Two-dimensional Spin Systems Research Articles

Emergent dimensional reduction of the spin sector in a model for narrow-band manganites

The widely used Double-Exchange model for manganites is shown to support various "striped" phases at filling fractions 1/n (n=3, 4, 5...), in the previously unexplored regime of narrow bandwidth and small Jahn-Teller coupling. Working in two dimensions, our main result is that these stripes can be individually spin flipped without a physically relevant change in the energy, i.e., we find a large groundstate manifold with nearly degenerate energies. The two-dimensional spin system thus displays an unexpected dynamically generated dimensional reduction into decoupled one-dimensional stripes, even though the electronic states remain two-dimensional. Relations of our results with recent literature addressing compass models in quantum computing are discussed.

Dynamics of entanglement in a two-dimensional spin system

We consider the time evolution of entanglement in a finite two-dimensional transverse Ising model. The model consists of a set of seven localized spin-$\frac{1}{2}$ particles in a two-dimensional triangular lattice coupled through nearest-neighbor exchange interaction in the presence of an external time-dependent magnetic field. The magnetic field is applied in different function forms: step, exponential, hyperbolic, and periodic. We found that the time evolution of the entanglement shows an ergodic behavior under the effect of the time-dependent magnetic fields. Also, we found that while the step magnetic field causes great disturbance to the system, creating rapid oscillations, the system shows great controllability under the effects of the other magnetic fields where the entanglement profile follows closely the shape of the applied field even with the same frequency for periodic fields. This follow-up trend breaks down as the strength of the field, the transition constant for the exponential and hyperbolic forms, or the frequency for periodic field increase leading to rapid oscillations. We observed that the entanglement is very sensitive to the initial value of the applied periodic field: the smaller the initial value is, the less distorted the entanglement profile is. Furthermore, the effect of thermal fluctuations is very devastating to the entanglement, which decays very rapidly as the temperature increases. Interestingly, although a large value of the magnetic field strength may yield a small entanglement, the magnetic field strength was found to be more persistent against thermal fluctuations than the small field strengths.

Ferromagnetically Coupled Shastry-Sutherland Quantum Spin Singlets in(CuCl)LaNb2O7

A thorough crystal structure determination at very low temperature of (CuCl)LaNb₂O₇, originally proposed as a spin-1/2 square-lattice antiferromagnet, is reported thanks to the use of single-crystal x-ray diffraction and powder neutron diffraction. State-of-the-art calculations (maximum entropy method) reveal that (CuCl)LaNb₂O₇ is orthorhombic with Pbam symmetry. First-principles calculations demonstrate that the dominant magnetic interactions are antiferromagnetic between fourth nearest neighbors with a Cu-Cl-Cl-Cu exchange path, which lead to the formation of spin singlets. The two strongest interactions between the singlets are ferromagnetic, which makes (CuCl)LaNb₂O₇ the first system of ferromagnetically coupled Shastry-Sutherland quantum spin singlets.

The Magnetic Properties of Mixed Ferrimagnetic Spin System

Based on Monte Carlo (MC) simulation, the magnetization behavior of mixed ferrimagnetic spin system with single-ion anisotropy under external field is investigated. It is assumed that the element of the mixed system is composed of spin-1 and spin-3/2 by turns. The simulated results indicate that there exist the magnetization curves at the ground state on the one-dimensional spin chain, two-dimensional spin system as well as three-dimensional spin system. It found that the size, anisotropy constant and spin configurations influence evidently the magnetic properties of the mixed system. Moreover, the magnetic plateaus and the phase diagrams of the systems can be well interpreted in terms of the simple calculation of energy.

