Antiferromagnetic Spin System Research Articles

Simulating frustrated antiferromagnets with quadratically driven QED cavities

We propose a class of quantum simulators for antiferromagnetic spin systems, based on coupled photonic cavities in presence of two-photon driving and dissipation. By modeling the coupling between the different cavities through a hopping term with negative amplitude, we solve numerically the quantum master equation governing the dynamics of the open system and determine its non-equilibrium steady state. Under suitable conditions, the steady state can be described in terms of the degenerate ground states of an antiferromagnetic Ising model. When the geometry of the cavity array is incommensurate with the antiferromagnetic coupling, the steady state presents properties which bear full analogy with those typical of the spin liquid phases arising in frustrated magnets.

Thermodynamic properties of a multiferroic antiferromagnetic spin system: The influence of Dzyaloshinskii Moriya interaction

In this paper, we address the influence of Dzyaloshinskii Moriya (DM) interaction on the thermodynamic properties of a multiferroic antiferromagnetic spin system using the spin wave theory (SWT) as a diagonalization method which, associated to the statistical physics, helps to evaluate the statistical sum. The basic factors in thermodynamics, such as the Boltzmann entropy and the specific heat capacity at thermal equilibrium, are obtained. Analyzing the numerical results, it follows that the DM interaction is the best candidate that can help to maintain in long time the system in its coherent state. Furthermore, we find that the influence of the DM interaction is more accentuated at low-temperature and that it enables the system to release heat energy. On the other hand, the fact that the specific heat capacity tends to the constant clearly shows that the system obeys the Dulong–Petit law. In addition, our results also show that for high magnetic field (greater than B[Formula: see text]=[Formula: see text]30 Tesla), the magnetic field dependence of both entropy and specific heat shows a peak-like behavior and that the DM interaction raises the corresponding critical magnetic field but lowers the peak amplitude. It follows that the spin-flop transition occurs in the system and that the strong magnetic field withdraw the antiferromagnetic phase. Overall, we find that the DM interaction is a promising candidate for the control of our system.

Long-Range Order, “Tower” of States, and Symmetry Breaking in Lattice Quantum Systems

In a quantum many-body system where the Hamiltonian and the order operator do not commute, it often happens that the unique ground state of a finite system exhibits long-range order (LRO) but does not show spontaneous symmetry breaking (SSB). Typical examples include antiferromagnetic quantum spin systems with Neel order, and lattice boson systems which exhibit Bose-Einstein condensation. By extending and improving previous results by Horsch and von der Linden and by Koma and Tasaki, we here develop a fully rigorous and almost complete theory about the relation between LRO and SSB in the ground state of a finite system with continuous symmetry. We show that a ground state with LRO but without SSB is inevitably accompanied by a series of energy eigenstates, known as the "tower" of states, which have extremely low excitation energies. More importantly, we also prove that one gets a physically realistic "ground state" by taking a superposition of these low energy excited states. The present paper is written in a self-contained manner, and does not require any knowledge about the previous works on the subject.

Quantized excitation spectra by magnon confinement in quasi-one-dimensional S=1 spin systems

We apply the infinite time-evolving-block-decimation algorithm to calculate the dynamical spin-structure factors of the quasi-one-dimensional (q1D) S=1 antiferromagnetic spin system with the single-ion anisotropy and the bond alternation. We find that excitation continuum originating from magnons is quantized, when the staggered field induced by the weak inter-chain interaction is taken into account. The excitation energies of the quantized excitation spectra are well explained by negative zeros of the Airy functions, when the easy-axis anisotropy is strong and the ground state is located deep in the N\'eel phase. This quantization of the magnon continuum is a counterpart of the spinon confinement, which has been recently discussed in q1D S=1/2 antiferromagnets. We further show that, when the staggered field exists, the quantized excitation spectra appear the phase boundary between the Haldane phase and the N\'eel phase of the phase diagram without the staggered field. However, the quantized excitation spectra disappear in the singlet dimer phase.

Robust Hund rule without Coulomb repulsion and exclusion principle in quantum antiferromagnetic chains of composite half spins

Quantum spin chains with composite spins have been used to approximate conventional chains with higher spins. For instance, a spin 1 (or ) chain was sometimes approximated by a chain with two (or three) spin ’s per site. However, little examination has been given as to whether this approximation, effectively assuming the first Hund rule per site, is valid and why. In this paper, the validity of this approximation is investigated numerically. We diagonalize the Hamiltonians of spin chains with a spin 1 and per site and with two and three spin ’s per site. The low energy excitation spectrum for the spin chain with M spin ’s per site is found to coincide with that of the corresponding conventional chain with one spin per site. In particular, we find that as the system size increases, an increasingly larger block of consecutive lowest energy states with maximal spin per site is observed, robustly supporting the first Hund rule even though the exclusion principle does not apply and the system does not possess Coulomb repulsion. As for why this approximation works, we show that this effective Hund rule emerges as a plausible consequence when applying to composite spin systems the Lieb–Mattis theorem, which is originally for the ground state of ferrimagnetic and antiferromagnetic spin systems.

