Ferromagnetic Resonance Response Research Articles

Rare earth doped M-type hexaferrites; ferromagnetic resonance and magnetization dynamics

M-type hexagonal barium ferrites come in the category of magnetic material that plays a key role in electromagnetic wave propagation in various microwave devices. Due to their large magnetic anisotropy and large magnetization, their operating frequency exceeds above 50 GHz. Doping is a way to vary its magnetic properties to such an extent that its ferromagnetic resonance (FMR) response can be tuned over a broad frequency band. We have done a complete FMR study of rare earth elements neodymium (Nd) and samarium (Sm), with cobalt (Co) as base, doped hexaferrite nanoparticles (NPs). X-ray diffractometry, vibrating sample magnetometer (VSM), and ferromagnetic resonance (FMR) techniques were used to characterize the microstructure and magnetic properties of doped hexaferrite nanoparticles. Using proper theoretical electromagnetic models, various parameters are extracted from FMR data which play important role in designing and fabricating high-frequency microwave devices.

Voltage-Tuned Transport Properties and Ferromagnetic Resonance in Lanthanum-Strontium-Manganite/Lead-Magnesium–Niobate-Lead-Titanate Multiferroic Heterostructures

We demonstrate piezostrain-induced modulation of transport and ferromagnetic resonance (FMR) properties in the La 0.5Sr0.5MnO3 (LSMO5)/0.7Pb(Mg1/3Nb2/3)O3 -0.3PbTiO3 (PMN-PT) (0 0 1) multiferroic heterostructures. The poling strain leads to the enhancement of the double exchange interaction and the reduction of Jahn–Teller electron-lattice distortion in the LSMO5 film, showing a maximum resistance decrease of 27% at 105 K, around which temperature the maximum magnetoresistance change of 10% is tuned by the piezostrain. The FMR response to the strain changes is probed by temperature-dependent electron spin resonance spectra, showing the largest FMR field shift of 220 Oe at the Neel temperature of 193 K. The magnetoelectric coupling behavior at the antiferromagnetic phase of LSMO5 film was dominated by the two-magnon scattering effect, which provides a new route for voltage-controllable magnetism in future spintronic devices.

Theory of ferromagnetic resonance driven by the combined action of spin-transfer torque and voltage-controlled magnetic anisotropy

An analytical study of the spectral line shape of ferromagnetic resonance (FMR) detected by spin rectification effect and driven by the combined action of spin-transfer torque (STT) and voltage-controlled magnetic anisotropy (VCMA) is developed. The system under consideration consists of a magnetic tunnel junction (MTJ). Explicit expressions for the symmetric and asymmetric components of the rectified voltage are derived, where the role of the VCMA, in-plane STT, and field-like torque is clearly identified and discussed. Typical geometrical configurations are particularly analyzed and compared with recent experimental results. The analytical findings show that the change of sign in the FMR response upon reversal of the magnetization is completely due to VCMA. By distinguishing in-plane, out-of-plane, and full magnetization reversal processes, it is shown that the VCMA induces a change of sign in the symmetric part for the in-plane and out-of-plane magnetization reversal, while the asymmetric part change its sign under a full and in-plane reversion of the magnetization. Explicit expressions of the symmetric and asymmetric contributions of the spectral line shape allow us to detect under what conditions the STT and VCMA can increase or decrease the FMR spectral line shape. The proposed theory allows access to a better understanding of the physics behind ferromagnetic resonance phenomena, promoting potential applications in STT+VCMA-based MTJs.

Ferromagnetic Resonance Measurement Using a Novel Short Circuited Coaxial Probe Technique

A versatile technique to characterize the ferromagnetic resonance (FMR) of ferrite samples using a short circuited coaxial probe is presented. The technique has sensitivity comparable to that of well-established methods besides its non-contact nature, broadband and local. Detailed theoretical approach and simulation studies (Proof of Concept) using HFSS are presented. Microwave measurements on different single crystal and polycrystalline samples (Yttrium Iron Garnet (Y3Fe5O12) YIG and Nickel Ferrite (NiFe2O4) NFO have been performed. We measured the FMR response of these samples as a function of frequency and the data showed the expected variation for both in plane and out of plane magnetic fields.

