Permalloy Stripes Research Articles

Axial and azimuthal spin-wave eigenmodes in rolled-up permalloy stripes

We experimentally realized rolled-up permalloy stripes to form three-dimensional ring-like ferromagnetic structures. By means of microwave absorption spectroscopy, we find multiple resonances occurring above a demagnetization field threshold which depends on the ring’s axial width. Our experimental data can be well modeled by assuming both axial and azimuthal spin-wave confinement.

Thermoelectric Detection of Ferromagnetic Resonance of a Nanoscale Ferromagnet

We present thermoelectric measurements of the heat dissipated due to ferromagnetic resonance of a Permalloy strip. A microwave magnetic field, produced by an on-chip coplanar strip waveguide, is used to drive the magnetization precession. The generated heat is detected via Seebeck measurements on a thermocouple connected to the ferromagnet. The observed resonance peak shape is in agreement with the Landau-Lifshitz-Gilbert equation and is compared with thermoelectric finite-element modeling. Unlike other methods, this technique is not restricted to electrically conductive media and is therefore also applicable to for instance ferromagnetic insulators.

Influence of Sample Geometry on Inductive Damping Measurement Methods

We study the precession frequency and effective damping of patterned permalloy thin films of different geometry using integrated inductive test structures. The test structures consist of coplanar wave guides fabricated onto patterned permalloy stripes of different geometry. The width, length and position of the permalloy stripe with respect to the center conductor of the wave guide are varied. The precession frequency and effective damping of the different devices is derived by inductive measurements in time and frequency domain in in-plane magnetic fields. While the precession frequencies do not reveal a significant dependence on the sample geometry we find a decrease of the measured damping with increasing width of the permalloy centered underneath the center conductor of the coplanar wave guide. We attribute this effect to an additional damping contribution due to inhomogeneous line broadening at the edges of the permalloy stripes which does not contribute to the inductive signal provided the permalloy stripe is wider than the center conductor. Consequences for inductive determination of the effective damping using such integrated reference samples are discussed.

Spin-wave damping in ferromagnetic stripes with inhomogeneous magnetization

A theory is presented for the interactions between the dipole-exchange spin waves in ferromagnetic nanowires with a stripe geometry. A Hamiltonian-based approach is used in order to extend earlier results for the linear (or noninteracting) spin waves to include the leading nonlinear processes due to three-magnon and four-magnon effects in a stripe. As well as the magnetic dipole-dipole and exchange terms in the Hamiltonian, the role of an applied magnetic field that can be either parallel or perpendicular to the stripe axis is considered. Within a diagrammatic perturbation method the contributions to the frequency shift and damping of the quantized spin waves are deduced. Numerical calculations are presented for Permalloy stripes, and it is shown that the damping in the transverse field case, where the magnetization may become strongly inhomogeneous, can be larger than that in the longitudinal field case. Comparisons are made with recent damping measurements for Permalloy stripes in a longitudinal field.

Generation of the second harmonic by spin waves propagating in microscopic stripes

We have studied experimentally the nonlinear frequency multiplication accompanying propagation of spin waves in microscopic Permalloy stripes. We find that a propagating spin wave efficiently generates another wave at the double frequency. By using an experimental technique with high spatial resolution, we show that the spatial distribution of the amplitude of the nonlinearly generated wave has a symmetry opposite that of the initial wave. We propose a qualitative model explaining this symmetry reversal.

Broadband Mag-Noise of Patterned Permalloy Thin Films

A Y-factor noise figure (NF) measurement method is developed to characterize high-frequency mag-noise of a 550 nm wide Permalloy strip array under different dc bias currents. The noise voltage density is obtained. The proposed lumped element transmission line model describes noise properties of the patterned Py array well. Measurement data show that rapid ferromagnetic resonance frequencies (FMR) shift induced by dc bias current is related to the excess magnetization fluctuation thermally created by the combined dc current Joule heating effects and orthogonal Oersted fields.

