Biquadratic Exchange Coupling Research Articles

Spin-glass-like behavior of low field magnetisation in multilayer (Gd/Si/Co/Si) n films

The results of experimental investigations of magnetic properties of multilayer (Gd/Si/Co/Si) n films in low magnetic fields are represented. The spin-glass-like behavior of magnetization is found. The role of biquadratic exchange coupling in a forming of magnetic state of system is discussed.

Surface and bulk spin waves in magnetic superlattices with biquadratic exchange coupling

A study is made of the bulk and surface spin wave modes propagating in magnetic superlattices that are composed of two simple cubic ferromagnetic materials which interact by bilinear and biquadratic exchange couplings at the interfaces. A transfer matrix treatment is employed with the calculations carried out for the exchange dominated regime within the framework of the Heisenberg model and taking into account the random phase approximation. The numerical results obtained show that from a certain value of the ratio R between the biquadratic and interfacial bilinear exchange couplings the surface acoustic modes are suppressed and only the optical modes are present.

Multifractal spectra of spin waves in Fibonacci magnetic superlattices with biquadratic exchange coupling

The multifractal properties are investigated for the bulk spin wave bands of quasiperiodic magnetic superlattices arranged according to the Fibonacci sequence. The superlattices are considered to be composed of layers of two simple cubic ferromagnetic materials. The layers are characterized by a bulk bilinear exchange coupling and they interact through an additional biquadratic exchange coupling at the interfaces. The function f( α), which describes the spectrum of singularities, is calculated for different values of the dimensionless in-plane wave vector k x a and ratio R= J bq / J bl I between the biquadratic and interfacial bilinear exchange couplings. Our results show the effects of the biquadratic exchange coupling on the bulk band structure, which becomes more disordered as the ratio R increases.

Magnetic interlayer exchange coupling in epitaxialFe/Si/Fe(001)studied by polarized neutron reflectometry

Polarized neutron reflectometry (PNR) has been used to investigate the magnetic interlayer coupling in a MBE-grown Fe/Si/Fe(001) sandwich at room temperature and at 10 K. Both the magnitude and orientation of the magnetic moments of the Fe layers are obtained from a rigorous analysis of the PNR data. Orthogonal configurations of the Fe magnetizations were observed, providing unambiguous evidence for the presence of a biquadratic term in the exchange coupling energy. The competition between the bilinear and biquadratic exchange couplings results in distinct orthogonal and antiparallel configurations of the Fe magnetizations at room temperature. A previously unresolved magnetic configuration in the room-temperature hysteresis curve was identified by the PNR measurements as a $180\ifmmode^\circ\else\textdegree\fi{}$ spin-flop transition. The dominant role of the biquadratic coupling at low temperatures is evident from the orthogonal configuration of the magnetizations at remanence in the measurements at $T=10\mathrm{K}.$ The magnetic configurations deduced by PNR are in good agreement with those obtained by fitting the magnetic hysteresis loops using a global energy minimum calculation.

Effects of the biquadratic exchange coupling on the localization and scaling laws of spin waves in Fibonacci superlattices

In this paper we study the spin wave spectra of quasiperiodic magnetic superlattices following a Fibonacci sequence. We consider superlattices that are composed of two simple cubic ferromagnetic materials which interact by bilinear and biquadratic exchange couplings at the interfaces. A transfer matrix treatment is employed with the calculations carried out for the exchange dominated regime within the framework of the Heisenberg model and taking into account the random phase approximation (RPA). The numerical results obtained show the effects of the biquadratic exchange coupling on the localization and scaling laws of the spin wave bulk bands.

4f–3d exchange coupling in Gd/X/Co (X=Pt, Cr) multilayers

We have studied the interlayer exchange coupling between Gd and Co through Pt and Cr spacers in a series of multilayers. Magnetization curves have been analyzed with a model, taking into account bilinear and biquadratic interlayer exchange couplings between Gd and Co. The interlayer exchange coupling constants have been determined as a function of the Pt or Cr spacer layer thickness.

Field induced biquadratic exchange in hard/soft ferromagnetic bilayers.

The appearance of biquadratic exchange coupling between soft Fe and hard SmCo thin layers is found. The remanent magnetization in the Fe layer reorients from parallel to perpendicular with respect to the SmCo easy axis after application of large enough negative field. To explain such an unexpected behavior in contacting ferromagnetic layers a model is proposed based on Slonczewski's fluctuating exchange mechanism. In our samples a partial remagnetization of the hard layer creates fluctuations of the bilinear interactions. The intralayer exchange averaging of the resulting magnetization fluctuations in the soft layer causes the observed biquadratic coupling.

In-plane magnetisation anisotropy of FeCr superlattices with biquadratic exchange coupling

Magnetisation anisotropy in non-collinear ordered (0 0 1)FeCr multilayers has been studied. It was found that the interplay between strong biquadratic exchange coupling and fourfold anisotropy causes change in magnetisation ‘easy’ and ‘hard’ axes during the magnetisation process. A simple phenomenological approach for extracting anisotropy and exchange parameters from magnetisation curves has been suggested.

