Ferromagnetic Resonance Modes Research Articles

Magnetic field controlled surface localization of ferromagnetic resonance modes in 3D nanostructures

By extending the current understanding and use of magnonics beyond conventional planar systems, we demonstrate the surface localization of ferromagnetic resonance (FMR) modes through the design of complex three-dimensional nanostructures. Using micromagnetic simulations, we systematically investigate woodpile-like scaffolds and gyroids — periodic chiral entities characterized by their triple junctions. The study highlights the critical role of demagnetizing fields and exchange energy in determining the FMR responses of 3D nanosystems, especially the strongly asymmetric distribution of the spin-wave mode over the system’s height. Importantly, the top–bottom dynamic switching of the surface mode localization across the structures in response to changes in magnetic field orientation provides a new method for controlling magnetization dynamics. The results demonstrate the critical role of the geometric features in dictating the dynamic magnetic behavior of three-dimensional nanostructures, paving the way for both experimental exploration and practical advances in 3D magnonics.

Broadband rectification of microwave current in magnetic tunnel junctions with perpendicular magnetic anisotropy

We experimentally studied the effect of broadband rectification of microwave current in magnetic tunnel junctions with perpendicular magnetic anisotropy with using the method of spin-transfer ferromagnetic resonance in a planar external magnetic field. It was found that the parameters of broadband rectification (frequency range, rectified voltage value and the region of existence of the ferromagnetic resonance mode) depend on the size of the sample and its shape. The maximum value of the rectified voltage was on a round elliptical sample of 100×150 nm. At the same time, the widest operating frequency range of approximately 2 GHz was observed on strongly elliptical MTJs with the size of 75×250 nm.

Large-angle analytical solution of magnetization precession in ferromagnetic resonance

Abstract Dynamics of magnetization M driven by microwave are derived analytically from the nonlinear Landau-Lifshitz-Gilbert equation. Analytical M and susceptibility are obtained self-consistently under a positive circularly polarized microwave field, h=(hcosωt,hsinωt,0), with frequency ω, which is perpendicular to a static field, H=(0,0,H). It is found that the orbital of M is always a cone along H. However, with increasing h the polar angle θ of M initially increases, then keeps 90° when h≥h 0=αω/γ in ferromagnetic resonance (FMR) mode, where α is Gilbert damping constant and γ is gyromagnetic ratio. These effects result in a nonlinear variation of FMR signal as h increases to h≥h 0, where the maximum of resonance peak decreases from a steady value, linewidth increases from a decreasing trend. These analytical solutions provide a complete picture of the dynamics of M with different h and H.

Spin-to-charge conversion via dual-mode ferromagnetic resonance in Ta/NiFe/FeMn/CoFeB multilayer

The precise engineering of microwave absorption frequencies is of paramount importance in the advancement of spintronic-based RF devices. In the pursuit of this objective, magnetic thin films demonstrate unrivaled efficacy in enabling external modulation of their microwave responses in a reconfigurable manner. Here, we demonstrate dual-frequency ferromagnetic resonance modes and corresponding spin-to-charge conversion efficiency in thin film structures comprising Ta/NiFe/FeMn/CoFeB multilayer. A systematic thickness variation of the NiFe layer (i.e., 4–20 nm) has been undertaken to elucidate the impact on both static and dynamic properties across the multilayer structure. The presence of two distinct magnetic layers manifests in the emergence of two-step magnetic hysteresis loops, which are incorporated with unique resonant modes. The separation between the resonant fields shows tunable properties with excitation frequencies, thereby offering a wide range of reconfigurable operating parameters. The effective damping parameter has shown a decrement with increasing thickness of the NiFe layers. The effective spin mixing conductance for the NiFe layer was found to be 7.4 ± 0.6 nm−2. The spin-to-charge conversion within these structures has been demonstrated through measurements of the inverse spin Hall effect. Systematic thickness variation revealed that the prominent voltage drop was observed in the NiFe layer compared to the CoFeB layer. Considering the opposite spin Hall angles of Ta and FeMn layer, the direction of the spin flow and spin-to-charge conversion efficiency are summarized.

