Localized Spin Waves Research Articles

INTRINSIC LOCALIZED MODES IN QUANTUM FERROMAGNETIC ISING–HEISENBERG CHAINS WITH SINGLE-ION UNIAXIAL ANISOTROPY

Based on the coherent-state method combined with the Dyson–Maleev representation of spin operators, the existence and properties of intrinsic localized spin-wave modes in quantum ferromagnetic Ising–Heisenberg chains with single-ion uniaxial anisotropy are investigated analytically in the semiclassical limit. With the help of the multiple-scale method combined with semidiscrete approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is found that, at the center of the Brillouin zone, a bright type intrinsic localized spin-wave mode can exist below the bottom of the linear spin-wave spectrum. Besides, we show that, at the boundary of the Brillouin zone, a dark type intrinsic localized spin-wave mode appears above the top of the linear spin-wave spectrum, which is different from the resonant nonpropagating kink mode.

Spin-Wave-Mode Coexistence on the Nanoscale: A Consequence of the Oersted-Field-Induced Asymmetric Energy Landscape

It has been argued that if multiple spin wave modes are competing for the same centrally located energy source, as in a nanocontact spin torque oscillator, that only one mode should survive in the steady state. Here, the experimental conditions necessary for mode coexistence are explored. Mode coexistence is facilitated by the local field asymmetries induced by the spatially inhomogeneous Oersted field, which leads to a physical separation of the modes, and is further promoted by spin wave localization at reduced applied field angles. Finally, both simulation and experiment reveal a low frequency signal consistent with the intermodulation of two coexistent modes.

Enhancement of spin wave excitation by spin currents due to thermal gradient and spin pumping in yttrium iron garnet/Pt

We investigate the interplay between spin currents produced by thermal gradients and spin pumping in hybrid yttrium iron garnet/Pt structures (YIG/Pt). By combining a spin pumping experiment with the application of a temperature gradient, we observe the excitation of local spin wave modes at the YIG/Pt interface. Strong enhancement of these modes was observed when the temperature gradient was applied along one direction and attenuation was observed by reversing the temperature gradient. The results provide support for a recent theoretical proposal, in which some spin wave modes are preferentially excited by spin currents traversing a YIG/Pt interface.

Current-induced localized spin wave interference in a ferromagnetic nanowire with a domain wall

Spin wave dispersion relations in a ferromagnetic nanowire with and without a domain wall are investigated by means of micromagnetic simulations. We confirm that the spin wave dispersion relation is shifted due to the spin wave Doppler effects, when the spin-transfer torque is applied. We also investigate the position-dependent ferromagnetic resonance spectra in the nanowire and find strong local spin wave interferences because of the formation of the standing wave due to reflections from a domain wall. It is observed that the spacing between the local spin wave constructive interferences is uniform, and it is revealed that the spacing is related with the spin wave Doppler shift.

Stability of the Landau state in square two-dimensional magnetic nanorings

We use a microscopic theory taking into account dipolar and nearest-neighbour exchange interactions to explore spin-wave excitations in two-dimensional square-shaped magnetic nanorings with the Landau state assumed as a magnetic state. From the spin-wave spectra, we determine the range of the dipolar-to-exchange interaction ratio in which the assumed state is stable. Various types of localized spin waves prove responsible for the transition to a new magnetic configuration. We found the transition forced by predominating exchange interactions size-independent in a wide range of both external and internal size of the ring.

Spin wave localization and softening in rod-shaped magnonic crystals with different terminations

The spin dynamics of simple cubic arrays of magnetic dipoles with the shape of elongated prisms is investigated in dependence of their terminations (flat or cusp) and of the applied field. We used two different calculation approaches: in the first, we solve the Landau-Lisfshits equation of motion of planar arrangements of magnetic dipoles; the static magnetization of the array is supposed to be uniform along the direction of the applied field, and the calculated modes have nodal planes perpendicular to the magnetization. In the second approach, we use the dynamical matrix method, which is a micromagnetic method, considers the exact (non-uniform) magnetic equilibrium configuration, and returns the complete set of magnetic eigenvalues/eigenmodes. Calculations show the existence of modes with different localization: low frequency modes, localized at the prism ends, and high frequency bulk modes, including the fundamental or quasi-uniform mode. We studied the internal field profile as a function of the termination details, the localization of spin modes, in particular of the lowest frequency mode, and the space resolved density of states. Finally, we address the soft modes of these systems, showing their frequency vs. applied field behavior in relation to the discontinuity of the magnetization curve, and investigating the symmetry transfer from the soft mode profile to the static magnetization, with possible applications.