Electrical Detection of Propagating Spin Waves Controlled by a Local Magnetic Field Induced by a DC Current

Propagation of spin waves was studied in electrical ways. Spin waves were excited locally in a permalloy strip by a microwave through a coplanar waveguide and were detected by an electrical technique based on spin rectification effect. By a local magnetic field induced by a DC current, the propagation of spin waves was suppressed in the permalloy strip. We demonstrated that spin wave excitation, manipulation and detection in permalloy strip are possible by electrical ways. And microwave leakage from the coplanar waveguide and local excitation of spin waves are discussed in this paper.

Spin-wave transduction at the submicrometer scale: Experiment and modeling

We report a complete study of spin-wave transduction combining microwave measurements performed over a frequency range of [1--15] GHz on Permalloy strips ($\text{thickness}=10--20\text{ }\text{nm}$, $\text{width}=2--8\text{ }\ensuremath{\mu}\text{m}$) and an accurate modeling of the experiment. This technique has been used recently to assess the spin polarization of the electrical current by measuring a current-induced spin-wave Doppler shift. We present here an electromagnetism calculation based on the magnetostatic wave theory combined with the Gilbert form of the damping that can be used directly as an optimization tool for future spin-wave experiments.

Nanostructured Magnonic Crystals with Size-Tunable Bandgaps

Just as a photonic crystal is a periodic composite composed of materials with different dielectric constants, its lesser known magnetic analogue, the magnonic crystal can be considered as a periodic composite comprising different magnetic materials. Magnonic crystals are excellent candidates for the fabrication of nanoscale microwave devices, as the wavelengths of magnons in magnonic crystals are orders of magnitude shorter than those of photons, of the same frequency, in photonic crystals. Using advanced electron beam lithographic techniques, we have fabricated a series of novel bicomponent magnonic crystals which exhibit well-defined frequency bandgaps. They are in the form of laterally patterned periodic arrays of alternating cobalt and permalloy stripes of various widths ranging from 150 to 500 nm. Investigations by Brillouin light scattering and computer modeling show that the dispersion spectrum of these crystals is strongly dependent on their structural dimensions. For instance, their first frequency bandgap is found to vary over a wide range of 1.4-2.6 gigahertz. Such a functionality permits the tailoring of the bandgap structure which controls the transmission of information-carrying spin waves in devices based on these crystals. Additionally, it is observed that the bandgap width decreases with increasing permalloy stripe width, but increases with increasing cobalt stripe width, and that the bandgap center frequency is more dependent on the stripe width of permalloy than that of cobalt. This information would be of value in the design of magnonic crystals for potential applications in the emerging field of magnonics.

Magnetostatic Interactions of Two-Dimensional Arrays of Magnetic Strips

AbstractA series of arrays consisting of Permalloy stripes with dimensions of 100 nm × 300 nm × 1500 nm was fabricated using electron beam nanolithography and magnetron sputtering followed by the lift-off process. In order to elucidate the effect of magnetostatic interactions among nanosized stripes on magnetic properties of the arrays, the separation between the stripes in different arrays was varied in the range between 100 nm and 2000 nm. Magnetic hysteresis loops of the arrays were measured using SQUID magnetometer for different orientations of the applied field with respect to the arrays. Magnetic anisotropy of the arrays was determined based on ferromagnetic resonance measurements at 9.8 GHz using EPR spectrometer. The measurements were carried out for different directions of in-plane magnetic bias filed. The angular dependence of the resonance field of the main resonant peak indicated presence of the uniaxial magnetic anisotropy due to elongated shape of the stripes. Comparison between angular curves of resonant fields for different arrays leads to the conclusion that increasing strength of magnetostatic interactions among the stripes leads to a suppression of the uniaxial anisotropy. The stripes separated by 2000 nm behave almost like non-interacting objects, but the effect of interactions becomes particularly significant for separations smaller than 600 nm. The properties of the arrays with the smallest separations resembled those of continuous films. Magnetostatic modes have been observed in the FMR spectra in addition to the main resonant peak. These modes are believed to result from dimensional confinement of lateral spinwaves in the magnetic stripes. No such modes were observed in the reference samples of solid Py films, with the in-plane applied magnetic field.