Low Gilbert damping and high perpendicular magnetic anisotropy in an Ir-coupled L10-FePd-based synthetic antiferromagnet

Thin ferromagnetic films possessing perpendicular magnetic anisotropy derived from the crystal lattice can deliver the requisite magnetocrystalline anisotropy density for thermally stable magnetic memory and logic devices at the single-digit-nm lateral size. Here, we demonstrate that an epitaxial synthetic antiferromagnet can be formed from L10 FePd, a candidate material with large magnetocrystalline anisotropy energy, through insertion of an ultrathin Ir spacer. Tuning of the Ir spacer thickness leads to synthetic antiferromagnetically coupled FePd layers, with an interlayer exchange field upwards of 0.6 T combined with a perpendicular magnetic anisotropy energy of 0.95 MJ/m3 and a low Gilbert damping of 0.01. Temperature-dependent ferromagnetic resonance measurements show that the Gilbert damping is mostly insensitive to temperature over a range of 20 K up to 300 K. In FePd|Ir|FePd trilayers with lower interlayer exchange coupling, optic and acoustic dynamic ferromagnetic resonance modes are explored as a function of temperature. The ability to engineer low damping and large interlayer exchange coupling in FePd|Ir|FePd synthetic antiferromagnets with high perpendicular magnetic anisotropy could prove useful for high performance spintronic devices.

Excitation of exchange spin waves in a magnetic insulator thin film at cryogenic temperatures

Spin waves and their quanta, magnons, are promising candidates for next-generation electronic devices, due to their low-power consumption and compatibility with radio-frequency-based electronic devices. For achieving magnon-based hybrid quantum systems for quantum memory and computation, the investigation of spin-wave propagation at cryogenic temperatures is highly required. In this article, we report the excitation and detection of exchange spin waves with wavelengths of tens of nanometers in an yttrium iron garnet (YIG) thin film at cryogenic temperatures. We find that the exchange spin waves are unidirectional in all temperature ranges, owing to the chiral dynamical dipolar coupling between the spin-wave mode in the YIG and the ferromagnetic resonance mode in the cobalt nanowire. Notably, a high exchange spin-wave group velocity of 2 km s−1 at 10 K is observed. Our results are promising for the development of high-speed and energy-efficient quantum magnonic devices operating at cryogenic temperatures.

MAGNETIC CORE APPLICATION IN A PLANAR RESONATOR WITH A YTTRIUM IRON GARNET FILM FOR ENHANCING STRONG PHOTON-MAGNON COUPLING

Subject and Purpose. This paper presents numerical simulation results on the transmission spectra of a split-ring resonator (SRR) loaded with a thin film of yttrium iron garnet (YIG). The application of a magnetic core in the SRR is proposed for increasing the photon-magnon (P-M) coupling strength. The anticrossing effect in the frequency dispersion behavior of the SRR modes and YIG film ferromagnetic resonance modes, namely SRR-YIG coupled modes, is identified. The dimensional parameters of the SRR with a magnetic core are calculated, taking care to preserve the design compactness and striving to obtain a maximum possible spin-number-normalized coupling strength for such a system. The work has been aimed at evaluating the efficiency of applying the magnetic core as a part of the planar microwave resonator to enhance the P-M coupling strength. Methods and Methodology. The transmission coefficient |S21| spectra of electromagnetic waves propagating through the planar resonator with the YIG film under the ferromagnetic resonance condition are numerically studied using the CST Studio Suite package in the frequency domain. The spatial distribution function of the magnetic field strength is calculated for the two scenarios of YIG film location: near the magnetic core (between the SRR and the feeding stripline) and inside the magnetic core (in the SRR center). Also, for each of these two scenarios, the transmission coefficient |S21| spectra of the wave propagation through the feeding stripline in the region of SRR-YIG coupled modes are simulated with and without the magnetic core. The dispersion curves of the SRR-YIG coupled modes are obtained in analytical terms. Results. It has been shown that the magnetic core application increases the P-M coupling strength 2.0 times in the scenario of YIG film location near the magnetic core (between the SRR and the feeding stripline). When the YIG film is inside the magnetic core (in the SRR center), the P-M coupling strength rises 2.3 times compared to similar cases without the magnetic core. Conclusions. The suggested magnetic core application can be used to increase the P-M coupling strength in the SRR — magnetic film resonant system, striving to develop effective microwave-to-optical converters and create efficient information exchange between quantum computers.

