Theory Of Ferromagnetic Resonance Research Articles

Terahertz magnetic resonance in MnCr2O4 under high magnetic field

Terahertz (THz) time-domain spectroscopy (THz-TDS) of polycrystalline MnCr2O4 was performed at <9 T and low temperatures. A resonance absorption in the sub-THz range with linear blueshifts was observed as the magnetic field was increased from 4 T to 9 T. These magnetism-driven absorptions originated from a ferromagnetic resonance, which agrees with low-field electron spin resonance measurements and ferromagnetic resonance theory. The low-temperature g-factors of MnCr2O4 were also obtained using THz-TDS. This work provides new insights into the spin dynamics of chromite spinel compounds in the THz region.

Multi-domain ferromagnetic resonance in magnetic van der Waals crystals CrI3 and CrBr3

Two-dimensional (2D) magnetic van der Waals crystals have received great attentions recently owing to their novel electronic and magnetic properties and rich potentials for low-dimensional and high-density spintronic devices. We investigated the magnetization dynamics of CrI3 and CrBr3 bulk single crystals by utilizing broadband ferromagnetic resonance (FMR) in a frequency range of 1 – 40 GHz and over a wide temperature range of 10 – 300 K. Complex features observed in the FMR spectra are quantitatively described by the multi-domain FMR theory. The minimum resonance frequency fmin in FMR spectra was recognized and analyzed as characteristics of the transition of the domain structure. Micromagnetic simulation on the domain structure and spin dynamics explains that the multi-domain structure exists under strong in-plane magnetic field for CrI3 and CrBr3 and significantly influences the magnetic dynamics properties. Our results also suggest that the linewidths of FMR spectra in CrI3 and CrBr3 are dominated by the magnetic inhomogeneous broadening.

Electrodynamic theory of ferromagnetic resonance and its applications in precise measurements of ferromagnetic linewidth, permeability tensor and saturation magnetization

This review paper describes the state of the art in measurements of ferromagnetic linewidth, permeability tensor and saturation magnetization employing electrodynamic theory of ferromagnetic resonance. It is shown that the electrodynamic theory allows significant improvements of measurement accuracy of these parameters with respect to the commonly used perturbation and magnetostatics theories. Contrary to the perturbation method the electrodynamic theory is not limited to small samples. It allows determination of the resonance frequencies and Q-factors for arbitrary size spherical and cylindrical gyromagnetic samples in suitably chosen metal enclosures. Results obtained with the electrodynamic theory for very small samples are identical to those obtained with perturbation and magnetostatics theories. Results of measurements of the ferromagnetic linewidth, permeability tensor and saturation magnetization at microwave frequencies are presented.

Broadband ferromagnetic resonance in Mn-doped Li ferrite nanoparticles

Lithium ferrites are well known materials due to their numerous technological applications especially in microwave devices. Mn-doped lithium ferrite nanoparticles were prepared by sol-gel technique by means of Pechini method, and then annealed at different temperatures in 250–1000 °C range. XRD confirms spinel formation with particle size in the 15–200 nm range, with increased size with annealing temperature. Microwave magnetoabsorption data of annealed lithium ferrite nanoparticles, obtained with a broadband system based on a network analyzer operating up to 8.5 GHz are presented. At fields up to 200 m T we can observe a broad absorption peak that shifts to higher frequencies with magnetic field according to ferromagnetic resonance theory. The amplitude of absorption, up to 85%, together with the frequency width of about 4.5 GHz makes this material suitable as wave absorber. Samples annealed at higher temperatures show a behaviour similar to polycrystalline samples, thus suggesting their multidomain character.

Ferromagnetic resonance in core-shell nanoparticles with multitype exchange anisotropy

A phenomenological model for magnetodynamics of core-shell nanoparticles is presented. The term core-shell implies, prima facie, that the spin structures (phases) of the particle components are different, no matter whether or not they are chemically identical. The model takes in two main assumptions. First, the interphase boundary is a thin (in comparison with the core and shell scales) transition layer with strongly inhomogeneous spin arrangement. Second, the shell is a granular structure consisting of spin-ordered crystallites with a wide spread of internal anisotropy, including a fraction of ones with extremely high coercivity. The framework developed on that basis, despite its simplicity, provides a unified explanation for the major specific properties of magnetic core-shell particles. Namely, (i) the growth of observed anisotropy field with reduction of the particle size, (ii) the presence of fixed unidirectional anisotropy, and (iii) the existence of rotatable anisotropy that emerges in a threshold manner under an external field. For a nanoparticle with the above-described core-shell architecture, a theory of ferromagnetic resonance with allowance for the superparamagnetic effect is worked out, and the ferromagnetic resonance absorption lines of noninteracting ensembles of such particles are presented. It is demonstrated that all the qualitatively different contributions to the core-shell-induced anisotropy could be evaluated from the data on a temperature sweep of the resonance field. Moreover, to do that, it suffices to use just the samples with random orientation of the particle axes. Preliminary assessment shows that a set of measurements for complete evaluation of the exchange-mediated anisotropies is feasible with the aid of a standard $X$-band spectrometer.

