Nonlinear Spin Research Articles

New solitons and periodic wave solutions for the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

We consider a nonlinear Schrödinger type equation in (2+1) dimensions. The proposed equation describes the nonlinear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semiclassical limit. We first construct three families of exact periodic solutions expressed in terms of Jacobi’s elliptic functions cn, sn and dn. We second consider the limit where the elliptic modulus approaches 1 to obtain bright and dark soliton solutions. Furthermore, we find a new type of soliton-like solution, illustrating the potentially rich set of wave solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation. Parametric conditions for the existence and uniqueness of exact solutions are presented. The derived structures of the obtained solutions offer a rich platform to study the nonlinear spin dynamics in magnetic materials.

Soliton stability in a square lattice model of an inhomogeneous helimagnet

In this paper, we propose a square lattice model to study the nonlinear spin excitations of an inhomogeneous helimagnet with bilinear, twist and anisotropic interactions in the semi classical limit. The dynamics is found to be governed by a nonlinear partial differential equation (pde) in (2 + 1) dimensions. The nonlinear excitations and the influence of different types of interactions are investigated using a perturbation technique. The effect of inhomogeneities in the system is demonstrated graphically in terms of soliton stability.

Zero-bias-field microwave dynamic magnetic properties in trapezoidal ferromagnetic stripe

Dynamic magnetization response of the axially magnetized ferromagnetic stripe with trapezoidal cross section has been studied. The stripe with beveled edges exhibits multiple resonant peaks modes under an in-plane microwave excitation compared with the single resonant of vertical edge surfaces. The complexity of the observed response is attributed to the spatially nonuniform equilibrium spin distribution at the stripe edges. Micromagnetic simulations identify spin waves as spatially localized mode at the modified edges. This one is also described by effective pinning boundary conditions taking into account finite-size effects, which is related to the exchange interaction, surface anisotropy and dipole–dipole interaction. These results provide detailed insights into the nonlinear spin dynamics of microstructures influenced by the edge properties.

Dark solitonic interaction and conservation laws for a higher-order [formula omitted]-dimensional nonlinear Schrödinger-type equation in a Heisenberg ferromagnetic spin chain with bilinear and biquadratic interaction

In this paper, a higher-order (2+1)-dimensional nonlinear Schrödinger-type equation is investigated, which describes the nonlinear spin dynamics of the (2+1)-dimensional Heisenberg ferromagnetic spin chain with bilinear and biquadratic interaction. Lax pair and infinite-number conservation laws are constructed, which could prove the existence of the multi-soliton solutions. Via the auxiliary function, bilinear forms and dark-soliton solutions are derived. Properties and interaction patterns for the dark solitons are investigated: (i) Effects on the dark solitons arising from the bilinear interaction, biquadratic interaction and lattice parameter are discussed. (ii) Through the asymptotic analysis, elastic and inelastic interaction between the two solitons is discussed analytically and graphically, respectively. Due to the elastic interaction, amplitudes and velocities of the two dark solitons remain unchanged with the distortion of the interaction area, except for certain phase shifts. However, in virtue of the inelastic interaction, amplitudes of the dark solitons reduce to zero, without the distortion. (iii) Elastic interaction among the three dark solitons is investigated, which implies that the properties of the elastic interaction among the three are similar to that between the two, except for the more complicated distortion. Inelastic–elastic interaction is also investigated, which implies that the interaction between the inelastic region and the dark soliton is elastic. (iv) Linear stability analysis is proposed, which is used to analyze the properties of modulation instability and proves that the dark solitons are modulationally stable.

Spin-current emission governed by nonlinear spin dynamics.

Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.

Soliton excitations and stability in a square lattice model of ferromagnetic spin system

We investigate the nature of nonlinear spin excitations in a square lattice model of ferromagnetic (FM) spin system with bilinear and biquadratic interactions. Using the coherent state ansatz combined with the Holstein–Primakoff (HP) bosonic representation of spin operators, the dynamics is found to be governed by a discrete nonlinear equation which possesses soliton solution. The modulational instability aspects of the soliton excitations are analysed for small perturbations in wave vectors.

Proposition of a Silica Nanoparticle-Enhanced Hybrid Spin-Microcantilever Sensor Using Nonlinear Optics for Detection of DNA in Liquid.

