Spin Wave Resonance Frequency Research Articles

Spin-wave resonance frequency and quantum fluctuation of the (anti)ferri-(anti)ferrimagnetic double-layer superlattice

The Hamiltonian of a four-sublattice simple cubic superlattice was solved by applying the linear spin-wave theory and the retarded Green's function technique. This study focused on the spin-wave resonance frequency, energy gap, sublattice magnetization, and quantum fluctuations of the system. The results show that the spin quantum number, interlayer (intralayer) exchange couplings, and intralayer anisotropy have a significant influence. In the ground state, the magnetizations of the sublattices are smaller than their spin quantum numbers, indicating the existence of quantum zero-point vibrations in the (anti)ferrimagnetic-(anti)ferrimagnetic bilayer system.

Spin wave resonance frequency in bilayer ferromagnetic films with the biquadratic exchange interaction

Abstract The dependences of spin wave resonance (SWR) frequency on the surface anisotropy field, interface exchange coupling, symmetry, biquadratic exchange (BQE) interaction, film thickness, and the external magnetic field in bilayer ferromagnetic films are theoretically analyzed by employing the linear spin wave approximation and Green’s function method. A remarkable increase of SWR frequency, except for energetically lower two modes, can be obtained in our model that takes the BQE interaction into account. Again, the effect of the external magnetic field on SWR frequency can be increased by increasing the biquadratic to interlayer exchange ratio. It has been identified that the BQE interaction is of utmost importance in improving the SWR frequency of the bilayer ferromagnetic films. In addition, for bilayer ferromagnetic films, the frequency gap between the energetically highest mode and lowest mode is found to increase by increasing the biquadratic to interlayer exchange ratio and film thickness and destroying the symmetry of the system. These results can be used to improve the understanding of magnetic properties in bilayer ferromagnetic films and thus may have prominent implications for future magnetic devices.

Magnetoelectric coupling in Ba:Pb(Zr,Ti)O3/Co40Fe40B20 nanoscale waveguides studied by propagating spin-wave spectroscopy

In this study, we report on the characterization of the magnetoelectric coupling coefficient in Ba-substituted Pb(Zr, Ti)O3/Co40Fe40B20 (BPZT/CoFeB) nanoscaled waveguides with lateral dimensions of 700 nm using propagating spin-wave spectroscopy. The characterization was conducted in a Damon–Eshbach configuration to maximize the magnetoelastic coupling strength, as predicted by strain distribution calculations using finite element simulations. The spin-wave resonance frequency is controlled by applying bias voltages on the magnetoelectric waveguide. The magnitude of the frequency shift was correlated with the strength of the magnetoelastic field, which reached a maximum value of 5.71 mT in our experiments. In addition, the results demonstrated that the coupling coefficient behavior is associated with the hysteretic ferroelectric nature of BPZT, reaching a maximum value of 1.69 mT/V.

Spin wave resonance frequency in ferromagnetic thin film with the biquadratic exchange interaction

Spin wave resonance (SWR) frequency in ferromagnetic thin film with the biquadratic exchange interaction, interlayer exchange coupling, film thickness, surface anisotropy field, and the external magnetic field has been investigated by using the linear spin-wave approximation and Green’s function techniques. In comparison to previous studies without considering the biquadratic exchange interaction, the SWR frequency behaviors of the energetically mid-higher modes were found to be highly sensitive to biquadratic exchange interaction. SWR frequencies of all modes are linearly proportional to external magnetic field. However, the SWR frequency has nonlinear dependence on the interlayer exchange coupling and surface anisotropy field. Moreover, the biquadratic exchange interaction enabled a considerable improvement in the effects of surface anisotropy field, interlayer exchange coupling, and external magnetic field on SWR frequency. Our results also reveal that a decrease in the SWR frequency of the corresponding mid-lower modes as the thickness of film is increased while the almost the same frequency gap between the energetically highest mode and lowest mode is obtained for the thicker film. These results could help improve the understanding of magnetic properties and promote magnetic materials applications in spintronic devices.