Magnon thermal Hall effect in kagome antiferromagnets with Dzyaloshinskii-Moriya interactions

We theoretically study magnetic and topological properties of antiferromagnetic kagome spin systems in the presence of both in- and out-of-plane Dzyaloshinskii-Moriya interactions. In materials such as the iron jarosites, the in-plane interactions stabilize a canted noncollinear "umbrella" magnetic configuration with finite scalar spin chirality. We derive expressions for the canting angle, and use the resulting order as a starting point for a spin-wave analysis. We find topological magnon bands, characterized by non-zero Chern numbers. We calculate the magnon thermal Hall conductivity, and propose the iron jarosites as a promising candidate system for observing the magnon thermal Hall effect in a noncollinear spin configuration. We also show that the thermal conductivity can be tuned by varying an applied magnetic field, or the in-plane Dzyaloshinskii-Moriya strength. In contrast with previous studies of topological magnon bands, the effect is found to be large even in the limit of small canting.

Order and excitations in site diluted quantum antiferromagnet in the triangular lattice

Abstract In this work we use the linear spin-wave approximation to study the quantum two-dimensional Heisenberg model on triangular lattice in the presence of nonmagnetic impurities. In particular we discuss how site disorder changes the ground-state properties of this important frustrated antiferromagnetic spin system. Our main focus is on the role of the nonmagnetic impurities which generates an influence of the quantum order-disorder transition and the effect of the ground-state spin structure in many spin systems.

Kink-like excitations in a square lattice model of an antiferromagnetic spin system

Introducing the Holstein–Primakoff (H-P) bosonic representation of spin operators, the coherent state ansatz and the time dependent variational principle, the dynamics of the square lattice model of an antiferromagnetic system is studied. The dynamics is found to be directed by a set of coupled nonlinear partial differential equations. Employing the multiple exponential function method, soliton excitation in the system is studied. Multiwave kink soliton solutions and their interaction properties are analysed.

Crystalline Motion of Interfaces Between Patterns

We consider the dynamical problem of an antiferromagnetic spin system on a two-dimensional square lattice $$\varepsilon \mathbb {Z}^2$$ with nearest-neighbour and next-to-nearest neighbour interactions. The key features of the model include the interaction between spatial scale $$\varepsilon $$ and time scale $$\tau $$ , and the incorporation of interfacial boundaries separating regions with microstructures. By employing a discrete-time variational scheme, a limit continuous-time evolution is obtained for a crystal in $$\mathbb {R}^2$$ which evolves according to some motion by crystalline curvatures. In the case of anti-phase boundaries between striped patterns, a striking phenomenon is the appearance of some “non-local” curvature dependence velocity law reflecting the creation of some defect structure on the interface at the discrete level.

Localized spin excitations in an antiferromagnetic spin system with D-M interaction.

The existence of localized spin excitations and spin deviations along the site in a one-dimensional antiferromagnet with Dzyaloshinski-Moriya (D-M) interaction has been studied using quasiclassical approximation. By introducing the Holstein-Primakoff bosonic representation of spin operators, the coherent state ansatz, and the time dependent variational principle, a discrete set of coupled nonlinear partial differential equations governing the dynamics is derived. Employing the multiple-scale method, one, two and three solitary wave solutions are constructed and depicted graphically.

Laser-induced polarization of a quantum spin system in the steady-state regime

The effect of the circularly polarized laser field on quantum spin systems in the steady-state regime, in which relaxation plays the central role, has been studied. The dynamical mean-field-like theory predicts several general results for the behavior of the time-average magnetization caused by the laser field. The induced magnetization oscillates with the frequency of the laser field (while Rabi-like oscillations, which modulate the latter in the dynamical regime, are damped by the relaxation in the steady-state regime). At high frequencies, that magnetization is determined by the value to which the relaxation process is directed. At low frequencies the slope of that magnetization as a function of the frequency is determined by the strength of the laser field. The anisotropy determines the resonance behavior of the time-averaged magnetization in both the ferromagnetic and antiferromagnetic cases with nonzero magnetic anisotropy. Nonlinear effects (in the magnitude of the laser field) have been considered. The effect of the laser field on quantum spin systems is maximal in resonance, where the time-averaged magnetization, caused by the laser field, is changed essentially. Out of resonance the changes in the magnetization are relatively small. The resonance effect is caused by the nonzero magnetic anisotropy. The resonance frequency is small (proportional to the anisotropy value) for spin systems with ferromagnetic interactions and enhanced by exchange interactions in the spin systems with antiferromagnetic couplings. We show that it is worthwhile to study the laser-field-induced magnetization of quantum spin systems caused by the high-frequency laser field in the steady-state regime in ``easy-axis'' antiferromagnetic spin systems (e.g., in Ising-like antiferromagnetic spin-chain materials). The effects of the Dzyaloshinskii-Moriya interaction and the spin-frustration couplings (in the case of the zigzag spin chain) have been analyzed.

