2D model (Zhitomirsky 2015 J. Phys.: Conf. Ser. 592 012110), is obtained with weak interlayer interaction, while the magnetization plateau vanishes at large J _c and other new states with z components of spins emerge. For [Formula: see text]-axis, an extra state, compared with 2D model, is obtained with a weak interlayer interaction. When J _c is large enough, only the state corresponding to the Umbrella phase in 2D model exits.

Frustrated Magnetism in Triangular Lattice TlYbS2 Crystals Grown via Molten Flux

The triangular lattice compound TlYbS₂ was prepared as large single crystals via a molten flux growth technique using sodium chloride. Anisotropic magnetic susceptibility measurements down to 0.4 K indicate a complete absence of long-range magnetic order. Despite this lack of long-range order, short-range antiferromagnetic interactions are evidenced through broad transitions, suggesting frustrated behavior. Variable magnetic field measurements reveal metamagnetic behavior at temperatures ≤2 K. Complex low temperature field-tunable magnetic behavior, in addition to no observable long-range order down to 0.4 K, suggest that TlYbS₂ is a frustrated magnet and a possible quantum spin liquid candidate.

Quantum Ising model on the frustrated square lattice

We investigate the role of a transverse field on the Ising square antiferromagnet with first (J_{1}) and second (J_{2}) neighbor interactions. Using a cluster mean-field approach, we provide a telltale characterization of the frustration effects on the phase boundaries and entropy accumulation process emerging from the interplay between quantum and thermal fluctuations. We found that the paramagnetic (PM) and antiferromagnetic phases are separated by continuous phase transitions. On the other hand, continuous and discontinuous phase transitions, as well as tricriticality, are observed in the phase boundaries between PM and superantiferromagnetic phases. A rich scenario arises when a discontinuous phase transition occurs in the classical limit while quantum fluctuations recover criticality. We also find that the entropy accumulation process predicted to occur at temperatures close to the quantum critical point can be enhanced by frustration. Our results provide a description for the phase boundaries and entropy behavior that can help to identify the ratio J_{2}/J_{1} in possible experimental realizations of the quantum J_{1}-J_{2} Ising antiferromagnet.

Quantum Spin Ice with Frustrated Transverse Exchange: From a π-Flux Phase to a Nematic Quantum Spin Liquid

Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalization, numerical linked-cluster and series expansions, we find that the previously studied U(1) quantum spin liquid, in its π-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.

The nature of spin excitations in the one-third magnetization plateau phase of Ba3CoSb2O9

Magnetization plateaus in quantum magnets—where bosonic quasiparticles crystallize into emergent spin superlattices—are spectacular yet simple examples of collective quantum phenomena escaping classical description. While magnetization plateaus have been observed in a number of spin-1/2 antiferromagnets, the description of their magnetic excitations remains an open theoretical and experimental challenge. Here, we investigate the dynamical properties of the triangular-lattice spin-1/2 antiferromagnet Ba₃CoSb₂O₉ in its one-third magnetization plateau phase using a combination of nonlinear spin-wave theory and neutron scattering measurements. The agreement between our theoretical treatment and the experimental data demonstrates that magnons behave semiclassically in the plateau in spite of the purely quantum origin of the underlying magnetic structure. This allows for a quantitative determination of Ba₃CoSb₂O₉ exchange parameters. We discuss the implication of our results to the deviations from semiclassical behavior observed in zero-field spin dynamics of the same material and conclude they must have an intrinsic origin.

Frustrated magnetic materials attract significant interest because their properties can become dominated by quantum fluctuations. Here the authors show that excitations in the plateau phase of a quantum magnet can be understood semiclassically even though the ground state involves strong quantum effects.

Structure of the magnetic excitations in the spin-1/2 triangular-lattice Heisenberg antiferromagnet Ba3CoSb2O9

A spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) is a prototypical frustrated quantum magnet, which exhibits remarkable quantum many-body effects that arise from the synergy between spin frustration and quantum fluctuation. The ground-state properties of a spin-1/2 TLHAF are theoretically well understood. However, the theoretical consensus regarding the magnetic excitations is limited. The experimental study of the magnetic excitations in spin-1/2 TLHAFs has also been limited. Here we show the structure of magnetic excitations in the spin-1/2 TLHAF Ba₃CoSb₂O₉ investigated by inelastic neutron scattering. Significantly different from theoretical expectations, the excitation spectrum has a three-stage energy structure. The lowest-energy first stage is composed of dispersion branches of single-magnon excitations. The second and third stages are dispersive continua accompanied by a columnar continuum extending above 10 meV, which is six times larger than the exchange interaction J = 1.67 meV. Our results indicate the shortcomings of the current theoretical framework.

Two-dimensional frustrated magnets are heavily studied because theories predict that quantum effects may lead to the emergence of fractionalized excitations. Ito et al. use inelastic neutron scattering to show that the excitation spectrum of Ba₃CoSb₂O₉ disagrees with current theoretical expectations.

Static and Dynamical Properties of the Spin-1/2 Equilateral Triangular-Lattice Antiferromagnet Ba_{3}CoSb_{2}O_{9}

We present single-crystal neutron scattering measurements of the spin-1/2 equilateral triangular-lattice antiferromagnet Ba_{3}CoSb_{2}O_{9}. Besides confirming that the Co^{2+} magnetic moments lie in the ab plane for zero magnetic field and then determining all the exchange parameters of the minimal quasi-2D spin Hamiltonian, we provide conclusive experimental evidence of magnon decay through observation of intrinsic line broadening. Through detailed comparisons with the linear and nonlinear spin-wave theories, we also point out that the large-S approximation, which is conventionally employed to predict magnon decay in noncollinear magnets, is inadequate to explain our experimental observation. Thus, our results call for a new theoretical framework for describing excitation spectra in low-dimensional frustrated magnets under strong quantum effects.