Oxide magnonics: Spin waves in functional magnetic oxides

Spin waves or their quanta magnons are collective excitations in magnetically ordered materials. Magnonics have recently attracted tremendous interest for building next-generation nanoscale devices and circuits with low-power consumption. Oxide materials provide an excellent platform for achieving highly efficient spin-wave excitation and transmission for magnonic applications with versatile functionalities. In this article, we review some recent advances for oxide-based magnonics, including both magnetic oxides for hosting spin waves and non-magnetic oxides for manipulating spin waves. First, we introduce recent development on coherent propagation and incoherent transport of magnons in thin-film iron garnets, low-damping ferrimagnetic oxides widely used in magnonics. Then, we discuss spin-wave chirality due to the inversion symmetry broken in magnetic oxides. Magnonics in antiferromagnetic oxides is also presented, where the spin-wave resonance frequency enters THz regime. Nanoscale spin textures, such as magnetic skyrmions, can be stabilized in magnetic oxides, and provide additional versatilities by coupling their dynamics with spin waves. Last but not the least, we highlight the electrical control of spin waves based on multiferroic oxides toward applications for hybrid magnonics.

Spin-wave diagnostics of ultrathin ferrite films

A method of nondestructive control of the layered structure of submicron ferrite films comparable to the thickness of the transition (diffusion) layer at the film-substrate interface was proposed. The control technique was based on measurements of spin-wave resonance frequencies and mathematical processing of the measurement results. It was found that the inhomogeneity of magnetization in the transition layer provides the condition of phase synchronism of electromagnetic waves (photons) and exchange spin waves (magnons). In the region of the synchronism points, the effects of hybridization of coupled waves appeared. In this case, hybrid quasi-spin and quasi-electromagnetic waves were excited in the film. The quasi-spin wave at the film-substrate interface had a purely electromagnetic character, which ensured a good matching with the external microwave tract. Near the plane of phase synchronism, there was an intensive redistribution of energy in favor of increasing the power of the quasi-spin wave. At the same time, the excitation region of the spin-wave resonance significantly narrowed. The proposed mechanism of photon-magnon conversion is applicable to any ferrite-dielectric structures with a boundary diffusion layer, and can be useful in the development of superminiature controlled devices for analog processing of microwave information signals.

Spin-wave resonance frequency and low-temperature properties of an antiferromagnetic graphene-like bilayer system

We studied the spin-wave resonance (SWR) frequency and low-temperature magnetization, internal energy, and specific heat of an antiferromagnetic graphene-like bilayer system with two sublattices by applying the retarded Green's function method and the linear spin-wave approximation. The numerical results show that two SWR frequencies in the system can be adjusted by changing the longitudinal magnetic field, interlayer (intralayer) exchange coupling, and intralayer anisotropy. These parameters greatly influence the magnetization, internal energy, and specific heat at low temperatures. Crossovers between the two sublattice magnetizations were observed for the different intralayer exchange couplings, which are affected by the quantum and thermal fluctuations.

Spin-wave resonance frequency in ferromagnetic thin film with the next nearest neighbor interaction

Linear spin-wave approximation and Green's function were used to study the dependence of spin wave resonance (SWR) frequency in a ferromagnetic film considering the external magnetic field, surface anisotropy, number of atomic layers, nearest and next nearest neighbor interaction. A systematic study of the SWR frequency as a function of external magnetic field, surface anisotropy, and next nearest neighbor interaction was performed. It demonstrates that the next nearest neighbor interaction affects strongly on the SWR frequencies of energetically higher modes, as well as the gap of resonance frequency between the highest and lowest energy modes is broaden as the next nearest neighbor interaction increasing. Moreover, we show that SWR frequencies at two higher energy modes are coincided when the surface anisotropy increases. Finally, as the thickness of film decreases, SWR frequency of the lowest energy mode is shifted to higher value. Thus, considering these effects in an opportune way, we are able to control the SWR frequency of the system.

Spin Wave Resonance Frequency in Ferromagnetic Homogeneous Bilayers with Next Nearest Neighbor Interaction

The effects of next nearest neighbor interaction, interface coupling, surface anisotropy, film thickness and symmetry on spin wave resonance (SWR) frequency in the ferromagnetic homogeneous bilayer...

