Two-dimensional Ising Antiferromagnet Research Articles

Dynamical signatures of thermal spin-charge deconfinement in the doped Ising model

The mechanism underlying charge transport in strongly correlated quantum systems, such as doped antiferromagnetic Mott insulators, remains poorly understood. Here we study the expansion dynamics of an initially localized hole inside a two-dimensional (2D) Ising antiferromagnet at variable temperature. Using a combination of classical Monte Carlo and a truncated basis method, we reveal two dynamically distinct regimes: A spin-charge confined region below a critical temperature $T^*$, characterized by slow spreading, and a spin-charge deconfined region above $T^*$, characterized by an unbounded diffusive expansion. The deconfinement temperature $T^*\approx 0.65 J_z$ we find is around the N\'eel temperature $T_{\rm N} = 0.567 J_z$ of the Ising background in 2D, but we expect $T^* < T_{\rm N}$ in higher dimensions. In both regimes we find that the mobile hole does not thermalize with the Ising spin background on the considered time scales, indicating weak effective coupling of spin- and charge degrees of freedom. Our results can be qualitatively understood by an effective parton model, and can be tested experimentally in state-of-the-art quantum gas microscopes.

Fractons from frustration in hole-doped antiferromagnets

Recent theoretical research on tensor gauge theories led to the discovery of an exotic type of quasiparticles, dubbed fractons, that obey both charge and dipole conservation. Here we describe physical implementation of dipole conservation laws in realistic systems. We show that fractons find a natural realization in hole-doped antiferromagnets. There, individual holes are largely immobile, while dipolar hole pairs move with ease. First, we demonstrate a broad parametric regime of fracton behavior in hole-doped two-dimensional Ising antiferromagnets viable through five orders in perturbation theory. We then specialize to the case of holes confined to one dimension in an otherwise two-dimensional antiferromagnetic background, which can be realized via the application of external fields in experiments, and prove ideal fracton behavior. We explicitly map the model onto a fracton Hamiltonian featuring conservation of dipole moment. Manifestations of fractonicity in these systems include gravitational clustering of holes. We also discuss diagnostics of fracton behavior, which we argue is borne out in existing experimental results.

Perpendicular susceptibility and geometrical frustration in two-dimensional Ising antiferromagnets: Exact solutions

Discovery of new materials and improved experimental as well as numerical techniques have led to a renewed interest in geometrically frustrated spin systems. However, there are very few exact results available that can provide a benchmark for comparison. In this work, we calculate exactly the perpendicular susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ for an Ising antiferromagnet with (i) nearest-neighbor pair interaction on a kagome lattice where strong frustration prevents long-range ordering and (ii) elementary triplet interactions on a kagome lattice which has no frustration but the system remains disordered down to zero temperature. By comparing with other known exact results with and without frustration, we propose that an appropriately temperature-scaled ${\ensuremath{\chi}}_{\ensuremath{\perp}}$ can be used as a quantitative measure of the degree of frustration in Ising spin systems.

Cluster algorithms for frustrated two-dimensional Ising antiferromagnets via dual worm constructions.

We report on the development of two dual worm constructions that lead to cluster algorithms for efficient and ergodic Monte Carlo simulations of frustrated Ising models with arbitrary two-spin interactions that extend up to third-neighbors on the triangular lattice. One of these algorithms generalizes readily to other frustrated systems, such as Ising antiferromagnets on the Kagome lattice with further neighbor couplings. We characterize the performance of both these algorithms in a challenging regime with power-law correlations at finite wave vector.

Ashkin-Teller criticality and weak first-order behavior of the phase transition to a fourfold degenerate state in two-dimensional frustrated Ising antiferromagnets.

We study the thermal phase transition of the fourfold degenerate phases (the plaquette and single-stripe states) in the two-dimensional frustrated Ising model on the Shastry-Sutherland lattice using Monte Carlo simulations. The critical Ashkin-Teller-like behavior is identified both in the plaquette phase region and the single-stripe phase region. The four-state Potts critical end points differentiating the continuous transitions from the first-order ones are estimated based on finite-size-scaling analyses. Furthermore, a similar behavior of the transition to the fourfold single-stripe phase is also observed in the anisotropic triangular Ising model. Thus, this work clearly demonstrates that the transitions to the fourfold degenerate states of two-dimensional Ising antiferromagnets exhibit similar transition behavior.

