Spin-wave Energy Research Articles

Магнитный отклик треугольного графона

We consider triangular graphone structure – a semi-hydrogenated layer of graphene with hydrogen atoms boned to one of its sub-lattices only. The response function of graphone to an external magnetic field is evaluated in general using the Heisenberg Hamiltonian model of the structure with exchange energy coefficient J 0 of unknown value (negative due to ferromagnetic behaviour of triangular graphone). The spin wave approach in the limit of near zero temperature is used for the description of the magnetisation. A specific case when the graphone is exposed to a magnetic pulse with a given carrier frequency is examined in greater depth. To obtain the magnetization response, integration over both the frequency space and momentum space is necessary. Due to inapplicability of the isotropic approximation for the given geometry of graphone, integration over momentum space is performed numerically. The calculations show that the resonance of the system occurs at frequencies which correspond to the upper limit of the spin wave energy band and the saddle points of the energy surface. Using these results, further experimental investigation based on THz or far-infrared spectroscopy can be performed, which can determine the as-yet-unknown exchange energy coefficient J 0 . The coefficient can in turn provide an estimate of a temperature range for which the spin wave approach utilised in our investigation is valid.

Enhanced spin wave propagation in magnonic rings by bias field modulation

We simulate the spin wave (SW) dynamics in ring structures and obtain the ω − k dispersion relations corresponding to the output waveguide. Different bias field configurations affect the transfer of SW power from one arm of the structure to the other arm. To this end, we show that circular or radial bias fields are more suitable for energy transfer across the ring than the conventional horizontal bias field Hx. The SW dispersion shows that modes excited, when the bias field is along the ring radius, are almost 10 dB higher in power when compared to the modal power in the case of Hx. This is also corroborated by the SW energy density in the receiving stub.

Spin-Wave Chirality and Its Manifestations in Antiferromagnets.

As first demonstrated by Tang and Cohen in chiral optics, the asymmetry in the rate of electromagnetic energy absorption between left and right enantiomers is determined by an optical chirality density. Here, we demonstrate that this effect can exist in magnetic spin systems. By constructing a formal analogy with electrodynamics, we show that in antiferromagnets with broken chiral symmetry, the asymmetry in local spin-wave energy absorption is proportional to a spin-wave chirality density, which is a direct counterpart of optical zilch. We propose that injection of a pure spin current into an antiferromagnet may serve as a chiral symmetry breaking mechanism, since its effect in the spin-wave approximation can be expressed in terms of additional Lifshitz invariants. We use linear response theory to show that the spin current induces a nonequilibrium spin-wave chirality density.

Internal dipolar field and soft magnons in periodic nanocomposite magnets

We study spin wave excitations in a three-dimensional nanocomposite magnet of exchange coupled hard (SmCo5) and soft (FeCo) phases. The dipolar interaction splits the spin wave energies into the upper and lower branches of the spin wave manifold. When the amount of the soft phase is increased the energy of low-lying spin excitations is considerably softened due to two reasons: (i) the low- lying mode locked into the soft phase region with a spin wave gap at k=0 which scales approximately proportional to the anisotropy constant of the soft phase and (ii) the internal dipolar field which comes from magnetic charges forming at hard-soft boundaries with normals parallel to the magnetization displaces the spin wave manifold toward the lower energies. With adding more soft phase the spin wave gap closes and the system moves to another ground state characterized by the magnetization mismatch between spins of the hard and soft phases.

Spin waves in the fcc lattice antiferromagnet: competing interactions, frustration, and instabilities in the Hubbard model

Spin waves in the type-III ordered antiferromagnetic state of the frustrated t-t′ Hubbard model on the face-centred-cubic (fcc) lattice are calculated to investigate finite-U-induced competing interaction and frustration effects on magnetic excitations and instabilities. Particularly strong competing interactions generated due to the interplay of fcc lattice geometry and magnetic order result in significant spin wave softening. The calculated spin wave dispersion is found to be in qualitative agreement with the measured spin wave dispersion in the pyrite mineral MnS2 obtained from inelastic neutron scattering experiments. Instabilities to other magnetic orders (type I, type II, spiral, non-collinear), as signalled by spin wave energies turning negative, are also discussed.

