Influence of exchange bias on spin torque ferromagnetic resonance for quantification of spin–orbit torque efficiency

Antiferromagnet(AFM)/ferromagnet(FM)heterostructure is a popular system for studying the spin–orbit torque(SOT)of AFMs.However,the interfacial exchange bias field induces that the magnetization in FM layer is noncollinear to the external magnetic field,namely the magnetic moment drag effect,which further influences the characteristic of SOT efficiency.In this work,we study the SOT efficiencies of IrMn/NiFe bilayers with strong interfacial exchange bias by using spin-torque ferromagnetic resonance(ST-FMR)method.A full analysis on the AFM/FM systems with exchange bias is performed,and the angular dependence of magnetization on external magnetic field is determined through the minimum rule of free energy.The ST-FMR results can be well fitted by this model.We obtained the relative accurate SOT efficiencyξ_(DL)=0.058 for the IrMn film.This work provides a useful method to analyze the angular dependence of ST-FMR results and facilitates the accurate measurement of SOT efficiency for the AFM/FM heterostructures with strong exchange bias.

Simultaneous resonance of an axially moving ferromagnetic thin plate under a line load in a time-varying magnetic field

In this paper,the simultaneous resonance of a ferromagnetic thin plate in a time-varying magnetic field,having axial speed and being subjected to a periodic line load,is studied.Based on the large deflection theory of thin plates and electromagnetic field theory,the nonlinear vibration differential equation of the plate is obtained by using the Hamilton′s principle and the Galerkin method.Then the boundary condition in which the longer opposite sides are clamped and hinged is considered.The dimensionless nonlinear differential equations are solved by using the method of multiple scales,and the analytical solution is given.In addition,the stability analysis is also carried out by using Lyapunov stability theory.Through numerical analysis,the variation curves of system resonance amplitude with frequency tuning parameter,magnetic field strength and external excitation amplitude are obtained.Different parameters that have significant effects on the response of the system,such as the thickness,the axial velocity,the magnetic field intensity,the position,and the frequency of external excitation,are considered and analyzed.The results show that the system has multiple solution regions and obvious nonlinear coupled characteristics.

Magnetoelastic combined resonance and stability analysis of a ferromagnetic circular plate in alternating magnetic field

The nonlinear combined resonance problem of a ferromagnetic circular plate in a transverse alternating magnetic field is investigated. On the basis of the deformation potential energy, the strain potential energy, and the kinetic energy of the circular plate, the Hamilton principle is used to induce the magnetoelastic coupling transverse vibration dynamical equation of the ferromagnetic circular plate. Based on the basic electromagnetic theory, the expressions of the magnet force and the Lorenz force of the circular plate are presented. A displacement function satisfying clamped-edge combined with the Galerkin method is used to derive the Duffing vibration differential equation of the circular plate. The amplitude-frequency response equations of the system under various combined resonance forms are obtained by means of the multi-scale method, and the stability of the steady-state solutions is analyzed according to the Lyapunov theory. Through examples, the amplitude-frequency characteristic curves with different parameters, the amplitude of resonance varying with magnetic field intensity and excitation force, and the time-course response diagram, phase diagram, Poincar′e diagram of the system vibration are plotted, respectively. The effects of different parameters on the amplitude and stability of the system are discussed. The results show that the electromagnetic parameters have a significant effect on the multi-valued attribute and stability of the resonance solutions, and the system may exhibit complex nonlinear dynamical behavior including multi-period and quasi-periodic motion.

Enhancement of ferromagnetic resonance in Al_2O_3-doped Co_2FeAl Heusler alloy film prepared by oblique sputtering

Large and variable in-plane uniaxial magnetic anisotropy in a nanocrystalline （Co2FeA1）97.8（Al2O3）2.2 soft magnetic thin film is obtained by an oblique sputtering method without being induced by magnetic field or post anneaiing. The in-plane uniaxiai magnetic anisotropy varies from 50 Oe to 180 Oe （1 Oe=79.5775 A·m-1） by adjusting the sample＇s position. As a result, the ferromagnetic resonance frequency of the film increases from 1.9 GHz to 3.75 GHz.