Nonlinear Propagation of Spin Waves in Microscopic Magnetic Stripes

We have studied experimentally with high spatial and temporal resolution propagation of intense spin waves in microscopic Permalloy stripes. We show that the nonlinearity of the spin system of metallic magnetic films together with microscopic-scale confinement effects lead to an anomalous nonlinear magnetic dynamics, such as a nonlinear spatial self-modulation of spin waves characterized by the repulsive nonlinearity. This phenomenon appears to be densely connected with the nonlinear damping in the system. We find that both of these effects develop synchronously on the nanosecond temporal scale.

Transformation of propagating spin-wave modes in microscopic waveguides with variable width

We have studied experimentally the propagation of spin waves in microscopic transversally magnetized permalloy stripe waveguides with variable width. Spatially resolved measurement based on the microfocus Brillouin light-scattering spectroscopy allowed a direct observation of transformations of propagating transverse spin-wave modes in the region of the width transition. Our experiments show that due to the variation in the internal demagnetizing fields caused by the width variation, an effective control of the spin-wave propagation can be achieved. In particular, a splitting of a spin-wave beam into two independent beams or preferred excitation of certain transverse spin-wave modes can be realized.

Field dependence of collective spin modes in transversely magnetized stripes with homogeneous and alternating width

Brillouin light scattering is used to study the spin-wave properties of arrays of closely spaced magnetic stripes with both homogeneous and alternating width, thickness of 30 nm, and edge-to-edge spacing of 55 nm. Experiments are performed with both the transferred wave vector and the applied magnetic field in the direction transverse to the length of the stripes, i.e., in the hard magnetization direction. When the transverse applied field is decreased from a relatively large value (0.15 T) down to zero, the overall direction of the stripe magnetization gradually switches from the transverse to the preferred longitudinal orientation, as confirmed by the shape of the Kerr hysteresis loops. The measured frequencies were compared to numerical calculations obtained for Permalloy stripe arrays by a microscopic dipole-exchange theory. A good overall agreement is achieved between experiment and theory, thanks to the inclusion of the dynamical interstripe dipolar coupling.

Spin waves of a current-injected thin ferromagnetic stripe

Within a micromagnetic model we present the theory of linearized spin waves of a current-carrying rectangular ferromagnetic stripe treated as a slab of infinite extent. After determining the nonuniform scissorlike magnetic ground state that results when a dc electric current is applied along an in-plane easy axis, we calculate both ferromagnetic resonances and spin-wave dispersion as a function of slab thickness. For Permalloy stripes less than $1\text{ }\ensuremath{\mu}\text{m}$ in thickness, increasing current stiffens the response of bulk spin waves, and their dispersion becomes increasingly asymmetric with respect to the easy axis---shifting to lower (higher) frequencies with (opposite) the direction of current. Also, the frequency and direction of propagation of the Damon-Eshbach surface mode are substantially modified by the current, with changed surface-mode behavior exhibited. Above $1\text{ }\ensuremath{\mu}\text{m}$ in thickness the lowest-lying resonance frequency of the Permalloy stripe softens to zero with increasing current and a gap opens up to finite wavelengths along the direction of current, indicative of a ground-state instability. We discuss the implication of our results to the characterization of the magnetic state of these rectangular structures.

Current-Induced Spin-Wave Doppler Shift

Spin transfer appears to be a promising tool for improving spintronics devices. Experiments that quantitatively access the magnitude of the spin transfer are required for a fundamental understanding of this phenomenon. By inductively measuring spin waves propagating along a permalloy strip subjected to a large electrical current, we observed a current-induced spin wave Doppler shift that we relate to the adiabatic spin transfer torque. Because spin waves provide a well-defined system for performing spin transfer, we anticipate that they could be used as an accurate probe of spin-polarized transport in various itinerant ferromagnets.

