Heisenberg Ferromagnet Research Articles

Spin correlations and colossal magnetoresistance inHgCr2Se4

This study aims to unravel the mechanism of colossal magnetoresistance (CMR) observed in n-type HgCr$_2$Se$_4$, in which low-density conduction electrons are exchange-coupled to a three-dimensional Heisenberg ferromagnet with a Curie temperature $T_C\approx$ 105 K. Near room temperature the electron transport exhibits an ordinary semiconducting behavior. As temperature drops below $T^*\simeq2.1T_C$, the magnetic susceptibility deviates from the Curie-Weiss law, and concomitantly the transport enters an intermediate regime exhibiting a pronounced CMR effect before a transition to metallic conduction occurs at $T<T_C$. Our results suggest an important role of spin correlations not only near the critical point, but also for a wide range of temperatures ($T_C<T<T^*$) in the paramagnetic phase. In this intermediate temperature regime the transport undergoes a percolation type of transition from isolated magnetic polarons to a continuous network when temperature is lowered or magnetic field becomes stronger.

Influence of quantum phase transition on spin conductivity in the anisotropic three-dimensional ferromagnetic model

We use the SU(3) Schwinger boson formalism to study the spin transport in the three-dimensional S=1 Heisenberg ferromagnet in the cubic lattice with an easy plane crystal field, considering first-, second- and third-neighbor interactions. We have got one single peak for the spin conductivity for this system at ω=ωk and a variation of the height of the peak with the parameters Dc and η, and hence an influence of the quantum phase transition, between the disordered paramagnetic phase and the ordered ones, on the spin conductivity of this system. We have considered the exchange interaction J1 as ferromagnetic and the interactions J2 and J3 as antiferromagnetic.

Triplet FFLO superconductivity in the doped Kitaev-Heisenberg honeycomb model

We provide analytical and numerical evidence of a spin-triplet FFLO superconductivity in the itinerant Kitaev-Heisenberg model (anti-ferromagnetic Kitaev coupling and ferromagnetic Heisenberg coupling) on the honeycomb lattice around quarter filling. The strong spin-orbit coupling in our model leads to the emergence of 6 inversion symmetry centers for the Fermi surface at non zero momenta in the first Brillouin zone. We show how the Cooper pairs condense into these non-trivial momenta, causing the spatial modulation of the superconducting order parameter. Applying a Ginzburg-Landau expansion analysis, we find that the superconductivity has three separated degenerate ground states with three different spin-triplet pairings. This picture is also supported by exact diagonalizations on finite clusters.

New insight into the thermodynamics of Heisenberg ferromagnets as inferred from high-temperature series

In search of a suitable equation of state for ferromagnets, we revise the information about the Heisenberg model obtainable from high-temperature series. Special attention is paid to the ratio χ3/χ4 (where χ⁢and⁢χ3 are the linear and cubic susceptibilities) related to Landau's quartic coefficient b. It is found in particular that both χ3/χ4 and b tend to a finite limit as T→TC. This limit is small — an order of magnitude smaller than predicted by Weiss's molecular field and similar theories — but contrary to the common belief, nonzero. This implies a rejection of the generally accepted critical-point exponents and a return to those of Landau: α=0, β=12, γ=1, etc.

Integrable hierarchies of Heisenberg ferromagnet equation

In this paper we consider the coupled Kadomtsev-Petviashvili system. From compatibility conditions we obtain the form of matrix operators. After using a gauge transformation, obtained a new type of Lax representation for the hierarchy of Heisenberg ferromagnet equation, which is equivalent to the gauge coupled Kadomtsev-Petviashvili system.

