Permalloy Stripes Research Articles

Spin-Cherenkov effect in a magnetic nanostrip with interfacial Dzyaloshinskii-Moriya interaction.

Spin-Cherenkov effect enables strong excitations of spin waves (SWs) with nonlinear wave dispersions. The Dzyaloshinskii-Moriya interaction (DMI) results in anisotropy and nonreciprocity of SWs propagation. In this work, we study the effect of the interfacial DMI on SW Cherenkov excitations in permalloy thin-film strips within the framework of micromagnetism. By performing micromagnetic simulations, it is shown that coherent SWs are excited when the velocity of a moving magnetic source exceeds the propagation velocity of the SWs. Moreover, the threshold velocity of the moving magnetic source with finite DMI can be reduced compared to the case of zero DMI. It thereby provides a promising route towards efficient spin wave generation and propagation, with potential applications in spintronic and magnonic devices.

Magnetic domain-wall dynamics in wide permalloy strips

Domain walls in soft permalloy strips may exhibit various equilibrium micromagnetic structures depending on the width and thickness of the strip, ranging from the well-known transverse and vortex walls in narrow and thin strips to double and triple vortex walls recently reported in wider strips [V. Est\'evez and L. Laurson, Phys. Rev. B {\bf 91}, 054407 (2015)]. Here we analyze the field driven dynamics of such domain walls in permalloy strips of widths from 240 nm up to 6 $\mu$m, using the known equilibrium domain wall structures as initial configurations. Our micromagnetic simulations show that the domain wall dynamics in wide strips is very complex, and depends strongly on the geometry of the system, as well as on the magnitude of the driving field. We discuss in detail the rich variety of the dynamical behaviors found, including dynamic transitions between different domain wall structures, periodic dynamics of a vortex core close to the strip edge, transitions towards simpler domain wall structures of the multi-vortex domain walls controlled by vortex polarity, and the fact that for some combinations of the strip geometry and the driving field the system cannot support a compact domain wall.

Domain wall dynamics along curved strips under current pulses: The influence of Joule heating

The current-induced domain wall dynamics along curved ferromagnetic strips is studied by coupling the magnetization dynamics to the heat transport. Permalloy strips with uniform and non-uniform cross section are evaluated, taking into account the influence of the electrical contacts used to inject the current pulses and the substrate on top of which the ferromagnetic strip is sited. Micromagnetic simulations indicate that the geometry and the non-ferromagnetic materials in the system play a significant role in the current-induced domain wall dynamics. Due to the natural pinning, domain walls are hardly affected by the spin-transfer torques when placed in uniform cross section strips under current pulses with reduced magnitude. On the contrary, the current-induced domain wall displacement is significantly different in strips with non-uniform cross section, where thermal gradients emerge as due to the Joule heating. It is found that these thermal gradients can assist or act against the pure spin-transfer torques, in agreement with the recent experimental observations.

Head-to-head domain wall structures in wide permalloy strips

We analyze the equilibrium micromagnetic domain wall structures encountered in Permalloy strips of a wide range of thicknesses and widths, with strip widths up to several micrometers. By performing an extensive set of micromagnetic simulations, we show that the equilibrium phase diagram of the domain wall structures exhibits in addition to the previously found structures (symmetric and asymmetric transverse walls, vortex wall) also double vortex and triple vortex domain walls for large enough strip widths and thicknesses. Also several metastable domain wall structures are found for wide and/or thick strips. We discuss the details of the relaxation process from random magnetization initial states towards the stable domain wall structure, and show that our results are robust with respect to changes of e.g. the magnitude of the Gilbert damping constant and details of the initial conditions.