Binding carriers to a nonmagnetic impurity in a two-dimensional square Ising antiferromagnet

A hole in a two-dimensional Ising antiferromagnet was believed to be infinitely heavy due to the string of wrongly oriented spins it creates as it moves, which should trap it near its original location. Trugman showed that, in fact, the hole acquires a finite effective mass due to contributions from so-called Trugman loop processes, where the hole goes nearly twice around closed loops, first creating and then removing wrongly oriented spins, and ending up at a different lattice site. This generates effective second- and third-nearest-neighbor hopping terms which keep the quasiparticle on the sublattice it was created on. Here, we investigate the trapping of the quasiparticle near a single attractive nonmagnetic impurity placed at one lattice site. We consider the two cases with the quasiparticle and impurity being on the same versus on different sublattices. The main result is that even though the quasiparticle can not see the bare disorder in the latter case, the coupling to magnons generates an effective renormalized disorder on its own sublattice which is strong enough to lead to bound states, which however have a very different spectrum than when the quasiparticle and impurity are on the same sublattice.

Aharonov-Bohm interference for a hole in a two-dimensional Ising antiferromagnet in a transverse magnetic field

We show that a proper consideration of the contribution of Trugman loops leads to a fairly low effective mass for a hole moving in a square lattice Ising antiferromagnet, if the bare hopping and the exchange energy scales are comparable. This contradicts the general view that because of the absence of spin fluctuations, this effective mass must be extremely large. Moreover, in the presence of a transverse magnetic field, we show that the effective hopping integrals acquire an unusual dependence on the magnetic field, through Aharonov-Bohm interference, in addition to significant retardation effects. The effects of the Aharonov-Bohm interference on the cyclotron frequency (for small magnetic fields) and the Hofstadter butterfly (for large magnetic fields) are analyzed.

Anisotropic spin dynamics in the frustrated chainCa3Co2O6detected by single-crystalC59oNMR

Static and dynamic magnetic properties are investigated by $^{59}\text{C}\text{o}$ NMR measurements on a single crystal of ${\text{Ca}}_{3}{\text{Co}}_{2}{\text{O}}_{6}$, a rare model of the ferromagnetic Ising chain coupled antiferromagnetically on a triangular lattice. Above a ferrimagnetic order transition temperature ${T}_{\text{N}}=25\text{ }\text{K}$, the static spin susceptibility probed by the $^{59}\text{C}\text{o}$ Knight shift shows anisotropic behavior in the temperature dependence, consistent with ferromagnetic interactions along the $c$-axis chain and antiferromagnetic interactions in the $ab$ plane. Correspondingly, the dynamical spin susceptibility obtained from the $^{59}\text{C}\text{o}$ nuclear spin-lattice relaxation rate is also highly anisotropic. The intrachain ferromagnetic correlation steeply develops below 300 K while the interchain antiferromagnetic one does below 120 K with the critical exponent expected in the two-dimensional Ising antiferromagnet. Below ${T}_{\text{N}}$, the low-energy excitation arising from the predominant spin-wave magnons has an anisotropic full gap, reflecting the strongly Ising nature. Clear microscopic evidence of the ferrimagnetic order is demonstrated in the $^{59}\text{C}\text{o}$ NMR spectra at 5 K. Rotation of the external magnetic field from the $ab$ plane to the $c$ axis shows the first-order transition from the ferrimagnetic to the fully polarized state. The ferrimagnetic state with the uniform magnitude of magnetic moment is observed even in the transverse field adjusted parallel to the $ab$ plane.

Ising antiferromagnet with mobile, pinned, and quenched defects

Motivated by recent experiments on (Sr,Ca,La)_14 Cu_24 O_41, a two-dimensional Ising antiferromagnet with mobile, locally pinned and quenched defects is introduced and analysed using mainly Monte Carlo techniques. The interplay between the arrangement of the defects and the magnetic ordering as well as the effect of an external field are studied.

Weakly coupled antiferromagnetic planes in single-crystalLiCoPO4

Neutron-scattering and magnetic susceptibility studies of single-crystal ${\mathrm{LiCoPO}}_{4}$ are reported. The neutron-diffraction results indicate that in the antiferromagnetic phase the moments are not strictly aligned along the b axis, as previously reported [R. P. Santoro et al., J. Phys. Chem. $27,$ 1192 (1996)], but are uniformly rotated from this axis by a small angle $(\ensuremath{\approx}4.6\ifmmode^\circ\else\textdegree\fi{}).$ This rotation breaks the mirror symmetry along the orthorhombic b axis. Symmetry considerations based on this rotation, on the magnetoelectric effect, and on a recently observed weak spontaneous magnetization along the spin direction, implying a so-far-unknown ferrimagneticlike kind of weak ferromagnetism, allow one to postulate the monoclinic magnetic point group ${2}^{\ensuremath{'}}.$ The diffraction data are analyzed in terms of weakly coupled two-dimensional Ising antiferromagnets. The large anisotropy in the susceptibility is explained in terms of the single-ion anisotropy and anisotropic exchange interactions. We argue that the alignment of the magnetic moments in the antiferromagnetic phase is determined by the single-ion anisotropy even though the exchange along this direction is the weakest.