Voltage-Controlled Spin-Wave Coupling in Adjacent Ferromagnetic-Ferroelectric Heterostructures

The manipulation of spin waves is the basis of $m\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}g\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}s$, one approach to the next generation of hardware for logic and data storage. The authors demonstrate the voltage-controlled transfer of spin-wave energy between adjacent ferrimagnetic-ferroelectric heterostructures. The coupling efficiency of the laterally coupled multiferroics can be tuned by independently varying applied magnetic and electric fields, which offers enticing prospects for magnonic devices.

Electronic structures, magnetic properties and spin-orbital coupling effects of aluminum nitride monolayers doped by 5d transition metal atoms: possible two-dimensional long-range magnetic orders

The magnetism of two-dimensional material is an important research topic. In particular, the long-range magnetic order of two-dimensional material is of great significance in theoretical research and practical application. According to the Mermin-Wagner theory, the isotropic Heisenberg model in a two-dimensional system cannot produce long-range magnetic orders at non-vanishing temperatures. Considering the existence of strong magnetic anisotropy, possible two-dimensional long-range magnetic orders may exist in 5d atom doped two-dimensional aluminum nitride (AlN) monolayer. This research is performed by first-principles calculations based on the density functional theory. Geometries, electronic structures, magnetic properties, and magnetic anisotropy energies from spin-orbital coupling effects in AlN monolayers doped by 5d transition metal atoms (Hf, Ta, W, Re, Os, Ir, Pt, Au, and Hg) are calculated. Four kinds of supercells are used in the calculation, i.e, 22, 33, 44, and 55, with one aluminum atom substituted by one 5d atom. Projection augmented wave method is used to describe the interaction between the valence electrons and the ions. The plane wave is used to expand the wave function of the valence electron. For an optimized geometry, the bond length between the 5d metal atom and the nearest N atom is the largest in Hg-doped supercells, which is 2.093 , followed by the Au, Hf, Pt, Ta, and Ir according to the order of bond length magnitude. For the densities of states (DOSs), obvious impurity energy levels appear in the forbidden bands. For all the supercells, spin-up and spin-down DOSs of Ta and Ir doped systems are symmetric, indicating non-magnetic states. DOSs of Hf, W, Re, and Os doped systems are asymmetric, indicating magnetic states. For Pt, Au, and Hg, DOSs are symmetric in 22 supercells, but asymmetric in the 33, 44, and 55 supercells. Total magnetic moments and the spin densities are also given. In 55 supercells, they are 1.00, 0.00, 0.39, 1.99, 1.17, 0.00, 1.00, 2.00, and 1.00 for Hf, Ta, W, Re, Os, Ir, Pt, Au, and Hg, respectively. The magnetic moment is mainly concentrated in the vicinity of the 5d atoms. The energy differences between ferromagnetic and antiferromagnetic states are calculated. For Hf, Re, Pt and Au systems, the differences in 48 supercells reach the maximum values of -187.2563 meV, 286.2320 meV, -48.0637 meV and -61.7889 meV, respectively. The results indicate that there is a strong interaction between the magnetic centers. Magnetic anisotropy energy originating from spin-orbital effect is calculated in the 44 supercells. For the Re system, it is the highest, reaching 11.622 meV. For W, Os, and Au, the values are larger than 1 meV, showing strong magnetic anisotropies. The magnetic anisotropy can produce a spin wave energy gap, resulting in long-range magnetic orders. Based on the results above, it is predicted that with appropriate 5d atoms and suitable doping concentration, two-dimensional long-range magnetic orders may exist in 5d transition metal atom doped AlN monolayers.

Nonlinear spin wave coupling in adjacent magnonic crystals

We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.

Mapping of spin wave propagation in a one-dimensional magnonic crystal

The formation and evolution of spin wave band gaps in the transmission spectrum of a magnonic crystal have been studied. A time and space resolved magneto inductive probing system has been used to map the spin wave propagation and evolution in a geometrically structured yttrium iron garnet film. Experiments have been carried out using (1) a chemically etched magnonic crystal supporting the propagation of magnetostatic surface spin waves, (2) a short microwave pulsed excitation of the spin waves, and (3) direct spin wave detection using a movable magneto inductive probe connected to a synchronized fast oscilloscope. The results show that the periodic structure not only modifies the spectra of the transmitted spin waves but also influences the distribution of the spin wave energy inside the magnonic crystal as a function of the position and the transmitted frequency. These results comprise an experimental confirmation of Bloch′s theorem in a spin wave system and demonstrate good agreement with theoretical observations in analogue phononic and photonic systems. Theoretical prediction of the structured transmission spectra is achieved using a simple model based on microwave transmission lines theory. Here, a spin wave system illustrates in detail the evolution of a much more general physical concept: the band gap.

