Nonlinear Spin Research Articles

Periodic solutions and Whitham modulation equations for the Lakshmanan–Porsezian–Daniel equation

In this paper, we adopt the improved finite-band integration method to find the periodic solutions of the Lakshmanan-Porsezian-Daniel (LPD) equation, which can be used to describe the nonlinear spin excitation with octupole-dipole interaction in the one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain. Based on this method, we obtain the one-phase periodic solutions of the LPD equation represented by the Weierstrass elliptic functions and Jacobi elliptic functions. Furthermore, we derive the Whitham velocities and Whitham modulation equations of the LPD equation based on the Riemann invariants.

Imaging and phase-locking of non-linear spin waves

Non-linear processes are a key feature in the emerging field of spin-wave based information processing and allow to convert uniform spin-wave excitations into propagating modes at different frequencies. Recently, the existence of non-linear magnons at half-integer multiples of the driving frequency has been predicted for Ni80Fe20 at low bias fields. However, it is an open question under which conditions such non-linear spin waves emerge coherently and how they may be used in device structures. Usually non-linear processes are explored in the small modulation regime and result in the well known three and four magnon scattering processes. Here we demonstrate and image a class of spin waves oscillating at half-integer harmonics that have only recently been proposed for the strong modulation regime. The direct imaging of these parametrically generated magnons in Ni80Fe20 elements allows to visualize their wave vectors. In addition, we demonstrate the presence of two degenerate phase states that may be selected by external phase-locking. These results open new possibilities for applications such as spin-wave sources, amplifiers and phase-encoded information processing with magnons.

Intrinsic Nonlinear Electric Spin Generation in Centrosymmetric Magnets.

We propose an intrinsic nonlinear electric spin generation effect, which can dominate in centrosymmetric magnets. We reveal the band geometric origin of this effect and clarify its symmetry characters. Asan intrinsic effect, it is determined solely by the material's band structure and represents a material characteristic. Combining our theory with first-principle calculations, we predict sizable nonlinear spin generation in single-layer MnBi_{2}Te_{4}, which can be detected in experiment. Our theory opens a new route for all-electric controlled spintronics in centrosymmetric magnets which reside outside of the current paradigm based on linear spin response.

Multiqudit interactions in molecular spins

We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of non-linear spin terms) and their multi-level structure. Finally, we calculate the long time dynamics for a pair of interacting molecular spins using the method of multiple scales analysis. This allows to find the set of 2-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information.

Modified generalized Darboux transformation and solitons for a Lakshmanan-Porsezian-Daniel equation

In this paper, a Lakshmanan-Porsezian-Daniel equation, which describes the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain with the octupole-dipole interaction, is investigated. With respect to the coherent amplitude of the spin deviation operator for the ferromagnetic spin chain in the coherent state, we construct a modified generalized Darboux transformation in which the multiple spectral parameters are involved, and the Nth-order semirational solutions in the determinant form, where N is a positive integer. Then, we obtain and analyze three types of the semirational solutions: Type-I degenerate soliton solutions which describe the degenerate solitons; Type-II degenerate soliton solutions which describe the interaction among the solitons and degenerate solitons; Type-III degenerate soliton solutions which describe the bound states among a set of the degenerate solitons. Generation conditions of the above semirational solutions are discussed. When the multiple solitons have the equal velocity, bound-state solitons are also constructed. Influence of β on the type-I degenerate solitons are graphically illustrated, where β denotes the strength of the higher-order linear and nonlinear effects in the equation.

Gap solitons in heterostructure magnonic crystal/semiconductor

The main features of the nonlinear spin wave propagating in the magnonic crystal/semiconductor (SC) layered heterostructure are studied. We demonstrate the possibility of double electric and magnetic control of the gap solitons parameters (their number, threshold of formation, velocity), bistability of spin waves, switching powers and nonlinear band gap shift in investigated structure. Our results show the possibility of nonlinear magnonics and SC electronics integration based on the proposed structure.

Nonlinear spin Hall effect in PT -symmetric collinear magnets

We theoretically investigate a nonlinear spin Hall effect in $\mathcal{PT}$-symmetric antiferromagnetic metals, which serve as an efficient spin current generator. We elucidate that an emergent spin-dependent Berry curvature dipole is a microscopic origin of the nonlinear spin Hall effect, which becomes nonzero with neither relativistic spin-orbit coupling, uniform magnetization, nor spin-split band structure. By analyzing a microscopic antiferromagnetic model without spin-orbit coupling for an intuitive understanding of the phenomena, we elucidate essential hopping processes and a condition to enhance the nonlinear spin Hall conductivity. We also provide a complete table to include useful correspondence among the N\'eel vector, odd-parity multipoles, nonlinear spin conductivity tensor, and candidate materials in all the $\mathcal{PT}$-symmetric black-and-white magnetic point groups.

