Interlayer exchange coupling in ferromagnet-semiconductor digital magnetic alloys

The interlayer exchange coupling in ferromagnet-semiconductor digital magnetic alloys in which monolyers (submonolayers) of transition metals are embedded into a semiconductor matrix is studied theoretically. A mechanism of an indirect exchange between ferromagnetic δ layers is proposed; it is based on the confinement of carriers in two-dimensional spin-polarized states inside the energy gap of the semiconductor. These appear due to strong potential and exchange carrier scattering by the δ layers. The interlayer exchange coupling is shown to occur through a nondegenerate semiconductor interlayer because of virtual electron excitations through an energy barrier separating these partly filled two-dimensional spin-polarized states and the edge of the bulk semiconductor band. The interlayer coupling intensity decreases exponentially with increasing distance between neighboring δ layers, and the type of this coupling can change from ferromagnetic into antiferromagnetic or vice versa as the interlayer thickness or the degree of filling the two-dimensional states increases.     

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.     

Coupling Stacking Orders with Interlayer Magnetism in Bilayer H-VSe_2

Stacking-dependent magnetism in van der Waals materials has caught intense interests.Based on the first principle calculations,we investigate the coupling between stacking orders and interlayer magnetic orders in bilayer H-VSe_2.It is found that there are two stable stacking orders in bilayer H-VSe_2,named AB-stacking and A'B-stacking.Under standard DFT framework,the A'B-stacking prefers the interlayer AFM order and is semiconductive,whereas the AB-stacking prefers the FM order and is metallic.However,under the DFT+U framework both the stacking orders prefer the interlayer AFM order and are semiconductive.By detailedly analyzing this difference,we find that the interlayer magnetism originates from the competition between antiferromagnetic interlayer super-superexchange and ferromagnetic interlayer double exchange,in which both the interlayer Se-4p_z orbitals play a crucial role.In the DFT+U calculations,the double exchange is suppressed due to the opened bandgap,such that the interlayer magnetic orders are decoupled with the stacking orders.Based on this competition mechanism,we propose that a moderate hole doping can significantly enhance the interlayer double exchange,and can be used to switch the interlayer magnetic orders in bilayer VSe_2.This method is also applicable to a wide range of semiconductive van der Waals magnets.     

Domain size and structure in exchange coupled [Co/Pt]/NiO/[Co/Pt] multilayers

We investigate the competing effects of interlayer exchange coupling and magnetostatic coupling in the magnetic heterostructure ([Co/Pt]/NiO/[Co/Pt]) with perpendicular magnetic anisotropy (PMA). This particular heterostructure is unique among coupled materials with PMA in directly exhibiting both ferromagnetic and antiferromagnetic coupling, oscillating between the two as a function of spacer layer thickness. By systematically tuning the coupling interactions via a wedge-shaped NiO spacer layer, we explore the energetics that dictate magnetic domain formation using high resolution magnetic force microscopy coupled with the magneto-optical Kerr effect. This technique probes the microscopic and macroscopic magnetic behavior as a continuous function of thickness and the interlayer exchange coupling, including the regions where interlayer coupling goes through zero. We see significant changes in domain structure based on the sign of coupling, and also show that magnetic domain size is directly related to the magnitude of the interlayer exchange coupling energy, which generally dominates over the magnetostatic interactions. When magnetostatic interactions become comparable to the interlayer exchange coupling, a delicate interplay between the differing energy contributions is apparent and energy scales are extracted. The results are of intense interest to the magnetic recording industry and also illustrate a relatively new avenue of undiscovered physics, primarily dealing with the delicate balance of energies in the formation of magnetic domains for coupled systems with PMA, defining limits on domain size as well as the interplay between roughness, domains and magnetic coupling.     

Quantum competitions between the effects of the interlayer exchange couplings and the magnetically structural symmetry in a four-layer ferrimagnetic superlattice

The magnon energy spectra, the sublayer magnetization and the quantum fluctuations in a ferrimagnetic superlattice consisting of four different magnetic sublayers are studied by employing the linear spin-wave approach and Green's function technique. The effects of the interlayer exchange couplings and the spin quantum numbers on the sublayer magnetization and the quantum fluctuations of the systems are discussed for three different spin configurations. The roles of quantum competitions among the interlayer exchange couplings and the symmetry of the different spin configurations have been understood. The magnetizations of some sublayers increase monotonously, while those of others can exhibit their maximum, and the quantum fluctuations of the whole superlattice system can show a minimum when one of the antiferromagnetic interlayer exchange couplings increases. This is due to the quantum competition/transmission of effects of the interlayer exchange couplings. When the spin quantum number of sublayers varies, the system goes through from a quantum region of small spin numbers to a classical region of large spin numbers. The quantum fluctuations of the system exhibit a maximum as a function of the spin quantum number of a sublayer, which is related with higher symmetry of the system. It belongs to the type III Shubnikov group of magnetic groups. This magnetically structural symmetry consists of not only the symmetry of space group, but also the symmetry of the direction and strength of spins.     

