Easy-plane Ferromagnet Research Articles

Interacting domain walls in an easy-plane ferromagnet

The Landau-Lifshitz equation for an anisotropic (easy-plane) ferromagnet is formulated as a Riemann-Hilbert problem on a Riemann surface of the spectral parameter. Exact multiple domain wall solutions can be obtained in a systematic and exhaustive manner by considering all possible pole arrangements on the Riemann surface. Explicit calculations for up to four poles have been carried out, yielding all possible double wall solutions, including states of colliding walls, breather modes of bound walls, and a set of solutions corresponding to marginally bound walls.

Magnon modes for a circular two-dimensional easy-plane ferromagnet in the cone state

We calculate the magnon modes in the presence of a vortex in a circular easy-plane ferromagnet with a magnetic field perpendicular to the plane of the magnet. We also determine the range of anisotropy and magnetic field for which the two vortex branches, known as light and heavy cone-state vortices, are stable. The analysis was done by combining analytical calculations in the continuum limit with numerical simulations of small discrete systems. For large enough systems the magnon modes are expressed by the S matrix for magnon-vortex scattering. For small systems the vortex structure and consequently the magnon scattering are affected by the finite size, for which a theory designed for isotropic magnets is extended here. The presence of magnetic field in combination with easy-plane anisotropy leads to a splitting of doublets both near a small magnetic field and when the magnetic field is comparable to the anisotropy field. Similar doublets with splitting determined by the magnetic field may be expected in the mode spectra of small magnetic particles.

Bloch walls in strongly driven easy-plane ferromagnets

We show that the action of strong rapidly oscillating transverse magnetic field in easy-plane ferromagnet gives rise to the appearance of effective biaxial magnetic anisotropy and new soliton solutions in the form of Bloch and Neel domain walls. Exact analytical expressions describing the conversion of a Neel wall into the stationary Bloch wall under dissipation are derived on the ground of the adiabatic approximation which are in good agreement with the numerical simulations of the basic strongly perturbed Landau-Lifshitz equation.

Vortices and magnetic structures of the target type in a two-dimensional ferromagnet with anisotropic exchange

Various types of magnetic structure in a two-dimensional Heisenberg ferromagnet are considered in a continuum approximation. The effect of anisotropic exchange and single-ion anisotropy on the vortex structure is analyzed. A new type of static magnetic structure (“target”) is predicted and investigated in an easy-plane ferromagnet.

Vortex Patterns in Layered Magnets with Nonmagnetic and Magnetic Impurities

Effects of a single-atom impurity on a small vortex-like soliton are studied in the two-dimensional (2D) Heisenberg model of layered magnets. In the 41 x 41 spin lattice with exchange parameters corresponding to the 2D easy-plane copper ferromagnet and the easy-axis manganese antiferromagnet a vortex-like structure and its energy are calculated in the presence of a single nonmagnetic or magnetic impurity. It is found that the in-plane and out-of-plane vortices are attracted to and centered on the impurity in the easy-plane magnet up to the almost isotropic limit. Layered Cu-halide compounds are found to be good candidates for experimental observation of stable, fixed vortex-antivortex patterns.

Scattering of vortex pairs in 2D easy-plane ferromagnets

Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of solitons in two dimensions. We investigate numerically and analytically the dynamics of such vortex pairs. In particular we simulate numerically the head-on collision of two pairs with different velocities for a wide range of the total linear momentum of the system. If the momentum difference of the two pairs is small, the vortices exchange partners, scatter at an angle depending on this difference, and form two new identical pairs. If it is large, the pairs pass through each other without losing their identity. We also study head-tail collisions. Two identical pairs moving in the same direction are bound into a moving quadrupole in which the two vortices as well as the two antivortices rotate around each other. We study the scattering processes also analytically in the frame of a collective variable theory, where the equations of motion for a system of four vortices constitute an integrable system. The features of the different collision scenarios are fully reproduced by the theory. We finally compare some aspects of the present soliton scattering with the corresponding situation in one dimension.

Two-dimensional Ising physics in quantum Hall ferromagnets

The close analogy between two-dimensional electron system states and conventional itinerant ferromagnets is used to analyze ordered many-body states in the integer quantum Hall regime. The possibility of in situ tuning between easy-plane and easy-axis quantum Hall ferromagnets is discussed for biased bilayer systems with total filling factor ν=3. Recent experiments on Ising quantum Hall systems are explained in terms of their unique domain wall physics. Issues including Ising critical temperatures, hysteresis loops and transport anisotropies are addressed using a combination of the self-consistent field technique, Hartree–Fock/RPA approximation, and exact diagonalization of the many-body Hamiltonian.