Gænice: A general model for magnon band structure of artificial spin ices

Arrays of artificial spin ices exhibit reconfigurable ferromagnetic resonance modes that can be leveraged and designed for potential applications. However, analytical and numerical studies of the frequency response of artificial spin ices have been restricted in scope due to the need of take into account nonlocal dipole fields in theoretical calculations or by long computation times in micromagnetic simulations. Here, we introduce Gænice, a framework to compute magnon dispersion relations of arbitrary artificial spin ice configurations. Gænice makes use of a tight-binding approach to compute the magnon bands. It also provides the user control over the interaction terms included, e.g., external field, shape anisotropy, exchange, and dipole, making Gænice useful for computing ferromagnetic resonances for a variety of structures, such as multilayers and ensembles of weakly or non-interacting nanoparticles. Because it relies on a semi-analytical model, Gænice is computationally inexpensive and efficient. This makes it an attractive tool for the exploration of large parameter spaces. We expect Gænice to help guide the development of novel artificial spin ices geometries and specific micromagnetic simulations for full quantitative verification.

Splitting phenomenon of ferromagnetic resonance spectra in NiFe films deposited on periodically rippled sapphire substrates

The splitting phenomenon of ferromagnetic resonance (FMR) spectra of Ni80Fe20 (NiFe) films deposited on periodically rippled sapphire substrates is studied experimentally with the help of micromagnetic simulation. The analyses show that the splitting of FMR spectra is related to the periodic ripple topography of films. When the applied magnetic field is perpendicular to the ripple direction, the effective field of periodically rippled films becomes inhomogeneous. The splitting of FMR spectra originates from localized FMR peaks corresponding to different regions with different effective field intensities in the rippled structure. Furthermore, the relative intensity and position between the split mode and the main FMR mode can be changed by designing ripple topography. This work would help understand the splitting phenomenon of FMR spectra for magnetic thin films deposited on the periodically rippled sapphire substrates.

Effect of thermal annealing on the magnetization reversal and spin dynamics in ferrimagnetic TbCo thin films

“Ferrimagnetic rare earth-transition metal alloys are promising materials for high-speed and low-power spintronic device applications due to their wide tunability in magnetic properties as a function of temperature and composition. Here, we report the influence of thermal annealing on the magnetization reversal and spin dynamics of ferrimagnetic Tb10Co90 thin films. We have used the co-sputtering technique for the deposition of two different thicknesses (20 nm and 25 nm) of the TbCo films. Annealing of the samples has been carried out in the vacuum at 350 °C for 1 h. The magnetization reversal and dynamic properties of the as-deposited and annealed films are studied using the magneto-optical Kerr effect and broadband ferromagnetic resonance measurements at room temperature, respectively. The hysteresis loops reveal an anisotropic reversal process. The anisotropy field reduces from 66 Oe to 38 Oe for 20-nm-thick films and 98 Oe to 31 Oe for 25-nm-thick films upon annealing. Consequently, thermal annealing has led to a large reduction (∼70 %) in inhomogeneous linewidth broadening of the ferromagnetic resonance modes. Gilbert damping constant is found to decrease from 0.027 to 0.021 for 20-nm-thick films, whereas it decreases from 0.043 to 0.019 for 25-nm-thick films. The results have been attributed to the enhanced crystallinity of the films as observed in the structural analysis using grazing incidence X-ray diffraction.”

Observation and Characterization of Multiple Resonance Modes in a Chiral Helimagnet CrNb3S6.

The chiral helimagnet CrNb3S6 hosts various temperature- and magnetic-field-stabilized chiral soliton lattices (CSLs) and corresponding exotic collective spin resonance modes, which make it an ideal candidate for future magnetic storage/memory and magnon-based information processing. While most studies have focused on characterizing various static spin textures in this chiral helimagnet, its corresponding collective dynamics have rarely been explored. This study systematically investigates the temperature- and magnetic-field-dependent magnetic dynamics of a single crystal of CrNb3S6 using broadband microwave spectroscopy. We observe an optical mode with a temperature-independent mode number in addition to Kittel-like ferromagnetic resonance (FMR) modes in the CSL phase, consistent with the temperature-independent normalized CSL period L(H)/L(0) based on the 1D chiral sine-Gordon model. Furthermore, combining theoretical model fitting and micromagnetic simulation, we provide a detailed phase diagram and temporal-spatial resolution of dynamic modes, which may help to develop high-frequency exchange-coupling-based spintronic devices.