Complete band gaps for magnetostatic forward volume waves in a two-dimensional magnonic crystal

We report on the formation of a complete band gap for spin waves in a two-dimensional magnonic crystal consisting of a periodic hole lattice. We go beyond the partial band gaps observed so far in that we apply a magnetic field perpendicular to the permalloy thin film. We explore the relevant geometrical parameters using micromagnetic simulations. In nanopatterned devices we obtain complete band gaps of up to 1.4 GHz. The magnetostatic forward volume waves addressed here overcome in particular spin-wave localization effects. These effects have led to complicated and highly anisotropic miniband formation or Bragg reflection in in-plane fields for a long time. We demonstrate how direct band-gap tailoring via geometrical lattice symmetries becomes possible in nanostructured magnetic antidot lattices.

Interaction of spin waves with dislocations in ferrodielectrics

It is demonstrated that the presence of dislocations in a ferromagnetic leads to localization of spin waves on it. The dispersion equation is derived and investigated, and the dependence of the localized wave amplitude on the distance to a dislocation is determined. The frequency interval separating the localized fluctuations from the volume ones is determined.

Nanoscale Spin Wave Localization Using Ferromagnetic Resonance Force Microscopy

We use the dipolar fields from a magnetic cantilever tip to generate localized spin wave precession modes in an in-plane magnetized, thin ferromagnetic film. Multiple resonances from a series of localized modes are detected by ferromagnetic resonance force microscopy and reproduced by micromagnetic models that also reveal highly anisotropic mode profiles. Modeled scans of line defects using the lowest-frequency mode provide resolution predictions of (94.5±1.5) nm in the field direction, and (390±2) nm perpendicular to the field.

Collective spin-wave excitations in a two-dimensional array of coupled magnetic nanodots

A general theory of collective spin-wave excitations in a two-dimensional array of magnetic nanodots coupled by magnetodipolar interaction is developed. The theory allows one to analytically calculate spectra, damping rates, excitation efficiencies, and other characteristics of spin waves in both periodic and aperiodic ground states of an array. It is demonstrated that all the properties of collective spin waves in an array existing in any spatially periodic ground state (e.g., ferromagnetic or chessboard antiferromagnetic) are determined by the same state-independent array's demagnetization tensor ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\mathbit{F}}}_{\mathbit{k}}$, which is determined by the spin-wave wave vector $\mathbit{k}$, the size and shape of the array's elements (nanodots), and the geometry of the array's lattice. The applications of the developed general theory are illustrated on particular examples: (i) spin waves in ferromagnetic and chessboard antiferromagnetic states of a square array, and (ii) localized spin-wave excitations associated with an isolated ``defect'' in a uniform ferromagnetic ground state of a square array.

Comment on “Mapping of localized spin-wave excitations by near-field Brillouin light scattering” [Appl. Phys. Lett. 97, 152502 (2010)

First Page

Localized domain-wall excitations in patterned magnetic dots probed by broadband ferromagnetic resonance

We investigate the magnetization dynamics in circular Permalloy dots with spatially separated magnetic vortices interconnected by domain walls (double vortex state). We identify a novel type of quasi one-dimensional (1D) localized spin wave modes confined along the domain walls, connecting each of two vortex cores with two edge half-antivortices. Variation of the mode eigenfrequencies with the dot sizes is in quantitative agreement with the developed model, which considers a dipolar origin of the localized 1D spin waves or so-called Winter's magnons [J. M. Winter, Phys. Rev. 124, 452 (1961)]. These spin waves are analogous to the displacement waves of strings and could be excited in a wide class of patterned magnetic nanostructures possessing domain walls, namely in triangular, square, circular, or elliptic soft magnetic dots.

Direct observation of a propagating spin wave induced by spin-transfer torque

Spin torque oscillators with nanoscale electrical contacts are able to produce coherent spin waves in extended magnetic films, and offer an attractive combination of electrical and magnetic field control, broadband operation, fast spin-wave frequency modulation, and the possibility of synchronizing multiple spin-wave injection sites. However, many potential applications rely on propagating (as opposed to localized) spin waves, and direct evidence for propagation has been lacking. Here, we directly observe a propagating spin wave launched from a spin torque oscillator with a nanoscale electrical contact into an extended Permalloy (nickel iron) film through the spin transfer torque effect. The data, obtained by wave-vector-resolved micro-focused Brillouin light scattering, show that spin waves with tunable frequencies can propagate for several micrometres. Micromagnetic simulations provide the theoretical support to quantitatively reproduce the results.

