Quantum Paramagnet Research Articles

Excitation spectrum and spin Hamiltonian of the frustrated quantum Ising magnet Pr3BWO9

We present a thorough experimental investigation on of the rare-earth based frustrated quantum antiferromagnet Pr3BWO9, a purported spin-liquid candidate on the breathing kagome lattice. This material possesses a disordered ground state with an unusual excitation spectrum involving a coexistence of sharp spin waves and broad continuum excitations. Nevertheless, we show through a combination of thermodynamic, magnetometric, and spectroscopic probes with detailed theoretical modeling that it should be understood in a completely different framework. The crystal field splits the lowest quasidoublet states into two singlets moderately coupled through frustrated superexchange, resulting in a simple effective Hamiltonian of an Ising model in a transverse magnetic field. While our neutron spectroscopy data do point to significant correlations within the kagome planes, the dominant interactions are out-of-plane, forming frustrated triangular spin-tubes through two competing ferro-antiferromagnetic bonds. The resulting ground state is a simple quantum paramagnet, where the presence of strongly hyperfine-coupled nuclear moments and weak structural disorder causes significant modifications to both thermodynamic and dynamic properties. Published by the American Physical Society 2024

Upper-branch thermal Hall effect in quantum paramagnets

Upper-branch thermal Hall effect in quantum paramagnets

Excitonic instability towards a Potts-nematic quantum paramagnet

Excitonic instability towards a Potts-nematic quantum paramagnet

Dynamical electric characteristics of a quantum paramagnet

We consider the quantum paramagnet with the coupling between spin and electric degrees of freedom. The dynamical electric characteristics of the system under the action of the ac electric field are calculated. It is shown that for the closed system the quadrupole spin moment oscillates with the frequency of the ac field. The oscillations are modulated by the Rabi-like frequency, while the amplitude of the modulation is minimal at resonance, at which the frequency of the electric field is equal to the double energy of spin excitation of the paramagnet. The open system in the steady-state regime manifests only oscillations with the frequency of the ac field. The calculated dynamical electric susceptibility is nonzero only for nonzero dc magnetic field, and, depending on the values of the single-ion magnetic anisotropy, can manifest nonmonotonic dependence on temperature, dc electric and magnetic fields.

CP2 skyrmions and skyrmion crystals in realistic quantum magnets

Magnetic skyrmions are nanoscale topological textures that have been recently observed in different families of quantum magnets. These objects are called CP1 skyrmions because they are built from dipoles—the target manifold is the 1D complex projective space, CP1 ≅ S2. Here we report the emergence of magnetic CP2 skyrmions in a realistic spin-1 model, which includes both dipole and quadrupole moments. Unlike CP1 skyrmions, CP2 skyrmions can also arise as metastable textures of quantum paramagnets, opening a new road to discover emergent topological solitons in non-magnetic materials. The quantum phase diagram of the spin-1 model also includes magnetic field-induced CP2 skyrmion crystals that can be detected with regular momentum- (diffraction) and real-space (Lorentz transmission electron microscopy) experimental techniques.