A two dimensional analytical model for the study of ferromagnetic resonance responses of single and multilayer films

An advanced analytical formulation to model the response of coplanar and stripline based broadband ferromagnetic resonance (FMR) for single and multilayer ferromagnetic films is presented. Several numerical examples are provided implementing the formulation. The model accounts for exchange interactions as well as exchange boundary conditions at the film surfaces and the film interfaces (in the case of multilayer films). The solutions to the Landau-Lifshitz equation and relevant Maxwell's equations are conducted in Fourier space and are transformed back to real space as required to ensure computational efficiency and to avoid length scale incompatibility due to the experiment geometry. This work presents several numerical examples pertaining to the effect of waveguide geometry and microwave eddy current shielding on the shape of coplanar and stripline FMR responses of single-layer ferromagnetic films. Additionally, the effect of microwave eddy current shielding and distance (dielectric spacer thickness) of the film from the transducer on the stripline FMR responses, dynamic magnetization, magnetic field strength, and precession angle for multilayer film samples is discussed.

Microwave magnetic properties of spinel ferrite films deposited by one-step electrochemical method

Spinel ferrites have been widely used in microwave devices due to their excellent electromagnetic properties. In this study, two kinds of spinel ferrite films, Fe3O4 and Co xFe3-xO4, were grown on Pt(111)/Ti/SiO2/Si substrates by one-step electrochemical deposition method. The XRD and SEM characterizations demonstrated that the orientation of the ferrite films changed from (111) to (100) with the increase of depositing time. The cobalt content within Co xFe3-xO4 films was studied in detail by EDS analysis. The ferromagnetic resonance (FMR) responses of the ferrite films were measured by the flip-chip method using a vector network analyzer (VNA). It showed that the FMR frequency of Fe3O4 films reached to 10.5GHz under an out-plane magnetic field of 5 kOe, while it reached to 27GHz under an in-plane magnetic field of 5kOe for Co xFe3-xO4 films. Meanwhile, whether the magnetic field was applied parallelly or perpendicularly, the resonant peaks were increased linearly with increasing the magnetic field, indicating that the films are promising candidates for applications in tunable wave-absorbing materials or other tunable frequency devices.

Theoretical Study of the Stripline Ferromagnetic Resonance Response of Metallic Ferromagnetic Films Based on an Analytical Model

We develop an advanced analytical model for calculating the broadband stripline ferromagnetic resonance (FMR) response for metallic ferromagnetic films, taking into account the exchange interaction as well as the exchange boundary conditions at the film surface. This approach leads to simple analytical expressions in the Fourier space. As a result, a numerical code which implements inverse Fourier transform of these equations is very quick. This allows us to explore a wide space of parameters as numerical examples of application of this theory. In particular, we investigate the joint effects of microwave eddy current shielding and magnetization pinning at the ferromagnetic film surfaces on the shape of the stripline FMR response of the film.

Ferromagnetic resonance of an heterogeneous multilayer system with interlayer exchange coupling: an accessible model