Brillouin light scattering study of the spin dynamics in nanoscale permalloy stripes: Theory and experiment

The spin-wave modes in nanoscale permalloy stripes are studied using Brillouin light scattering for the case where an external magnetic field is applied transversely to the length of the stripes. By adjusting the magnitude of this external field, the overall magnetization may be varied between the approximately transverse and longitudinal orientations. The observed spin-wave frequencies are analysed using a recently developed microscopic dipole-exchange theory that is particularly appropriate when the magnetization displays strong spatial inhomogeneity. Comparison between theory and experiment for the two sizes of stripes studied gives fairly good agreement, allowing the magnetic parameters of permalloy to be deduced. A small magnetic anisotropy of the easy-plane type is shown to play an important role.

High-frequency characterization of Permalloy nanosized strips using network analyzer ferromagnetic resonance

We report on the dynamic properties of Permalloy nanostrips at gagahertz frequencies. The thickness of the strips is 100nm, strip width is 300nm, strip spacing is 1μm, and length is 0.3–100μm; aspect ratios are 1:1, 1:2, 1:3, 1:5, 1:10, and 1:333. The dynamic behavior was studied by network analyzer ferromagnetic resonance (FMR) using Permalloy strips on a coplanar waveguide in flip-chip geometry. The FMR mode frequencies (fr) can be controlled by the aspect ratio as well as by the applied magnetic field (H). In longer strips (1:10 and 1:333), the excitation frequencies show a soft mode behavior (Heff=990Oe) when the field is along the hard axis. However, along the easy axis (along the strip length), fr increases with applied field. At a field of 3kOe, fr values are almost independent of aspect ratio along the easy axis except for the 1:1 strip. Along the hard axis, the frequencies are strongly dependent upon the aspect ratio. We also observed that the frequency linewidths of the strips are dependent on the aspect ratio.

The rf magnetic-field vector detector based on the spin rectification effect

Ferromagnetic resonances on three Permalloy strips under an in-plane external magnetic field are detected electrically. By measuring and analyzing the angular dependence of the photovoltage induced by the spin rectification effect, an approach is demonstrated for making microwave detectors capable of detecting the rf magnetic field vector at subwavelength scale.

Influence of easy magnetization axis orientation on magnetization reversal in permalloy strips

AbstractWe studied the effect of easy magnetization axis orientation with respect to the strip direction on magnetization reversal process in permalloy strips by measuring the magnetoresistance (MR), the magneto‐optic Kerr effect (MOKE), and the real‐time domain evolution. The three strips were patterned on a single chip with the easy‐axis orientation of each strip relative to the longitudinal direction by around 0, 30, and 60°, respectively. The overall shape of field‐dependent MR was mostly governed by the anisotropic magnetoresistance. The longitudinal MR ratio was significantly increased with increasing angle between the easy axis and the bar direction. Several MR steps were observed during the magnetization reversal in 0 and 30° bars, and the simultaneous measurement of the MOKE and the domain images identified that the MR steps were associated with evolution of the magnetic domains. In addition a resistance contribution from the domain walls was also observed. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

非一様電流による磁壁駆動のマイクロマグネティックシミュレーション

Herein, we introduce a classical expression for describing a spin-polarized current, and propose the effect of a spin-polarized current with a spatial distribution in a micromagnetic framework. The electric current was calculated on the basis of the resistance between neighboring cells in the calculation region. The effect of a spin-polarized current crossing a domain wall in a thin and narrow permalloy strip with a notch was elucidated by micromagnetic calculation. When the magnetic strip has a notch, the highest current density around the notch in the magnetic strip is dominant for domain wall motion. The critical current density increases as the notch size increases. Below the critical current, the domain wall tends to vibrate around the notch. The natural frequency of the wall vibration spectrum increases as the notch size increases, whereas it is almost independent of the current density.