Magnetization in quasiperiodic magnetic multilayers with biquadratic exchange coupling

A theoretical study of the magnetization curves of quasiperiodic magnetic multilayers is presented. We consider structures composed by ferromagnetic films (Fe) with interfilm exchange coupling provided by intervening nonferromagnetic layers (Cr). The theory is based on a realistic phenomenological model, which includes the following contributions to the free magnetic energy: Zeeman, cubic anisotropy, bilinear, and biquadratic exchange energies. The experimental parameters used here are based on experimental data recently reported, which contain sufficiently strong biquadratic exchange coupling.

Interplay of antiferromagnetic coupling in copper/permalloy combination multilayers

The evolution of the giant magnetoresistance (GMR) effect in sputtered combination multilayers (CMLs) of type Py1.8nm//{(Cu1.8nm/Py1.6nm)N/(Cu0.9nm/Py1.6nm)N}y with Py (permalloy=Ni81Fe19) has been investigated at room temperature. It is shown that the GMR characteristic of these CMLs can be phenomenologically predicted, if the physical properties are known, i.e., the GMR effect amplitude, double layer conductance, and bilinear and biquadratic antiferromagnetic exchange coupling constants of the two underlying {Cu/Py}N base systems at the first (Cu0.9nm) and second (Cu1.8nm) antiferromagnetic coupling maximum (AFCM). The GMR characteristic of the simplest CML with N=1 is, e.g., determined by averaging the bilinear and biquadratic exchange coupling constants of the two base systems. The GMR characteristics of CML with N⩾2 are a superposition of that of the underlying {Cu/Py}N base systems weighted by the fraction of the corresponding double layer conductance. Furthermore, it is demonstrated that the CMLs are interesting from an application point of view since they combine the temperature stability of the underlying {Cu/Py}N base system at the second AFCM with a larger GMR effect amplitude.

Biquadratic interlayer exchange coupling in epitaxial Fe/Si/Fe

We have studied the biquadratic exchange coupling in epitaxially grown Fe/Si/Fe. The temperature and thickness dependence of the biquadratic coupling strength were determined unambiguously by fitting the easy- and hard-axis magneto-optical Kerr effect loops. The origin of the biquadratic coupling can be fully understood in terms of Slonczewski’s loose spins mechanism.

Antiferromagnetic coupling in fcc Fe overlayers on Ni/Cu(100)

Magnetic properties of ultrathin fcc Fe overlayers on Ni/Cu(100) have been determined to study the influence of a magnetic interface. Three regions of different magnetic behavior are distinguished by magneto-optic Kerr ellipsometry, in line with previous studies of Fe/Co/Cu(100) and Fe/Ni/Cu(100). These magnetic states are closely related to the film structure. Above 10 monolayers (ML), the iron films are homogeneously magnetized and adopt the bcc phase. Very thin films up to 2.5 ML are homogeneously magnetized as well but show an fcc structure in conjunction with a $(4\ifmmode\times\else\texttimes\fi{}1)$ reconstruction. The most complex magnetic properties characterize Fe films between 5 and 10 ML. In this thickness range the iron films are not homogeneously magnetized. Instead ferromagnetism is only observed at the Fe film surface and the Fe/Ni film interface. The surface magnetization is apparently correlated with an enlarged atomic volume at the surface and a $(2\ifmmode\times\else\texttimes\fi{}1)$ surface reconstruction. Additionally, the magnetic Ni substrate induces ferromagnetic order in the Fe film at the Fe/Ni interface. The coupling of the two ferromagnetic portions of the film shows a strong temperature dependence. This is attributed to the temperature dependence of the bilinear and biquadratic exchange coupling. At low temperature an antiferromagnetic coupling between the two ferromagnetic portions is observed. With increasing temperature this is followed by a canted spin arrangement and finally a ferromagnetic coupling.

Self-similar magnetoresistance of Fibonacci ultrathin magnetic films

We study numerically the magnetic properties (magnetization and magnetoresistance) of ultra-thin magnetic films (Fe/Cr) grown following the Fibonacci sequence. We use a phenomenological model which includes Zeeman, cubic anisotropy, bilinear and biquadratic exchange energies. Our physical parameters are based on experimental data recently reported, which contain biquadratic exchange coupling with magnitude comparable to the bilinear exchange coupling. When biquadratic exchange coupling is sufficiently large a striking self-similar pattern emerges.

Pinholes in antiferromagnetically coupled multilayers: Effects on hysteresis loops and relation to biquadratic exchange

We present a micromagnetic study of the influence of ferromagnetic bridges between consecutive ferromagnetic layers in antiferromagnetically coupled multilayers. The model is compared with experimental results for hysteresis loops obtained from the multilayer systems Co-Cu and FeNi-Ag. The presence of pinholes in Cu-Co multilayers is confirmed by transmission electron microscopy. We demonstrate that low densities of ferromagnetic pinholes in such multilayers are sufficient to give rise to significant deviations from the expected bilinear interlayer coupling and modify the observed interlayer oscillatory exchange coupling. The effects of pinholes can be simulated in certain cases by biquadratic exchange coupling, and we propose a magnetic phase diagram which correlates the apparent bilinear and biquadratic couplings to the pinholes density, size, and interlayer exchange strength.