Activation studies of pseudospin quantum Hall ferromagnets in double quantum wells

We study pseudospin quantum Hall ferromagnets realized in a strongly coupled double-quantum-well structure. The pseudospin dependence of the Coulomb interactions leads to magnetic anisotropy. Activation energies measured as a function of the single-particle gap, i.e. the pseudospin Zeeman energy, reveal a striking difference between the easy-axis and easy-plane ferromagnets. In the limit of zero single-particle gap, we observe a novel low-energy excitation, reminiscent of Skyrmions, for the ν=4 easy-axis ferromagnet. We discuss the reduced gap in terms of topological charge excitations in the domain walls.

Charge excitations in easy-axis and easy-plane quantum Hall ferromagnets.

We study charge excitations in quantum Hall ferromagnets realized in a symmetric quantum well. Landau levels (LLs) with different subband and orbital indices crossing at the Fermi level act as up and down pseudospin levels. The activation energy measured as a function of the pseudospin Zeeman energy, Delta(Z), reveals easy-plane and easy-axis ferromagnetism for LL filling of nu = 3 and 4, respectively, for which the crossing levels have parallel and antiparallel spin. For nu = 4, we observe a sharp reduction in the gap for Delta(Z)-->0, which we discuss in terms of a topological excitation in domain walls akin to Skyrmions.

Internal modes and magnon scattering on topological solitons in two-dimensional easy-axis ferromagnets

We study the magnon modes in the presence of a topological soliton in a 2d Heisenberg easy-axis ferromagnet. The problem of magnon scattering on the soliton with arbitrary relation between the soliton radius R and the "magnetic length" Delta_0 is investigated for partial modes with different values of the azimuthal quantum numbers m. Truly local modes are shown to be present for all values of m, when the soliton radius is enough large. The eigenfrequencies of such internal modes are calculated analytically on limiting case of a large soliton radius and numerically for arbitrary soliton radius. It is demonstrated that the model of an isotropic magnet, which admits an exact analytical investigation, is not adequate even for the limit of small radius solitons, R<<Delta_0: there exists a local mode with nonzero frequency. We use the data about local modes to derive the effective equation of soliton motion; this equation has the usual Newtonian form in contrast to the case of the easy-plane ferromagnet. The effective mass of the soliton is found.

Discrete breathers in classical spin lattices

Discrete breathers (nonlinear localised modes) have been shown to exist in various nonlinear Hamiltonian lattice systems. In the present paper we study the dynamics of classical spins interacting via Heisenberg exchange on spatial $d$-dimensional lattices (with and without the presence of single-ion anisotropy). We show that discrete breathers exist for cases when the continuum theory does not allow for their presence (easy-axis ferromagnets with anisotropic exchange and easy-plane ferromagnets). We prove the existence of localised excitations using the implicit function theorem and obtain necessary conditions for their existence. The most interesting case is the easy-plane one which yields excitations with locally tilted magnetisation. There is no continuum analogue for such a solution and there exists an energy threshold for it, which we have estimated analytically. We support our analytical results with numerical high-precision computations, including also a stability analysis for the excitations.

Effect of a negative biquadratic interaction on the phase states and spectra of coupled magnetoelastic waves of an easy-plane ferromagnet

The spectra of the coupled magnetoelastic waves of an easy-plane ferromagnet with a negative biquadratic interaction are investigated. It is shown that in this case the existence region of the quadrupolar phase is narrowed substantially in comparison with the case of a positive biquadratic interaction. The phase diagram of the system is constructed.

Superfluid properties of double-layer quantum Hall ferromagnets

Because of the degeneracy of 2D electron system Landau levels, quantum Hall systems exhibit a wide variety of non-trivial electron–electron interaction effects. Double-layer systems with small layer separations have broken symmetry ground states that can be regarded either as easy-plane ferromagnets or as excitonic superfluids. In this contribution we discuss the superfluid properties of quantum Hall ferromagnets.

