Quantum Paramagnet Research Articles

Thermal Transport and Strong Mass Renormalization inNiCl2−4SC(NH2)2

Several quantum paramagnets exhibit magnetic-field-induced quantum phase transitions to an antiferromagnetic state that exists for H c1 ≤ H ≤ H c2. For some of these compounds, there is a significant asymmetry between the low- and high-field transitions. We present specific heat and thermal conductivity measurements in NiCl2-4SC(NH2)2, together with calculations which show that the asymmetry is caused by a strong mass renormalization due to quantum fluctuations for H ≤ H c1 that are absent for H ≥ H c2. We argue that the enigmatic lack of asymmetry in thermal conductivity is due to a concomitant renormalization of the impurity scattering.

Master Equation in Phase Space for a Spin in an Arbitrarily Directed Uniform External Field

The time evolution equation for the probability density function of spin orientations in the phase space representation of the polar and azimuthal angles is derived for the nonaxially symmetric problem of a quantum paramagnet subjected to a uniform magnetic field of arbitrary direction. This is accomplished by first rotating the coordinate system into one in which the polar axis is collinear with the field vector, then writing the reduced density matrix equation in the new coordinate system as an explicit inverse Wigner-Stratonovich transformation so that the phase space master equation may be derived just as in the axially symmetric case [Yu.P. Kalmykov et al., J. Stat. Phys. 131:969, 2008]. The properties of this equation, resembling the corresponding Fokker-Planck equation, are investigated. In particular, in the large spin limit, S→∞, the master equation becomes the classical Fokker-Planck equation describing the magnetization dynamics of a classical paramagnet in an arbitrarily directed uniform external field.

Family of Exactly Solvable Models with an Ultimate Quantum Paramagnetic Ground State

We present a family of two-dimensional frustrated quantum magnets solely based on pure nearest-neighbor Heisenberg interactions which can be solved quasiexactly. All lattices are constructed in terms of frustrated quantum cages containing a chiral degree of freedom protected by frustration. The ground states of these models are dubbed ultimate quantum paramagnets and exhibit an extensive entropy at zero temperature. We discuss the unusual and extensively degenerate excitations in such phases. Implications for thermodynamic properties as well as for decoherence free quantum computation are discussed.

The ground state phase diagram of the quantumJ1–J2 spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice

We have studied the ground state phase diagram of the quantum spin-1/2 frustrated Heisenberg antiferromagnet on a square lattice by using theframework of the differential operator technique. The Hamiltonian is solvedby using an effective-field theory for a cluster with two spins (EFT-2). Themodel is described using the Heisenberg Hamiltonian with two competingantiferromagnetic interactions: nearest neighbor (NN) with different coupling strengthsJ1 andJ1′ alongthe x and y directions and next nearest neighbor (NNN) with couplingJ2. We propose a functional for the free energy (similar to the Landau expansion)and using Maxwell construction we obtain the phase diagram in the (λ, α) space,where λ = J1′/J1 and α = J2/J1. We obtain three different states depending on the values ofλ andα: antiferromagnetic (AF), collinear antiferromagnetic (CAF)and quantum paramagnetic (QP). For an intermediate regionλ1 < λ < 1 we observe a QP state between the ordered AF and CAF phases, which disappears forλ above some critical value . We find a second-order phase transition between the AF and QP phases and a first-ordertransition between the CAF and QP phases. The boundaries between these orderedphases merge at the quantum triple point (QTP). Below this QTP there is again adirect first-order transition between the AF and CAF phases, with a behaviorapproximately described by the classical line .