Angular dependent study on ferromagnetic resonance and spin excitations by spin rectification

We report angular dependent spin rectification spectra which are applied to studying spin excitations in single permalloy stripe. Based on planar Hall effect, those spin excitations generate special resonant dc Hall voltages, which have been characterized as functions of the amplitude and direction of applied magnetic field. Through high angular resolution 2D mappings, the evolutions of different spin excitation can be directly presented, and the dynamic magnetic parameters such as the gyromagnetic ratio, effective exchange field, as well as the quantized numbers of standing spin waves can be accurately determined through fitting the angular evolution of each resonance.

Ferromagnetic Resonance Line Shapes in Permalloy Strips at Low Magnetic Fields

Spin rectification line shapes for ferromagnetic resonance in swept, low external bias fields differ significantly from widely investigated high-field resonant spectra. The anomaly in the low-field case may originate from magnetization rotation associated with magnetic anisotropy and demagnetization. The low-field, rectified voltage spectra are also sensitive to the relative phase and polarization of the microwave field. Ferromagnetic thin strips thus have the potential for use as polarization- and phase-resolved microwave detectors at low fields.

Bolometer detection of magnetic resonances in nanoscaled objects

We report on a nanoscaled thermocouple (ThC) as a temperature sensor of a highly sensitive bolometer for probing the dissipative damping of spin dynamics in nanosized Permalloy (Py) stripes. The Au-Pd ThC based device is fabricated by standard electron beam lithography on a 200 nm silicon nitride membrane to minimize heat dissipation through the substrate. We show that this thermal sensor allows not only measurements of the temperature change on the order of a few mK due to the uniform resonant microwave (MW) absorption by the Py stripe but also detection of standing spin waves of different mode numbers. Using a 3D finite element method, we estimate the absorbed MW power by the stripe in resonance and prove the necessity of using substrates with an extremely low heat dissipation like a silicon nitride membrane for successful thermal detection. The voltage responsivity and the noise equivalent power for the ThC-based bolometer are equal to 15 V W−1 and 3 nW Hz−1/2, respectively. The ThC device offers a magnetic resonance response of 1 nV/(μB W) corresponding to a sensitivity of 109 spins and a temperature resolution of 300 μK under vacuum conditions.

Ferromagnetic resonance micromagnetic studies in patterned permalloy thin films and stripes

We present micromagnetic simulations of ferromagnetic resonance in patterned permalloy films and isolated stripes. Films of the total thickness 20 nm or 40 nm are patterned in the form of 1D periodic structures with rectangular profile (rectangular grooves of depth varying from zero up to the film thickness) and in-plane period of 500 nm. The direction of the applied dc magnetic field is varied in the film plane from the direction parallel to the stripes to perpendicular one. The thickness of the patterned elements and direction of the bias field affect essentially the resonance peaks (changing their position, amplitude and number) and the corresponding dynamical magnetization profiles. We simulated from one up to three ferromagnetic resonance peaks and found the areas of microwave magnetization localization for them.

Spin wave non-reciprocity and beating in permalloy by the time-resolved magneto-optical Kerr effect

We studied the propagation characteristics of spin wave modes in a permalloy stripe by time-resolved magneto-optical Kerr effect techniques. We observed a beating interference pattern in the time domain under the influence of an electrical square pulse excitation at the centre of the stripe. We also probed the non-reciprocal behaviour of propagating spin waves with a dependence on the external magnetic field. Spatial dependence studies showed that localized edge mode spin waves have a lower frequency than the spin waves at the centre of the stripe, due to the varying magnetization vector across the width of the stripe.

Magnetic shielding for DAMPE electromagnetic calorimeter PMTs

The magnetic characteristics of R5610A-01 photomultiplier tubes are studied in this paper. The experimental data shows that the gain of R5610A-01 loses about 53% when the magnetic field is 3 Gs along its +X axis. A cylinder of one-layer permalloy strip is able to reduce the effect of a 3 Gs magnetic field on the PMT gain to less than 1%.