We theoretically propose a method based on the combination of a nonlinear optical mass sensor using a hybrid spin-microcantilever and the nanoparticle-enhanced technique, to detect and monitor DNA mutations. The technique theoretically allows the mass of external particles (ssDNA) landing on the surface of a hybrid spin-microcantilever to be detected directly and accurately at 300 K with a mass responsivity 0.137 Hz/ag in situ in liquid. Moreover, combined with the nanoparticle-enhanced technique, even only one base pair mutation in the target DNA sequence can be identified in real time accurately, and the DNA hybridization reactions can be monitored quantitatively. Furthermore, in situ detection in liquid and measurement of the proposed nonlinear optical spin resonance spectra will minimize the experimental errors.

Spin-polarized electron transport through magnetic poly-BIPO molecule: the role of soliton–antisoliton separation

Spin-polarized transport through a one-dimensional metal/poly-BIPO/metal model junction with the soliton–antisoliton separation is investigated. Nonlinear spin and charge densities are considered in magnetic poly-BIPO molecule, as a neutral soliton and charged antisoliton with different separations. The calculations are performed based on Su–Schrieffer–Heeger Hamiltonian which is extended with Heisenberg and Hubbard Hamiltonians to include the spin and electron–electron interactions. The spin-dependent transport properties are obtained within the framework of the Landauer–Buttiker formalism based on Green’s function theory. This study demonstrates the reduction in current and spin polarization as the separation between soliton and antisoliton centers is increased. We have found that when the soliton–antisoliton separation is less than 14 sites, the spin polarization is almost 100 % plato, over the voltage ranges more than 0.3 V. Also the energy differences between the soliton–antisoliton mid-gap states for up- and down-spin electrons and the Fermi energy of the system are reduced. However, for the soliton–antisoliton separation lengths more than 14 sites, these quantities tend to constant values with enhancement of the distance between the excitation centers.

Alkali-Metal Spin Maser

Quantum measurement is a combination of a read-out and a perturbation of the quantum system. We explore the nonlinear spin dynamics generated by a linearly polarized probe beam in a continuous measurement of the collective spin state in a thermal alkali-metal atomic sample. We demonstrate that the probe-beam-driven perturbation leads, in the presence of indirect pumping, to complete polarization of the sample and macroscopic coherent spin oscillations. As a consequence of the former we report observation of spectral profiles free from collisional broadening. Nonlinear dynamics is studied through exploring its effect on radio frequency as well as spin noise spectra.

Strong Second-Harmonic Generation in Atomic Layered GaSe.

Nonlinear effects in two-dimensional (2D) atomic layered materials have recently attracted increasing interest. Phenomena such as nonlinear optical edge response, chiral electroluminescence, and valley and spin currents beyond linear orders have opened up a great opportunity to expand the functionalities and potential applications of 2D materials. Here we report the first observation of strong optical second-harmonic generation (SHG) in monolayer GaSe under nonresonant excitation and emission condition. Our experiments show that the nonresonant SHG intensity of GaSe is the strongest among all the 2D atomic crystals measured up to day. At the excitation wavelength of 1600 nm, the SHG signal from monolayer GaSe is around 1-2 orders of magnitude larger than that from monolayer MoS2 under the same excitation power. Such a strong nonlinear signal facilitates the use of polarization-dependent SHG intensity and SHG mapping to investigate the symmetry properties of this material: the monolayer GaSe shows 3-fold lattice symmetry with an intrinsic correspondence to its geometric triangular shape in our growth condition; whereas the bilayer GaSe exhibits two dominant stacking orders: AA and AB stacking. The correlation between the stacking orders and the interlayer twist angles in GaSe bilayer indicates that different triangular GaSe atomic layers have the same dominant edge configuration. Our results provide a route toward exploring the structural information and the possibility to observe other nonlinear effects in GaSe atomic layers.

Nonlinear vibration analysis of a spinning shaft with multi-disks

In this study the stability of a rotor system, which is comprised of a simply supported nonlinear spinning shaft with multi-rigid disk, near to the major critical speeds is investigated. The nonlinearity is due to the stretching and large amplitude. The influence of rotary inertia and gyroscopic effects are included, however, shear deformation is ignored. To analyze the nonlinear equations of motion, the method of multiple scales is applied to the ordinary differential equations of motion. The influences of different parameter such as number of disks, disk mass moment of inertia, rotational speed, external damping, and position of disks on the forward and backward linear frequencies, steady state response, stability and bifurcations of the rotor system are investigated. It is seen that in the higher rotational speeds, the backward frequency is increasing with an increase of number of disks, and in the lower rotational speeds, the backward frequency is decreasing with an increase of number of disks. By increasing number of disks, bifurcations occur in the lower speeds therefore, the instability occurrence for large number of disk is at speeds lower than that regarding to the low number of disks. By an increase of disk mass moment of inertia, the amplitude and the hardening effect decrease.