The quantum spin-1/2 J1–J2 antiferromagnet on a stacked square lattice: a study of effective-field theory in a finitecluster

The ground state phase diagram of the quantum spin-1/2 Heisenberg antiferromagnet in the presence of nearest-neighbor (J1) andnext-nearest-neighbor (J2) interactions (J1–J2 model) on a stacked square lattice, where we introduce an interlayer coupling throughnearest-neighbor bonds of strength , is studied within the framework of the differential operator technique.The Hamiltonian is solved by effective-field theory in a cluster withN = 4 spins (EFT-4). We obtain the sublattice magnetizationmA for the ordered phases: antiferromagnetic (AF) and collinear (CAF—collinearantiferromagnetic). We propose a functional for the free energyΨμ(mμ) (μ = A, B) to obtain thephase diagram in the λ–α plane, where and α = J2/J1. Dependingon the values of λ and α, we found different ordered states (AF and CAF) and a disorderedstate (quantum paramagnetic (QP)). For an intermediate regionα1c(λ) < α < α2c(λ) we observe a QP phasethat disappears for λ below some critical value . For α < α1c(λ) and α > α2c(λ), andbelow λ1, we have the AF and CAF semi-classically ordered states, respectively. Atα = α1c(λ) a second-order transition between the AF and QP states occurs and atα = α2c(λ) a first-order transition between the AF and CAF phases takes place. The boundariesbetween these ordered phases merge at the critical end point , where . Above this CEP there is again a direct first-order transition betweenthe AF and CAF phases, with a behavior described by the pointαc independentof λ ≥ λ1.

Equilibrium susceptibilities of superparamagnets: longitudinal and transverse, quantumand classical

The equilibrium susceptibility of uniaxial paramagnets is studied in a unified frameworkwhich permits us to connect traditional results of the theory of quantum paramagnets,S = 1/2,1,3/2,..., with molecularmagnetic clusters, S∼5,10,20 all the way up (S = 30,50,100,...,) to the theory of classical superparamagnets. This is done using standard tools ofquantum statistical mechanics and linear-response theory (the Kubo correlatorformalism). Several features of the temperature dependence of the susceptibility curves(crossovers, peaks, deviations from Curie law) are studied and their scalings withS identified and characterized. Both the longitudinal and transverse susceptibilities arediscussed, as well as the response of the ensemble with anisotropy axes oriented at random.For the latter case a simple approximate formula is derived too, and its range of validityassessed, which could be used in the modelization of experiments.

The Heisenberg antiferromagnet on the square-kagomé lattice

e lattice. This magnetic system belongs to the class of highly frustrated spin systems with an innite non-trivial degeneracy of the classical ground state as it is also known for the Heisenberg antiferromagnet on the kagom · and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet with a nite spin gap and with a large number of non-magnetic excitations within this gap. We also discuss the magnetization versus eld curve that shows a plateaux as well as a macroscopic magnetization jump to saturation due to independent localized magnon states. These localized states are highly degenerate and lead to interesting features in the low-temperature thermodynamics at high magnetic elds such as an additional low-temperature peak in the specic heat and an enhanced magnetocaloric effect.

A “Star” Antiferromagnet: A Polymeric Iron(III) Acetate That Exhibits Both Spin Frustration and Long‐Range Magnetic Ordering