We present a general model for the coupled magnetic resonances of an exchange interacting multilayer system, which can be implemented without complex analytical calculations or numerical simulations. The model allows one to study the spin wave modes of a multilayer structure with any number of layers, accounting for individual uniaxial and cubic anisotropies, and (static and dynamic) demagnetizing and external fields as well, assuming that only the interlayer exchange coupling mechanism is relevant between such magnetic layers. This scheme is applied to recent measurements of a NiFe/CoFe bilayer, and to studying the influence of the strength of ferromagnetic and antiferromagnetic exchange interactions and the applied field orientation on the spin wave modes and intensities of the ferromagnetic resonance response. We find that the acoustic oscillation mode tends to stabilize in frequency if the magnetizations of the layers are parallel to each other, while the optical mode stabilizes when the magnetizations are antiparallel. Furthermore, we find that each oscillation mode is governed by either the NiFe or the CoFe. The modes swap the governing layer as the perpendicular field increases, inducing a gap between their frequencies, which appears to be proportional to the exchange coupling. Finally, we find that the field linewidth of the bilayer due to Gilbert damping has a dependence on the frequency very similar to the linear dependence of the linewidth in single layers. The theoretical scheme presented here can be further used to explore magnetization dynamics in different multilayer architectures—such as exchange springs, structures with perpendicular magnetic anisotropy, and complex compositions of layer stacks—and can be useful as a basis to study multilayers with chiral and dipolar interactions.

Cantilever detected ferromagnetic resonance in thin Fe50Ni50, Co2FeAl0.5Si0.5 and Sr2FeMoO6 films using a double modulation technique

In this work we introduce a new method, which employs commercial piezo-cantilevers, for a ferromagnetic resonance (FMR) detection from thin, nm-size, films. Our setup has an option to rotate the sample in the magnetic field and it operates up to the high microwave frequencies of 160GHz. Using our cantilever based FMR spectrometer we have investigated a set of samples, namely quasi-bulk and 84nm film Co2FeAl0.5Si0.5 samples, 16nm Fe50Ni50 film and 150nm Sr2FeMoO6 film. Low frequency and room temperature test of our setup using 84nm Co2FeAl0.5Si0.5 film yielded a result identical to a standard X-Band spectrometer, namely a single line with quite small linewidth. Our measurements at low temperatures and high frequencies revealed a quite strong FMR response detected in all samples. The FMR spectra share common features, such as the emergence of the second line with an opposite angular dependence, and a drastic increase of the linewidths with increasing microwave frequency. We believe that these findings are results of the complicated dynamics of the magnetization at low temperatures and high frequencies, which we were able to probe using our cantilever based FMR setup.

Sensitivity Enhancement of a Pd/Co Bilayer Film for Hydrogen Gas Sensing Using a Perpendicular-to-Plane Ferromagnetic Resonance Configuration

Previously, it has been shown that the strength of the perpendicular magnetic anisotropy (PMA) of thin palladium (Pd)–cobalt (Co) bilayer films can be modified when hydrogen gas is absorbed by the Pd layer. In our recent work, we showed that the ferromagnetic resonance (FMR) response of this material is sensitive to the changes in PMA upon exposure of Pd to hydrogen gas. As such, a simple, compact, and contactless hydrogen gas sensor could exploit the FMR-based detection of the reversible hydrogen-gas-induced changes in PMA. The magnitude of the FMR peak shift is critical to determining detection sensitivity: the higher the FMR peak shift at a given hydrogen gas concentration, the higher the sensitivity. Here, we demonstrate that the detection sensitivity is enhanced when the static magnetic field is applied perpendicular to the film plane. This is due to the frequency large shift, which is eight times larger than in the in-plane FMR configuration studied previously. An analysis based on the Kittel equation for FMR frequencies of an FM film is carried out in order to understand the mechanism of sensitivity enhancement. The result is important for optimizing Pd/Co bilayered thin films for use in novel platforms for hydrogen gas sensing.

Microwave magnetic dynamics in ferromagnetic metallic nanostructures lacking inversion symmetry

In this work, we carried out systematic experimental and theoretical investigations of ferromagnetic resonance (FMR) responses of quasi-two-dimensional magnetic objects—macroscopically long stripes with nanoscale cross-section made of ferromagnetic metals. We were interested in the impact of the symmetries of this geometry on the FMR response. Three possible scenarios from which the inversion symmetry break originated were investigated, namely: (1) from the shape of the stripe cross-section, (2) from the double-layer structure of the stripes with exchange coupling between the layers, and (3) from the single-side incidence of the microwave magnetic field on the plane of the stripe array. The latter scenario is a characteristic of the stripline FMR configuration. It was found that the combined effect of the three symmetry breaks is much stronger than the impacts of each of these symmetry breaks separately.

