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

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.

Effect of annealing time on the exchange coupling interactions and microstruc-ture of nanocomposite Pr_(7.5)Dy_1Fe_(71)Co_(15)Nb_1B_(4.5) ribbons

The influence of annealing time on the magnetic properties and microstructure of nanocomposite Pr7.5Dy1Fe71Co15Nb1B4.5 ribbons was systematically investigated by the methods of vibrating sample magnetometer （VSM）, X-ray diffraction （XRD） and high resolution transmission electron microscopy （HRTEM）. Interaction domains derived from strong exchange coupling interactions between hard and soft magnetic grains were imaged using magnetic force microscopy （MFM）. Maximum remanence, intrinsic coercivity, and maximum energy product values were obtained in the ribbons annealed at 700℃ for 15 min, which were composed of Pr2（Fe, Co）14B, α-（Fe, Co）, and slight Pr2（Fe, CO）17 phases. Although Jr, Hci, and （Bn）max decreased gradually with further increase of annealing time, it is emphasized that comparatively high Jr and Hci and （BH）max were obtained in a wide annealing time period of 15 to 360 min. The shape of initial magnetization curves and hysteresis loops change as a function of annealing time, indicating different magnetization reversal routes, which can be fully explained by the corresponding microstructure.

Effect of chromium interlayer on magnetic exchange coupling of SmCo/Cr/TbFeCo multilayer thin films

A series of SmCo/Cr/TbFeCo multilayer thin films with perpendicular anisotropy were prepared by RF- magnetron sputtering system, and the effects of Cr interlayer thickness on magnetic properties and interlayer exchange coupling were investigated. It was found that the magnetic properties varied with the thickness of Cr interlayer, especially the values of saturation magnetization Ms and the coercivity Hc fluctuated periodically with the thickness of Cr interlayer. STM images revealed that the variation of coercivity Hc was attributed to the microstructure change of SmCo layer influenced by Cr interlayer, and the variation of Ms was related to interlayer exchange coupling.

Effect of exchange coupling on magnetic property in Sm–Co/α-Fe layered system

The hysteresis loops as well as the spin distributions of Sm-Co/a-Fe bilayers have been investigated by both three- dimensional （3D） and one-dimensional （1D） micromagnetic calculations, focusing on the effect of the interface exchange coupling under various soft layer thicknesses ts. The exchange coupling coefficient Alas between the hard and soft ,layers varies from 1.8 x10-6 erg/cm to 0.45 x 10-6 erg/cm, while the soft layer thickness increases from 2 nm to 10 nm. As the exchange coupling decreases, the squareness of the loop gradually deteriorates, both pinning and coercive fields rise up monotonically, and the nucleation field goes down. On the other hand, an increment of the soft layer thickness leads to a significant drop of the nucleation field, the deterioration of the hysteresis loop squareness, and an increase of the remanence. The simulated loops based on the 3D and 1D methods are consistent with each other and in good agreement with the measured loops for Sm-Co/a-Fe multilayers.

Exchange-coupling-induced fourfold magnetic anisotropy in CoFeB/FeRh bilayer grown on SrTiO_(3)(001)

Exchange coupling across the interface between a ferromagnetic(FM)layer and an antiferromagnetic(AFM)or another FM layer may induce a unidirectional magnetic anisotropy and/or a uniaxial magnetic anisotropy,which has been extensively studied due to the important application in magnetic materials and devices.In this work,we observed a fourfold magnetic anisotropy in amorphous Co Fe B layer when exchange coupling to an adjacent Fe Rh layer which is epitaxially grown on an SrTiO_(3)(001)substrate.As the temperature rises from 300 K to 400 K,Fe Rh film undergoes a phase transition from AFM to FM phase,the induced fourfold magnetic anisotropy in the Co Fe B layer switches the orientation from the Fe Rh<110>to Fe Rh<100>directions and the strength is obviously reduced.In addition,the effective magnetic damping as well as the two-magnon scattering of the Co Fe B/Fe Rh bilayer also remarkably increase with the occurrence of magnetic phase transition of Fe Rh.No exchange bias is observed in the bilayer even when Fe Rh is in the nominal AFM state,which is probably because the residual FM Fe Rh moments located at the interface can well separate the exchange coupling between the below pinned Fe Rh moments and the Co Fe B moments.