The preparation of new geometrically spin-frustrated magnetic materials that approximate theoretical models is a challenge. Although theMermin–Wagner theorem indicates that long-range magnetic order can exist in two dimensions at zero Kelvin, order can be destroyed either by quantum fluctuations or geometric frustration even at this temperature. Theoretical studies indicate that the ground state of a spin-1/2 Heisenberg antiferromagnet is most likely to be semiclassically ordered. However, the interplay of geometric frustration and quantum fluctuations has been found to give rise to a paramagnetic ground state without semi-classical long-range order in two types of lattice. The first of these lattices is the famous Kagom+ lattice (T8) and the second is the so-called “star” lattice (T9; Scheme 1), which may serve as a new example of a quantum paramagnet. 5] The triangles are corner-sharing in the Kagom+ lattice whereas they are separated by a bridge in the star lattice, which means that their next-nearest-neighbor exchange interactions are different. 5] The magnetic J exchange pathways in the Kagom+ lattice are all equivalent, whereas the intra-triangular JT pathway in the star lattice is weaker than the inter-triangular JD pathway. In contrast to the rapid development of Kagom+-type antiferromagetic lattices 7] and related, geometrically spin-frustrated lattices, there appears to date to be no report of a compound with a genuine star lattice. Triangular clusters with superexchange pathways, such as the widely employedM3(m3-O) clusters, whereMmay be Fe , Fe, Co, Ni, Cu, V, or Cr, can be used to generate frustrated lattices, including the desired magnetically frustrated star lattice. This star lattice can be described in vertex notation as 3.12 (see Scheme S1 in the Supporting Information), a lattice that is a uniform, three-connected twodimensional net with large voids. Three-connected node subunits that prefer to bond in a planar fashion, such as the basic cationic iron(III) carboxylate cluster [Fe3(m3-O)(mO2CR)6L3] , where L may be water, methanol, or pyridine, must be used to avoid three-dimensional connections. These carboxylate clusters are good potential building blocks because they are easily prepared, prefer planar bonding, and the R groups and L ligands can easily be varied. The cationic [Fe3(m3-O)(m-O2CR)6L3] + moiety has previously served as a sixor three-connected node (see Scheme S2 in the Supporting Information) to form either threeor zero-dimensional porous frameworks depending upon the nature of the carboxylate, which may be either fully or partially substituted by dicarboxylates; the L ligands are usually retained as terminal ligands. Although no example is known to date, it should be possible to substitute the L ligands located in the triangular [Fe3(m3-O)(m-O2CR)6L3] + cation plane with other bridging bidentate ligands that are better at both mediating antiferromagnetic interactions and producing a two-dimensional star lattice. Herein, we report the use of bidentate acetate bridging ligands to link [Fe3(m3-O)(mOAc)6] + cations together to form [Fe3(m3-O)(m-OAc)6(H2O)3][Fe3(m3-O)(m-OAc)7.5]2·7H2O (1), a new compound with the desired star lattice. Single-crystal X-ray diffraction studies of 1 at 293 and 90 K revealed that isolated [Fe3(m3-O)(m-OAc)6(H2O)3] + cations (Figure 1) occupy the dodecagonal channels formed by the stacking of acetate-bridged [Fe3(m3-O)(m-OAc)7.5] 1/2 anionic layers; the dihedral angle between the triangular [Fe3(m3-O)(m-OAc)6(H2O)3] + cations and the [Fe3(m3-O)(mScheme 1. A comparison of the Kagom (T8, left) and star (T9, right) lattices with indication of the magnetic J exchange pathways.

Field-driven phase transitions in a quasi-two-dimensional quantum antiferromagnet

We report magnetic susceptibility, specific heat, and neutron scattering measurements as a function of applied magnetic field and temperature to characterize the S = 1/2 quasi-two-dimensional (2D) frustrated magnet piperazinium hexachlorodicuprate (PHCC). The experiments reveal four distinct phases. At low temperatures and fields the material forms a quantum paramagnet with a 1 meV singlet triplet gap and a magnon bandwidth of 1.7 meV. The singlet state involves multiple spin pairs some of which have negative ground state bond energies. Increasing the field at low temperatures induces 3D long-range antiferromagnetic order at 7.5 Tesla through a continuous phase transition that can be described as magnon Bose–Einstein condensation. The phase transition to a fully polarized ferromagnetic state occurs at 37 Tesla. The ordered antiferromagnetic phase is surrounded by a renormalized classical region. The crossover to this phase from the quantum paramagnet is marked by a distinct anomaly in the magnetic susceptibility which coincides with closure of the finite temperature singlet–triplet pseudo gap. The phase boundary between the quantum paramagnet and the Bose–Einstein condensate features a finite temperature minimum at T = 0.2 K, which may be associated with coupling to nuclear spin or lattice degrees of freedom close to quantum criticality.