Neutron scattering study of the magnetic phase diagram of underdoped YBa2Cu3O6+x

We present a neutron triple-axis and resonant spin-echo spectroscopy study of the spin correlations in untwinned YBa2Cu3O6+x single crystals with x=0.3, 0.35 and 0.45 as a function of temperature and magnetic field. As the temperature T→0, all samples exhibit static incommensurate magnetic order with propagation vector along the a-direction in the CuO2 planes. The incommensurability δ increases monotonically with hole concentration, as it does in La2−xSrxCuO4 (LSCO). However, δ is generally smaller than in LSCO at the same doping level, and there is no sign of a reorientation of the magnetic propagation vector at the lowest doping levels. The intensity of the incommensurate Bragg reflections increases linearly with magnetic field for YBa2Cu3O6.45 (superconducting Tc=35 K), whereas it is field independent for YBa2Cu3O6.35 (Tc=10 K). These results fit well into a picture in which superconducting and spin-density wave order parameters coexist, and their ratio is controlled by the magnetic field. They also suggest that YBa2Cu3O6+x samples with x∼0.5 exhibit incommensurate magnetic order in the high fields used for the recent quantum oscillation experiments on this system, which likely induces a reconstruction of the Fermi surface. We present neutron resonant spin-echo measurements (with energy resolution ∼1 μeV) for T≠0 that demonstrate a continuous thermal broadening of the incommensurate magnetic Bragg reflections into a quasi-elastic peak centered at excitation energy E=0, consistent with the zero-temperature transition expected for a two-dimensional spin system with full spin–rotation symmetry. Measurements on YBa2Cu3O6.45 with a conventional triple-axis spectrometer (with energy resolution ∼100 μeV) yield a characteristic crossover temperature TSDW∼30 K for the onset of quasi-static magnetic order. Upon further heating, the wavevector characterizing low-energy spin excitations progressively approaches the commensurate antiferromagnetic wavevector, and the incommensurability vanishes in an order-parameter-like fashion at an ‘electronic liquid crystal’ onset temperature TELC∼150 K. Both TSDW and TELC increase continuously as the Mott-insulating phase is approached with decreasing doping level. These findings are discussed in the context of current models of the interplay between magnetism and superconductivity in the cuprates.

Finite-size scaling behavior in trapped systems

Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in the presence of a confining magnetic field which varies with distance |x| to a "trap center," proportionally to (|x|/ℓ)p, where p>0 . On a strip geometry, the competition between the "trap size" ℓ and the strip width L is analyzed in the context of a generalized finite-size scaling ansatz. In the low-field regime ℓ >> L, we use conformal-invariance concepts in conjunction with a linear-response approach to derive the appropriate (p-dependent) limit of the theory, which agrees very well with numerical results for magnetization profiles. For high fields ℓ ≲ L, correlation-length scaling data broadly confirm an existing picture of p-dependent characteristic exponents. Standard spin-1/2 and spin-1 Ising systems are considered, as well as the Blume-Capel model.

Exact calculation of entanglement in a19-site two-dimensional spin system

Using the Trace Minimization Algorithm, we carried out an exact calculation of entanglement in a 19-site two-dimensional transverse Ising model. This model consists of a set of localized spin-1/2 particles in a two dimensional triangular lattice coupled through exchange interaction J and subject to an external magnetic field of strength h. We demonstrate, for such a class of two-dimensional magnetic systems, that entanglement can be controlled and tuned by varying the parameter $\lambda$ = h/J in the Hamiltonian and by introducing impurities into the systems. Examining the derivative of the concurrence as a function of $\lambda$ shows that the system exhibits a quantum phase transition at about $\lambda_c$ = 3.01, a transition induced by quantum fluctuations at the absolute zero of temperature.

Bound states in two-dimensional spin systems near the Ising limit: A quantum finite-lattice study

We analyze the properties of low-energy bound states in the transverse-field Ising model and in the XXZ model on the square lattice. To this end, we develop an optimized implementation of perturbative continuous unitary transformations. The Ising model is studied in the small-field limit which is found to be a special case of the toric code model in a magnetic field. To analyze the XXZ model, we perform a perturbative expansion about the Ising limit in order to discuss the fate of the elementary magnon excitations when approaching the Heisenberg point.