Origin of Nonlinear Damping Due to Mode Coupling in Auto-Oscillatory Modes Strongly Driven by Spin-Orbit Torque

We investigate the physical origin of nonlinear damping due to mode coupling between several auto-oscillatory modes driven by spin-orbit torque in constricted Py/Pt heterostructures by examining the dependence of auto-oscillation on temperature and applied field orientation. We observe a transition in the nonlinear damping of the auto-oscillation modes extracted from the total oscillation power as a function of drive current, which coincides with the onset of power redistribution amongst several modes and the crossover from linewidth narrowing to linewidth broadening in all individual modes. This indicates the activation of another relaxation process by nonlinear magnon-magnon scattering within the modes. We also find that both nonlinear damping and threshold current in the mode-interaction damping regime at high drive current after transition are temperature independent, suggesting that the mode coupling occurs dominantly through a non-thermal magnon scattering process via a dipole or exchange interaction rather than thermally excited magnon-mediated scattering. This finding presents a promising pathway to overcome the current limitations of efficiently controlling the interaction between two highly nonlinear magnetic oscillators to prevent mode crosstalk or inter-mode energy transfer and deepens understanding of complex nonlinear spin dynamics in multimode spin wave systems.

Nonlinear spin excitations in a Heisenberg antiferromagnet with NNN and D–M interactions

Spin deviation vs site number in an inhomogeneous (site dependent) antiferromagnet incorporating next nearest neighbour (NNN) and Dzyaloshinski–Moriya (D–M) interactions along with nearest neighbour and anisotropic interactions is investigated. In this context, a model Hamiltonian for 1D inhomogeneous antiferromagnetic spin system with site dependent inhomogenities is constructed. Glauber coherent state representation along with H-P representation is applied to derive the Heisenberg equation of motion. The dynamics in the continuum level is investigated using the Sine–Cosine (SC) function method and the results are analysed graphically.

Nonbistable rectified linear unit-based gain-dissipative Ising spin network with stochastic resonance effect

The gain-dissipative Ising machine (GIM), comprising a nonlinear transfer function and spin interaction feedback, is one of the most promising quantum analog annealers. However, previous GIM constructions have been limited to only bistable nonlinear transfer functions with low noise intensity condition. To provide a new insight and broaden the potential design of GIMs, we construct a nonbistable rectified linear unit-based gain-dissipative Ising spin network (RISN). In contrast to the traditional GIM, spin dynamics analysis in the uncoupled state proves that RISN is nonbistable. Furthermore, it is demonstrated that the proposed RISN can effectively solve combinatorial optimization problems with a high noise level, which can be regarded as a stochastic resonance phenomenon. The proposed configuration, which does not comply with known conclusions, can become a stepping-stone for new GIM designs.

Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study

In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.

Possibility of Raising the Frequency of RF Limiters Using the Nonlinear Spin Wave–Electromagnetic Interaction in Ferrites With High Saturation Magnetization

Physics of the spin wave&#x2013;electromagnetic (EM) interaction is investigated for RF limiter applications, by looking at the magnetization <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> and its deviation <inline-formula> <tex-math notation="LaTeX">$\Delta M$ </tex-math></inline-formula> through equations of motion. Exchange effects are examined, and a complete magnetodynamics equation is developed and looked at for both the fundamental- and second-harmonic frequencies. Nonlinear conversion of energy occurs between the first and second harmonics. It is shown here that the usual operating frequencies for RF limiters, in the range of 1.5&#x2013;15-GHz frequencies, can be lifted up into the much higher frequencies of the 40&#x2013;60-GHz range by a new formula developed from fundamental spin wave&#x2013;EM interactions in magnetic material characterized by a magnetization <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>. The treatment is self-contained in which all of the information needed to understand the magnetics aspect for RF applications is provided.