Neutron scattering from a coordination polymer quantum paramagnet

Inelastic neutron scattering measurements are reported for a powder sample of the spin-1/2 quantum paramagnet $\rm Cu(Quinoxaline)Br_2$. Magnetic neutron scattering is identified above an energy gap of 1.9 meV. Analysis of the sharp spectral maximum at the onset indicates that the material is magnetically quasi-one-dimensional. Consideration of the wave vector dependence of the scattering and polymeric structure further identifies the material as a two-legged spin-1/2 ladder. Detailed comparison of the data to various models of magnetism in this material based on the single mode approximation and the continuous unitary transformation are presented. The latter theory provides an excellent account of the data with leg exchange $J_{\parallel}=2.0$ meV and rung exchange $J_{\perp}=3.3$ meV.

Quantum Criticality in an Organic Magnet

Exchange interactions between S=1/2 sites in piperazinium hexachlorodicuprate produce a frustrated bilayer magnet with a singlet ground state. We have determined the field-temperature phase diagram by high field magnetization and neutron scattering experiments. There are two quantum critical points: Hc1=7.5 T separates a quantum paramagnet phase from a three dimensional, antiferromagnetically ordered state while Hc2=37 marks the onset of a fully polarized state. The ordered phase, which we describe as a magnon Bose-Einstein condensate (BEC), is embedded in a quantum critical regime with short range correlations. A low temperature anomaly in the BEC phase boundary indicates that additional low energy features of the material become important near Hc1.

Field-induced quantum phase transition in the quasi 1D XY-like antiferromagnet Cs2CoCl4

We explore the magnetic excitations as a function of applied field in the quasi 1D s=12 XY-like magnet Cs2CoCl4. A transition from spin–flop antiferromagnetic order to a quantum paramagnet occurs at the critical field BC=2.15T and fields higher than 2.5T fully align the spins along the field. In the spin–flop phase gapped scattering continua dominate, identified with the creation of pairs of quantum domain walls. In the saturated phase sharp peaks are observed, as expected for magnons in a ferromagnetically ordered ground state.

Anisotropy-induced quantum critical behavior of magnetite nanoparticles at low temperatures

The classical, thermally driven transition from ferrimagnets to superparamagnets in Fe 3O 4 nanoparticles can be converted into another quantum phase by a transverse microwave magnetic field or by a strong internal anisotropic field. These fields, perpendicular to the Ising axis, can destroy the magnetic long-range order to quantum paramagnets as the fields exceed some critical values. We have exploited the spin resonance spectrometer to determine the dynamic spin susceptibility and the critical exponent γ, which is a power-law dependent spanning of the quantum critical point. Quantum phase transition observed at low temperatures for small magnetite nanoparticles induced by strong surface anisotropic field illustrates the fascinating interplay between thermal and quantum fluctuations in the vicinity of a quantum critical point.

Parisi symmetry of the many-body quantum theory of randomly interacting fermionic systems