Highly relativistic spin-gravity coupling for fermions

Descriptions of highly relativistic fermions in a gravitational field in the classical (nonquantum) and quantum approaches are discussed. The results following from the Mathisson-Papapetrou equations for a fast spinning particle in Schwarzschild's and Kerr's background are considered. Numerical estimates for electron, proton and neutrino in the gravitational field of black holes are presented.The general relativistic Dirac equation is analyzed from the point of view it is using for the adequate description of highly relativistic fermions in a gravitational field, in the linear and nonlinear spin approximation. It is necessary to have some corrected Dirac equation for a highly relativistic fermion with strong spin-gravity coupling.

Study of the nonlinear Rashba spin splitting in AlGaN/GaN heterostructures by the perturbative expansion method

By considering the energy dispersion of the conduction subband and using the perturbative expansion method, the dependence of all order contributions to the Rashba coefficient (α) and nonlinear Rashba spin splitting (ΔE) in AlGaN/GaN quantum wells (QWs) on the in-plane wave vector (k//) are studied. The zeroth-order contribution to α only comes from the heterointerface, and does not depend on k//. The first-order correction α(1) contributing from the well (ΓW(1)) and the barrier (ΓB(1)) are not related to k//, but the contribution from the heterointerface (ΓInter(1)) and the higher corrections to α all depend on k//. So the zeroth-order contribution to ΔE and the first-order correction ΔE(1) contributing from the well and barrier increase linearly with k//, while the contribution to ΔE(1) from the heterointerface and the higher corrections to ΔE all increase nonlinearly with k//. Therefore, the linear Rashba model could be assumed as an approximation of the nonlinear Rashba model, and the difference between the two models is relatively minute at small wave vectors, especially for wide-gap semiconductors.

Collision and propagation of electromagnetic solitons in an antiferromagnetic spin ladder medium

Soliton collisions constitute one of the central topics of nonlinear-wave dynamics. We demonstrate an inelastic collision between the electromagnetic solitons in a two coupled Heisenberg spin ladder. The interplay of bilinear ferromagnetic coupling with antiferromagnetic rung and diagonal coupling along with the magnetic field component of the electromagnetic wave (EMW) has been studied by solving the Maxwell’s equation together with the two coupled Landau–Lifshitz nonlinear spin equations for the magnetization of the medium. The magnetization dynamics of the spin ladder under the influence of EMW is governed by a two coupled generalized derivative nonlinear Schro¨dinger (CGDNLS) equations. We employ the Ba¨cklund transformation to solve CGDNLS equations and construct the one and two-soliton solutions. We explicitly construct two soliton solutions to the CGDNLS equations in the framework of Hirota’s bilinearization method. We bring out clearly the various features underlying the fascinating shape changing collisions of electromagnetic solitons both in the absence and presence of antiferromagnetic diagonal coupling.

Non-Gilbert-damping Mechanism in a Ferromagnetic Heusler Compound Probed by Nonlinear Spin Dynamics.

The nonlinear decay of propagating spin waves in the low-Gilbert-damping Heusler film Co_{2}Mn_{0.6}Fe_{0.4}Si is reported. Here, two initial magnons with frequency f_{0} scatter into two secondary magnons with frequencies f_{1} and f_{2}. The most remarkable observation is that f_{1} stays fixed if f_{0} is changed. This indicates, that the f_{1} magnon mode has the lowest instability threshold, which, however, cannot be understood if only Gilbert damping is present. We show that the observed behavior is caused by interaction of the magnon modes f_{1} and f_{2} with the thermal magnon bath. This evidences a significant contribution of the intrinsic magnon-magnon scattering mechanisms to the magnetic damping in high-quality Heusler compounds.