Direct visualization of surface phase of oxygen molecules physisorbed on Ag(111) surface: A two-dimensional quantum spin system

We report on the real-space observation of the two-dimensional distorted triangular lattice of physisorbed oxygen $({\mathrm{O}}_{2})$ molecules on an Ag(111) surface by low-temperature scanning tunneling microscopy. The physisorbed state of the ${\mathrm{O}}_{2}$ monolayers was confirmed by measuring their thermal stability, which showed good agreement with previous thermal desorption spectroscopy. The distortion of the observed lattice was reproduced quantitatively by considering the intermolecular exchange interaction in Monte Carlo calculations, indicating a critical role of antiferromagnetic ordering of ${\mathrm{O}}_{2}$ spins. In tunneling spectra, the Kondo resonance was not observed on the ${\mathrm{O}}_{2}$ layer at 4.7 K unlike the case of physisorbed ${\mathrm{O}}_{2}$ on Ag(110). These results indicate that an intrinsic $S=1$ spin of the ${\mathrm{O}}_{2}$ molecules was preserved to form a two-dimensional antiferromagnetic quantum spin system on the surface.

Inapproximability for Antiferromagnetic Spin Systems in the Tree Nonuniqueness Region

A remarkable connection has been established for antiferromagnetic 2-spin systems, including the Ising and hard-core models, showing that the computational complexity of approximating the partition function for graphs with maximum degree Δ undergoes a phase transition that coincides with the statistical physics uniqueness/nonuniqueness phase transition on the infinite Δ-regular tree. Despite this clear picture for 2-spin systems, there is little known for multispin systems. We present the first analog of this in approximability results for multispin systems. The main difficulty in previous inapproximability results was analyzing the behavior of the model on random Δ-regular bipartite graphs, which served as the gadget in the reduction. To this end, one needs to understand the moments of the partition function. Our key contribution is connecting: (i) induced matrix norms, (ii) maxima of the expectation of the partition function, and (iii) attractive fixed points of the associated tree recursions (belief propagation). The view through matrix norms allows a simple and generic analysis of the second moment for any spin system on random Δ-regular bipartite graphs. This yields concentration results for any spin system in which one can analyze the maxima of the first moment. The connection to fixed points of the tree recursions enables an analysis of the maxima of the first moment for specific models of interest. For k -colorings we prove that for even k , in a tree nonuniqueness region (which corresponds to k < Δ) there is no FPRAS, unless NP = RP, to approximate the number of colorings for triangle-free Δ-regular graphs. Our proof extends to the antiferromagnetic Potts model, and, in fact, to every antiferromagnetic model under a mild condition.

Non-equilibrium thermo-field dynamics for anti-ferromagnetic spin system

The non-equilibrium thermo-field dynamics for an anti-ferromagnetic spin system interacting with a phonon reservoir is proposed for the case of a non-bilinear unperturbed Hamiltonian, which includes not only a bilinear part but also a non-bilinear part, in the spin–wave approximation. The two kinds of quasi-particle operators are introduced, and their forms are derived for the semi-free boson fields. It is shown that the two quasi-particles decay exponentially with the frequencies and life-times which are different from each other. It is also shown that each quasi-particle changes to the other tilde quasi-particle through the spin–phonon interaction. The spin–spin correlation functions and longitudinal magnetization for the anti-ferromagnetic spin system under an external static magnetic field are derived in the forms convenient for the perturbation expansions. The expectation values of the spin–wave energy and longitudinal magnetization and the spin–spin correlation functions are investigated numerically for an anti-ferromagnetic system of one-dimensional infinite spins interacting with a damped phonon-reservoir, in the region valid for the lowest spin–wave approximation and the narrowing-limit approximation in which the relaxation times of the spin system are much larger than the correlation time of the phonon reservoir. The two-point Green’s function of the semi-free spin–wave for the anti-ferromagnetic spin system is derived by introducing the thermal quartet notation, and it is given in a form of 4×4 matrix.