Static and dynamic properties of single-chain magnets with sharp and broad domain walls

We discuss time-quantified Monte-Carlo simulations on classical spin chains with uniaxial anisotropy in relation to static calculations. Depending on the thickness of domain walls, controlled by the relative strength of the exchange and magnetic anisotropy energy, we found two distinct regimes in which both the static and dynamic behavior are different. For broad domain walls, the interplay between localized excitations and spin waves turns out to be crucial at finite temperature. As a consequence, a different protocol should be followed in the experimental characterization of slow-relaxing spin chains with broad domain walls with respect to the usual Ising limit.

Field tunable localization of spin waves in antidot arrays

We show that magnetic spin wave resonance modes in an antidot patterned array are sensitive to small changes in the magnetic configuration near dots, resulting in strong localization effects as the field is increased. Frequencies measured using ferromagnetic resonance from an antidot array patterned from a NiFe/IrMn bilayer are interpreted using micromagnetic calculations, and it is shown that the observed field dependence of the resonance response can be attributed to strong interdot localization of spin waves. This field tunable localization is created by stray fields produced by magnetic poles at the dot surfaces.

The effect of the single-spin defect on the stability of the in-plane vortex state in 2D magnetic nanodots

The aim of this study is to analyse the stability of the single in-plane vortex state in two-dimensional magnetic nanodots with a nonmagnetic impurity (single-spin defect) at the centre. Small square and circular dots including up to a few thousand of spins are studied by means of a microscopic theory with nearest-neighbour exchange interactions and dipolar interactions fully taken into account. We calculate the spin-wave frequencies versus the dipolar-to-exchange interaction ratio d to find the values of d for which the assumed state is stable. Transitions to other states and their dependence on d and the vortex size are investigated as well, with two types of transition found: vortex core formation for small d values (strong exchange interactions), and in-plane reorientation of spins for large d values (strong dipolar interactions). Various types of localized spin waves responsible for these transitions are identified.

Magnetic Field Dependence of the Lowest-Frequency Edge-Localized Spin Wave Mode in a Magnetic Nanotriangle

An understanding of the spin dynamics of nanoscale magnetic elements is important for their applications in magnetic sensing and storage. Inhomogeneity of the demagnetizing field in a non-ellipsoidal magnetic element results in localization of spin waves near the edge of the element. However, relative little work has been carried out to investigate the effect of the applied magnetic fields on the nature of such localized modes. In this study, micromagnetic simulations are performed on an equilateral triangular nanomagnet to investigate the magnetic field dependence of the mode profiles of the lowest-frequency spin wave. Our findings reveal that the lowest-frequency mode is localized at the base edge of the equilateral triangle. The characteristics of its mode profile change with the ground state magnetization configuration of the nanotriangle, which, in turn, depends on the magnitude of the in-plane applied magnetic field.

Low-energy coherent Stoner-like excitations inCaFe2As2

Using linear-response density-functional theory, magnetic excitations in the striped phase of CaFe$_{2}$As$_{2}$ are studied as a function of local moment amplitude. We find a new kind of excitation: sharp resonances of Stoner-like (itinerant) excitations at energies comparable to the N{\'{e}}el temperature, originating largely from a narrow band of Fe $d$ states near the Fermi level, and coexist with more conventional (localized) spin waves. Both kinds of excitations can show multiple branches, highlighting the inadequacy of a description based on a localized spin model.

Spin wave localization in a triangular nanomagnet

Brillouin measurements have been carried out on a low density array of 20 nm thick Ni80Fe20 equilateral triangles with an edge length of 190 nm, under an in-plane magnetic field applied perpendicular to one edge of the triangular magnets. The dynamical matrix method is employed to identify the observed spin wave modes. Most of the observed modes can be classified into different categories based on their mode profiles, with modes in each category characterized by the same number of nodal lines along the direction of the applied field but having different spatial localization. Hybrid modes with different numbers of nodal lines in different regions of the nanomagnet are also found to exist. The spatial localization and the spatial variation in the spin wave character for the observed modes have been calculated based on the spin wave well model. Calculations based on the simple model give reasonable agreement with numerical results obtained by the dynamical matrix method.

Mapping of localized spin-wave excitations by near-field Brillouin light scattering

We report on the experimental study of the spatial characteristics of high-frequency spin-wave modes localized at the edges of micrometer-size in-plane magnetized permalloy ellipses. Using a near-field Brillouin light scattering technique, we have mapped the modes with the spatial resolution of few tens of nanometers. We show that the width of the localization area strongly depends on the applied magnetic field and reduces to about 85 nm for high fields. We also demonstrate that the existing theoretical models do not appropriately describe spatial characteristics of the modes.