A first theoretical realization of honeycomb topological magnon insulator

It has been recently shown that in the Heisenberg (anti)ferromagnet on the honeycomb lattice, the magnons (spin wave quasipacticles) realize a massless two-dimensional (2D) Dirac-like Hamiltonian. It was shown that the Dirac magnon Hamiltonian preserves time-reversal symmetry defined with the sublattice pseudo spins and the Dirac points are robust against magnon–magnon interactions. The Dirac points also occur at nonzero energy. In this paper, we propose a simple realization of nontrivial topology (magnon edge states) in this system. We show that the Dirac points are gapped when the inversion symmetry of the lattice is broken by introducing a next-nearest neighbour Dzyaloshinskii–Moriya (DM) interaction. Thus, the system realizes magnon edge states similar to the Haldane model for quantum anomalous Hall effect in electronic systems. However, in contrast to electronic spin current where dissipation can be very large due to Ohmic heating, noninteracting topological magnons can propagate for a long time without dissipation as magnons are uncharged particles. We observe the same magnon edge states for the XY model on the honeycomb lattice. Remarkably, in this case the model maps to interacting hardcore bosons on the honeycomb lattice. Quantum magnetic systems with nontrivial magnon edge states are called topological magnon insulators. They have been studied theoretically on the kagome lattice and recently observed experimentally on the kagome magnet Cu(1-3, bdc) with three magnon bulk bands. Our results for the honeycomb lattice suggests an experimental procedure to search for honeycomb topological magnon insulators within a class of 2D quantum magnets and ultracold atoms trapped in honeycomb optical lattices. In 3D lattices, Dirac and Weyl points were recently studied theoretically, however, the criteria that give rise to them were not well-understood. We argue that the low-energy Hamiltonian near the Weyl points should break time-reversal symmetry of the pseudo spins. Thus, recovering the same criteria in electronic systems.

Classification of magnons in rotated ferromagnetic Heisenberg model and their competing responses in transverse fields

Competing orders is a general concept to describe various quantum phases and transitions in various materials. One efficient way to investigate competing orders is to first classify different class of excitations in a given quantum phase, then study their competing responses under various external probes. This strategy may not only lead to deep understanding of the quantum phase itself, but also its deep connections to various other quantum phases nearby. We implement this approach by studying the Rotated Ferromagnetic Heisenberg model (RFHM) in two different transverse fields $h_x$ and $h_z$ which can be intuitively visualized as studying spin-orbit couplings (SOC) effects in 2d Ising or anisotropic XY model in a transverse field. At a special SOC class, it was known that the RFHM at a zero field owns an exact ground state called Y-x state. It supports non only the commensurate C-C$_0$ and C-C$_{\pi} $ magnons, but also the in-commensurate C-IC magnons. These magnons are non-relativistic, not contained in the exact ground state, so need to be thermally excited. Their dramatic response under the longitudinal $ h_y $ field was recently worked out by the authors. Here we find they respond very differently under the two transverse fields. Any $h_x$ ($h_z$) changes the collinear Y-x state to a canted co-planar YX-x (YZ-x) state which suffers quantum fluctuations. The C-C$_0$, C-C$_{\pi} $ and C-IC magnons sneak into the quantum ground state, become relativistic and play leading roles even at $ T=0 $. We map out the boundaries among the C-C$_0$, C-C$_{\pi} $ and C-IC magnons, especially the detailed evolution of the C-IC magnons inside the canted phases. As $h_x$ ($h_z$) increases further, the C-C$_0$ magnons always win the competition and emerge as the seeds to drive a transition from the YX-x (YZ-x) to the X-FM ( Z-FM ) which is shown to be in the 3d Ising universality class.

On a integrable deformations of Heisenberg supermagnetic model

The Heisenberg supermagnet model which is the supersymmetric generalization of the Heisenberg ferromagnet model is an important integrable system. We consider the deformations of Heisenberg supermagnet model under the two constraint 1. S2 = S for S ∈ USPL(2/1)/S(L(1/1) × U(1)) and 2. S2 = 3S − 2I S ∈ USPL(2/1)/S(U(2) × U(1)). By means of the gauge transformation, we construct the gauge equivalent counterparts, i.e., the super generalized Hirota equation and Gramman odd nonlinear Schrödinger equation.