Critical Spin Dynamics in the Two-Dimensional Percolating Ising Antiferromagnet, Rb2CocMg1-cF4

We performed inelastic neutron-scattering experiments with high energy resolution, in order to investigate the critical spin dynamics in the two-dimensional (2D) Ising antiferromagnet, Rb 2 Co c Mg 1- c F 4 , with c =0.6, 0.65, 0.7 and 1, above the percolation threshold c p ( c p =0.593 for a square lattice). First, we have confirmed the dynamical scaling for the homogeneous system ( c =1), and the observed dynamical critical exponent ( z =2.01±0.05) was very close to that obtained from recent numerical studies. Next, the observed spin dynamics in the dilute systems could be described by the temperature dependence expected by the standard scaling theory, the power of the reduced temperature, however, the values of the exponents deviate from those predicted by the 2D Ising model and increase as c approaches to c p from the homogeneous limit. Also, the observed spin dynamics for c close c p was in a quantitatively good agreement with that predicted by the model for critical spin dynamics in a percolating Is...

Crossover from pure Ising to random-exchange dominated behavior of the two-dimensional antiferromagnetRb2Co1−xMgxF4

The temperature dependence of the uniform susceptibility, chi, of diluted two-dimensional Ising antiferromagnets Rb2Co1-xMgxF4,0<=x<=0.4, is investigated in the limit of vanishing external field. Novel data for x = 0.15 are compared with those obtained for x = 0 and 0.4 by Breed et al. (1969) and Ikeda (1983), respectively. Whereas in the pure case, x = 0, Fishers (1962) "energetic contribution" dominates, Aharony et al.s (1979,1986) "random contribution" becomes increasingly important with increasing x. Taking into account both terms not only with respect to the global ordering temperature, TN(x), but also in relation to the "local" phase transition temperatures TN throughout the Griffiths regime,TN(x)<=TN<=TN(0), a satisfactory quantitative description of chi vs. T is deduced for any x above the percolation threshold.

Polarized neutron scattering investigations of the magnetic structure of La 8Cu 7O 19 single crystals

The magnetic properties of the perovskite-related compound La 8Cu 7O 19 were investigated by means of full-polarization analysis of scattered neutrons. Transition to the magnetic ordered state has features of a two-dimensional (2D) Ising antiferromagnet. Magnetic structure below Neel temperature 103(3) K has a propagation vector (0.5 0.5 0).

Dynamics of domains in diluted antiferromagnets

We investigate the dynamics of two-dimensional site-diluted Ising antiferromagnets. In an external magnetic field these highly disordered magnetic systems have a domain structure which consists of fractal domains with sizes on a broad range length scales. We focus on the dynamics of these systems during the relaxation from a long-range ordered initial state to the disordered fractal-domain state after applying an external magnetic field. The equilibrium state with applied field consists of fractal domains with a size distribution which follows a power law with an exponential cutoff. The dynamics of the systems can be understood as a growth process of this fractal-domain state in such a way that the equilibrium distribution of domains develops during time. Following these ideas quantitatively we derive a simple description of the time dependence of the order parameter. The agreement with simulations is excellent.

Spin correlations in percolating networks with fractal geometry

Using neutron-scattering techniques, we have investigated the magnetic correlations in dilute antiferromagnets close to the percolation threshold, in which the magnetic connectivity takes a fractal form. Recent experimental results concerning the self-similarity of the magnetic order, and magnetic excitations in two-dimensional Ising and threedimensional Heisenberg antiferromagnets are presented.

Unitary transformation treatment of a single hole in an Ising antiferromagnet

The behavior of a single hole in a two-dimensional Ising antiferromagnet (t-J z model), is studied in the generalized Dyson-Maleev representation, where the spins are mapped on boson operators and the hole is described as a spinless fermion. The formal similarity with Frohlich's polaron Hamiltonian suggests that thet-J z model can be approximately diagonalized by means of two successive unitary transformations, analogous to those used by Lee, Low, and Pines in their intermediate-coupling treatment of the polaron. Our approach yields an upper bound to the exact ground state energy, as well as the corresponding ground state eigenvector. Fork=0 our energy bound is remarkably close to the result of the self-consistent Born approximation over a wide range of the coupling parameter, which includes the range typically assumed for the high-T c materials. The ground state eigenvector is used to calculate the spatial distribution of bosons (spin deviations) surrounding the hole. Here our results are qualitatively very similar to those obtained in previous work, showing that our ground state eigenvector accounts quite well for the small size of the “spin polaron” in thet-J z model.