Enhancement of Brillouin light scattering signal with anti-reflection layers on magnetic thin films

The significant enhancement of Brillouin light scattering (BLS) spectroscopy intensity in a ferromagnetic thin film with an additional dielectric anti-reflection layer is experimentally investigated. The anti-reflection layer thickness dependent BLS measurements on ferromagnetic layers are performed systematically. Consequently, we observe that BLS signals are dramatically enhanced by more than 450% at a specific dielectric layer thickness due to the pure optical effect. Because of the large signal enhancements, the errors of the spin wave resonance peak frequencies are noticeably reduced as well. Since many magnetic properties such as the saturation magnetization, the surface anisotropy, and the exchange stiffness constant are determined by the spin wave resonance frequencies from the BLS spectra, the additional anti-reflection layer can help to improve the reliability of BLS experiments. Especially, the BLS signal improvement plays a crucial role in the precise determination of the interfacial Dzyaloshinskii-Moriya interaction (iDMI) energy density, since the iDMI energy density is calculated from the difference of Stokes and anti-Stokes resonance frequencies, which is typically order of 1 GHz.

Spin wave resonance in symmetrical/asymmetrical bilayer ferromagnetic films

The dependence of spin wave resonance (SWR) frequency on the surface anisotropy, the interlayer coupling, the ferromagnetic layer thickness and the external magnetic field in the bilayer ferromagnetic film have been investigated by using the linear spin wave approximation and Green’s function technique. We find that the SWR frequency of the ferromagnetic bilayer film are shifted to higher values corresponding to those of above factors, respectively. The lowest four modes can be controlled by the surface anisotropy of A, B layer and the symmetry of the film. The SWR frequency of the energetically lowest mode is no affected except for applied magnetic field. A notable rapidly increasing behavior appears in frequency with the increasing of interlayer coupling.

Spin-wave resonance frequency in ferromagnetic thin film with interlayer exchange coupling and surface anisotropy

We have investigated the dependence of spin-wave resonance(SWR) frequency on the surface anisotropy, the interlayer exchange coupling, the ferromagnetic layer thickness, the mode number and the external magnetic field in a ferromagnetic superlattice film by means of the linear spin-wave approximation and Green's function technique. The SWR frequency of the ferromagnetic thin film is shifted to higher values corresponding to those of above factors, respectively. It is found that the linear behavior of SWR frequency curves of all modes in the system is observed as the external magnetic field is increasing, however, SWR frequency curves are nonlinear with the lower and the higher modes for different surface anisotropy and interlayer exchange coupling in the system. In addition, the SWR frequency of the lowest (highest) mode is shifted to higher (lower) values when the film thickness is thinner. The interlayer exchange coupling is more important for the energetically higher modes than for the energetically lower modes. The surface anisotropy has a little effect on the SWR frequency of the highest mode, when the surface anisotropy field is further increased.

Spin Wave Resonance Frequency in the Bilayer Ferromagnetic Film

The dependence of spin wave resonance (SWR) frequency on the surface anisotropy, the interlayer and interfacial coupling, the ferromagnetic layer thickness and the external magnetic field in the bilayer ferromagnetic film have been investigated by using the linear spin wave approximation and Green’s function technique. We find that the SWR frequency of the ferromagnetic bilayer films are shifted to higher values corresponding to those of above factors, respectively. The mode of the energetically highest can be controlled by the interfacial coupling, the thickness and the symmetry of the film. The SWR frequency of mode number m = 1 is almost flat except for applied magnetic field. Analytical details and the validity of the method are shown and discussed.

Effect of antiferromagnetic interfacial coupling on spin-wave resonance frequency of multi-layer film

We investigate the spin-wave resonance (SWR) frequency in a bicomponent bilayer and triple-layer films with antiferromagnetic or ferromagnetic interfacial couplings, as function of interfacial coupling, surface anisotropy, interface anisotropy, thickness and external magnetic field, using the linear spin-wave approximation and Green’s function technique. The microwave properties for multi-layer magnetic film with antiferromagnetic interfacial coupling is different from those for multi-layer magnetic film with ferromagnetic interfacial coupling. For the bilayer film with antiferromagnetic interfacial couplings, as the lower (upper) surface anisotropy increases, only the SWR frequencies of the odd (even) number modes increase. The lower (upper) surface anisotropy does not affect the SWR frequencies of the even (odd) number modes. For the multi-layer film with antiferromagnetic interfacial coupling, the SWR frequency of modes m=1, 3 and 4 decreases while that of mode m=2 increases with increasing thickness of the film within a proper parameter region. The present results could be useful in enhancing our fundamental understanding and show the method to enhance and adjust the SWR frequency of bicomponent multi-layer magnetic films with antiferromagnetic or ferromagnetic interfacial coupling.