Quantum paramagnetism in a non-Kramers rare-earth oxide: Monoclinic Pr2Ti2O7

Little is so far known about the magnetism of the ${A}_{2}{B}_{2}{\mathrm{O}}_{7}$ monoclinic layered perovskites that replace the spin-ice supporting pyrochlore structure for ${r}_{A}/{r}_{B}>1.78$. We show that high quality monoclinic ${\mathrm{Pr}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ single crystals with a three-dimensional network of non-Kramers ${\mathrm{Pr}}^{3+}$ ions that interact through edge-sharing superexchange interactions, form a singlet ground-state quantum paramagnet that does not undergo any magnetic phase transitions down to, at least, 1.8 K. The chemical phase stability, structure, and magnetic properties of the layered perovskite ${\mathrm{Pr}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ were investigated using x-ray diffraction, transmission electron microscopy, and magnetization measurements. Synthesis of polycrystalline samples with the nominal compositions of ${\mathrm{Pr}}_{2}{\mathrm{Ti}}_{2+x}{\mathrm{O}}_{7}$ ($\ensuremath{-}0.16\ensuremath{\le}x\ensuremath{\le}0.16$) showed that deviations from the ${\mathrm{Pr}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ stoichiometry lead to secondary phases of related structures including the perovskite phase ${\mathrm{Pr}}_{2/3}{\mathrm{TiO}}_{3}$ and the orthorhombic phases ${\mathrm{Pr}}_{4}{\mathrm{Ti}}_{9}{\mathrm{O}}_{24}$ and ${\mathrm{Pr}}_{2}{\mathrm{TiO}}_{5}$. No indications of site disordering (stuffing and antistuffing) or vacancy defects were observed in the ${\mathrm{Pr}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ majority phase. A procedure for growth of high-structural-quality stoichiometric single crystals of ${\mathrm{Pr}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ by the traveling solvent floating zone method is reported. Thermomagnetic measurements of single-crystalline ${\mathrm{Pr}}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7}$ reveal an isolated singlet ground state that we associate with the low-symmetry crystal electric-field environments that split the ($2J+1=9$)-fold degenerate spin-orbital multiplets of the four differently coordinated ${\mathrm{Pr}}^{3+}$ ions into 36 isolated singlets resulting in an anisotropic temperature-independent van Vleck susceptibility at low $T$. A small isotropic Curie term is associated with 0.96(2)% noninteracting ${\mathrm{Pr}}^{4+}$ impurities.

Influence of the ac magnetic field on the elastic and electric characteristics of a quantum paramagnet

It is shown that electric, piezoelectric, and elastic characteristics of the orthorhombic quantum paramagnet depend on the applied ac magnetic field, collinear to the dc one. The dependence is due to the renormalization of the quadrupole spin susceptibility. In the dynamical regime, the quadrupole susceptibility oscillates with the frequency of the ac field, and with the Rabi-like frequency. In the steady-state regime, the quadrupole susceptibility oscillates with the frequency of the ac field only about the renormalized with respect to the initial one value. That renormalization can change the values of the electric, piezoelectric, and elastic characteristics of the system.

Grüneisen parameters in the quantum paramagnet with the magnetoelectric coupling

It is shown theoretically that magnetic Grüneisen parameter for the quantum orthorhombic paramagnet manifests features similar to the ones observed in many-body quantum spin systems at critical points. For the paramagnet with the strong coupling between the spin and electric subsystems, we have introduced the electric Grüneisen parameter, which is the characteristic of the electrocaloric effect in the system. The low-temperature behavior of both Grüneisen parameters is determined by the crossover points of the spectrum of the quantum paramagnet.

Higher-order topological quantum paramagnets

Quantum paramagnets are strongly-correlated phases of matter where competing interactions frustrate magnetic order down to zero temperature. In certain cases, quantum fluctuations induce instead topological order, supporting, in particular, fractionalized quasi-particle excitations. In this work, we investigate paradigmatic spin models and show how magnetic frustration can also give rise to higher-order topological properties. We first study the frustrated Heisenberg model in a square lattice, where a plaquette valence bond solid appears through the spontaneous breaking of translational invariance. Despite the amount of effort that has been devoted to study this phase, its topological nature has so far been overlooked. By means of tensor network simulations, we establish how such state belongs to a higher-order symmetry-protected topological phase, where long-range plaquette order and non-trivial topology coexist. This interplay allows the system to support excitations that would be absent otherwise, such as corner-like states in the bulk attached to dynamical topological defects. Finally, we demonstrate how this higher-order topological quantum paramagnet can also be induced by dipolar interactions, indicating the possibility to directly observe this phase using atomic quantum simulators.

Higher-order topology and corner triplon excitations in two-dimensional quantum spin-dimer models

The concept of free fermion topology has been generalized to $d$-dimensional phases that exhibit $(d-n)$-dimensional boundary modes, such as zero-dimensional (0D) corner excitations. Motivated by recent extensions of these ideas to magnetic systems, we consider 2D quantum paramagnets formed by interacting spin dimers with dispersive triplet excitations. We propose two examples of such dimer models, where the spin-gapped bosonic triplon excitations are shown to host bands with nontrivial higher-order topology. We demonstrate this using real-space Bogoliubov--de Gennes calculations that reveal the existence of mid-bandgap corner triplon modes as a signature of higher-order bulk topology. We provide an understanding of the higher-order topology in these systems via a computation of bulk topological invariants as well as the construction of edge theories, and study their phase transitions as we tune parameters in the model Hamiltonians. We also discuss possible experimental approaches for detecting the emergent corner triplon modes.