Unitary transformation treatment of a single hole in an Ising antiferromagnet

The motion of a single hole in a two-dimensional Ising antiferromagnet ( t − J z model) is studied in a representation, where the spins are treated in the linear spin-wave approximation and the hole is described as a spinless fermion. The formal similarity with Fröhlich's polaron Hamiltonian suggests that the t − J z model can be approximately diagonalized by means of two successive unitary transformations, analogous to those used by Lee, Low, and Pines in their intermediate-coupling treatment of the polaron. The first one is the lattice version of the Jost transformation, and its effect on the Hamiltonian is that the latter becomes diagonal in the hole operators. The remaining pure boson part is then subject to a displaced-oscillator transformation to eliminate all terms linear in the boson operators. The resulting energy E(k) is a rigorous upper bound to the exact ground state energy and, for k = 0, compares well with analytic results based on the retraceable path approximation.

Light scattering from magnetic-energy fluctuations in the one-dimensional Heisenberg antiferromagnet KCuF3.

Inelastic light scattering by magnetic-energy fluctuations has been observed in the one-dimensional Heisenberg antiferromagnet ${\mathrm{KCuF}}_{3}$ using a conventional Raman spectrometer. The scattering, having a peak in the cross section at zero frequency and completely distinguished from Rayleigh scattering, is observed over an extremely wide range of temperature above ${\mathit{T}}_{\mathit{N}}$=39 K. The scattered light is strongly polarized and its line profile around zero frequency is well fitted on a Lorentzian curve. The cross section increases with increasing temperature above ${\mathit{T}}_{\mathit{N}}$. Our experimental data are well explained by the theory which Halley developed introducing the hydrodynamic form for the correlation function of magnetic-energy density given by Halperin and Hohenberg. The absence of such inelastic scattering in ${\mathrm{K}}_{2}$${\mathrm{CoF}}_{4}$ (a two-dimensional Ising antiferromagnet) and ${\mathrm{K}}_{2}$${\mathrm{CuF}}_{4}$ (a two-dimensional Heisenberg ferromagnet) in a Raman spectrum is also discussed.

Intercalation of n-alkylamines in iron thiohypophosphate (FePS3)

The intercalation of linear alkylamines (C1-C4) in the two-dimensional (2D) Ising antiferromagnet, FePS3, has been investigated. Intercalation proceeds with a dilation of the interlayer distance. The expansion (approximately 3.8 angstrom) is the same for all four amine molecules, suggesting that they are oriented flat with respect to the layers. From an analysis of the products of deintercalation, it is concluded that the intercalated species are the alkylammonium cations and neutral amine molecules. The intercalated compounds are highly moisture sensitive, as reflected in the chemical nature of the intercalated species. Charge neutrality of the lattice after intercalation is preserved by the loss of Fe2+ ions from the lattice. These Fe2+ ions are further oxidized to form superparamagnetic Fe2O3 clusters, as confirmed by Mossbauer spectra and magnetic measurements. This was further corroborated by in situ EPR studies. The Fe-57 Mossbauer spectra of the intercalated compounds showed evidence for two species other than Fe2O3. On the basis of the observed isomer shifts and quadrupole splittings, they have been assigned to Fe2+ in an environment similar to that in FePS3 and in a distorted FePS3 environment. The temperature and field dependence of the magnetic susceptibility of single crystals of the amine-intercalated FePS3 have been measured. Their magnetic behavior shows many of the features expected of a 2D Ising antiferromagnet with random defects, Fe1-xPS3, in agreement with the mechanism of intercalation.

Monte Carlo Twist Method Applied to the Two-Dimensional Ising Antiferromagnets in Magnetic Fields: Tests of the Method and Critical-Point Amplitudes

We apply our Monte Carlo twist method to the antiferromagnetic Ising model on square lattices in several uniform fields imposing fixed boundary conditions. We have estimated the critical temperature T c and critical exponent ν at each field. The former well agree with the analytic results of Müller-Hartmann and Zittartz, and the latter are all close to ν=1. We have calculated the finite-size critical-point amplitude of the interfacial free energy Ξ 0 which is believed to be universal. Our estimate of Ξ 0 at zero field is in good agreement with the analytic result of Abraham and Švrakić. We also report for the first time estimates of Ξ 0 at finite fields. Further, comparison is made with results of Mon and Jasnow.