Synthesis, structural characterization and broadband ferromagnetic resonance in Li ferrite nanoparticles

Lithium ferrites are well known materials due to its numerous technological applications especially in microwave devices. Lithium ferrite nanoparticles were prepared by sol-gel technique by means of Pechini method, and then annealed at different temperatures in 250–1000 °C range. XRD confirms spinel formation with particles sizes in 15–700 nm range, with increased size with annealing temperature, whereas FTIR and Raman measurement confirm that single phase lithium ferrite with ordered cationic structure is obtained. Microwave magnetoabsorption data of the annealed lithium ferrite nanoparticles were obtained with a broadband system based on a network analyzer that operates up to 8.5 GHz. At fields up to 200 mT we can observe a broad absorption peak that shifts to higher frequencies with magnetic field according to ferromagnetic resonance theory. The amplitude of absorption, up to 85%, together with the frequency width of about 5.5 GHz makes this material suitable as wave absorber. FMR parameters like resonance field, linewidth and broadening are analyzed in order to obtain the characteristic parameters and analyze the microwave behaviour.

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.

Magnetic properties and simulated structure of granular nanothickness in magnetic films in a pre-percolation area

Multilayered (CoFeB)m(SiO2)100−m nanogranular film composites are probed via ferromagnetic resonance (FMR) spectroscopy. When the layer thickness is 1.0 to 2.6 nm and magnetic phase concentrations remain in the percolation range, the FMR field in these nanosystems reveals no dependence on the magnetic composite layer thickness. The observed phenomena are explained in the context of the FMR theory, and the relationship between the magnetic granule shape and absorbed electromagnetic radiation is established as well.

Ferromagnetic resonance in a dilute suspension of uniaxial superparamagnetic particles

A consistent theory of ferromagnetic resonance in a dilute suspension of superparamagnetic particles with uniaxial anisotropy of arbitrary strength is presented. The developed approach is used for studying the high-frequency response of a magnetic fluid at different temperatures. It is shown that in a certain temperature interval the absorption line splits into two components. The width of this interval is essentially dependent on the magnitude of the particle anisotropy.

Temperature and magnetic field dependence ofrare−earth↔ironexchange resonance mode in a magnetic oxide studied with femtosecond magneto-optical Kerr effect

In magnetic materials, the exchange is the strongest quantum interaction due to the Pauli exclusion principle. For that reason it can induce high-frequency modes ${f}_{\mathrm{exch}}$ of the magnetization precession. In this work we investigate these modes over a wide range of temperatures ($50--300\phantom{\rule{0.16em}{0ex}}\text{K}$) and magnetic fields up to $10T$ in a bismuth-doped garnet with perpendicular magnetic anisotropy by performing femtosecond magneto-optical pump-probe experiments. Near the compensation temperature ${T}_{M}$ the divergence of $1/{f}_{\mathrm{exch}}(T)$ allows identifying unambiguously ${f}_{\mathrm{exch}}$ with the rare-earth $\ensuremath{\leftrightarrow}$ iron exchange mode. In addition, at low temperature ${f}_{\mathrm{exch}}$ is independent of the field as usually observed. In contrast, we find that near ${T}_{M},\phantom{\rule{0.28em}{0ex}}{f}_{\mathrm{exch}}$ decreases linearly with an increasing magnetic field. This behavior is explained in the context of the ferromagnetic resonance theory by including the perturbation term linear in the external applied field ${H}_{\mathrm{ext}}$.

Ферромагнитный резонанс в суспензии наночастиц с одноосной анизотропией

A kinetic theory of ferromagnetic resonance in a suspension of nanoparticles with uniaxial anisotropy of arbitrary strength is proposed. The presented approach explicitly takes into account thermal fluctuations of magnetic moment for the dispersed particles and specifies the orientational distribution function of their anisotropy axes at any external field and temperature. The developed theory is used for studying the high-frequency response of a magnetic fluid at different temperatures. It is shown that in a certain temperature interval the absorption line splits into two components. The resonance field, corresponding to the first one, is almost temperature-independent and close to the value for an isotropic magnet. The second component appears only at reduced temperatures, when orientational texturing of the suspension occurs due to the action of magnetizing field. As the temperature of the system goes down, that latter component shifts towards lower fields. The width of this interval is essentially dependent on the magnitude of the particle anisotropy and the precession damping constant. Received 12 . 09 .2016; accepted 04 . 10 .2016