Skyrmion size evolution with interlayer exchange coupled ferromagnetic nanostructures

Skyrmions are viewed as the basic elements for the future generation of magnetic memories. Their small sizes and good dynamical properties give them the ability to store and transport information easily. In this paper, we used micromagnetic simulation to study the contribution of interlayer exchange coupling and the geometrical confinement on scaling magnetic skyrmions. We started the work by comparing the utility of interlayer exchange coupling to the perpendicular magnetic field in scaling magnetic skyrmions. Then, we investigated the effect of combining the interlayer exchange coupling and geometrical confinement to reduce skyrmions size.     

Oscillatory interlayer exchange coupling and its temperature dependence in [Pt/Co]3/NiO/[Co/Pt]3 multilayers with perpendicular anisotropy

Interlayer exchange coupling that oscillates between antiferromagnetic and ferromagnetic as a function of NiO thickness has been observed in [Pt(5 A)/Co(4 A)](3)/NiO(t(NiO) A)/[Co(4 A)/Pt(5 A)](3) multilayers with out-of-plane anisotropy. The period of oscillation corresponds to approximately 2 monolayers of NiO. This oscillatory behavior is possibly attributed to the antiferromagnetic ordering in NiO. The antiferromagnetic interlayer exchange coupling for the 11 A NiO layer shows an increase in coupling strength with increasing temperature, in agreement with the quantum interference model of Bruno for insulating spacer layers. A coexistence of exchange biasing and antiferromagnetic interlayer exchange coupling has been observed below T=250 K.     

Magnetic resonance in multilayer Gd/Si/Co magnetic films

The magnetic properties of multilayer Gd/Si/Co magnetic films are experimentally studied by electron magnetic resonance and analyzed theoretically. The introduction of a semiconductor silicon interlayer is found to substantially affect the magnetic interlayer coupling and the magnetic dynamics of the system. The interlayer coupling is shown to be ferromagnetic for the (Gd/Si)_n films and to be antiferromagnetic for the (Gd/Si/Co/Si)_n films. The temperature dependences of the exchange parameters and the gyromagnetic ratios are determined. Possible mechanisms responsible for the formation of the interlayer coupling are discussed.     

Interlayer magnetic coupling in multilayer magnetic Fe/Cr/Fe systems

The interlayer magnetic coupling of iron layers as a function of the chromium spacer thickness and temperature has been studied for three-layer epitaxial Fe/Cr/Fe films by the methods of Kerr magnetometry and Mandelstam-Brillouin scattering. The results obtained indicate that the short-period component of the interlayer exchange is related to the spin density wave in the chromium spacer.     

Noncollinear interlayer exchange in Fe/Cr/Fe magnetic structures with different interface roughnesses

The interaction of iron layers through a chromium spacer in Fe/Cr/Fe trilayers with different roughnesses of interfaces was studied by the Kerr magnetometry and Mandel’shtam-Brillouin light scattering techniques so as to trace the interlayer exchange coupling of the Fe layers depending on the Cr spacer thickness and the sample temperature. It is established that, in a broad range of these parameters, the interlayer exchange in Fe/Cr/Fe structures with sufficiently smooth interfaces is adequately described using the proximity magnetism and half-angle coupling models taking into account the antiferromagnetic properties of chromium. As the interface roughness increases, the well-known biquadratic exchange model becomes valid. This is evidence for the decisive role of the magnetic stiffness of a Cr spacer and the structure of interfaces on the noncollinear exchange coupling in Fe/Cr/Fe trilayers.     

Interlayer exchange coupling,crystalline and magnetic structure in Fe/CsCl–FeSi multilayers grown by molecular beam epitaxy

Crystalline and magnetic structure as well as the interlayer exchange coupling in MBE grown Fe/FeSi multilayers are investigated. From conversion electron Mössbauer spectroscopy and ion beam channeling measurements the spacer FeSi material is found to be stabilized in a crystalline metastable metallic FeSi phase with the CsCl structure. Strong non-oscillatory interlayer exchange coupling is identified with magnetometry and synchrotron Mössbauer reflectometry. From the fits of the time spectrum and the resonant ?—? scans a model for the sublayer magnetization of the multilayer is deduced.

     

The influence of interlayer exchange coupling on magnetic ordering in Fe/V superlattices

The relation between the interlayer exchange coupling and magnetic order is addressed, using Fe/V(0 0 1) superlattices as a model system. Large decrease in the ordering temperature (T_c) is observed with decreasing interlayer exchange coupling. The effective exponents of the magnetization were determined to be larger than 0.5 for all the samples, which is strongly deviating from the classical values of both two- and three-dimensional systems. This effect can partially be ascribed to the presence of boundaries, invoked by the finite number of magnetic layers.     