Temperature-dependent interlayer exchange coupling strength in synthetic antiferromagnetic [Pt/Co]_2/Ru/[Co/Pt]_4 multilayers

In this work, we experimentally investigated the thermal stability of the interlayer exchange coupling field(Hex) and strength(-Jiec) in synthetic antiferromagnetic(SAF) structure of [Pt(0.6)/Co(0.6)]2/Ru(tRu)/[Co(0.6)/Pt(0.6)]4multilayers with perpendicular anisotropy. Depending on the thickness of the spacing ruthenium(Ru) layer, the observed interlayer exchange coupling can be either ferromagnetic or antiferromagnetic. The Hexwere studied by measuring the magnetization hysteresis loops in the temperature range from 100 K to 700 K as well as the theoretical calculation of the-Jiec. It is found that the interlayer coupling in the multilayers is very sensitive to the thickness of Ru and temperature. The Hexexhibits either a linear or a non-linear dependence on the temperature for different thickness of Ru. Furthermore, our SAF multilayers show a high thermal stability even up to 600 K(Hex= 3.19 kOe,-Jiec= 1.97 erg/cm~2 for tRu=0.6 nm, the unit 1 Oe = 79.5775 A·m-1), which was higher than the previous studies.

Large coercivity and unconventional exchange coupling in manganese-oxide-coated manganese gallium nanoparticles

The microstructures and magnetic properties of nanoparticles, each composed of an antiferromagnetic （AFM） manganese-oxide shell and a ferromagnetic-like core of manganese-gallium （MnGa） compounds, are studied. The coreshell structure is confirmed by transmission electron microscope （TEM）. The ferromagnetic-like core contains three kinds of MnGa binary compounds, i.e., ferrimagnetic （FI） DO22-type MnaGa, ferromagnetic （FM） Mn8Gas, and AFM DO19-type Mn3Ga, of which the first two correspond respectively to a hard magnetic phase and to a soft one. Decoupling effect between these two phases is found at low temperature, which weakens gradually with increasing temperature and disappears above 200 K. The exchange bias （EB） effect is observed simultaneously, which is caused by the exchange coupling between the AFM shell and FM-like core. A large coercivity of 6.96 kOe （1Oe = 79.5775 A·m^-1） and a maximum EB value of 0.45 kOe are achieved at 300 K and 200 K respectively.

Providing insight into exchange coupling within nanomagnetism:mechanism,micromagnetic simulation,synthesis and biomedical application

Exchange coupling within nanomagnetism is a rapidly evolving field with significant implications for that plays a crucial role in the development of magnetic nanomaterials.Manipulating exchange coupling interaction enables the magnetic systems to overcome limitations associated with size-dependent magnetic behavior within nano scale,thereby improving their magnetic properties and providing for superior performance in biomedical applications compared with single-phase magnetic materials.Understanding the underlying mechanism of exchange coupling and its impact on macroscopic magnetic properties is crucial for the design and application of such magnetic materials.This review provides an overview of recent advances in interfacial exchange coupling among different magnetic modalities-ferromagnetism,ferrimagnetism,and antiferromagnetism-based on core-shell magnetic nanoparticles(MNPs).Additionally,this review discusses micromagnetic simulations to gain insights into the relationship between the microscopic magnetic structure(size,shape,composition,and exchange coupling)and the resulting macroscopic properties.The controlled synthesis of MNPs is summarized,including one-step method and two-step method.The precise manipulation of interfacial characteristics is of great importance,albeit challenging,as it allows for the finetuning of magnetic properties tailored for specific applications.The review also explores potential applications of coreshell MNPs in magnetic resonance imaging,hyperthermia therapy,targeted drug delivery,and advanced neuromodulation.