Synthesis, Structural and Magnetic Properties of the Solid Solution (CuCl1-xBrx)LaNb2O7 (0 ≤x ≤1)

The two-dimensional (2D) quantum spin system (CuCl)LaNb2O7 has a spin-singlet ground state with a gap of 2.3 meV, while the isostructural material (CuBr)LaNb2O7 displays collinear antiferromagnetic order at TN = 32 K. Here we report on the synthesis of solid solution (CuCl1-xBrx)LaNb2O7 (0 < x < 1), and its structural and magnetic properties by means of magnetic susceptibility, high-field magnetization, and neutron diffraction studies. The x-dependence of cell parameters follows Vegards law, verifying the uniform distribution of Cl and Br atoms at the halide site, though a more complex structural evolution is inferred from an opposing correlation between the intra- and interlayer cell distances (vs. x). 5%-Br substitution is found to induce antiferromagnetic order with TN = 7 K, consistent with a recent mSR study, and the magnetic structure is collinear, having a significantly reduced moment. Further Br substitution leads to a linear increase in TN up to x = 1. These results indicate that (CuCl)LaNb2O7 is located in the vicinity of the quantum phase boundary.

Nonequilibrium structures and slow dynamics in a two-dimensional spin system with competing long-range and short-range interactions

We present a lattice spin model that mimics a system of interacting particles through a short-range repulsive potential and a long-range attractive power-law decaying potential. We perform a detailed analysis of the general equilibrium phase diagram of the model at finite temperature, showing that the only possible equilibrium phases are the ferromagnetic and the antiferromagnetic ones. We then study the nonequilibrium behavior of the model after a quench to subcritical temperatures, in the antiferromagnetic region of the phase diagram region, where the pair interaction potential behaves in the same qualitative way as in a Lennard-Jones gas. We find that even in the absence of quenched disorder or geometric frustration, the competition between interactions gives rise to nonequilibrium disordered structures at low enough temperatures that strongly slow down the relaxation of the system. This nonequilibrium state presents several features characteristic of glassy systems such as subaging, nontrivial fuctuation dissipation relations, and possible logarithmic growth of free-energy barriers to coarsening.

Scaling behaviour of magnetic transitions in Ni3V2O8

We have studied phase transitions in multiferroic Ni3V2O8, through dielectric measurements and by investigating the effects of Zn doping. The divergence of the dielectric constant near T L = 6.4 K can be approximately fit by power law behaviour, but exhibits different critical exponents above and below T L . The two higher temperature magnetic transitions in (Ni1−x Zn x )3V2O8, are strongly suppressed as the Zn doping fraction x is increased. The rates of the suppression of both T H and T L with x are consistent with two-dimensional spin systems, with the suppression of T H consistent with Ising spins and the suppression of T L consistent with Heisenberg spins.

Topological excitations in a two-dimensional spin system with high spin s ≥1

We construct a class of topological excitations of a mean field in a two-dimensional spin system represented by a quantum Heisenberg model with high powers of exchange interaction. The quantum model is associated with a classical one (the continuous classical analogue) that is based on a Landau-Lifshitz like equation, and describes large-scale fluctuations of the mean field. On the other hand, the classical model is a Hamiltonian system on a coadjoint orbit of the unitary group SU($2s {+} 1$) in the case of spin $s$. We have found a class of mean field configurations that can be interpreted as topological excitations, because they have fixed topological charges. Such excitations change their shapes and grow preserving an energy.

Scaling behavior of domain walls at theT=0ferromagnet to spin-glass transition

We study domain-wall excitations in two-dimensional random-bond Ising spin systems on a square lattice with side length L, subject to two different continuous disorder distributions. In both cases an adjustable parameter allows to tune the disorder so as to yield a transition from a spin-glass ordered ground state to a ferromagnetic groundstate. We formulate an auxiliary graph-theoretical problem in which domain walls are given by undirected shortest paths with possibly negative distances. Due to the details of the mapping, standard shortest-path algorithms cannot be applied. To solve such shortest-path problems we have to apply minimum-weight perfect-matching algorithms. We first locate the critical values of the disorder parameters, where the ferromagnet to spin-glass transition occurs for the two types of the disorder. For certain values of the disorder parameters close to the respective critical point, we investigate the system size dependence of the width of the the average domain-wall energy (~L^\theta) and the average domain-wall length (~L^df). Performing a finite-size scaling analysis for systems with a side length up to L=512, we find that both exponents remain constant in the spin-glass phase, i.e. \theta ~- 0.28 and df~1.275. This is consistent with conformal field theory, where it seems to be possible to relate the exponents from the analysis of Stochastic Loewner evolutions (SLEs) via df-1=3/[4(3+\theta)]. Finally, we characterize the transition in terms of ferromagnetic clusters of spins that form, as one proceeds from spin-glass ordered to ferromagnetic ground states.