MAGNETICALLY TUNABLE FERRITE-DIELECTRIC LEFT-HANDED METAMATERIAL

In this paper, a magnetically tunable metamaterial is proposed and studied. The metamaterial is based on the combination of ferrite sheets and dielectric rods. The tunable property is originated from the ferromagnetic resonance and electric response of dielectric rods. The retrieved electromagnetic parameters and transmission characteristic showed that by simultaneously inspiring the ferromagnetic resonance and electric resonance, composite metamaterial can possess double-negative band in the resonant state. Moreover, this band was tunable by adjusting applied magnetic fields. The simulations and experiments verified that the composite metamaterial clearly displayed a tunable feature. The proposed method is simple in designing tunable metamaterials.

A rigorous two-dimensional model for the stripline ferromagnetic resonance response of metallic ferromagnetic films

In this work, we constructed a two-dimensional numerical model for calculation of the stripline ferromagnetic resonance (FMR) response of metallic ferromagnetic films. We also conducted numerical calculations by using this software. The calculations demonstrated that the eddy current contribution to the FMR response decreases with a decrease in the stripline width. The most important manifestations of the conductivity (eddy current) effect are excitation of the higher-order standing spin waves across the film thickness in the materials for which the standing spin wave peaks would be absent in cavity FMR measurements and strong dependence of the off-resonance series conductance of the stripline on the stripline width. Whereas the contribution of the eddy currents to the stripline FMR response can be very significant, because wide striplines (100 μm+) are conventionally used for the FMR measurements, it is negligible in the case of excitation of spin waves, just because very narrow stripline transducers (0.5–5 μm wide) are required in order to excite spin waves in metallic ferromagnetic films in a noticeable frequency/applied field range.

The effects of Dzyaloshinskii-Moriya interactions on the ferromagnetic resonance response in nanosized devices

The effects of Dzyaloshinskii-Moriya interaction (DMI) on the ferromagnetic resonance response are investigated in nanometer-sized disks using 3D micromagnetics with the inclusion of DMI energy. A rich complexity is found in the effects on the spinwave eigenmodes and their behavior when varying parameters. Two distinct results are demonstrated: first, unique DMI modes are found to form, instead of the expected modes forming in the absence of DMI and they can be uniquely accessed using field rotation; and second, modal evolution with the DMI parameter involves distinct modal twisting and rotations.

Seed influence on the ferromagnetic resonance response of Co/Ni multilayers

The effect of Pd and Ru seed layers on the magnetic properties of [Co/Ni]N multilayers with varying number of bilayer repeats N is investigated using vector network analyzer ferromagnetic resonance. The effective anisotropy field HKeff is found to increase with N for Ru seed, but decreases for Pd until N = 15. As N is increased beyond 15, HKeff decreases for both seeds. In contrast, the damping parameter α decreases with N regardless of the seed, showing a 1/N dependence. Taking spin pumping into account, the intrinsic damping α0 for both Pd and Ru seeds reduce to α0 ≈ 0.01. These results demonstrate that there can be a strong influence of the seed/Co interface on anisotropy, especially for sufficiently low N, but not necessarily on α0.

Splitting of spin-wave modes in thin films with arrays of periodic perturbations: theory and experiment

A joint theoretical–experimental study focusing on the description of the ferromagnetic resonance response of thin films in the presence of periodic perturbations introduced on the upper film surface is presented. From the viewpoint of theory, these perturbations may exist in the form of any kind of one- or two-dimensional rectangular defect arrays patterned onto one surface of the magnetic film. Indeed, the defects may be pits or bumps, or ion-implanted regions with a lower saturation magnetization. The complete set of response functions, given by the components of the frequency and wave-vector dependent dynamic magnetic susceptibility tensor of the film exposed to microwave excitation, are provided and are used to explain the experimental data. This allows us to obtain the response of the system due to microwave absorption, from which the zero wave-vector spin-wave modes in the field-frequency spectra, including their intensity, are calculated. Explicit calculations for periodic defects featuring the shape of stripes, dots and rectangles are given in detail, as well as experimental results for stripe-like defects prepared either by topographical depressions or by ion implantation of thin magnetic films. The excellent agreement of the theoretical and experimental results manifests the validity of the presented model.