The observation of non-homogeneous FMR modes in multilayer Fe/Cr structures

The spectrum of excitations in [Fe/Cr] n structures with a non-collinear magnetic ordering was studied by means of the FMR technique. The measurements were carried out at room temperature in the frequency range of 9.5–37 GHz with both static and microwave magnetic fields lying in the film plane. Along with the acoustic FMR mode several additional modes were observed in the longitudinal pumping configuration. The resonance spectrum of an infinite magnetic superlattice was calculated analytically on the basis of the biquadratic exchange coupling model. Both cases were considered: external magnetic field H parallel and perpendicular to the film plane. It was shown that the observed additional FMR modes correspond to the excitation of standing spin waves with wave vectors perpendicular to the superlattice plane.

Effect of biquadratic exchange coupling on magnetoresistance and magnetization process in magnetic bilayer systems

An improved model is proposed to deal with the magnetic bilayer systems taking into account the contribution of the anisotropy energy and biquadratic exchange coupling to elaborate on the evolution of the magnetoresistance (MR) ratio and magnetization process. The results indicate that the characteristic behavior of the MR ratio depends distinctly on both the biquadratic coupling constant and the layer thickness. The profile of the MR ratio was found to vary from an inverted bell shape to a concave pyramid with increasing biquadratic coupling strength, and decays sharply with the layer thickness. This model calculation helps us to provide a venue for further understanding the MR or giant magnetoresistance behavior of the magnetic multilayer system.

Biquadratic coupling in sputtered Fe/Cr/Fe still in need of a new mechanism

The bilinear (J1) and biquadratic (J2) exchange coupling constants were measured in sputtered trilayers of (100) Fe(40 Å)/Cr(s)/Fe(40 Å) for several Cr spacer layer thicknesses in the range s=8–35 Å and as a function of temperature T, using magneto-optical Kerr effect magnetometry, Brillouin light scattering, and ferromagnetic resonance. In the samples in the range s=8–13 Å, corresponding to the first antiferromagnetic peak of J1, J2 follows J1 with a room temperature ratio J2/J1≅0.1, while in the range 25–35 Å, corresponding to the second antiferromagnetic peak, J2 also follows J1 but with a much larger ratio J2/J1≅1. This result, as well as the temperature dependence of J2 in all samples but the one with s=15 Å, cannot be explained by any of the intrinsic or extrinsic mechanisms that have been proposed for the origin of the biquadratic exchange coupling in Fe/Cr/Fe.

Hydrogen induced changes of the interlayer coupling in Fe (3)/V ( x) superlattices ( x=11–16)

The effect of hydrogen on the magnetic exchange coupling between iron layers through vanadium spacer layers has been studied with magneto-optical Kerr effect experiments in Fe (3)/V ( x) superlattices. Here x refers to the number of V monolayers varying from 11 to 16 and the Fe layer thickness is fixed at three monolayers. Without hydrogen the superlattice is antiferromagnetic (AFM) for x between 12 and 14 and ferromagnetic (FM) in all other cases. With hydrogen loading the coupling can be switched from AFM to FM and vice versa. As previously observed with neutron reflectivity measurements (Hjörvarsson et al., Phys. Rev. Lett. 79 (1997) 901) the change of the interlayer coupling upon hydrogen uptake is not simply due to the expansion of the non-magnetic vanadium spacer layer but more likely to the distortion of the Fermi surface. Bilinear and biquadratic exchange couplings can be recognized by the magnetic hysteresis loops and their coupling energies have been extracted by fits to the curves. For all samples the easy axis of the magnetization is in the plane without any preferred in-plane direction. Hydrogen loading does not affect the magnetic anisotropy of these samples.

Bilinear and biquadratic interlayer exchange coupling in sputtered Co/Cu multilayers damaged with residual gas impurities

The oscillatory indirect exchange coupling exhibited by magnetic/nonmagnetic metal multilayers is known to be highly sensitive to structural defects. We have measured the effects on coupling of residual gas atoms in sputtered Co/Cu multilayers. We have used a simple technique to selectively probe particular parts of the multilayer stack. A large reduction in the giant magnetoresistance has been observed when gas impurity atoms are introduced into the middle of the Cu spacer layers, with a corresponding increase in the remanence of the sample. These changes are shown to be consistent with overwhelmingly strong biquadratic coupling between the Co layers. This leads to the moments in adjacent layers being no longer collinear in zero applied field, which we have confirmed by other measurements. We discuss the applicability of the various theoretical models of biquadratic coupling to our observations.

Exchange couplings between two Fe layers in Fe/Al/Fe/Ni-Fe/NiO sandwiches

Exchange couplings between two Fe layers have been investigated in polycrystalline Fe/Al/Fe/Ni-Fe/NiO and Fe/Al/Fe/Ni-Fe sandwiches. Linear exchange couplings between the two Fe layers were strong and ferromagnetic when the thickness of the Al spacer was between 0.7 and 2.2 nm. We observed biquadratic exchange couplings (90 degree couplings) when the thickness of the Al spacer was between 2.5 and 4.0 nm.