We show that fermion systems with random and frustrated interactions display a strong coupling between glassy order and fermionic correlations, which culminates in the implementation of Parisi replica permutation symmetry breaking (RPSB) in their zero-temperature quantum field theories. RPSB effects, setting in below fermionic de Almeida--Thouless (dAT) lines, become stronger as the temperature T decreases and play a crucial role for many physical properties within the entire low-$T$ regime. The Parisi ultrametric structure is shown to determine the dynamic behavior of fermionic correlations (Green's functions) for large times and for the corresponding low-energy excitation spectra, which is predicted to affect transport properties in metallic (and superconducting) spin glasses. Thus we reveal the existence and the detailed form of a number of quantum-dynamical fingerprints of the Parisi scheme. These effects, being strongest as $\stackrel{\ensuremath{\rightarrow}}{T}0,$ are contrasted with the replica-symmetric nature of the critical field theory of quantum spin glass transitions at $T=0,$ which display only small corrections at low T from RPSB. RPSB effects moreover appear to influence the loci of the ground state transitions at ${O(T}^{0})$ and hence the phase diagrams. From explicit solutions for arbitrary T we find a representation of the Green's function in the $T=0$ limit. This leads to a map of the fermionic (insulating) spin glass solution to the local limit of a Hubbard model with random repulsive interaction. This map holds for any number of replica-symmetry-breaking steps K. We obtain the distribution of the Hubbard interaction U and its dependence on the order of RPSB. A generalized mapping between metallic spin glass and random U Hubbard model is conjectured. We also suggest that the new representation of the Green's function at $T=0$ can be used for generalizations to superconductors with spin glass phases. Further generalizations due to Coulomb effects including a crossover from four-state per site to effectively three-state per site models in the $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty}$ limit are briefly considered. We compare our spin glass results with recent $d=\ensuremath{\infty}$ (clean) Hubbard model analyses, paying particular attention to the common role of the corresponding Onsager reaction fields. We also present details of the phase diagrams, emphasizing the important role of the chemical potential $\ensuremath{\mu}.$ The insulating fermionic Ising spin glass model is shown to reveal different entangled magnetic instabilities and phase transitions. We review tricritical phenomena related to the strong correspondence between charge and spin fluctuations and controlled by quantum statistics. A comparison with the diluted Sherrington-Kirkpatrick (SK) spin glass and with classical spin 1 models such as the Blume-Emery-Griffiths model is given. Our detailed analysis for the infinite-range model shows that spin glass order must decay discontinuously as $\ensuremath{\mu}$ exceeds a critical value, provided T is below the tricritical ${T}_{c3}$ and that the $T=0$ transition is of classical type. RPSB occurs in any case on the irreversible side of the (modified) dAT lines for the fermionic SK model and hence at least everywhere within a fermionic spin glass phase. Although the critical field theory of the quantum paramagnet to spin glass transition in metallic systems remains replica symmetric at $T=0,$ with only small corrections at low T from RPSB, the phase diagram is affected at ${O(T}^{0})$ by RPSB. Generalizing our results for the fermionic Ising spin glass we consider modifications in phase diagrams of models with spin and charge quantum dynamics such as metallic spin glasses.

Universal relaxational dynamics near two-dimensional quantum critical points

We describe the nonzero temperature (T), low frequency (\omega) dynamics of the order parameter near quantum critical points in two spatial dimensions (d), with a special focus on the regime \hbar\omega << k_B T. For the case of a `relativistic', O(n)-symmetric, bosonic quantum field theory we show that, for small \epsilon=3-d, the dynamics is described by an effective classical model of waves with a quartic interaction. We provide analytical and numerical analyses of the classical wave model directly in d=2. We describe the crossover from the finite frequency, "amplitude fluctuation", gapped quasiparticle mode in the quantum paramagnet (or Mott insulator), to the zero frequency "phase" (n >= 2) or "domain wall" (n=1) relaxation mode near the ordered state. For static properties, we show how a surprising, duality-like transformation allows an exact treatment of the strong-coupling limit for all n. For n=2, we compute the universal T dependence of the superfluid density below the Kosterlitz-Thouless temperature, and discuss implications for the high temperature superconductors. For n=3, our computations of the dynamic structure factor relate to neutron scattering experiments on La_{1.85}Sr_{0.15}CuO_4, and to light scattering experiments on double layer quantum Hall systems. We expect that closely related effective classical wave models will apply also to other quantum critical points in d=2.

Magnetic Gaps Related to Spin Glass Order in Fermionic Systems

We provide evidence for spin glass related magnetic gaps in the fermionic density of states below the freezing temperature. Model calculations are presented and proposed to be relevant for explaining resistivity measurements which observe a crossover from variable range to activated behavior. The magnetic field dependence of a hard gap and the low temperature decay of the density of states are given. In models with fermion transport a new metal-insulator transition is predicted to occur due to the spin glass gap, anteceding the spin glass to quantum paramagnet transition at smaller spin density. Important fluctuation effects due to finite range frustrated interactions are estimated and discussed.