Static and dynamic magnetic characteristics in concentric permalloy nanorings

Magnetic nanodisks and nanorings have been focus of attention for quite some time due to their applicability in magnetic memory devices. In this paper, static and dynamic magnetic properties of Permalloy concentric thin ring nanostructures are reported as a function of the number of rings by using micromagnetic simulations. The maximum outer radius (R) and thickness (t) of the concentric rings are fixed at 100 nm and 20 nm respectively. The distance between any two neighbouring rings is always maintained equal to the width of each ring while the number of nanorings is increased starting from one to five. In-plane magnetic hysteresis loops show that in all cases, the remanence and coercivity values are found to be almost zero while vortex state is exhibited with opposite helicity in adjacent nanorings. When the number of nanorings reach five, the narrowest hysteresis loop is observed with almost no hysteresis at all. Dynamic susceptibility spectra was computed by relaxing the system from a out of plane saturated state followed by an in-plane excitation using a small field pulse. In most of the cases, the in plane magnetic field pulse excites azimuthal spin wave modes. The resonance frequency corresponding to these excitation modes depends on the remanent configuration and the number of peaks increase with increment in the number of rings. The ferromagnetic resonance mode that is common for all the samples considered, moves towards lower frequency with increase in number of concentric rings.

Field angle dependent resonant dynamics of artificial spin ice lattices

Artificial spin ice structures which are networks of coupled nanomagnets arranged on different lattices that exhibit a number of interesting phenomena are promising for future information processing. We report reconfigurable microwave properties in artificial spin ice structures with three different lattice symmetries namely square, kagome, and triangle. Magnetization dynamics are systematically investigated using field angle dependent ferromagnetic resonance spectroscopy. Two distinct ferromagnetic resonance modes are observed in square spin ice structures in contrast with the three well-separated modes in kagome and triangular spin ice structures that are spatially localized at the center of the individual nanomagnets. A simple rotation of the sample placed in magnetic field results in the merging and splitting of the modes due to the different orientations of the nanomagnets with respect to the applied magnetic field. Magnetostatic interactions are found to shift the mode positions after comparing the microwave responses from the array of nanomagnets with control simulations with isolated nanomagnets. Moreover, the extent of the mode splitting has been studied by varying the thickness of the lattice structures. The results have potential implications for microwave filter-type applications which can be operated for a wide range of frequencies with ease of tunability.

Special features of low-temperature microwave ferromagnetic resonance in nanometer ferrite layer patterned by macroporous silicon substrate

Experimental magnetic resonance spectra for nanometer ferrite brand 1SCh4 layer deposited on macroporous silicon substrate, obtained at T = 300 and 4.2 K in the frequency ranges of 5–15 and 60–75 GHz, respectively, were analyzed. In addition to the ferromagnetic resonance mode, additional peaks were found in the magnetoresonance spectra. An analysis using the known theoretical concepts of the modern spin dynamic theory, together with the results of micromagnetic simulation, showed the formation of spin-wave oscillation modes that arise due to the structurization of the ferrite layer by a substrate of macroporous silicon.

Out-of-plane Ferromagnetic Resonance and Surface Spin Wave Modes in Ni80Fe20 Film on Ripple-Patterned Sapphire Substrate

The study of surface magnetic anisotropy of magnetic films is beneficial to understanding the behaviors of films at high frequencies and further promoting their high-frequency magnetic applications. We investigated the out-of-plane ferromagnetic resonance (FMR) and surface spin wave modes in 40-nm Ni80Fe20 (NiFe) films deposited on ripple-patterned sapphire substrate with periodicity and a flat sapphire substrate by broad-band FMR technique. When measuring the FMR of the film on ripple-patterned substrate, the in-plane angle (\U0001d711 H of the external applied magnetic field was along the direction of the ripples (\U0001d711 H = 90°) and perpendicular to the ripple direction (\U0001d711 H = 0°) respectively. The spin-wave resonance spectra consisting of up to two surface spin wave (SSW) modes were observed as the external magnetic field polar angle θH varied from “in-plane configuration” (θH = 90° ) to “out-of-plane configuration” (θH = 0°). As the decrease of θH , the two surface spin excitations disappeared in sequence and further only FMR mode was observed in the region θH which was smaller than the “critical angle” θc . The θc of \U0001d711 H = 90° is found to be different from that for \U0001d711 H = 0°. The dependences of field shift vs. out-of-plane angles θH for each SSW mode were analyzed by the surface inhomogeneity model. From the model, the surface anisotropy constants Ks of films were obtained. The results show that the values of surface anisotropy constants for the two SSW modes are different. Compared with the film sputtered on flat sapphire substrate, after introducing ripple-patterned substrate, the variation of Ks is only on the order of 0.01 erg/cm2 for the film of this thickness.