Interlayer exchange coupling in iron/silicon nanostructures

A superexchange mechanism is considered for the interlayer exchange coupling in Fe/Si nanostructures. It is assumed that the most important role in this mechanism is played by iron-silicon interfaces, in whose immediate vicinity the contact-induced ferromagnetic phase of body-centered iron monosilicide forms and spin-polarized interface states arise. The magnetic coupling between iron layers is accomplished by means of the interaction of interface states through the normal-semiconductor spacer layer and involves both intraband and interband processes. The nonmonotonic character of the dependence of the interband exchange coupling on the spacer thickness and composition (the occurrence of a maximu, the change in shape, the possible sign reversal of the bilinear component) is caused by competition between the ferro-and antiferromagnetic super-exchange components and by the complex character of the spacer electronic spectrum (in particular, by the occurrence of several equivalent extrema in the semiconductor bands). This model qualitatively reproduces the main features of the mechanism of interlayer exchange coupling in real Fe/Si nanostructures.     

T(3/2) dependence of the interlayer exchange coupling in ferromagnetic multilayers

The temperature dependence of the interlayer exchange coupling in ferromagnetic films coupled across nonmagnetic spacers is determined via in situ ferromagnetic resonance experiments for various systems. Clear evidence for a T(3/2) law is found over a wide temperature regime.     

Phase transition “polydomain state-single-domain state” with exchange springs in the antiferromagnetic interlayer of the spin-valve structure

The phase transition “polydomain state-single-domain state” with exchange springs in the antiferromagnetic interlayer of the spin-valve ferromagnet-antiferromagnet-ferromagnet structure, which occurs as the ratio of the interlayer thickness to the width of atomic steps on the interfaces between the layers increases, has been investigated using mathematical simulation. The critical value of this ratio, at which the phase transition occurs, and the deflection of exchange springs that appear at the interfaces between the layers have been determined in a wide range of values of the single-ion anisotropy constant.     

Specific Heat of a Two-Layer Magnetic Superlattice

The specific heats of both a two-layer ferromagnetic superlattice and atwo-layer ferrimagnetic one are studied. It is found that the spin quantumnumbers, the interlayer and intralayer exchange couplings, the anisotropy,the applied magnetic field, and the temperature all affect the specificheat of these superlattices. For both the ferromagnetic and ferrimagneticsuperlattices, the specific heat decreases with increasing the spin quantumnumber, the absolute value of interlayer exchange coupling, intralayerexchange coupling, and anisotropy, while it increases with increasingtemperature at low temperatures. When an applied magnetic field is enhanced, the specific heat decreases in the two-layer ferromagnetic superlattice, while it is almost unchanged in the two-layer ferrimagnetic superlattice at low field range at low temperatures.     

The mechanism of interlayer exchange coupling in iron-chromium type nanostructures

A mechanism of the interlayer exchange coupling in layered structures of the Fe/Cr(001) type with rough interfaces is proposed. The theory is based on a model of the charge-induced spin density wave (SDW) formed in the chromium layer. It is shown that the effective magnetic coupling between thick ferromagnetic layers arises due to variations of the SDW vector orientation in the antiferromagnetic layer over a characteristic length ζ determined by the exchange stiffness of chromium. A general expression for the effective magnetic coupling energy E(ψ) as a function of the angle ψ between magnetic moments of the ferromagnetic layers is obtained and numerically analyzed for an arbitrary value of the parameter ρζ, where ρ is the density of monoatomic steps on the interface. For ρζ?1, the form of E(ψ) is typical of a model with the “ biquadratic” interaction, while in the case of ρζ?1, the dependence obtained differs significantly. The proposed mechanism is used to interpret the results of measurements of the interlayer exchange coupling in Fe/Cr(001) structures.     

Frequency in Middle of Magnon Band Gap in a Layered Ferromagnetic Superlattice

The frequency in middle of magnon energy band in a five-layer ferromagnetic superlattice is studied by using the linear spin-wave approach and Green's function technique. It is found that four energy gaps and corresponding four frequencie in middle of energy gaps exist in the magnon band along K_x direction perpendicular to the superlattice plane. The spin quantum numbersand the interlayer exchange couplings all affect the four frequencies in middle of the energy gaps. When all interlayer exchange couplings are same, the effect of spin quantum numbers on the frequency ω_g1 in middle of the energy gap Δω₁₂ is complicated, and the frequency ω_g1 depends on the match of spin quantum numbers in each layer. Meanwhile, the frequencies ω_g2, ω_g3, and ω_g4 in middle of other energy gaps increase monotonously with increasing spin quantum numbers. When the spin quantum numbersin each layer are same, the frequencies ω_g1, ω_g2, ω_g3, and ω_g4 all increasemonotonously with increasing interlayer exchange couplings.     

The study of exchange coupling in NiFe/Cu/IrMn trilayer structures by MOKE and FMR measurements

The exchange coupling strength of NiFe/Cu/IrMn trilayer films was examined with both a new magneto optical Kerr effect (MOKE) method developed for the exchange coupling field determination and ferromagnetic resonance (FMR) measurements. We found that the value for exchange coupling field obtained by the MOKE technique coincided with FMR result with high accuracy. Other peculiarities of FMR measurements due to interlayer exchange coupling such as angular dependence of resonance field on Cu spacer thickness are also shown in the article.