Theoretical investigation of ferromagnetic resonance in a ferromagnetic thin film with external stress anisotropy

We use the ferromagnetic resonance(FMR)method to study the properties of ferromagnetic thin film,in which external stress anisotropy,fourfold anisotropy and uniaxial anisotropy are considered.The analytical expressions of FMR frequency,linewidth and the imaginary part of magnetic susceptibility are obtained.Our results reveal that the FMR frequency and the imaginary part of magnetic susceptibility are distinctly enhanced,and the frequency linewidth or field linewidth are broadened due to a strong external stress anisotropy field.The hard-axis and easy-axis components of magnetization can be tuned significantly by controlling the intensity and direction of stress and the in-plane uniaxial anisotropy field.

Active ferromagnetic shimming of the permanent magnet for magnetic resonance imaging scanner

This paper presents an approach of active ferromagnetic shimming for C-type permanent magnetic resonance imaging （MRI） magnet. It is designed to reduce inhomogeneity of magnetostatic field of C-type permanent magnet to meet the stringent requirement for MRI applications. An optimal configuration （locations and thicknesses） of active ferromagnetic pieces is generated through calculation according to the initial field map and the demanded final homo- geneity specifications. This approach uses a minimisation technique which makes the sum of squared magnetic moment minimum to restrict the amount of the active ferromagnetic material used and the maximal thickness of pieces stacked at each hole location in the shimming hoards. Simulation and experimental results verify that the method is valid and efficient.

Picosecond time-resolved X-ray ferromagnetic resonance measurements at Shanghai synchrotron radiation facility

An experimental picosecond time-resolved X-ray ferromagnetic resonance(TR-XFMR)apparatus with a time resolution of 13 ps(RMS)or 31 ps(FWHM)was constructed and demonstrated in the 07U and 08U1A soft X-ray beamlines at the Shanghai Synchrotron Radiation Facility(SSRF)using pump-probe detection and X-ray magnetic circular dichroism(XMCD)spectroscopy.Element and time-resolved ferromagnetic resonance was excited by continuous microwave phase-locking of the bunch clock within the photon beam during synchrotron radiation and was characterized by detecting the magnetic circular dichroism signals of the elements of interest in the magnetic films.Using this equipment,we measured the amplitude of the element-specific moment precession during ferromagnetic resonance(FMR)at 2 GHz in a single Ni81Fe19layer.

Effect of interface magnetization depinning on the frequency shift of ferromagnetic and spin wave resonance in YIG/GGG films

Nowadays the yttrium iron garnet(Y3Fe5O12, YIG) films are widely used in the microwave and spin wave devices due to their low damping constant and long propagation distance for spin waves. However, the performances, especially the frequency stability, are seriously affected by the relaxation of the interface magnetic moments. In this study, the effect of out-of-plane magnetization depinning on the resonance frequency shift(△ fr) was investigated for 3-μm YIG films grown on Gd3Ga5O12(GGG)(111) substrates by liquid-phase epitaxy. It is revealed that the ferromagnetic resonance(FMR) and spin wave propagation exhibit a very slow relaxation with relaxation time τ even longer than one hour under an out-of-plane external magnetic bias field. The △ fr span of 15.15–24.70 MHz is observed in out-of-plane FMR and forward volume spin waves. Moreover, the △ fr and τ depend on the magnetic field. The △ fr can be attributed to that the magnetic moments break away from the pinning layer at the YIG/GGG interface. The thickness of the pinning layer is estimated to be about9.48 nm to 15.46 nm according to the frequency shifting. These results indicate that △ fr caused by the pinning layer should be addressed in the design of microwave and spin wave devices, especially in the transverse magnetic components.

STRUCTURE AND FERROMAGNETIC RESONANCE OF Fe/Cu SUPERLATTICES

Metallic Fe/Cu superlattice films on glass substrates were prepared by a dc-magnetion sputtering system.The modulation behaviors and the crystal structures of the films were ex- amined by X-ray diffraction and transmission electron microscopy(TEM)respectively. Their magnetic properties were studied by means of ferromagnetic resonnance spectrometer and the vibrating sample magnetometer.The results show that there exists a strong magnetic coupling between the neighbouring Fe layers and it is the coupling that affectes the magnetic properties of these superlattice films.