An Effective Method of Magnetic Hyperthermia Based on the Ferromagnetic Resonance Phenomenon

Nickel and cobalt ferrite nanoparticles have been synthesized using the chemical precipitation method; the nanoparticle sizes were found to be 63 ± 22 and 26 ± 4 nm, respectively. The static hysteresis loops and Mössbauer spectra have been measured. It is shown that cobalt ferrite powders are magnetically harder than nickel ferrite powders. Ferromagnetic resonance (FMR) curves have been studied. It is found that the FMR absorption for cobalt ferrite is observed at room temperature and above. The time dependences of the nanoparticle warm-up under FMR conditions have been measured. The maximum temperature changes for nickel ferrite and cobalt ferrite particles are 8 and 11 K, respectively. Using the example of cobalt ferrite powder, the possibility of effectively heating of particles in the FMR mode in their own field without using a DC magnetic field source is shown. The observed effect can be used in magnetic hyperthermia.

Heating of magnetic powders in the ferromagnetic resonance mode at a frequency of 8.9 GHz

Nickel ferrite nanoparticles 4 nm in size were synthesized by chemical deposition. Subsequent annealing at T=700oC for 5 h led to an increase in the particle size to 63 nm. The Mossbauer spectra and the frequency-field dependences of ferromagnetic resonance have been measured. It has been shown that freshly prepared powders are superparamagnetic at room temperature. The kinetic dependences of the heating of nanoparticles in the ferromagnetic resonance mode at a frequency of 8.9 GHz were measured. It was found that the maximum rate of temperature increase in this mode for a ferromagnetic powder is an order of magnitude greater than for the superparamagnetic state (1.2 and 0.13 K/s, respectively). The latter is determined by the saturation magnetization of the studied powders. Keywords: ferromagnetic resonance, superparamagnetic powders, relaxation frequency, frequency-field dependence, heating of powders.

Нагрев магнитных порошков в режиме ферромагнитного резонанса на частоте 8.9 GHz

Nickel ferrite nanoparticles 4 nm in size were synthesized by chemical deposition. Subsequent annealing at T=700℃ for 5 h led to an increase in the particle size to 63 nm. The Mössbauer spectra and the frequency-field dependences of ferromagnetic resonance have been measured. It has been shown that freshly prepared powders are superparamagnetic at room temperature. The kinetic dependences of the heating of nanoparticles in the ferromagnetic resonance mode at a frequency of 8.9 GHz were measured. It was found that the maximum rate of temperature increase in this mode for a ferromagnetic powder is an order of magnitude greater than for the superparamagnetic state (1.2 and 0.13 K/s, respectively). The latter is determined by the saturation magnetization of the studied powders.

Strong photon–magnon coupling at microwave and millimeter-wave frequencies in planar hybrid circuits

Photon–magnon hybrid systems have potential applications in modern information processing technologies. Although planar hybrid circuits based on split ring resonators have shown strong coherent photon–magnon coupling, none of those operates at millimeter-wave frequencies. With specially designed electric-field-coupled resonators, strong coupling between resonator modes and ferromagnetic resonance modes (either in-plane or out-of-plane) was experimentally observed in two circuits working at 4.1 and 30 GHz. Their dynamics were well described by quantum models. The miniature, integrable, and physically robust circuits pave a way for planar photon–magnon hybrid systems at even higher frequencies, demonstrating the possibility to integrate magnon-based systems with millimeter-wave devices.

Optimizing magnetic/dielectric matching in permalloy/carbonized cotton fiber composites by strain-tunable ferromagnetic resonance and defect-induced dielectric polarization

• The ferromagnetic resonance modes could be tuned by stress caused by the shrinkage of the carbon fibers. • The ferromagnetic resonance frequency fr is proportional to the stress σ with the relationship of fr = 1.52 × σ + 9.38. • The simultaneous tunability of ferromagnetic resonance and dielectric polarization can be realized in permalloy/carbon fiber composites. Electromagnetic losses in composites could be synergistically controlled by permeability and permittivity, associated with multiple ferromagnetic resonances and dielectric polarization. However, it is still challenging for simultaneous tunability for both the terms in a magnetic/dielectric composite system. Here, we demonstrate the tunable ferromagnetic resonances and the enhanced dielectric losses at gigahertz frequencies in permalloy/carbonized cotton fiber composites with different annealing temperatures. It is theoretically confirmed that the stress field acting on the magnetic permalloy layer increases with increasing temperature because of the shrinkage of the dielectric carbonized cotton fibers, resulting in multiple ferromagnetic resonances, in which there is a linear relationship ( f r = 1.52 × σ + 9.38 ) between the resonance frequency ( f r ) and the stress ( σ ). The present work provides a fundamental insight into understanding the micromagnetic dynamics of the magnetic/dielectric composite system.