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.

Ferromagnetic Resonance Study on the Permalloy Submicron Rectangular Arrays Prepared by Electron Beam Lithography

In this paper, we report a ferromagnetic resonance study on the permalloy film of submicron sized rectangular arrays prepared by electron beam lithography and the theoretical simulation to the non uniform demagnetizing effect and ferromagnetic resonance data. By theoretical simulation, the magnetization, gyromagnetic ratio and g value of the sample are determined. The theoretical curves of the dependence of the resonance field on the field orientation φ H fit well with the experimental data. When the steady magnetic field is applied near the film normal, a series of additional regular peaks (up to eight ) appeared in the FMR spectrum on the low field side of the main FMR peak. The resonance field of these side peaks decreases linearly with the peak number. The possible physical mechanism of these multiple peaks was discussed.

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.

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.

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.

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.

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.

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.

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.

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.

Interfacial DMI in Fe/Pt thin films grown on different buffer layers

We study the interfacial Dzyaloshinskii-Moriya interactions(i-DMI)of Fe/Pt bilayers grown on Si substrates with MgO,SiO_(2),or Ta each as a buffer layer on the basis of wave-vector-resolved Brillouin light scattering(BLS)measurement.The obtained i-DMI energy values for Fe/Pt on MgO,Ta,and SiO_(2) buffer layers are 0.359,0.321,and 0.274 mJ/m~2,respectively.The large i-DMI value observed in Fe/Pt system on the MgO buffer layer can be attributed to the good interfacial quality and the Rshaba effect at the MgO/Fe interface.Moreover,the MgO/Fe/Pt system,benefiting from better sample quality,exhibits a lower damping factor.Furthermore,layer-resolved first-principles calculations are carried out to gain a more in-depth understanding of the origin of the i-DMI in the Fe/Pt system.The results indicate that in the Fe(110)/Pt(111)system,the substantial DMI energy between Fe spins at the interface is related to a significant change in spin-orbit coupling(SOC)energy in the neighboring Pt layer.In contrast,for the MgO(002)/Fe(002)system,both the DMI and its related SOC energy are concentrated at the interfacial Fe layer.Our investigation will provide a valuable insight into the spintronic community in exploring novel devices with chirality dependence.

Twisted Integration of Complex Oxide Magnetoelectric Heterostructures via Water‑Etching and Transfer Process

Manipulating strain mode and degree that can be applied to epitaxial complex oxide thin films have been a cornerstone of strain engineering.In recent years,lift-off and transfer technology of the epitaxial oxide thin films have been developed that enabled the integration of heterostructures without the limitation of material types and crystal orientations.Moreover,twisted integration would provide a more interesting strategy in artificial magnetoelectric heterostructures.A specific twist angle between the ferroelectric and ferromagnetic oxide layers corresponds to the distinct strain regulation modes in the magnetoelectric coupling process,which could provide some insight in to the physical phenomena.In this work,the La_(0.67)Sr_(0.33)MnO_(3)(001)/0.7Pb(Mg_(1/3)Nb_(2/3))O_(3)-0.3PbTiO_(3)(011)(LSMO/PMN-PT)heterostructures with 45.and 0.twist angles were assembled via water-etching and transfer process.The transferred LSMO films exhibit a fourfold magnetic anisotropy with easy axis along LSMO<110>.A coexistence of uniaxial and fourfold magnetic anisotropy with LSMO[110]easy axis is observed for the 45°Sample by applying a 7.2 kV cm^(−1)electrical field,significantly different from a uniaxial anisotropy with LSMO[100]easy axis for the 0°Sample.The fitting of the ferromagnetic resonance field reveals that the strain coupling generated by the 45°twist angle causes different lattice distortion of LSMO,thereby enhancing both the fourfold and uniaxial anisotropy.This work confirms the twisting degrees of freedom for magnetoelectric coupling and opens opportunities for fabricating artificial magnetoelectric heterostructures.

Characterization of a Y-type hexagonal ferrite-based frequency tunable microwave absorber

A Y-type hexaferrite rod with the composition of Ba2COl.8Cuo.2Fe12022 was presented as an absorbing material with high absorb- anee. Its high absorbance and wide absorption band result from ferromagnetic resonance （FMR） that is self-biased by strong shape and mag- netocrystaUine anisotropy fields. Around the FMR frequency the specimen of the ferrite rods exhibits very high absorbance and the FMR frequency can be tuned by the rod dimension. In addition to the high absorbance and the wide tunable absorption band, the microwave ab- sorber has another advantage of light weight due to the use of the ferrite rods instead of ferrite slabs.

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.

Giant anisotropy of magnetic damping and significant in-plane uniaxial magnetic anisotropy in amorphous Co40Fe40B20 films on GaAs(001)

Tuning magnetic damping constant in dedicated spintronic devices has important scientific and technological implications. Here we report on anisotropic damping in various compositional amorphous CoFeB films grown on GaAs(001) substrates. Measured by a vector network analyzer-ferromagnetic resonance (VNA-FMR) equipment, a giant magnetic damping anisotropy of 385%, i.e., the damping constant increases by about four times, is observed in a 10-nm-thick Co40Fe40B20 film when its magnetization rotates from easy axis to hard axis, accompanied by a large and pure in-plane uniaxial magnetic anisotropy (UMA) with its anisotropic field of about 450 Oe. The distinct damping anisotropy is mainly resulted from anisotropic two-magnon-scattering induced by the interface between the ferromagnetic layer and the substrate, which also generates a significant UMA in the film plane.

Dynamics of magnetization in ferromagnet with spin-transfer torque

We review our recent works on dynamics of magnetization in ferromagnet with spin-transfer torque. Driven by constant spin-polarized current, the spin-transfer torque counteracts both the precession driven by the effective field and the Gilbert damping term different from the common understanding. When the spin current exceeds the critical value, the conjunctive action of Gilbert damping and spin-transfer torque leads naturally the novel screw-pitch effect characterized by the temporal oscillation of domain wall velocity and width. Driven by space- and time-dependent spin-polarized current and magnetic field, we expatiate the formation of domain wall velocity in ferromagnetic nanowire. We discuss the properties of dynamic magnetic soliton in uniaxial anisotropic ferromagnetic nanowire driven by spin-transfer torque, and analyze the modulation instability and dark soliton on the spin wave background, which shows the characteristic breather behavior of the soliton as it propagates along the ferromagnetic nanowire. With stronger breather character, we get the novel magnetic rogue wave and clarify its formation mechanism. The generation of magnetic rogue wave mainly arises from the accumulation of energy and magnons toward to its central part. We also observe that the spin-polarized current can control the exchange rate of magnons between the envelope soliton and the background, and the critical current condition is obtained analytically. At last, we have theoretically investigated the current-excited and frequency-adjusted ferromagnetic resonance in magnetic trilayers. A particular case of the perpendicular analyzer reveals that the ferromagnetic resonance curves, including the resonant location and the resonant linewidth, can be adjusted by changing the pinned magnetization direction and the direct current. Under the control of the current and external magnetic field, several magnetic states, such as quasi-parallel and quasi-antiparallel stable states, out-of-plane precession, and bistable states can be realized. The precession frequency can be expressed as a function of the current and external magnetic field.