Magnetic Field Induced Quantum Spin Liquid in the Two Coupled Trillium Lattices of K_{2}Ni_{2}(SO_{4})_{3}.

Quantum spin liquids are exotic states of matter that form when strongly frustrated magnetic interactions induce a highly entangled quantum paramagnet far below the energy scale of the magnetic interactions. Three-dimensional cases are especially challenging due to the significant reduction of the influence of quantum fluctuations. Here, we report the magnetic characterization of K_{2}Ni_{2}(SO_{4})_{3} forming a three-dimensional network of Ni^{2+} spins. Using density functional theory calculations, we show that this network consists of two interconnected spin-1 trillium lattices. In the absence of a magnetic field, magnetization, specific heat, neutron scattering, and muon spin relaxation experiments demonstrate a highly correlated and dynamic state, coexisting with a peculiar, very small static component exhibiting a strongly renormalized moment. A magnetic field B≳4 T diminishes the ordered component and drives the system into a pure quantum spin liquid state. This shows that a system of interconnected S=1 trillium lattices exhibits a significantly elevated level of geometrical frustration.

Quantum paramagnetism and magnetization plateaus in a kagome-honeycomb Heisenberg antiferromagnet

A spin-1/2 Heisenberg model on a honeycomb lattice is investigated by doing triplon analysis and quantum Monte Carlo calculations. This model, inspired by ${\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4}$), has three different antiferromagnetic exchange interactions (${J}_{A}, {J}_{B}, {J}_{C}$) on three different sets of nearest-neighbor bonds which form a kagome superlattice. While the model is bipartite and unfrustrated, its quantum phase diagram is found to be dominated by a quantum paramagnetic phase that is best described as a spin-gapped hexagonal-singlet state. The N\'eel antiferromagnetic order survives only in a small region around ${J}_{A}={J}_{B}={J}_{C}$. The magnetization produced by the external magnetic field is found to exhibit plateaus at 1/3 and 2/3 of the saturation value, or at 1/3 alone, or no plateaus. Notably, the plateaus exist only inside a bounded region within the hexagonal-singlet phase. This study provides a clear understanding of the spin-gapped behavior and magnetization plateaus observed in ${\mathrm{Cu}}_{2}{(\mathrm{pymca})}_{3}({\mathrm{ClO}}_{4}$), and also predicts the possible disappearance of 2/3 plateau under pressure.

Resummation-based quantum Monte Carlo for quantum paramagnetic phases

For spin rotational symmetric models with a positive-definite high-temperature expansion of the partition function, a stochastic sampling of the series expansion upon partial resummation becomes logically equivalent to sampling an uncoloured closely-packed loop-gas model in one higher dimension. Based on this, we devise quantum Monte Carlo updates that importance-sample loop configurations for general $SU(N)$ in fundamental and higher-symmetric representations. The algorithmic performance systematically improves with increase in (continuous) $N$ allowing efficient simulation of quantum paramagnets. The underlying reason for the increased efficacy is the correspondence of quantum paramagnetic phases like valence bond solids to short-loop phases on the loop-gas side rather than the particular value of $N$. This also gives a connection between Sandvik's $JQ$ model class and classical loop-gas models in the deconfined universality class.

Finite-temperature topological phase transitions of spin- j systems in Uhlmann processes: General formalism and experimental protocols

The Uhlmann process is built on the density matrix of a mixed quantum state and offers a way to characterize topological properties at finite temperatures. We analyze an ideal spin-j quantum paramagnet in a magnetic field undergoing an Uhlmann process and derive general formulae of the Uhlmann phase and Loschmidt amplitude for arbitrary j as the system traverses a great circle in the parameter space. A quantized jump of the Uhlmann phase signifies a topological quantum phase transition (TQPT) of the underlying process, which is accompanied by a zero of the Loschmidt amplitude. The exact results of j=1/2 and j=1 systems show topological regimes that only survive at finite temperatures but not at zero temperature, and the number of TQPTs is associated with the winding number in the parameter space. Our results pave the way for future studies on finite-temperature topological properties, and possible experimental protocols and implications for atomic simulators and digital simulations are discussed.