Exact localized and oscillatory solutions of the nonlinear spin and pseudospin symmetric Dirac equations

We derive exact analytic solutions of nonlinear Dirac equations with Kerr-like cubic nonlinearity. The equations model, among many physical systems, a Bose-Einstein condensate confined by a two-dimensional honeycomb optical lattice as well as relativistic solitons in optical waveguide arrays. The nonrelativistic limit of the solutions is derived, and the role of the nonlinearity on localization is discussed. The possibility of realizing some of these solutions in waveguide arrays and Bose-Einstein condensates is pointed out.

Self-oscillations of spins in a nanodimensional spin waveguide with localized sources of spin-polarized current

Spin oscillations and their phase synchronization are discovered in a spin 1D waveguide (nanowire) after the local injection of a spin-polarized current in the vertical (perpendicular) geometry of magnetization. The mode composition of nonlinear spin self-oscillations is analyzed for a single nano-oscillator using the effect of spin transfer torque with regard to spin wave runaway over the 1D waveguide and synchronized spin self-oscillations at current pumping by two nano-oscillators. It is shown specifically that, along with simple (“nontopological”) oscillation modes, in which singular points in the oscillation amplitude spatial distribution are absent, the 1D waveguide may support modes with pole-type singular points inside the current pumping domain, which are characteristic of the geometry of a precessing 2π-domain boundary. A diagram for frequency- and current-detuning-synchronized spin self-oscillations that are excited by two spin nano-oscillators in the 1D spin waveguide is constructed.

Nonlinear valley and spin currents from Fermi pocket anisotropy in 2D crystals.

The controlled flow of spin and valley pseudospin is key to future electronics exploiting these internal degrees of freedom of carriers. Here, we discover a universal possibility for generating spin and valley currents by electric bias or temperature gradient only, which arises from the anisotropy of Fermi pockets in crystalline solids. We find spin and valley currents to the second order in the electric field as well as their thermoelectric counterparts, i.e., the nonlinear spin and valley Seebeck effects. These second-order nonlinear responses allow two unprecedented possibilities to generate pure spin and valley flows without net charge current: (i) by an ac bias or (ii) by an arbitrary inhomogeneous temperature distribution. As examples, we predict appreciable nonlinear spin and valley currents in two-dimensional (2D) crystals including graphene, monolayer and trilayer transition-metal dichalcogenides, and monolayer gallium selenide. Our finding points to a new route towards electrical and thermal generations of spin and valley currents for spintronic and valleytronic applications based on 2D quantum materials.

Magnetization boundary conditions at a ferromagnetic interface of finite thickness

We develop a systematic approach to derive boundary conditions at an interface between two ferromagnetic materials in the continuous medium approximation. The approach treats the interface as a two-sublattice material, although the final equations connect magnetizations outside of the interface and therefore do not explicitly depend on its structure. Instead, the boundary conditions are defined in terms of some average properties of the interface, which may also have a finite thickness. In addition to the interface anisotropy and symmetric exchange coupling, this approach allows us to take into account coupling resulting from inversion symmetry breaking in the vicinity of the interface, such as the Dzyaloshinskii-Moriya antisymmetric exchange interaction. In the case of negligible interface anisotropy and Dzyaloshinskii-Moriya exchange parameters, the derived boundary conditions represent a generalization of those proposed earlier by Barnaś and Mills and are therefore named ‘generalized Barnaś–Mills boundary conditions’. We demonstrate how one could use the boundary conditions to extract parameters of the interface via fitting of appropriate experimental data. The developed theory could be applied to modeling of both linear and non-linear spin waves, including exchange, dipole-exchange, magnetostatic, and retarded modes, as well as to calculations of non-uniform equilibrium micromagnetic configurations near the interface, with a direct impact on the research in magnonics and micromagnetism.

NONLINEAR SPIN WAVES IN GRAPHENE STRUCTURES

Basing on Dirac equation for interacting massless fermions, we propose a nonlinear model that describes a possible mechanism of ferromagnetism in graphene structures, resulting from electron–electron interaction and spontaneous breaking of spin symmetry of valence electrons. Qualitative predictions of the model are important for practical applications in spintronics. Localized kink–antikink patterns of valence electron spin density on the graphene surface are calculated, their interaction is described, and, finally, the formation of their quasi-bound metastable states (breathers) is investigated. The spectrum of breathers is calculated in both the analytical and the numerical form. Possible inverted population of the appropriate states may be used to generate quantum coherent nonlinear spin waves that can find practical applications in nanoelectronics and spintronics.