Spin wave dynamics in Heisenberg ferromagnetic/antiferromagnetic single-walled nanotubes

The spin wave dynamics, including the magnetization, spin wave dispersion relation, and energy level splitting, of Heisenberg ferromagnetic/antiferromagnetic single-walled nanotubes are systematically calculated by use of the double-time Green’s function method within the random phase approximation. The role of temperature, diameter of the tube, and wave vector on spin wave energy spectrum and energy level splitting are carefully analyzed. There are two categories of spin wave modes, which are quantized and degenerate, and the total number of independent magnon branches is dependent on diameter of the tube, caused by the physical symmetry of nanotubes. Moreover, the number of flat spin wave modes increases with diameter of the tube rising. The spin wave energy and the energy level splitting decrease with temperature rising, and become zero as temperature reaches the critical point. At any temperature, the energy level splitting varies with wave vector, and for a larger wave vector it is smaller. When pb=π, the boundary of first Brillouin zone, spin wave energies are degenerate, and the energy level splittings are zero.

Quantum Theory of Spin Wave Gap in Ultrathin Magnetic Films

A simple quantum model is presented for the spin wave energy gap in single-layer and thin magnetic films that include both the magnetic out-of-plane and in-plane anisotropies. The films are assumed to be under the influence of the out-of-plane direction of the applied magnetic field at zero temperature. The calculated equations present a nonzero spin wave gap at zero magnetic field which is strongly affected by anisotropies. The effects of the film thickness and the role of the applied field are also examined. We discuss the results in connection with experimental data reported for nanocrystalline amorphous CoFeB films with growth-induced anisotropy.

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.

Magnetic field induced spin-wave energy focusing

Local temperature variations induced by spin-wave propagation are studied using a model that couples nonuniform magnetization dynamics and heat flow. We show that the remote heating at the sample edge reported recently [T. An et al., Nat. Mater. 12, 549 (2013)] is due to the geometry-induced gradual reduction of the effective field. We demonstrate that the same effect can be achieved by a reduction in the external field instead of a constriction at the edge and, furthermore, that both the location and the amount of energy to be delivered to the lattice can be controlled accurately this way.

Transport measurements of the spin-wave parameters of thin Mn films

This paper provides an experimental description and theoretical explanation of how disorder affects electronic transport in antiferromagnetic thin films. The authors find a quantum correction to the conductivity which survives to high disorder strength because of a high rate of inelastic scattering of electrons off of gapped antiferromagnetic spin waves. The data provide first-time estimates of the spin-wave energy gap and exchange energy derived solely from transport measurements. The focus on the unexplored effect of antiferromagnetism on electronic transport provides new perspectives on the role of electronic transport and spin alignment in disordered magnetic systems.

The investigation of Neutron Scattering In Spin Waves Theory of Ferromagnetic Crystals

Inelastic neutron scattering, probing the temporal spin-spin correlation at the different microscopic scale, is a powerful technique to study the magnetic behaviour of ferromagnetic crystals. In addition, high penetration power of neutron in samples has made it as a useful way for spin-spin interaction in neutron scattering. Changes in the magnetic cross section in term of different energy transfer and temperatures are calculated for nickel and iron as transition metals in Heisenberg model versus spin wave theory by considering atomic form factor. Finally, the effect of magnetic structure and behaviour of crystal in measuring cross-section shows that increasing temperature results in the Cross-section increase Also, the existence of propagating spin waves below Tc is compared in Ni and Fe in different momentum transfers. The relation of spin wave energy with temperature dependence of nickel has created different behaviour in the changes of cross section rather than iron.