Ferromagnetic resonance in Co/Pt multilayers

Out-of-plane angular dependence of ferromagnetic resonance spectra was measured in sputtered Co/Pt multilayers and analyzed with the Landau-Lifshitz-Gilbert equation. The effective demagnetizing field 4πMeff is found to increase with decreasing tPt and decreasing 1/tco, which can be considered as a result of interplay between the interlayer coupling and a lowdimensional effect. The g factor increases with increasing tpt and decreasing tCo, indicating contribution of spin-polarization of Pt atoms and additional contribution of orbital moment of Co atoms. The in-plane resonance line-width increases with decreasing too and increases with increasing tPt.

Voltage control of ferromagnetic resonance and spin waves

The voltage control of magnetism has attracted intensive attention owing to the abundant physical phenomena associated with magnetoelectric coupling. More importantly, the techniques to electrically manipulate spin dynamics, such as magnetic anisotropy and ferromagnetic resonance, are of great significance because of their potential applications in high-density memory devices, microwave signal processors, and magnetic sensors. Recently, voltage control of spin waves has also been demonstrated in several multiferroic heterostructures. This development provides new platforms for energyefficient, tunable magnonic devices. In this review, we focus on the most recent advances in voltage control of ferromagnetic resonance and spin waves in magnetoelectric materials and discuss the physical mechanisms and prospects for practical device applications.

INTERLAYER COUPLING AND FERROMAGNETIC RESONANCE IN Fe-Si/Cr MULTILAYERS

Fe-Si/Cr multilayers with amorphous Fe-Si magnetic layers and Cr nonmagnetic layers were prepared by an rf-sputtering method.When the thickness of the Cr layers varies from 0.5 to 6 nm, the interlayer coupling oscillates periodically from ferromagnetic to antiferromagnetism. For each sample only one wide uniform resonance peak is detected by the ferromagnetic resonance. The uniform resonance field Hb and the resonance line width △H_b oscillate periodically as the thickness of the Cr layers increases, which is related to the oscillation of the interlayer coupling from ferromagnetic to antiferromagnetism.The oscillation period is about 1.5nm.

FERROMAGNETIC RESONANCE STUDIES OF Co/CoFe_2O_4 MULTILAYERS

The Co/CoFe2O4 multilayers have been grown on the glass substrate using sputtering techniques. In these films the Co layers were measured to have the fcc structure with [11] axis perpendicular to the film plane, and the CoFe2O4 layers are amorphous. Ferromagnetic resonance measurements have been made as a function of the external magnetic field orientation in a plane perpendicular to the film. The effective magnetization, effective anisotropy constant and interface anisotropy constant have been determined. The influence of Co layers thickness on magnetic properties was discussed.

Ferromagnetic resonance frequency shift model of laminated magnetoelectric structure tuned by electric field

Based on Smith-Beljers theory and classical laminate theory, an explicit model is proposed for the ferromagnetic resonance （FMR） frequency shift of a stress-mediumed laminated magnetoelectric structure tuned by an electric field. This model can effectively predict the experimental phenomenon that the FMR frequency increases under a parallel magnetic field and decreases under a perpendicular magnetic field when the electric field ranges from - 10 kV/m to 10 kV/m. Besides, this theory further shows that the FMR frequency increases monotonically as the angle between the direction of the external magnetic field and the outside normal direction of the laminated structure increases, and the frequency will increase as great as 7 GHz. In addition, when the angle reaches a certain critical value, the external electric field fails to tune the FMR frequency. When the angle is above the critical value, the increase of the electric field induces the FMR frequency to increase, and the opposite scenario happens when it is below the critical value. When the angle is 90~ （parallel magnetic field）, the FMR frequency is the most sensitive to the change of the electric field.