Green’s function theory of ferromagnetic resonance in magnetic superlattices with damping

We explore a quantum Green’s-function method to study the resonance absorption of magnetic materials. The relationship between the resonance magnon (spin wave) density and the resonance frequency of a superlattice consisting of two magnetic layers with damping and antiferromagnetic interlayer exchange coupling is studied. The effects of temperature, interlayer coupling, anisotropy, external magnetic field and damping on the the resonance frequency and resonance magnon density are investigated. The resonance excitation probability for a magnon is proportional to the resonance magnon density. In the classic methods, the imaginary part of magnetic permeability represents the resonance absorption in magnetic materials. In the quantum approach, the resonance magnon density can be used to estimate the strength of the resonance absorption. In the present work, a quantum approach is developed to study resonance absorption of magnetic materials and the results show the method to obtain a magnetic multilayered materials with both high resonance frequency and high resonance absorption.

FMR and Magnetic Properties of (CoFeB)&lt;sub&gt;m&lt;/sub&gt;(SiO&lt;sub&gt;2&lt;/sub&gt;)&lt;sub&gt;1&lt;/sub&gt;&lt;sub&gt;00&lt;/sub&gt;&lt;sub&gt;-m &lt;/sub&gt;Nanocomposite

Multilayer nanogranular film structures (CoFeB)m(SiO2)100-mhave been investigated by ferromagnetic resonance (FMR). It is shown experimentally that for these films which magnetic phase content is below percolation threshold the variation of FMR fields is not related to the thickness of magnetic layers but can be explained by variation of the shape (elongation) of spheroidal magnetic granules. The observed results are explained within standard phenomenological FMR theory.

Spin precession mapping at ferromagnetic resonance via nuclear resonant scattering of synchrotron radiation.

We probe the spin dynamics in a thin magnetic film at ferromagnetic resonance by nuclear resonant scattering of synchrotron radiation at the 14.4keV resonance of ^{57}Fe. The precession of the magnetization leads to an apparent reduction of the magnetic hyperfine field acting at the ^{57}Fe nuclei. The spin dynamics is described in a stochastic relaxation model adapted to the ferromagnetic resonance theory by Smit and Beljers to model the decay of the excited nuclear state. From the fits of the measured data, the shape of the precession cone of the spins is determined. Our results open a new perspective to determine magnetization dynamics in layered structures with very high depth resolution by employing ultrathin isotopic probe layers.

Ferromagnetic resonance in ϵ-Co magnetic composites

We investigate the electromagnetic properties of assemblies of nanoscale ϵ-cobalt crystals with size range between 5 to 35 nm, embedded in a polystyrene matrix, at microwave (1–12 GHz) frequencies. We investigate the samples by transmission electron microscopy imaging, demonstrating that the particles aggregate and form chains and clusters. By using a broadband coaxial-line method, we extract the magnetic permeability in the frequency range from 1 to 12 GHz, and we study the shift of the ferromagnetic resonance (FMR) with respect to an externally applied magnetic field. We find that the zero-magnetic field ferromagnetic resonant peak shifts towards higher frequencies at finite magnetic fields, and the magnitude of complex permeability is reduced. At fields larger than 2.5 kOe the resonant frequency changes linearly with the applied magnetic field, demonstrating the transition to a state in which the nanoparticles become dynamically decoupled. In this regime, the particles inside clusters can be treated as non-interacting, and the peak position can be predicted from Kittelʼs FMR theory for non-interacting uniaxial spherical particles combined with the Landau–Lifshitz–Gilbert equation. In contrast, at low magnetic fields this magnetic order breaks down and the resonant frequency in zero magnetic field reaches a saturation value reflecting the interparticle interactions as resulting from aggregation. Our results show that the electromagnetic properties of these composite materials can be tuned by external magnetic fields and by changes in the aggregation structure.

Magnetoabsorption and magnetic hysteresis in Ni ferrite nanoparticles

Nickel ferrite nanoparticles were prepared by a modified sol-gel technique employing coconut oil, and then annealed at different temperatures in 400-1200 oC range. This route of preparation has revealed to be one efficient and cheap technique to obtain high quality nickel ferrite nanosized powder. Sample particles sizes obtained with XRD data and Scherrer's formula lie in 13 nm to 138 nm, with increased size with annealing temperature. Hysteresis loops have been obtained at room temperature with an inductive method. Magnetic field induced microwave absorption in nanoscale ferrites is a recent an active area of research, in order to characterize and explore potential novel applications. In the present work microwave magnetoabsorption data of the annealed nickel ferrite nanoparticles are presented. These data have been obtained with a system based on a network analyzer that operates in the frequency range 0 - 8.5 GHz. At fields up to 400 mT we can observe a peak according to ferromagnetic resonance theory. Sample annealed at higher temperature exhibits different absorption, coercivity and saturation magnetization figures, revealing its multidomain character.