Microwave-Induced DC Response of Spin Wave Resonance Driven by an Anisotropic Built-In Field in a Permalloy Thin Strip

The microwave-induced dc response has been investigated in an in-plane magnetized permalloy strip. The spin wave resonances (SWRs) are observed. The SWR signals get anomalously suppressed when the direction of the specimen or the amplitude of the microwave frequencies is changed. Such suppression occurs at frequencies of less than 11 GHz, while the resonant field is as weak as less than 200 Oe. They are finally quantitatively interpreted by introducing an anisotropic built-in magnetic field that describes the shape anisotropy of the specimen.

Coupling of spinwave modes in wire structures

We investigate the magnon dispersion of spinwaves propagating in a Permalloy stripe and compare it to a plain film. We use a Scanning Kerr Microscope to directly image their spatial propagation- and decay properties as well as micromagnetic simulations to extract additional information about the static magnetization distribution. For low external fields, we find anti-crossings for the dispersion branches corresponding to different transverse wave vectors that also occur as minima of the decay length for the spinwave.

An integrated planar magnetic micropump

This paper presents an integrated magnetic micropump that uses in-plane compliance-based check valves and a magnetically actuated membrane. The device, which allows for simple fabrication and system integration with other functional elements, consists of two functional layers both fabricated from poly(dimethylsiloxane) (PDMS). The upper PDMS layer provides a compliant membrane with an electroplated thin-film permalloy strip for actuation, while the lower PDMS layer incorporates microfluidic components including the microchannels, pump chamber, and a pair of check valves for flow regulation. The PDMS check valves, each having a compliant flap in contact with a stiff stopper to allow for unidirectional fluid flow with minimized leakage, are located at the inlet and outlet of the pump chamber, respectively. As such, the unidirectional flow at a controlled volumetric rate can be readily generated in accordance with the pumping actions. Systematic characterization of the micropump has been performed by studying the dependence of its pumping flow rate on the driving frequency of magnetic actuation, and the back pressure. Experimental results show that this micropump is capable of generating fluid flow of 0.15 μL/min at the frequency of 2Hz, corresponding to a volume resolution of 1 nL per stroke, and working reliably against a maximum back-pressure of 550Pa, demonstrating the potential application of this micropump for various integrated lab-on-a-chip systems.

The Role of the Oersted Field on the Current-Driven Domain Wall Dynamics Along Wires With Square Cross Section

Current-driven domain wall dynamics in long Permalloy strips with square cross section, taking into account the influence of the Oersted field and the nonadiabatic spin-torque term, are studied in this work. Depending on the size of the square cross section two types of domain wall configurations can be nucleated, transverse or Bloch-point walls. The transverse wall dynamics showed a linear relation between the wall velocity and the applied current density. Also seen for this type of wall is that its dynamic is practically unaffected by either the presence of the Oersted field or the value of the nonadiabatic parameter, and its behavior resembles the one seen in cylindrical wires as it also does not have a Walker breakdown. In the case of the Bloch-point wall there is a threshold current density in order to promote the wall movement and it also depends on the value of the nonadiabatic parameter. The effect of the Oersted field for some values of the nonadiabatic parameter is the increase of the wall's velocity and reduction of its width. For values above 1013 A · m-2 the wall transforms into complex unstable structures.

Kerr-Imaged Edge-Curling Wall Effects of Narrow Magnetic Cores

Magnetic cores produced by laminating alternating magnetic/nonmagnetic layers have been shown to eliminate closure domains by linking flux vertically between magnetic layers at the edge of the film. Closure domains, which do not contribute significantly to the permeability, are undesired in patterned magnetic cores for transformers since they reduce the inductance. The inductance of narrow magnetic core transformers was found to drop with increasing frequency. Kerr images of these cores reveal partial closure domains at the edges, which explain the inductance behavior. Edge domain effects are explained based upon energy models of laminated Permalloy strips.