Nonlinear optical Hall effect of few-layered NbSe2

${\mathrm{NbSe}}_{2}$ is one of metallic two-dimensional (2D) transition-metal dichalcogenide (TMDC) materials. Because of broken crystal inversion symmetry, large spin splitting is induced by Ising-type spin-orbit coupling in odd-number-layered ${\mathrm{NbSe}}_{2}$, but absent for even-number-layered ${\mathrm{NbSe}}_{2}$ with the inversion symmetry. In this paper we numerically calculate nonlinear optical charge and spin Hall conductivities of few-layered ${\mathrm{NbSe}}_{2}$ based on an effective tight-binding model which includes ${d}_{{z}^{2}}$, ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$, and ${d}_{xy}$ orbitals of Nb atoms. We show that the nonlinear optical Hall conductivity for the second harmonic generation (SHG) process has a nonvanishing value in odd-number-layered ${\mathrm{NbSe}}_{2}$. Also, we provide a nonlinear optical selection rule in few-layered ${\mathrm{NbSe}}_{2}$ and their polarization dependencies. Furthermore, for the even-number-layered case, the nonlinear optical Hall currents can be generated by applying electric fields which break inversion symmetry. We also discuss that the nonlinear optical Hall effect is expected to occur in TMDC materials in general. Thus, our results will serve to design potential opt-spintronics devices based on 2D materials to generate the spin Hall current by SHG.

Nonlinear signal processing with magnonic superlattice with two periods

In this work, we provide investigations of nonlinear spin wave propagation in magnonic superlattice. Magnonic superlattice is a ferromagnetic film loaded on a dielectric ceramic substrate with the copper grating with two periods. It is shown that a superlattice with two periods allows the formation of narrower bandgaps as compared to magnonic crystal with one period. Nonlinear effects, such as the generation of spin wave excitations at half-frequency, caused by first-order parametric processes, and a nonlinear shift of the bandgap, caused by a change in the longitudinal component of magnetization with an increase in the input signal power, are revealed. For the experimental study, the Brillouin light scattering spectroscopy was used, and the theoretical model was built using the transfer matrix method.

Nonlinear magnon spin Nernst effect in antiferromagnets and strain-tunable pure spin current

In this paper, we study the spin Nernst effect of magnons in the nonlinear response regime. We derive the formula for the nonlinear magnon spin Nernst current by solving the Boltzmann equation and find out that it is described by an extended Berry curvature dipole of magnons. The nonlinear magnon spin Nernst effect is expected to occur in various N\'eel antiferromagnetic materials even without the Dzyaloshinskii-Moriya interaction. In particular, the nonlinear spin Nernst current in the honeycomb and diamond lattice antiferromagnets can be controlled by strain/pressure.

Enormous soliton solutions to a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation

In our current study, we will extract enormous, impressive soliton solutions to a (2+1)-dimensional Heisenberg ferromagnetic spin chains with bilinear and anisotropic interactions in the semi classical limit. The suggested model has its wide importance for many magnetism phenomena. Specially, it is very momentous in modern magnetism theory in which the nonlinear long-range ferromagnetic ordering magnetism can be explained. Moreover, it describes the characteristic of magnetism to many insulating crystals as well as interaction spins. The ferromagnetism plays fundamental role in modern technology and industry and it is principal for many electrical and electromechanical devices such as electromagnets, electric motors, generators etc. We will document various types of the soliton solutions by using four various techniques to extract the soliton configuration behaviors arising from the magnet dynamics model. The techniques that are used to derive these types of soliton solutions are the extended direct algebraic method, the extended simple equation method, the solitary wave ansatz method and the Paul-Painleve approach method. The expected achieved soliton solutions will offer a rich podium to study the nonlinear spin dynamics in magnetic materials. The achieved soliton solutions are new compared with that achieved previously by other authors who used different techniques.

Dynamical plane wave solutions for the Heisenberg model of ferromagnetic spin chains with beta derivative evolution and obliqueness

The oblique plane waves with their dynamical behaviors for a (2+1)-dimensional nonlinear Schrödinger equation (NLSE) having beta derivative spatial-temporal evolution are investigated. In order to study such phenomena, NLSE is converted to a nonlinear ordinary differential equation with a planar dynamical system by considering the variable wave transform with obliqueness and the properties of the beta derivative. Some more new general forms of analytical solutions, like bright, dark, singular, and pure periodic solutions of NLSE are constructed by employing the auxiliary ordinary differential equation method and the extended simplest equation method. The effect of obliqueness and beta derivative parameter on several types of wave structures along with the phase portrait diagrams are reported by considering some special values of parameters for the existence of attained solutions. It is found that the planar dynamical system is not supported by any type of orbit for Θ=450. It is also confirmed from the obtained solutions that no plane waves are generated for Θ=450. The presented studies on bifurcation analysis and analytical solutions for (2+1)-dimensional NLSE would be very useful to understand the physical scenarios of nonlinear spin dynamics in magnetic materials for Heisenberg models of ferromagnetic spin chains.