Competing exchange interactions in multiferroic and ferrimagnetic CaBaCo4O7

Competing exchange interactions can produce complex magnetic states together with spin-induced electric polarizations. With competing interactions on alternating triangular and kagome layers, the swedenborgite CBO may have one of the largest measured spin-induced polarizations of about 1700 nC/cm$^2$ below its ferrimagnetic transition temperature at 70 K. Powder neutron-diffraction data, magnetization measurements, and spin-wave resonance frequencies in the THz range reveal that the complex spin order of multiferroic CBO can be described as a triangular array of c-axis chains ferrimagnetically coupled to each other in the ab plane. Magnetostriction on bonds that couple those chains produces the large spin-induced polarization of CBO.

Spin-wave resonance frequency in a multi-layer film

The spin-wave resonance (SWR) frequency in a ferromagnetic bilayer or triple-layer film (for bilayer or triple-layer films, including symmetric and asymmetric films) with single-ion anisotropy has been studied by using the linear spin-wave approximation and Green’s function technique. The effects of interfacial coupling, surface anisotropy, interface anisotropy, bulk anisotropy and external magnetic field on the SWR frequency have been investigated. For a ferromagnetic bilayer or triple-layer film, the SWR frequencies (for the same spin-wave modes) all increase with increasing external magnetic field, surface anisotropy, interface anisotropy and bulk anisotropy and with decreasing film thickness. As the interfacial coupling increases, the SWR frequencies of some modes increase, while the SWR frequencies of the other modes do not change. The SWR frequencies of a triple-layer film are different from those of a bilayer film and the SWR frequencies of an asymmetric film are also different from those of a symmetric film. The present results show the method to enhance and adjust the SWR frequency of ferromagnetic multi-layer films.

Spin-wave resonance frequency in a ferromagnetic thin film

The spin-wave resonance (SWR) frequency in a ferromagnetic thin film with single-ion surface and bulk anisotropies has been studied by using the linear spin-wave approximation and Green's function techniques. The effects of surface and bulk anisotropies, film thickness, spin quantum number, and external magnetic field on the SWR frequency have been investigated. It is found that the SWR frequencies all increase, as the external magnetic field, the bulk anisotropy, and the spin quantum number increase, respectively. The surface anisotropy affects strongly the SWR frequencies of the middle and low modes (except for the lowest one). With large bulk anisotropy, the surface anisotropy affects mainly the resonance frequency of the lowest spin-wave mode. As the film thickness decreases, the SWR frequency of the same mode increases. The present results direct the method to enhance and adjust the SWR frequency of ferromagnetic thin films.

Interaction of Ultrasonic Waves with Thin Magnetic Films

We discuss the interaction of an externally generated ultrasonic wave with a thin magnetic film, and the generation of phonons by driving such a film with a microwave field. Several geometries are considered. If the frequency of the driving wave is close to one of the spin-wave resonance frequencies of the film, we exhibit an exact solution to the phonon equation of motion in the presence of one-magnon-one-phonon terms in the magneto-elastic coupling. Some difficulties present in an earlier theory are eliminated.We find a contribution to the spin wave resonance linewidths from the one-magnon-one-phonon terms. For the $n=0$ term of a Ni film, we estimate the magneto-elastic coupling may make a contribution to the linewidth of roughly ten percent of the total linewidth. If we denote this contribution to the linewidth by ${{\ensuremath{\Gamma}}_{n}}^{(\mathrm{pn})}$ and the total linewidth by ${\ensuremath{\Gamma}}_{n}$, then we show that study of the interaction of an externally generated ultrasonic wave with the film provides a direct measure of the ratio $\frac{{{\ensuremath{\Gamma}}_{n}}^{(\mathrm{pn})}}{{\ensuremath{\Gamma}}_{n}}$. The presence of a poor acoustical impedance match at a film surface is shown to introduce a factor in the expression for ${{\ensuremath{\Gamma}}_{n}}^{(\mathrm{pn})}$ periodic in the external magnetic field, for a film of fixed thickness.