Standing spin waves in magnonic crystals

The features of standing spin waves (SWs) excited during ferromagnetic resonance in three different one-dimensional magnonic crystals (MC) are intensively studied. The investigated magnonic crystals were: an array of air-spaced cobalt stripes, an array of air-spaced permalloy (Py) stripes, and a bi-component MC composed of alternating Co and Py stripes. All MC structures were made by etching technique from Co and Py thin films deposited onto Si substrates. Two configurations are considered with the in-plane external magnetic field applied parallel or perpendicular to the stripes. The supporting calculations are performed by the finite element method in the frequency domain. A number of intensive SW modes occurred in periodic structures under ferromagnetic resonance conditions as a consequence of standing spin waves excitation. These modes were analyzed theoretically in order to explain the origins of SW excitations. With the support of numerical calculations, we analyze also the possible scenarios for the occurrence of standing SWs in the investigated structures. It is demonstrated that the SW propagation length is an important factor conditioning the standing SW formation in MCs.

Thermoelectric Detection of Spin Waves

We report on the thermoelectric detection of spin waves in Permalloy stripes via the anomalous Nernst effect. Spin waves are locally excited by a dynamic magnetic field generated from a microwave current flowing in a coplanar waveguide placed on top of a Permalloy stripe, which acts as a waveguide for spin waves. Electric contacts at the ends of the Permalloy stripe measure a dc voltage generated along the stripe. Magnetic field sweeps for different applied microwave frequencies reveal, with a remarkable signal-to-noise ratio, an electric voltage signature characteristic of spin-wave excitations. The symmetry of the signal with respect to the applied magnetic field direction indicates that the anomalous Nernst effect is responsible; Seebeck effects, anisotropic magnetoresistance, and voltages due to spin-motive forces are excluded. The dissipation of spin waves causes local heating that drains into the substrate, giving rise to a temperature gradient perpendicular to the sample plane, resulting in the anomalous Nernst voltage.

Effect of magnetization pinning on the spectrum of spin waves in magnonic antidot waveguides

We study the spin-wave spectra in magnonic antidot waveguides (MAWs) for two limiting cases (strong and negligible) of the surface anisotropy at the ferromagnet/air interface. The MAWs under investigation have the form of a thin stripe of permalloy with a single row of periodically arranged antidots in the middle. The introduction of a magnetization pinning at the edges of the permalloy stripe and the edges of antidots is found to modify the spin-wave spectrum. This effect is shown to be necessary for magnonic gaps to open in the considered systems. Our study demonstrates that the surface anisotropy can be crucial in the practical applications of MAWs and related structures and in the interpretation of experimental results in one- and two-dimensional magnonic crystals. We used three different numerical methods, i.e., plane waves method (PWM), finite difference method, and finite element method to validate the results. We showed that PWM in the present formulation assumes pinned magnetization, while in micromagnetic simulations special care must be taken to introduce pinning.

Two-dimensional spectroscopic imaging of individual ferromagnetic nanostripes

We use ferromagnetic-resonance force microscopy to spectroscopically image the edge modes in individual 700 nm and 400 nm wide Permalloy stripes with a spatial resolution on the order of 200 nm. The imaging clearly identifies some resonances as edge modes in stripes in a case where mode identification by comparison with micromagnetic modeling is not clear. Combined spectroscopic and spatial scans reveal clear differences in the edge mode resonances at opposite edges of the stripes as well as inhomogeneity along the length of the stripe.

Direct observation of nonlinear four-magnon scattering in spin-wave microconduits

We demonstrate the intrinsic nonlinear dynamics of spin waves due to four-magnon scattering processes in a micrometer sized permalloy stripe. Spin waves are excited by a microwave current transmitted through a coplanar waveguide and the spin-wave spectrum is locally probed by Brillouin light scattering microscopy for a wide range of excitation powers. We find a transition from a purely monochromatic excitation of spin waves at low microwave powers to a large broadening of the spectrum above a certain threshold power. The spectral distributions of the measured spin waves show a unique profile, which is in excellent agreement with theoretical expectations for four-magnon scattering processes.