The structure dependence of exchange bias in ferromagnetic/antiferromagnetic bilayers

The structure dependence of exchange bias in ferromagnetic/antiferromagnetic （FM/AF） bilayers has been investigated in detail by extending Slonczewski＇s ＇proximity magnetism＇ idea. Here three important parameters are discussed for FM/AF bilayers, i.e. interracial bilinear exchange coupling J1, interracial biquadratic （spin-flop） exchange coupling J2 and antiferromagnetic layer thickness tAF. The results show that both the occurrence and the variety of the exchange bias strongly depend on the above parameters. More importantly, the small spin-flop exchange coupling may result in an exchange bias without the interracial bilinear exchange coupling. However, in general, the spin-flop exchange coupling cannot result in the exchange bias. The corresponding critical parameters in which the exchange bias will occur or approach saturation are also presented.

The rotational anisotropies in the ferromagnetism/antiferromagnetism 1/ antiferromagnetism 2 exchange bias structures

The rotational anisotropies in the exchange bias structures of ferromagnetism/antiferromagnetism 1/antiferro- magnetism 2 are studied in this paper. Based on the model, in which the antiferromagnetism is treated with an Ising mean field theory and the rotational anisotropy is assumed to be related to the field created by the moment induced on the antiferromagnetic layer next to the ferromagnetic layer, we can explain why in experiments for ferromag- netism （FM）/antiferromagntism 1 （AFM1）/antiferromagnetism 2 （AFM2） systems the thickness-dependent rotational anisotropy value is non-monotonic, i.e. it reaches a minimum for this system at a specific thickness of the first anti- ferromagnetic layer and exhibits oscillatory behaviour. In addition, we find that the temperature-dependent rotational anisotropy value is in good agreement with the experimental result.

Ru thickness-dependent interlayer coupling and ultrahigh FMR frequency in FeCoB/Ru/FeCoB sandwich trilayers

The antiferromagnetic(AFM) interlayer coupling effective field in a ferromagnetic/non-magnetic/ferromagnetic(FM/NM/FM) sandwich structure, as a driving force, can dramatically enhance the ferromagnetic resonance(FMR) frequency. Changing the non-magnetic spacer thickness is an effective way to control the interlayer coupling type and intensity, as well as the FMR frequency. In this study, Fe Co B/Ru/Fe Co B sandwich trilayers with Ru thickness(tRu) ranging from 1 A to 16 A are prepared by a compositional gradient sputtering(CGS) method. It is revealed that a stress-induced anisotropy is present in the Fe Co B films due to the B composition gradient in the samples. A tRu-dependent oscillation of interlayer coupling from FM to AFM with two periods is observed. An AFM coupling occurs in a range of 2 A ≤ tRu≤ 8 A and over 16 A, while an FM coupling is present in a range of tRu< 2 A and 9 A ≤ tRu≤ 14.5 A. It is interesting that an ultrahigh optical mode(OM) FMR frequency in excess of 20 GHz is obtained in the sample with tRu= 2.5 A under an AFM coupling. The dynamic coupling mechanism in trilayers is simulated, and the corresponding coupling types at different values of tRuare verified by Layadi’s rigid model. This study provides a controllable way to prepare and investigate the ultrahigh FMR films.

Magnetic properties of soft layer/FePt-MgO exchange coupled composite perpendicular recording media

The magnetic properties of exchange coupled composite （ECC） media that are composed of perpendicular magnetic recording media FePt MgO and two kinds of soft layers have been studied by using an x-ray diffractometer, a polar Kerr magneto-optical system （PMOKE） and a vibrating sample magnetometer （VSM）. The results show that ECC media can reduce the coercivities of perpendicular magnetic recording media FePt-MgO. The ECC media with granular-type soft layers have weaker exchange couplings between magnetic grains and the magnetization process, for ECC media of this kind mainly follow the Stoner Wohlfarth model.