Metallic spin glasses

Recent work on the zero-temperature phases and phase transitions of strongly random electronic systems is reviewed. The transition between the spin glass and quantum paramagnet is examined, for both metallic and insulating systems. Insight gained from the solution of infinite-range models leads to a quantum field theory for the transition between a metallic quantum paramagnetic and a metallic spin glass. The finite-temperature phase diagram is described and crossover functions are computed in mean-field theory. A study of fluctuations about mean field leads to the formulation of scaling hypotheses.

Quantum phase transitions involving a change in polarization.

The geometric Berry's phase of the many-body wave function can be used to characterize changes in the electric polarization at quantum phase transitions that take place as one parameter of the Hamiltonian is adiabatically changed. Transitions which involve a discontinuous change in macroscopic polarization are of topological nature, and occur whenever the system exhibits planes of inversion symmetry. We have applied these ideas to a variety of strongly correlated lattice fermion models in one and two dimensions; in particular, the three-band Hubbard model in ${\mathrm{CuO}}_{2}$ planes in the parent compounds of high-temperature superconductors. For spin-1/2 fermions, we find that the transition between a quantum paramagnet and an antiferromagnet is one of those topological transitions, thus establishing an interesting relation between electric polarization and antiferromagnetism. Interesting consequences emerge when one considers insulators separated by domain walls: A net accumulation of charge at the interface results, which is easily calculated from the Berry's phase change at the domain wall. We discuss the connection to the recently proposed (and experimentally observed) ``microscopic stripes'' in nickelate and insulating cuprate materials. \textcopyright{} 1996 The American Physical Society.

Quantum field theory of metallic spin glasses

We introduce an effective field theory for the vicinity of a zero temperature quantum transition between a metallic spin glass (``spin density glass'') and a metallic quantum paramagnet. Following a mean field analysis, we perform a perturbative renormalization-group study and find that the critical properties are dominated by static disorder-induced fluctuations, and that dynamic quantum-mechanical effects are dangerously irrelevant. A Gaussian fixed point is stable for a finite range of couplings for spatial dimensionality $d > 8$, but disorder effects always lead to runaway flows to strong coupling for $d \leq 8$. Scaling hypotheses for a {\em static\/} strong-coupling critical field theory are proposed. The non-linear susceptibility has an anomalously weak singularity at such a critical point. Although motivated by a perturbative study of metallic spin glasses, the scaling hypotheses are more general, and could apply to other quantum spin glass to paramagnet transitions.

Landau theory of quantum spin glasses of rotors and Ising spins.

We consider quantum rotors or Ising spins in a transverse field on a $d$-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors, and with the transverse field for the Ising spins. For a suitable distribution of exchange constants, these models display spin glass and quantum paramagnet phases and a zero temperature quantum transition between them. An earlier exact solution for the critical properties of a model with infinite-range interactions can be reproduced by minimization of a Landau effective-action functional for the model in finite $d$ with short-range interactions. The functional is expressed in terms of a composite spin field which is bilocal in time. The mean-field phase diagram near the zero temperature critical point is mapped out as a function of temperature, strength of the quantum coupling, and applied fields. The spin glass ground state is found to be replica symmetric, with replica symmetry breaking appearing only at finite temperatures. Next we examine the consequences of fluctuations about mean-field for the critical properties. Above $d=8$, and with certain restrictions on the values of the Landau couplings, we find that the transition is controlled by a Gaussian fixed point with mean-field critical exponents. For couplings not attracted by the Gaussian fixed point above $d=8$, and for all physical couplings below $d=8$, we find runaway renormalization group flows to strong coupling. General scaling relations that should be valid even at the strong coupling fixed point are proposed and compared with Monte Carlo simulations.