Permalloy Dots Research Articles

Ferromagnetic resonance force microscopy studies of arrays of micron size permalloy dots

The dynamic magnetic properties of micron-sized permalloy disks have been investigated using magnetic resonance force microscopy. From local spectroscopy data, information about the global sample properties is obtained. The experimental results are in good agreement with theoretical predictions, which account for magnetostatic modes with quantized in-plane wave vector. Ferromagnetic resonance spectral features due to the permalloy dots in close proximity to the micromagnetic probe tip provide two-dimensional images of the sample.

Superconducting memory based on ferromagnetism

Answering to the need for dense superconducting memories, the authors propose a memory concept that combines ferromagnetic dots for the storage of the data and Josephson junctions for their readout. Good scalability is expected for large scale integration. Exploratory memory cells have been implemented using 3μm Nb technology and Permalloy dots. Nonvolatile data storage at 300K was demonstrated.

Origin of fourfold anisotropy in square lattices of circular ferromagnetic dots

We discuss the fourfold anisotropy of the in-plane ferromagnetic resonance field ${H}_{r}$, found in a square lattice of circular Permalloy dots when the interdot distance $a$ becomes comparable to the dot diameter $d$. The minimum ${H}_{r}$ along the lattice ⟨11⟩ axes and the maximum along the ⟨10⟩ axes differ by $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{Oe}$ at $a∕d=1.1$. This anisotropy, not expected in uniformly magnetized dots, is explained by a mechanism of nonuniform magnetization $\mathbf{m}(\mathbf{r})$ in a dot in response to dipolar forces in the patterned magnetic structure under strong enough applied field. It is well described by an iterative solution of a continuous variational procedure.

Theory of spin wave modes in tangentially magnetized thin cylindrical dots: A variational approach

We present a theoretical study of the quantized spin wave spectrum in tangentially magnetized cylindrical thin magnetic dots. Low-energy spin waves in magnetic dots may be subdivided into four families: Damon-Eshbach like, backward like, mixed, and end modes. Frequencies and mode profiles are found using a variational approach based on carefully chosen trial functions. The variational method has the advantage that it can be used for large dots that are not practical to treat using numerical finite-element methods. Results for small dots generated using the variational method compare well with micromagnetic results. The variational method is demonstrated with an analysis of data obtained from experimental Brillouin light scattering data from saturated thin cylindrical Permalloy dots. Our approach allows for the definition of parameters describing important contributions to the spin wave energies. As an example, we show that a variational parameter $ϵ$ provides a measure of spin wave localization near the dot border for one class of modes.

Soft magnetic dot as a linear flux amplifier

It has been demonstrated that the critical current versus the applied flux relationship of an Al superconducting loop enclosing a soft Permalloy magnetic dot has a variable field-dependent phase. It is, therefore, possible to use this structure as a magnetic flux amplifier for applications in superconducting quantum interference devices. The dimensions of a single-domain Permalloy dot were selected in such a way that the preferential orientation of the magnetization is rotated from the perpendicular direction. By increasing an applied magnetic field, the magnetization of the dot rotates towards the out-of-plane direction. This magnetization rotation provides a flux gain and an enhancement of the field sensitivity. In the low-field regime, where the structure was investigated, the magnetization of the dot changes linearly with the applied flux and the flux gain is constant. As a result of a pronounced shape anisotropy, the flux gain can be tuned by adjusting the dimensions of the dot.

Normal mode splitting in interacting arrays of cylindrical permalloy dots

Brillouin light scattering has been exploited to study the dependence of the spin-wave spectrum on the interdot distance in squared arrays of circular permalloy dots with radius R=100nm, thickness L=50nm, and interdot spacing (s) variable in the range between 50 and 800nm. The experimental data have been satisfactorily reproduced using a micromagnetic approach which solves the discretized Landau-Lifshitz-Gilbert equation over a 3×3 matrix of differently spaced circular dots and performing a local Fourier transform. This approach enabled us to clarify that, on reducing the s∕R ratio, some of the normal modes existing within each isolated dot increase their frequency retaining their own character. The fundamental mode, instead, splits into three modes characterized by different profiles of the dynamic magnetization. For all these modes, hybriditazion effects have also been observed.

Detection of the domain structure change using magnetotransport for a series of circular Permalloy dots

The magnetic structure of a magnetic dot depends on its geometrical factors such as thickness and dot size and can be either a multidomain state or a vortex state. The magnetoresistance (MR) of a series of magnetic dots with diameters ranging from 0.3to5μm was measured to investigate the correlation between domain-structure and magnetotransport properties. A dot with a diameter of less than 2μm has a domain of vortex state at remanence and demonstrates similar reversible MR results. Moreover, the behaviors of MR show clear changes corresponding to the domain-structure change from vortex to multidomain states with an increasing dot diameter. Data can be qualitatively described by the anisotropic magnetoresistive effect. Hence, our results show that the magnetotransport can be a tool to detect the magnetic domain structure of a submicron magnetic dot.