Voltage control magnetism and ferromagnetic resonance in an Fe_(19)Ni_(81)/PMN-PT heterostructure by strain

Voltage control magnetism has been widely studied due to its potential applications in the next generation of information technology.PMN-PT,as a single crystal ferroelectric substrate,has been widely used in the study of voltage control magnetism because of its excellent piezoelectric properties.However,most of the research based on PMN-PT only studies the influence of a single tensile(or compressive)stress on the magnetic properties due to the asymmetry of strain.In this work,we show the effect of different strains on the magnetic anisotropy of an Fe_(19)Ni_(81)/(011)PMN-PT heterojunction.More importantly,the(011)cut PMN-PT generates non-volatile strain,which provides an advantage when investigating the voltage manipulation of RF/microwave magnetic devices.As a result,a ferromagnetic resonance field tunability of 70 Oe is induced in our sample by the non-volatile strain.Our results provide new possibilities for novel voltage adjustable RF/microwave magnetic devices and spintronic devices.

Progress of novel diluted ferromagnetic semiconductors with decoupled spin and charge doping: Counterparts of Fe-based superconductors

Diluted ferromagnetic semiconductors（DMSs） that combine the properties of semiconductors with ferromagnetism have potential application in spin-sensitive electronic（spintronic） devices. The search for DMS materials exploded after the observation of ferromagnetic ordering in Ⅲ-Ⅴ（Ga,Mn）As films. Recently, a series of DMS compounds isostructural to iron-based superconductors have been reported. Among them, the highest Curie temperature TCo f 230 K has been achieved in（Ba,K）（Zn,Mn）2As2. However, most DMSs, including（Ga,Mn）As, are p-type, i.e., the carriers that mediate the ferromagnetism are holes. For practical applications, DMSs with n-type carriers are also advantageous. Very recently,a new DMS Ba（Zn,Co）2As2 with n-type carriers has been synthesized. Here we summarize the recent progress on this research stream. We will show that the homogeneous ferromagnetism in these bulk form DMSs has been confirmed by microscopic techniques, i.e., nuclear magnetic resonance（NMR） and muon spin rotation（μSR）.

Microwave ferromagnetic properties of as-deposited Co_2FeSi Heusler alloy films prepared by oblique sputtering

The Co2FeSi films are deposited on Si （100） substrates by an oblique sputtering method at ambient temperature. It is revealed that the microwave ferromagnetic properties of Co2FeSi films are sensitive to sample position and sputtering power. It is exciting that the as-deposited films without any magnetic annealing exhibit high in-plane uniaxial anisotropy fields in a range of 200 Oe-330 Oe （1 Oe = 79.5775 A.m ^-1）, and low coercivities in a range of 5 Oe-28 Oe. As a result, high self-biased ferromagnetic resonance frequency up to 4.75 GHz is achieved in as-deposited oblique sputtered films. These results indicate that Co2FeSi Heusler alloy films are promising in practical applications of RF/microwave devices.

Terahertz magnetic resonance in MnCr_(2)O_(4)under high magnetic field

Terahertz(THz)time-domain spectroscopy(THz-TDS)of polycrystalline MnCr_(2)O_(4)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 MnCr_(2)O_(4)were also obtained using THz-TDS.This work provides new insights into the spin dynamics of chromite spinel compounds in the THz region.

双层铁磁薄膜中层间耦合和面外各向异性对系统共振频率的影响

本文采用能量极小原理,重点讨论了层间双线性耦合、双二次型耦合和面外单轴各向异性对双层铁磁薄膜中铁磁共振频率的影响。分别从三个方面讨论光学模和声学模共振频率对层间双线性耦合、双二次型耦合以及面外单轴各向异性的依赖。结果表明,层间双线性耦合和双二次型耦合可以提高光学模的共振频率。然而,面外单轴各向异性会降低光学模和声学模的共振频率,尤其是对声学模的影响更加明显。此外,对于光学模,双二次型耦合比双线性耦合更为重要。这些结果有助于新型微波器件的设计。

基于磁控溅射制备的YIG薄膜结构与磁性能

使用射频磁控溅射在衬底上沉积了纳米级YIG薄膜,借助X射线衍射仪、振动样品磁强计、铁磁共振等研究了溅射气压、溅射功率和退火温度对于所制薄膜结构与磁性能的影响,并基于唯象方程拟合出薄膜样品的Gilbert阻尼系数。