Breathers on elliptic function background for a generalized nonlinear Schrödinger equation with higher-order terms

A generalized nonlinear Schrödinger equation with higher-order terms, which is derived as a model for the nonlinear spin excitations in the one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin, is investigated. Firstly, in view of Riccati equations associated with the Lax pair, the Darboux transformation of a generalized nonlinear Schrödinger equation is presented. Secondly, the complicated Jacobi elliptic functions as seed solutions are considered so that much more fascinating solutions and dynamical properties can be obtained. Based on the above discussion, breathers in the presence of two kinds of Jacobian elliptic functions dn and cn are constructed. Finally, the dynamical properties of such solutions are analyzed by drawing the three-dimensional figures. The structures of these solutions are influenced by the higher-order operator. More importantly, the method provided in this paper can also be adopted to construct breathers on the elliptic functions background of other higher-order nonlinear integrable equations.

Synthesis, tailoring the optical properties of insulating alkaline-earth metal oxide (MgO) with dopants of transition metal (Cu) and vibrating sample magnetometer measurements

X-ray diffraction studies on MgO with copper dopants show the solubility limit of copper up to 3% preferably with f.c.c. (face centered cubic) structures. With doped of copper exceeding 3% in MgO. XRD showed phase changes with dopants of copper at 5% and exceeding 5% in MgO. Composites of two different crystalline phases are expected to appear (may be f.c.c cubic and f.c. triclinic). This confirmed to the fact that substitution or replacement of magnesium ions with copper ions would result into composite structures. Secondary phase appeared with exceeding 3% copper doping in MgO in the form of CuO as spherical nanoparticles and the same could be for MgO as spherical nanoparticles. EDX confirmed this behavior for copper dopants in MgO.With UV–visible absorption spectra, the quantum confinement effect is attributed to defects produced with dopants of copper ions as interstials in MgO within a limit of one to three percent. The observed size of MgO with SEM is 90.85 nm and the band gap is 4.68eV which are indicative of the transitions from insulating to dielectric behavior or to topological insulator.Experimental results of a.c. magnetic susceptibility with VSM on magnesium oxide and varying dopants of copper in MgO even with composite structures and phase changes show an antiferromagnetic behavior. This antiferromagnetic behavior is a manifestation of ‘topological insulator’ with enhanced dielectricity. Spin fluctuations due to nonlinear spin dynamics, triggered gyroscopic behavior in the nanomaterials, thereby producing quasiparticles of electrons and holes (vacant quantum states of electrons) as Majorana Fermions. Step transitions with upward and downward peaks of magnetization in MgO, with 3% copper ions concentrations and MgO with 8% copper ions concentration show ‘skyrmion like’ excitations with decreasing trends due to phase changes and composite structures but accompanied with negative slopes thereby maintaining ‘antiferromagnetic behavior’ as manifestations of topological insulators. Other samples of MgO with 1%, 5% and 10% copper ions concentrations showed antiferromagnetic behavior. With proper selection of copper dopants in MgO, various kinks of ‘spin fluctuations’ as manifestations of magnetic excitations can be produced to making these materials useful for diverse categories of devices.Mathematical result is proposed for eigenfunctions (shape profiles) and energy eigenvalues by considering the quasiparticles of energy fields for electrons and holes as Majorana Fermions with twisting and twigging in a braided configuration with QED behavior.

Comprehensive theory of second-order spin photocurrents

The spin photocurrents, direct currents induced by light, hold great promise for introducing new elements to spintronics. However, a general theory for spin photocurrents in real materials which is applicable to systems with spin-orbit coupling or noncollinear magnetism is absent. Here, we develop such a general theory of second-order spin photocurrents. We find that the secondorder spin photocurrents can be classified into Drude, Berry curvature dipole, shift, injection, and rectification currents, which have different physical origins and symmetry properties. Surprisingly, our theory predicts a direct pure spin rectification current in an insulator induced by photons with energies lower than the material band gap. This phenomenon is absent in the case of the charge photocurrent. We find that the pure spin current of BiTeI induced by subgap light is large enough to be observable in experiments. Moreover, the subgap pure spin photocurrent is highly tunable with the polarization of light and the flowing direction of the spin photocurrent. This study lays the groundwork for the study of nonlinear spin photocurrents in real materials and provides a route to engineer light-controlled spin currents.