Vortex magnetodynamics: Ferromagnetic resonance in permalloy dot arrays

Permalloy dot arrays (square lattices of 100, 200, 500, and 1000 nm dots, 40 nm thick) have been fabricated using e-beam lithography. Hysteresis loops show vortex states at remanence in all samples. Variable frequency ferromagnetic resonance was used to probe the dynamics of both vortex and single domain states. The uniform resonance mode is present at fields above the vortex annihilation when field sweeping up and vortex nucleation field when field sweeping down. In the vortex state multiple resonances are observed in the 500 and 1000 nm samples, but interestingly, not in the 100 and 200 nm. In the frequency/field dispersion curve, these vortex resonances exhibit optical mode characteristics, whereas the uniform mode exhibits the expected acoustic mode behavior. Resonance modes corresponding to the annihilation and creation field (transition from vortex to single domain or verse versa) are also observed and discussed.

Microwave spectrum of square Permalloy dots: Quasisaturated state

We report on an experimental and theoretical study of the spin-wave spectrum $(1--20\phantom{\rule{0.3em}{0ex}}\mathrm{GHz})$ in square Permalloy dots ($30\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick, $3\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ wide) subjected to a saturating in-plane field $(10--150\phantom{\rule{0.3em}{0ex}}\mathrm{mT})$. By changing the pumping geometry, we could favor the excitation of modes with different spatial profiles. Spin-wave frequencies and mode profiles were estimated using both numerical calculations (a micromagnetic simulation and a diagonalization of the dynamical matrix) and approximate methods (use of a quantization condition and of a simplified micromagnetic edge potential). Comparison between the measurements and those calculations allows us to identify unambiguously up to 13 modes. Among those modes, we distinguish magnetostatic waves quantized both parallel (i) and perpendicular (ii) to the magnetization, spin-wave wells (iii), and a mode condensation feature (iv) resulting from a large density of states close to a minimum in the spin-wave dispersion.

Magnetic Vortex Core Dynamics in Cylindrical Ferromagnetic Dots

We report direct imaging by means of x-ray photoemission electron microscopy of the dynamics of magnetic vortices confined in micron-sized circular permalloy dots that are 30 nm thick. The vortex core positions oscillate on a 10 ns time scale in a self-induced magnetostatic potential well after the in-plane magnetic field is turned off. The measured oscillation frequencies as a function of the aspect ratio of the dots are in agreement with theoretical calculations presented for the same geometry.

Shifting and Pinning of a Magnetic Vortex Core in a Permalloy Dot by a Magnetic Field

Magnetic pinning in thin films seems to be a major research subject in the near future, as it is involved in all switching processes which include a movement of a domain wall or a magnetic vortex. We used Lorentz transmission electron microscopy and vortex pinning at artificial pinning sites to investigate the pinning behavior of magnetic vortices for the first time with high spatial resolution.

Spin dynamics in thin nanometric elliptical Permalloy dots: A Brillouin light scattering investigation as a function of dot eccentricity

Brillouin light scattering (BLS) spectra have been measured in arrays of cylindrical Permalloy dots with elliptical cross section, $200\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ wide, $15\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick, and eccentricities from 1 to 3. Several spin modes are observed and their frequencies tracked as a function of the direction of the applied $1.5\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$ magnetic field $\mathbit{H}$. The experimental data are interpreted within the framework of the recently introduced dynamical matrix method to calculate spin excitations in magnetic particles. We find that the mode frequencies strongly depend on the eccentricity of the dots and on the direction of the applied field. For fields along the principal axes the solutions can be classified into: (i) modes localized near the particle ends, (ii) modes with nodal lines perpendicular to $\mathbit{H}$ (backwardlike modes), (iii) modes with nodal lines parallel to $\mathbit{H}$ (Damon-Eshbach-like modes) and (iv) modes with both parallel and perpendicular nodal lines. In cases where the frequencies of two modes in different families are similar, some hybridization between the modes is observed. For $\mathbit{H}$ along nonsymmetry directions only the modes of type (i) remain reasonably well defined, other modes can at best be described as hybrids of modes in the above categories. Determining which of the modes is active in BLS experiments leads to excellent agreement with the experimental results.

Linear magnetic flux amplifier

By measuring the critical current versus the applied magnetic field Ic(Φ) of an Al superconducting loop enclosing a soft Permalloy magnetic dot, we demonstrate that it is feasible to design a linear magnetic flux amplifier for applications in superconducting quantum interference devices. The selected dimensions of a single-domain Permalloy dot provide that the preferential orientation of the magnetization is rotated from the perpendicular direction. By increasing an applied magnetic field, the magnetization of the dot coherently rotates toward the out-of-plane direction, thus providing a flux gain and an enhancement of the sensitivity. As a result of a pronounced shape anisotropy, the flux gain generated by the dot can be tuned by adjusting the dimensions of the dot.