Pseudospin anisotropy classification of quantum Hall ferromagnets

Broken symmetry ground states with uniform electron density are common in quantum Hall systems when two Landau levels simultaneously approach the chemical potential at integer filling factor $\nu$. The close analogy between these two-dimensional electron system states and conventional itinerant electron ferromagnets can be emphasized by using a pseudospin label to distinguish the two Landau levels. As in conventional ferromagnets, the evolution of the system's state as external field parameters are varied is expected to be sensitive to the dependence of ground state energy on pseudospin orientation. We discuss the predictions of Hartree-Fock theory for the dependence of the sign and magnitude of the pseudospin anisotropy energy on the nature of the crossing Landau levels. We build up a classification scheme for quantum Hall ferromagnets that applies for single layer and bilayer systems with two aligned Landau levels distinguished by any combination of real-spin, orbit-radius, or growth direction degree-of-freedom quantum numbers. The possibility of in-situ tuning between easy-axis and easy-plane quantum Hall ferromagnets is discussed for biased bilayer systems with total filling factors $\nu=3$ or $\nu=4$. Detailed predictions are made for the bias dependence of pseudospin reversal properties in $\nu=3$ bilayer systems.

Gakel’–Turov oscillations in iron borate

Dependence of the amplitude of transverse sound passed through a basal plate of easy-plane weak ferromagnet FeBO 3 on a magnetic field H, parallel to the plate is investigated in experiment at T=77 K. This dependence is of the oscillating form. The phenomenon is caused by magnetic birefringence of transverse sound, being the analog of Cotton–Mouton optical effect. In acoustics this effect is associated with magnetic additions appearing in elastic modules upon transition from a paramagnetic phase to an antiferromagnetic one. However, the theory of magnetoacoustic birefringence for homogeneously magnetized crystals, valid for MnCO 3, is unable to explain the experiment for FeBO 3. A model, taking into account the experimental boundary conditions and inhomogeneous distribution of magnetization in the sample of iron borate is constructed. Calculations based on this model describe the experiment satisfactorily.

Magnetoelastic coupling and long-range magnetic ordering in two-dimensional ferromagnets

In the present work the spectra of elementary excitations of a 2D easy-plane ferromagnet with the account of magnetoelastic coupling are investigated. It has been shown that the presence of magnetoelastic coupling results in the stabilization of long-range magnetic order. The Curie temperature has been evaluated.

Scattering of a radially symmetric spin wave on a magnetic vortex in a two-dimensional easy-plane ferromagnet

The scattering amplitude for a radially symmetric spin wave (azimuthal number m=0) on a vortex in an easy-plane ferromagnet is found by analytical and numerical calculations in the long-wavelength approximation (wave number much larger than the inverse size of the vortex core). It is found that the scattering amplitude of a radially symmetric spin wave is smaller than that for a translational mode (m=±1) with the same value of the wave number.

Switching between different vortex states in two-dimensional easy-plane magnets due to an ac magnetic field

Using a discrete model of two-dimensional easy-plane classical ferromagnets, we propose that a rotating magnetic field in the easy plane can switch a vortex from one polarization to the opposite one if the amplitude exceeds a threshold value, but the backward process does not occur. Such switches are indeed observed in computer simulations.

Antiferromagnetic resonance in CuB2O4 single crystal

The frequency-field, temperature, and angular dependences of the antiferromagnetic resonance parameters for the tetragonal CuB2O4 single crystal are studied in the frequency range 2.6–80 GHz and at temperatures of 4.2–30 K. The results obtained confirm the fact that, in the high-temperature state in the range 10–21 K, this compound is an easy-plane weak ferromagnet. The temperature dependence of the Dzyaloshinski field is determined. An abrupt change observed in the frequency-field dependence of the magnetic resonance at T=4.2 K and H ⊥ C 4 indicates the transition to the weak ferromagnetic state induced by the external field H ⊥. The phase diagram for CuB2O4 is constructed on the H ⊥-T coordinates. It is demonstrated that, in the low-temperature state, the magnetic moments of copper ions remain in the basal plane, but the weak ferromagnetism is absent.

Spin mapping, phase diagram, and collective modes in double-layer quantum Hall systems atν=2

An exact spin mapping is identified to simplify the recently proposed hard-core boson description (Demler and Das Sarma, Phys. Rev. Lett., to be published) of the bilayer quantum Hall system at filling factor 2. The effective spin model describes an easy-plane ferromagnet subject to an external Zeeman field. The phase diagram of this effective model is determined exactly and found to agree with the approximate calculation of Demler and Das Sarma, while the Goldstone-mode spectrum, order parameter stiffness and Kosterlitz-Thouless temperature in the canted antiferromagnetic phase are computed approximately.