Field-Induced Microwave Absorption in Ni Ferrite Nanoparticles

Ferrite nanoparticles are in the last years a matter of strong interest due to the fact that nanoscale materials possess size-dependent optical, electronic, magnetic, thermal, mechanical, and chemical properties that are comparable to or superior to those of bulk material counterparts, as well as its potential applications in sensors or microwave devices. Nickel ferrites, which are well-known technological materials in various electronic devices, were prepared in the form of nanoparticles by a modified sol-gel technique employing coconut oil, and then annealed at different temperatures in the 400 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C-1200 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">°</sup> C range. This route of preparation has been revealed to be one efficient and cheap technique to obain high-quality nickel ferrite nanosized powder. Sample particle sizes obtained with X-ray diffraction data and Scherrer's formula lie in 13-138 nm, with increased size with annealing temperature. Magnetic field-induced microwave absorption in nanoscale ferrites is a recent an active area of research, in order to characterize and explore potential novel applications. In the present work, microwave magnetoabsorption data of the annealed nickel ferrite nanoparticles are presented. These data have been obtained with a system developped in our laboratory, based on a network analyzer that operates in the frequency range 0-8.5 GHz. We can observe a resonance peak with applied fields of up to 400 mT. The results are interpreted on the basis of ferromagnetic resonance theory.

Magnetic and microwave absorbing properties of Ti and Co substituted M-hexaferrites in Ka-band frequencies (26.5 ~ 40 GHz)

Magnetic and microwave absorbing properties of M-hexaferrites have been investigated in Ka-band frequencies (26.5 ~ 40 GHz) with substitution of Ti+4 and Co+2 ions for Fe+3 sites. The powders of composition BaFe12-2xTixCoxO19 were prepared by conventional ceramic processing, where the substitution ratio x was varied from 0.0 to 2.0. With the calcined powders, polycrystalline bulk and composite sheet samples were prepared for the evaluation of magnetic and microwave absorbing properties. VSM measurements indicate that the saturation magnetization and coercivity of the M-hexaferrites decrease with the substitution of Ti and Co, which is attributed to the reduction in crystal anisotropy field by changing of easy-axis of magnetization from c-axis to basal plane. Ferromagnetic resonance frequency with the peak magnetic loss is decreased sensitively with the substitution of Ti and Co, which is well consistent with ferromagnetic resonance theory. Theoretical estimation of matching frequency and matching thickness for zero wave reflection is made using the solution map of impedance matching. A wide bandwidth of microwave absorption is predicted in the composite samples containing the ferrite powders of x = 0.5 in Ka-band frequencies.

Theory of ferromagnetic resonance in perpendicularly magnetized nanodisks: Excitation by the Oersted field

We present theoretical studies of ferromagnetic resonance in perpendicularly magnetized nanodisks, wherein spin waves are excited through the ac modulation of the dc transport current injected into the disk. We have nanopillars in mind in our analysis, where spin-polarized current is injected from a metallic ferromagnet elsewhere in the structure. We argue that in a limit described, the modulation of the Oersted field generated by the transport current is the dominant spin-wave excitation mechanism, and our studies explore this limit. We calculate the critical current above which the nominal ferromagnetic state becomes unstable through studies of the linewidth of the lowest spin-wave mode, which vanishes when the critical current is reached. We find that as the applied Zeeman field ${H}_{0}$ is decreased from values above $4\ensuremath{\pi}{M}_{S}$, the critical current has a minimum when ${H}_{0}\ensuremath{\sim}4\ensuremath{\pi}{M}_{S}$ to increase for values of the external field below this value.

Analysis of the ferromagnetic resonance spectra of aggregates of magnetite nanoparticles formed by a magnetic field

The ferromagnetic resonance (FMR) spectra of magnetite nanoparticles in aqueous solutions and solid polymer films were analyzed at different particle concentrations, matrix rigidities, temperatures, external magnetic effects, and positions of flat samples in the field of the spectrometer. The formation of linear aggregates of nanoparticles under the influence of magnetic fields is the major factor that changes the FMR spectrum shape and position. The results were analyzed in terms of phenomenological theory of FMR. The applicability of the equations of phenomenological theory was verified, and the fraction of nanoparticles in linear aggregates was evaluated.