Scanning magnetoresistive microscopy study of quasi-static magnetic switching in mesoscopic square dots: observation of field-driven transition between flux-closure states

We used newly developed scanning magnetoresistance microscopy (SMRM) to observe time-lapsed magnetic domain images during magnetic switching in square Permalloy dots. Unlike magnetic force microscopy, the SMRM images measure the absolute local magnetic field from any microstructure. SMRM works in an external magnetic field, allowing the measurement of evolution of quasi-static domain structures. We observed a complete magnetic reversal in 5 /spl mu/m Permalloy dots from a positively saturated state to a negatively saturated state via a mixture of flux-closure states. We also observed field-driven transitions between the various flux closure states at low fields. There appears to be a distribution of switching field and mode, even for geometrically identical dots. This work demonstrates the novel capability of the SMRM technique and the rich switching physics of magnetic square dots.

Magnetization reversal in patterned double-vortex structures

The magnetization reversal process for micron and submicron disk-shaped dots is controlled by successive nucleation, displacement, and annihilation of a magnetic vortex. Here the reversal process for a system involving two ferromagnetic disks separated by a nonmagnetic spacer is investigated experimentally, analytically, and numerically. Permalloy (Ni80Fe20 or Py) dots with thicknesses of up to 40nm and diameters of 0.5–2.5μm separated by a copper spacer (1–45nm thick) were considered. Micromagnetic simulations indicate that the disks will each support oppositely directed vortices at remanence and also show the hysteresis of the coupled structures. The calculations are compared to hysteresis loops and x-ray photoemission electron microscopy images of Py∕Cu∕Py dots produced by electron-beam lithography and magnetron sputtering.

True Single Domain and Configuration-Assisted Switching of Submicron Permalloy Dots Observed by Electron Holography

The switching behavior of submicron circular Permalloy nanomagnets has been investigated. Electron holography provides a magnetic resolution of down to 10 nm. This allows us to observe in detail the switching and to measure the induction within single nanodots with diameters down to 150 nm at a thickness of 6 nm. Particles of these dimensions show a single domain state during the whole switching process which takes place at external fields of only a few 100 A/m. For larger or thicker particles the magnetization reversal runs via the formation of a C state or an intermediate vortex state.

Magnetic field dependence of quantized and localized spin wave modes in thin rectangularmagnetic dots

The magnetic field dependences of the frequencies of standing spin-wavemodes in a tangentially magnetized array of thin rectangular permalloy dots(800 × 550 nm) were measured experimentally by a Brillouin light scattering technique and calculatedtheoretically using an approximate size-dependent quantization of the spin-wavevectorcomponents in the dipole-exchange dispersion equation for spin waves propagating in acontinuous magnetic film. It was found that the inhomogeneous internal bias magnetic fieldof the dot has a strong influence on the profiles of the lowest spin-wave standing modes. Inaddition, the dynamic magnetization distributions found for both longitudinally andtransversely magnetized long magnetic stripes gives a good approximation for modedistributions in a rectangular dot magnetized along one of its in-plane sides. Anapproximate analytic theory of exchange-dominated spin-wave modes, strongly localizedalong the dot edge that is perpendicular to the bias magnetic field, is developed. Agood quantitative agreement with the results of the BLS experiment is found.

Correlated vortex chiralities in interacting permalloy dot patterns

Magnetostatic interactions in different polycrystalline permalloy dot patterns for dots with diameter 900nm and thickness 30nm are investigated through magnetic force microscopy imaging, magneto-optic Kerr effect measurements, and micromagnetic simulations. Magnetization reversal occurs through vortex nucleation∕annihilation. Vortex nucleation and annihilation fields for different interacting arrays were observed to vary with pattern type and with the applied field direction and were shown to follow the prediction of a simple point-dipole model. The vortex chirality was established by imaging vortices in a small applied field. The vortex chirality distribution was determined for different arrays and a well-defined ordering phenomenon of the vortex chirality was observed in two-dot and zigzag-dot chain patterns as well as in a honeycomb array of dots. Micromagnetic simulations well account for the type of vortex chirality ordering observed and attribute it to magnetostatic interactions that induce correlated C-state magnetization configurations among nearest neighbor dots prior to vortex nucleation.

Switching of Single Domain Permalloy Dots Observed by Electron Holography

Extended abstract of a paper presented at Microscopy and Microanalysis 2004 in Savannah, Georgia, USA, August 1–5, 2004.

Nonuniform magnetization reversals in elliptical permalloy dots

Reversible and irreversible magnetization processes of the single-domain elliptical permalloy dot are studied by simulation. The magnetization curve of the reversible process obtained by applying the field along the hard axis of the elliptical dot is almost linear, as is the case in the single-domain ellipsoidal particle. Due to the occurrence of the non uniform reversal, the switching field is reduced significantly compared to that predicted by the Stoner–Wohlfarth model. The nucleation fields of elliptical dots are calculated as a function of ellipse's aspect ratio, and the function reveals a step-like behavior.