Theoretical Studies on the Spin Exchange Interaction in Copper(II) Complexes Coordinated with Nitronyl Nitroxide

Nitronyl nitroxide radical 1, NIT (4, 4, 5, 5-tetramethyl-4, 5-dihydro-1H-imidazolyl-1- oxyl-3-oxide) and copper(II) chloride complexes with nitronyl nitroxide 2, [Cu(NITPh)2Cl2] (NITPh = 2-phenyl-4, 4, 5, 5-tetramethyl-imidazoline-1-oxyl-3-oxide) were studied with density functional theory (DFT). The magnetic orbital analysis reveals that the antiferromagnetic coupling for complex 2 is due to the antibonding s*-orbital overlap between 22x-yd(Cu) and p* (NO) orbitals. Also, spin population and atomic charge distribution analysis suggest that for AFS of complex 2 the antiferromagnetic coupling between the radical ligands and the copper(II) ion originates from the spin delocalization induced by the a electron transfer from p*(NO) to 22x-yd(Cu) orbital.

Surface states modulated exchange interaction in Bi2Se3/thulium iron garnet heterostructures

We investigate the modulation of magnetic anisotropy of thulium iron garnet(TmIG)films by interfaced Bi2Se3 thin films.High quality epitaxial growth of Bi2Se3 films has been achieved by molecular beam epitaxy on TmIG films.By the method of ferromagnetic resonance,we find that the perpendicular magnetic anisotropy(PMA)of TmIG can be greatly strengthened by the adjacent Bi2Se3 layer.Moreover,the competition between topological surface states and thickness dependent bulk states of Bi2Se3 gives rise to the modulation of PMA of the Bi2Se3/TmIG heterostructures.The interfacial interaction can be attributed to the enhanced exchange coupling between Fe^3+ions of TmIG mediated by topological surface electrons of Bi2Se3.

Nanocrystalline exchange-coupled Pr-Fe-B permanent magnets

Nanocomposite Pr2Fe14B/α-Fe permanent magnets were prepared by melt spinning and subsequent crystallizahon of Pr8Fe86B6, amorphous Precursnors. The microstructure is a two-phase nanocomposite of Pr2 Fe14 B and softmagnetic α-Fe with an average size of 30nm. X-ray diffration, Thermomagnetic analysis and TEM analy0sis indicatetha amorphous Pr8Fe86B6, alloy crystallizes through the process of Am→Am→Am'+α-Fe→Pr2Fe23B3+α-Fe-Pr2Fe14B+α-FeThe highest value of remanence (Br), cocreivity (Hci) and maximum energy Product ((BH)max) of the nanocrystallinealloys are 1.10T, 340 kA/m and 110 kJ/m3 respechvely, exhibihng remarkable remanence enhancement. The effect ofannaling temperature and time on the microstructure and magnetic properties was also studied. The resultS show thatappropriate annealing temperature and time are important for obtaining the optimal microstructure and the bestmagnetic properties.

Magnetic anisotropy,exchange coupling and Dzyaloshinskii–Moriya interaction of two-dimensional magnets

The two-dimensional(2D)magnets provide novel opportunities for understanding magnetism and investigating spin related phenomena in several atomic thickness.Multiple features of 2D magnets,such as critical temperatures,magnetoelectric/magneto-optic responses,and spin configurations,depend on the basic magnetic terms that describe various spins interactions and cooperatively determine the spin Hamiltonian of studied systems.In this review,we present a comprehensive survey of three types of basic terms,including magnetic anisotropy that is intimately related with longrange magnetic order,exchange coupling that normally dominates the spin interactions,and Dzyaloshinskii–Moriya interaction(DMI)that favors the noncollinear spin configurations,from the theoretical aspect.We introduce not only the physical features and origin of these crucial terms in 2D magnets but also many correlated phenomena,which may lead to the advance of 2D spintronics.