The role of orbital order in the stabilization of the (π, 0) ordered magnetic state in a minimal two-band model for iron pnictides

Spin wave excitations and stability of the (π, 0) ordered magnetic state are investigated in a minimal two-band itinerant-electron model for iron pnictides. Presence of hopping anisotropy generates a strong ferro-orbital order in the dxz and dyz Fe orbitals in the (π, 0) state. The orbital order sign is as observed in experiments. The induced ferro-orbital order strongly enhances the spin wave energy scale and stabilizes the magnetic state by optimizing the strength of the emergent antiferromagnetically and ferromagnetically spin couplings through optimal band fillings in the two orbitals. The calculated spin-wave dispersion is in quantitative agreement with neutron scattering measurements. Finite inter-orbital Hund's coupling is shown to further enhance the spin wave energies state by coupling the two magnetic sub-systems. A more realistic two-band model with less hopping anisotropy is also considered, which yields not only the circular hole pockets but also correct ferro-orbital order and emergent F spin coupling.

Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite size spin chains with a chiral spin ground state observed on bi-atomic Fe chains deposited on Iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya (DM) coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff (HP) boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the non-collinear nature of the classical ground state, there is a significant zero point reduction of the ground state magnetization of the spin spiral. Second, the two lowest energy spin waves are edge modes in the spin spiral state that, above a critical field the results into a collinear ferromagnetic ground state, become confined bulk modes. Third, in the spin spiral state, the spin wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Magnonic band structure, complete bandgap, and collective spin wave excitation in nanoscale two-dimensional magnonic crystals

We present the observation of a complete bandgap and collective spin wave excitation in two-dimensional magnonic crystals comprised of arrays of nanoscale antidots and nanodots, respectively. Considering that the frequencies dealt with here fall in the microwave band, these findings can be used for the development of suitable magnonic metamaterials and spin wave based signal processing. We also present the application of a numerical procedure, to compute the dispersion relations of spin waves for any high symmetry direction in the first Brillouin zone. The results obtained from this procedure has been reproduced and verified by the well established plane wave method for an antidot lattice, when magnetization dynamics at antidot boundaries is pinned. The micromagnetic simulation based method can also be used to obtain iso--frequency countours of spin waves. Iso--frequency contours are analougous of the Fermi surfaces and hence, they have the potential to radicalize our understanding of spin wave dynamics. The physical origin of bands, partial and full magnonic bandgaps has been explained by plotting the spatial distribution of spin wave energy spectral density. Although, unfettered by rigid assumptions and approximations, which afflict most analytical methods used in the study of spin wave dynamics, micromagnetic simulations tend to be computationally demanding. Thus, the observation of collective spin wave excitation in the case of nanodot arrays, which can obviate the need to perform simulations may also prove to be valuable.

Quasi-2D J1–J2 antiferromagnet Zn2VO(PO4)2 and its Ti-substituted derivative: A spin-wave analysis

In this study, we present non-linear spin wave analysis of a quasi-2D spin-12J1–J2 antiferromagnet at the parameter regime relevant for the recently studied compound Zn2VO(PO4)2. We obtain the temperature dependence of the spin wave energy, susceptibility and magnetization using Green's function technique and Tyablikov's decoupling or Hartree–Fock factorization. The comparison of our numerical results with the experimental findings is discussed. Magnetic structure factor is calculated and compared with powder neutron diffraction data. We also study the spin wave behavior of the compound Zn2Ti0.25V0.75O(PO4)2 obtained by partial chemical substitution of Ti at V sites of the compound Zn2VO(PO4)2 [Kanungo, et al., Phys. Rev. B 87 (2013) 054431]. Due to the superlattice structure of the spin lattice, the substituted compound possesses multiple spin wave modes. The spin wave analysis confirms the quasi-1D nature of the substituted system.

Magnetic excitations in ferromagnetic phase of MnP

Inelastic neutron scattering experiments were performed on an intermetallic compound, MnP. We used a newly developed High Resolution Chopper Spectrometer, HRC, for energy transfers E≤75meV, besides various triple axis spectrometers; LTAS for energy transfers E≤2meV, TOPAN for E≤7.5meV and TAS-1 for E≤35meV. Spin wave excitations were observed in the ferromagnetic phase of MnP in the entire Brillouin zone along the a⁎- and b⁎-axes. The zone boundary energies of spin waves were determined to be around 60meV along the a⁎-axis and around 75meV along the b⁎-axis, and the dispersion relations showed two branches for both axes. The observed dispersion relations of spin waves were well described by an isotropic Heisenberg interaction adding a single ion anisotropy with two sub-lattices.