Critical dielectric susceptibility at a magnetic BEC quantum critical point

Magnetic-field-induced phase transitions are investigated in the frustrated gapped quantum paramagnet Rb$_{2}$Cu$_{2}$Mo$_3$O$_{12}$ through dielectric and calorimetric measurements on single-crystal samples. It is clarified that the previously reported dielectric anomaly at 8~K in powder samples is not due to a chiral spin liquid state as has been suggested, but rather to a tiny amount of a ferroelectric impurity phase. Two field-induced quantum phase transitions between paraelectric and paramagnetic and ferroelectric and magnetically ordered states are clearly observed. It is shown that the electric polarization is a secondary order parameter at the lower-field (gap closure) quantum critical point but a primary one at the saturation transition. Having clearly identified the magnetic Bose-Einstein condensation (BEC) nature of the latter, we use the dielectric channel to directly measure the critical divergence of BEC susceptibility. The observed power-law behavior is in very good agreement with theoretical expectations for three-dimensional BEC. Finally, dielectric data reveal magnetic presaturation phases in this compound that may feature exotic order with unconventional broken symmetries.

Strong-coupling expansion of multi-band interacting models: Mapping onto the transverse-field [formula omitted]-[formula omitted] Ising model

We investigate a class of two-dimensional two-band microscopic models in which the inter-band repulsive interactions play the dominant role. We first demonstrate three different schemes of constraining the ratios between the three types of inter-band interactions – density-density, spin exchange, and pair-hopping – that render the model free of the fermionic sign-problem for any filling and, consequently, amenable to efficient Quantum Monte Carlo simulations. We then study the behavior of these sign-problem-free models in the strong-coupling regime. In the cases where spin-rotational invariance is preserved or lowered to a planar symmetry, the strong-coupling ground state is a quantum paramagnet. However, in the case where there is only a residual Ising symmetry, the strong-coupling expansion maps onto the transverse-field J1-J2 Ising model, whose pseudospins are associated with local inter-band magnetic order. We show that by varying the band structure parameters within a reasonable range of values, a variety of ground states and quantum critical points can be accessed in the strong-coupling regime, some of which are not realized in the weak-coupling regime. We compare these results with the case of the single-band Hubbard model, where only intra-band repulsion is present, and whose strong-coupling behavior is captured by a simple Heisenberg model.

External electric field and strain effects in a quantum paramagnet

Influence of the external electric field and the external strain on a quantum paramagnetic insulator is studied. It is shown that the external electric field and/or strain can cause drastic changes in the magnetic characteristics of the paramagnet.

Piezoelectric and magneto-elastic effects in a quantum paramagnet

Electric, piezoelectric, and elastic characteristics of the orthorhombic quantum paramagnet are calculated. Using the exact analytical solution it was shown that the electric permittivity, piezoelectric, and elastic modules can manifest strong dependences on the values of the external magnetic, electric field, external strain, and temperature.

Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks

The recent progress in the optimization of two-dimensional tensor networks [H.-J. Liao, J.-G. Liu, L. Wang, and T. Xiang, Phys. Rev. X 9, 031041 (2019)] based on automatic differentiation opened the way towards precise and fast optimization of such states and, in particular, infinite projected entangled-pair states (iPEPS) that constitute a generic-purpose Ansatz for lattice problems governed by local Hamiltonians. In this work, we perform an extensive study of a paradigmatic model of frustrated magnetism, the J_1-J_2J1−J2 Heisenberg antiferromagnet on the square lattice. By using advances in both optimization and subsequent data analysis, through finite correlation-length scaling, we report accurate estimations of the magnetization curve in the N'eel phase for J_2/J_1 \le 0.45J2/J1≤0.45. The unrestricted iPEPS simulations reveal an U(1)U(1) symmetric structure, which we identify and impose on tensors, resulting in a clean and consistent picture of antiferromagnetic order vanishing at the phase transition with a quantum paramagnet at J_2/J_1 \approx 0.46(1)J2/J1≈0.46(1). The present methodology can be extended beyond this model to study generic order-to-disorder transitions in magnetic systems.

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.