Strong Eddy-Current Shielding of Ferromagnetic Resonance Response in Sub-Skin-Depth-Thick Conducting Magnetic Multilayers

Exchange-coupled nonmagnetic metal (NM) and ferromagnetic metal (FM) multilayers are crucial for microwave magnonic and spintronic devices. These layered materials usually have total thicknesses smaller than the microwave skin depth. By using a stripline broadband ferromagnetic resonance spectroscopy technique, we experimentally demonstrate that the amplitude of the magnetization precession in the FM layer is strongly diminished by the shielding effect of microwave (612GHz) eddy currents circulating in the NM capping layers.

Static and dynamic magnetic properties of Ni80Fe20anti-ring nanostructures

The static and dynamic behavior of Ni${}_{80}$Fe${}_{20}$ anti-ring arrays has been systematically investigated using broadband ferromagnetic resonance (FMR) spectroscopy, magneto-optical Kerr effect (MOKE), and magnetic force microscopy (MFM). The unit cell of this periodic lattice represents a hole in a continuous film, with an elliptical nanodot placed in the middle of the hole. The FMR responses display multiple absorption peaks due to the superposition of the absorptions from the anti-dot and the central nanomagnet (dot) regions of the anti-ring structures. Interestingly, for fixed anti-ring geometry, the static and dynamic behavior is markedly sensitive to the thickness of the structure due to complicated spatial distributions of the demagnetizing field. Direct MFM imaging reveals that at remanence, the central nanomagnets are in a single-domain state, for small sample thicknesses, whereas for larger thicknesses, they display a multidomain or vortex state. This observation is in good agreement with both FMR and MOKE data. All our results agree well with micromagnetic simulations.

Metallic spintronic thin film as a hydrogen sensor

We investigate the ferromagnetic resonance response of palladium-cobalt bi-layer thin films to hydrogen charging at atmospheric pressure. We find that hydrogen absorption by the palladium capping layer results in the narrowing and shifting of the ferromagnetic resonance line of the underlying cobalt. We explain the observed phenomena as originating from reduction in the spin pumping effect and from variation in the magnetic anisotropy of the cobalt layer through an interface effect. The shift of the resonance frequency or field is the easiest to detect. We utilize this to demonstrate functionality of the bi-layer film as a hydrogen sensor.

Impact of conducting nonmagnetic layers on the magnetization dynamics in thin-film magnetic nanostructures

Through rigorous numerical simulations with an improved finite-difference time-domain algorithm consistent with a linearized Landau-Lifshitz-Gilbert equation and Hoffmann interlayer exchange boundary conditions, we investigate theoretically broadband ferromagnetic resonance response of single-layer and bilayer magnetic film nanostructures closely contacting with nonmagnetic metal layers. We show that the nonmagnetic capping/seed layers decrease the nonuniformity of the magnetic field inside the magnetic films, which decreases the effect of dominating first higher-order standing spin-wave mode observable in broadband ferromagnetic resonance spectrometry. We also demonstrate that the conductivity of a microstrip line inducing a microwave Oersted field in the magnetic films insignificantly affects the frequency and linewidth of the resonances. However, it exerts a shielding effect on the magnetic field and thus reduces the amplitude of the resonance peaks. Finally, we argue that in experiments involving spin wave detection in insulating magnetic films via the inverse spin-Hall effect voltage, the platinum electrode should be placed away from the microstrip line. Our findings will be useful for the design and optimization of spintronic devices for spin-based data-storage and processing.