Spin-Singlet Ground State in the Two-Dimensional Frustrated Triangular Lattice: YbAl3C3

We present the highly frustrated phenomena observed in YbAl 3 C 3 with a spin gap. The inelastic neutron spectra of low-lying magnetic excitations at low temperatures are quite similar to those of SrCu 2 (BO 3 ) 2 and (CuCl)LaNb 2 O 7 that exhibit a dimer ground state in a two-dimensional quantum spin system. The structure of the first excited triplet state is directly clarified by inelastic neutron scattering experiments with a higher energy resolution. Furthermore, it becomes clear that the characteristic magnetic excitations remain within a high-temperature region. The result of the specific heat measurement also shows an anomaly associated with the formation of dimerized Yb ions. We conclude that a long-range magnetic order is suppressed by a large geometrical spin frustration, resulting in the stabilization of the dimer ground state.

状態推定遅延を含む2次元量子スピン制御系の安定化

状態推定遅延を含む2次元量子スピン制御系の安定化

Exact mapping between classical and topological orders in two-dimensional spin systems

Motivated by the duality between site-centered spin and bond-centered spin in one-dimensional system, which connects two different constructions of fermions from the same set of Majorana fermions, we show that two-dimensional models with topological orders can be constructed from certain well-known models with classical orders characterized by symmetry breaking. Topology-dependent ground state degeneracy, vanishing two-point correlation functions, and unpaired Majorana fermions on boundaries emerge naturally from such construction. The approach opens a different way to construct and characterize topological orders.

Canonical sequence method applied to a two-dimensional spin system

A number of years ago, Horn and Weinstein introduced a novel nonperturbative method, the t-expansion, for calculating ground-state expectation values for Hamiltonian systems. Recently Samaj et al. have generalized the t-expansion technique and the related connected moments expansion to a more general canonical sequence. In the present work we have expounded upon this work and have applied this to the two-dimensional square anisotropic XXZ Heisenberg model.

Effects of interchain frustration on the phase transition in two-dimensional spin systems

Effects of interchain frustration on the phase transition in two-dimensional spin systems

A Novel Ordered Phase in SrCu2(BO3)2 under High Pressure

We report results of 11 B NMR and susceptibility measurements on the quasi two-dimensional frustrated dimer spin system SrCu 2 (BO 3 ) 2 under high pressure. At 2.4 GPa and in a magnetic field of 7 T, NMR lines split with decreasing temperature in two steps. A gradual splitting below T = 30 K breaking the four-fold symmetry of magnetic response is followed by a further sudden splitting below 3.6 K. The latter indicates a magnetic phase transition, which is also marked by a kink in the susceptibility at 1.44 GPa. From the magnetic hyperfine shift data, we conclude that the low- T phase has a doubled unit cell containing two types of dimers, one in a nearly singlet state and the other with a finite magnetization down to T = 0.

Magnetic structure and magnetic excitations in the two-dimensional spin system of the Cu3B2O6 compound

This paper reports on the results of measurements of the magnetic susceptibility, heat capacity, neutron scattering, muon spin relaxation, and electron paramagnetic resonance in Cu3B2O6 for the study of the ground state of the spin system of this compound. The results obtained suggest that, at a temperature of 10 K, the spin subsystem of the crystal, which consists of single spins and clusters of pairs and fours of spins interacting with one another, undergoes a transition to a state representing a superposition of the singlet (for clusters) and magnetically ordered (for single spins) states.