Dynamics of a bond-disorderedS=1quantum magnet nearz=1criticality

Neutron scattering is used to study NiCl$_{2-2x}$Br$_{2x}\cdot$4SC(NH$_2$)$_2$, $x=0.06$, a bond-disordered modification of the well-known gapped $S=1$ antiferromagnetic quantum spin system NiCl$_{2}\cdot$4SC(NH$_2$)$_2$. The magnetic excitation spectrum throughout Brillouin zone is mapped out at $T=60$ mK using high-resolution time-of-flight spectroscopy. It is found that the dispersion of spin excitation is renormalized, as compared to that in the parent compound. The lifetime of excitations near the bottom of the band is substantially decreased. No localized states are found below the gap energy $\Delta\simeq0.2$ meV. At the same time, localized zero wave vector states are detected above the top of the band. The results are consistent with a more or less continuous random distribution of bond strengths, and a discrete, possibly bimodal, distribution of single-ion anisotropies in the disordered material.

Superconducting Phase in λ-(BEDT-STF)2GaCl4 at High Pressures

Electrical resistivity measurements under pressure were conducted on the organic conductor λ-(BEDT-STF)2GaCl4, which is situated between λ-(ET)2GaCl4 and λ-(BETS)2GaCl4. Magnetic susceptibility was also measured at ambient pressure. A drop in resistivity, which is associated with the superconducting transition, was observed at Tc ≈ 5 K above 1.22 GPa. The superconducting phase was confirmed by pair-breaking under a magnetic field. This is the first observation of superconductivity in λ-(BEDT-STF)2GaCl4. The temperature dependence of spin susceptibility suggests a two-dimensional antiferromagnetic spin system without any magnetic ordering. The phase adjacent to the superconducting phase in λ-type systems is not the antiferromagnetic phase, unlike the case for κ-(ET)2X.

Intrinsic life-time and external manipulation of Néel states in antiferromagnetic adatom spins on semiconductor surfaces

It has been proposed that antiferromagnetic Fe adatom spins on semiconductor Cu–N surfaces can be used to store information (Loth et al 2012 Science 335 196). Here, we investigate spin dynamics of such antiferromagnetic systems through Monte Carlo simulations. We find out the temperature and size laws of switching rates of Néel states and show that the Néel states can become stable enough for the information storage when the number of spins reaches one or two dozens of the Fe spins. We also explore promising methods for manipulating the Néel states. These could help realize information storage with such antiferromagnetic spin systems.

Inequalities between ground-state energies of Heisenberg models

The Lieb–Schupp inequality is the inequality between ground state energies of certain antiferromagnetic Heisenberg spin systems. In our paper, the numerical value of energy difference given by Lieb–Schupp inequality has been tested for spin systems in various geometries: chains, ladders and quasi-two-dimensional lattices. It turned out that this energy difference was strongly dependent on the class of the system. The relation between this difference and a fall-off of a correlation function has been empirically found and formulated as a conjecture.

Observation of the Thermal Conductivity due to Spins in the One-Dimensional Antiferromagnetic Ising-Like Spin System ACoX3 (A = Rb, Cs; X = Cl, Br)

Thermal conductivity measurements have been carried out for single crystals of the onedimensional (1D) antiferromagnetic (AF) Ising-like spin system ACoX3 (A = Rb, Cs; X = Cl, Br). A shoulder originating from the thermal conductivity due to spin excitations, \k{appa}?spin, has been observed around 60 K in the temperature dependence of the thermal conductivity along the c-axis parallel to spin chains for every ACoX3. To our knowledge, this is the first observation of ?\k{appa}spin in 1D AF Ising-like spin systems. It has been found that the magnitude of ?\k{appa}spin in ACoX3 is a little smaller than those in 1D AF Heisenberg spin systems. The reason is discussed in terms of the Heisenberg-like character in ACoX3.

Approximation Algorithms for Two-State Anti-Ferromagnetic Spin Systems on Bounded Degree Graphs

We show that for the anti-ferromagnetic Ising model on the Bethe lattice, weak spatial mixing implies strong spatial mixing. As a by-product of our analysis, we obtain what is to the best of our knowledge the first rigorous proof of the uniqueness threshold for the anti-ferromagnetic Ising model (with non-zero external field) on the Bethe lattice. Following a method due to Weitz [15], we then use the equivalence between weak and strong spatial mixing to give a deterministic fully polynomial time approximation scheme for the partition function of the anti-ferromagnetic Ising model with arbitrary field on graphs of degree at most $$d$$ , throughout the uniqueness region of the Gibbs measure on the infinite $$d$$ -regular tree. By a standard correspondence, our results translate to arbitrary two-state anti-ferromagnetic spin systems with soft constraints. Subsequent to a preliminary version of this paper, Sly and Sun [13] have shown that our results are optimal in the sense that, under standard complexity theoretic assumptions, there does not exist a fully polynomial time approximation scheme for the partition function of such spin systems on graphs of maximum degree $$d$$ for parameters outside the uniqueness region. Taken together, the results of [13] and of this paper therefore indicate a tight relationship between complexity theory and phase transition phenomena in two-state anti-ferromagnetic spin systems.