The free energy in a class of quantum spin systems and interchange processes

We study a class of quantum spin systems in the mean-field setting of the complete graph. For spin S=12, the model is the Heisenberg ferromagnet, and for general spin S∈12N, it has a probabilistic representation as a cycle-weighted interchange process. We determine the free energy and the critical temperature (recovering results by Tóth and by Penrose when S=12). The critical temperature is shown to coincide (as a function of S) with that of the q = 2S + 1 state classical Potts model, and the phase transition is discontinuous when S ≥ 1.

Quantum breathers in XXZ ferromagnetic chains with on-site easy-plane anisotropy

The existence and properties of quantum breathers in a one-dimensional XXZ ferromagnetic Heisenberg spin chain with single-ion easy-plane anisotropy are investigated analytically in the Hartree approximation. We show that the system can support the appearance of quantum breathers, and discuss their existence conditions and properties. In addition, our results show that, for quantum breathers in this system, both the corresponding energy and magnetic moment are quantized.

Verification of a New Quantum Simulation Approach through Its Application to Heisenberg-Like Models

A quantum simulation approach facilitated by the self-consistent algorithm was applied in the present work to ferromagnetic and antiferromagnetic three-dimensional Heisenberg lattices consisting of S = 1 spins. Consequently, the calculated spontaneous magnetizations for the two sorts of lattices are precisely consistent with mean-field theory in the whole temperature range. Especially, the numerical results, such as magnetizations, total energies and total free energies per mole of spins, show no size eects. Thus, the physical properties of a huge bulk magnet can be estimated by performing simulation for a very tiny sample, so that the computational time can be greatly saved.

Spin transport in the frustrated anisotropic two-dimensional ferromagnet in the square lattice

Abstract We use the SU(3) Schwinger boson formalism together with the Kubo theory of the linear response to study the spin transport in the two-dimensional S=1 frustrated anisotropic Heisenberg ferromagnet in a square lattice with easy-plane single-ion anisotropy and considering the second-neighbor interaction in the diagonal and the third-neighbor interaction ( J 1 – J 2 – J 3 model). The AC spin conductivity σ reg ( ω ) is determined for several values of the critical single-ion parameter D, and the frustration parameters J2 and J3. We have calculated the dynamic structure factor too, S ( q → , ω ) , for this model and obtained a behaviour exponentially decreasing for the damping Γq with the decreasing of q = | q → | towards q → 0 .

Coherent magnon dynamics in ferromagnetic models with nonuniform magnetic field and correlated disorder

In this work we investigated the nature of the one-magnon eigenstates in a disordered chain at the presence of a non-uniform magnetic field. In our study, we analyzed the one-dimensional ferromagnetic Heisenberg model within the one-magnon framework. The spin-spin interaction was considered as a correlated disorder distribution with power law spectrum S(k)∝k−α. By using numerical methods we calculated the time evolution of a initially localized Gaussian wave-packet. Our results reveal that for weak correlations (α<1), the magnetic wave-packet remains localized around the initial position and for α>1, we got an oscillatory profile similar to the Bloch-like phenomenology. We calculate the frequency of these oscillations and observed that it is in a good agreement with the semi-classical approach traditionally used to explain the Block-like oscillatory behavior.

Joint Density of States Calculation Employing Wang–Landau Algorithm

Joint density of states (JDoS), which depends both on energy and another variable like order parameter provides more information than the conventional density of states (DoS) which depend only on energy. Calculation of JDoS requires huge computational time. In this paper we employ two level method to calculate JDoS which requires relatively much less computational time. We demonstrate this method on a two dimensional Ising spin system, lattice spin model of double strand DNA (dsDNA) and Heisenberg ferromagnet.