Anisotropic exchange coupling interaction between hard-hard magnetic grains in sintered SrFe_(12)O_(19)ferrites

Exchange coupling interaction in sintered magnetic materials is generally isotropic.In this study,the anisotropic exchange coupling interaction was found in sintered oblate cylindrical SrFe_(12)O_(19)(SrM)specimens obtained by the SrM nanopowders synthesized via a hydrothermal method.According to Henkel plots,the exchange coupling interaction between hard-hard magnetic grains was found in both as-pressed and sintered specimens.However,the exchange coupling interaction can only be found in the in-plane direction but not in the out-of-plane direction for thel sintered specimens.By building a model of a grain configuration,this anisotropy of the exchange coupling interaction was ascribed to the vertically arranged plate-like SrM grains with micrometers in width but nanometers in thickness,which was confirmed by morphologies of cross sections in fractured specimens.

Effect of zirconium content on exchange coupling and magnetization reversal of nanocrystalline Nd_(12.3)Fe_(81.7-x)Zr_xB_6 alloy

The effect of Zr content on exchange coupling and magnetization reversal of the Ndl2.3Fe81.7_xZrxB6 （x=0-3.0） ribbons was systematically investigated. Interaction domains were imaged by magnetic force microscopy （MFM）. The strength of interactions determined by Wohlfarth＇s analysis increased first with Zr content x increasing, reached the maximum value at x=l.5, and then decreased with x further increasing. Initial magnetization curves and dependence of coercivity and remanence on applied magnetic field showed that the mechanism of coercivity in all samples was mainly of exchange coupling pinning type, which was enhanced with x increasing. It was found by three-dimensional atom probe （3DAP） that Zr atoms did not partition into the Nd2Fe14B hard magnetic phase, but significantly enriched at the interfacial region.

The influence of interface exchange coupling on the demagnetization process for perpendicularly oriented FePt/α-Fe/FePt trilayers

The influence of the interface exchange coupling on the magnetization reversal process for a FePt/α-Fe/FePt tri-layer structure has been studied through a micromagnetic approach.The analytical formula of the nucleation field has been derived.It is found that the nucleation field increases as the interface coupling constant rises.Especially when the thickness of the soft layer is small,the influence of the exchange coupling on the nucleation field is significant.The angular distributions of the magnetization for various exchange coupling constants have been obtained by numerical calculation.It is found that the angular distribution of the magnetization is discontinuous at the interface of the hard and soft layers.In the meantime,the pinning field decreases with the increase of the thickness of the soft layer and the exchange coupling constant.

Effect of Ga addition on the magnetic properties and microstructure of nanocrystalline Nd_(12.3)Fe_(81.7)B_(6.0) ribbons

Nd 12.3 Fe 81.7 x Ga x B 6.0 （x = 0-1.8） ribbons were prepared by melt spinning at 22 m/s and subsequent annealing treatment. The influences of Ga addition and annealing conditions on the magnetic properties and microstructure of the nanocrystalline alloys were systematically investigated. After being annealed at 620℃ for 20 min, the J r and H ci increased from 0.85 T and 582.6 kA/m for Ga-free sample to 0.97 T and 734.6 kA/m for the x = 0.9 sample, respectively. The （BH） max for the x = 0.9 sample increased by about 40% from 96.3 to 135.5 kJ/m 3 compared with that of the Ga-free one. The significant improvement of magnetic properties originated from the refinement of grains in the samples by introducing Ga, which led to a stronger exchange coupling between the neighboring grains in comparison with that in Ga-free samples. The microstructure and magnetic properties of the samples depended strongly on annealing parameters, while the sensitivity of micro-structure to annealing conditions could be significantly suppressed by the addition of Ga element.