Spin-1 [formula omitted] ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice: A bosonic approach

We examine the phase diagram of the spin-1 J1−J2−J3 ferromagnetic Heisenberg model with an easy-plane crystal field on the cubic lattice, in which J1 is the ferromagnetic exchange interaction between nearest neighbors, J2 is the antiferromagnetic exchange interaction between next-nearest neighbors and J3 is the antiferromagnetic exchange interaction between next-next-nearest neighbors. Using the bond-operator formalism, we investigate the phase transitions between the disordered paramagnetic phase and the ordered ones. We show that the nature of the quantum phase transitions changes as the frustration parameters (J2J1, J3J1) are varied. The zero-temperature phase diagram exhibits second- and first-order transitions, depending on the energy gap behavior. Remarkably, we find a disordered nonmagnetic phase, even in the absence of a crystal field, which is suggested to be a quantum spin liquid candidate. We also depict the phase diagram at finite temperature for some values of crystal field and frustration parameters.

Six dimensional QCD at two loops

We construct the six dimensional Quantum Chromodynamics (QCD) Lagrangian in a linear covariant gauge and subsequently renormalize it at two loops in the MSbar scheme. The coupling constant corresponding to the gauge interaction is asymptotically free for all numbers of quark fields, Nf. Analysing the beta-functions yields a rich spectrum of fixed points. For instance, the conformal window in the six dimensional theory is at Nf = 16 for the SU(3) colour group. The critical theory structure is similar to that of an O(N) scalar theory in eight dimensions. Using the large N expansion the latter is shown to be in the same universality class as the Heisenberg ferromagnet. Similarly using the large Nf expansion, six dimensional QCD is shown to be in the same class as the two dimensional non-abelian Thirring model and four dimensional QCD. Abelian gauge theories are also renormalized at high loops in six and eight dimensions. It is shown that the gauge parameter only appears in the electron anomalous dimension at one loop, similar to four dimensions.

Importing spontaneous polarization into a Heisenberg ferromagnet for a potential single-phase multiferroic

A novel two-dimensional Heisenberg ferromagnet, [C6H5(CH2)4NH3]2[CuCl4], exhibits ferroelastic, ferroelectric and ferromagnetic transitions at 337, 143 and 7.8 K, respectively.

Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling.

We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.

Erratum: “The connection between vortex-like topological excitations and conventional excitations in quantum ferromagnetic spin systems on two-dimensional lattice and their stability”

In this paper, we present a scheme for the construction of quantum states of vortex-like topological excitations corresponding to spin-1/2 strongly XY-anisotropic nearest neighbor Heisenberg ferromagnet on two-dimensional lattice. The procedure involving Pauli spin basis states is carried out corresponding to both infinite dilute limit and finite density limit of vortex/anti-vortex. It is found that the corresponding quantum mechanical states representing charge 1 quantum vortices/anti-vortices can be expressed as linear combinations of single magnon states, composite multi-magnon states and the ground state. Detailed calculations show that these states are quantum mechanically stable states of the Hamiltonian only when the system size exceeds certain threshold value. Our analysis indicates that the interactions between different magnon modes can very well generate these topological excitations. Possible applications of our calculations to real magnetic systems are also discussed. Magnetic measurements probing spin dynamics may be undertaken to verify the existence of the threshold size for the stability of vortices.

The connection between vortex-like topological excitations and conventional excitations in quantum ferromagnetic spin systems on two-dimensional lattice and their stability

In this paper, we present a scheme for the construction of quantum states of vortex-like topological excitations corresponding to spin-1/2 strongly XY-anisotropic nearest neighbor Heisenberg ferromagnet on two-dimensional lattice. The procedure involving Pauli spin basis states is carried out corresponding to both infinite dilute limit and finite density limit of vortex/anti-vortex. It is found that the corresponding quantum mechanical states representing charge 1 quantum vortices/anti-vortices can be expressed as linear combinations of single magnon states, composite multi-magnon states and the ground state. Detailed calculations show that these states are quantum mechanically stable states of the Hamiltonian only when the system size exceeds certain threshold value. Our analysis indicates that the interactions between different magnon modes can very well generate these topological excitations. Possible applications of our calculations to real magnetic systems are also discussed. Magnetic measurements probing spin dynamics may be undertaken to verify the existence of the threshold size for the stability of vortices.