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.     

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.     

MAGNETIC POLARIZATION OF Pd SPACERS AND OSCILLATORY EXCHANGE COUPLING BETWEEN Fe AND Pd LAYERS IN Fe/Pd MULTILAYERS

Ay oscillatory behavior in specific saturation magnetization of Fe/Pd multilayers is observed. The conversion electron M?ssbauer spectroscopy and other experiments indicate that this behavior is caused by the magnetic polarization of Pd spacers, which alternates between positive and negative polarization with respect to the magnetic moments of Fe layers. The interlayer coupling between two Fe layers always keeps ferromagnetic. Then, the interlayer couplings in ferromagnetic metal/nearly ferromagnetic metal multilayers were calculated By using the model of Barnas. The results of calculation prove that the above phenomenon might appear under some condition. The influence of magnetic polarization potential of spacers and interface chemical potential on the interlayer couplings is also discussed.     

Low-energy band structure very sensitive to the interlayer distance in Bernal-stacked tetralayer graphene

We have investigated Bernal-stacked tetralayer graphene as a function of interlayer distance and perpendicular electric field by using density functional theory calculations. The low-energy band structure was found to be very sensitive to the interlayer distance, undergoing a metal-insulator transition. It can be attributed to the nearest-layer coupling that is more sensitive to the interlayer distance than are the next-nearest-layer couplings. Under a perpendicular electric field above a critical field, six electric-field-induced Dirac cones with mass gaps predicted in tight-binding models were confirmed, however, our density functional theory calculations demonstrate a phase transition to a quantum valley Hall insulator, contrasting to the tight-binding model prediction of an ordinary insulator.     

The Role of Intermixing in the Phase Determination of the Interlayer Exchange Coupling in Multilayers: Application to Fe-Cr Superlattices

The phase of the short-range interlayer exchange coupling oscillations in Fe n Cr m superlattices is expressed in terms of the intermixing at the Fe-Cr as well as at the Cr-Fe interfaces. The interdiffusion is modeled through stochastic algorithms, which presupposes floating of the atoms on the surface of the sample during the epitaxial growth. It automatically leads to the different chemical and magnetic structure of Fe on Cr and Cr on Fe interfaces. Self-consistent calculations of the magnetic moments are performed on the basis of the periodic Anderson model. Although short-range (2 monolayers (ML)) oscillations of exchange coupling were detected for all considered structures, its amplitude and phase strongly depend on the interface alloying. Introduction of the same intermixing at both interfaces does not change the phase as compared to the ideal superlattices with sharp interfaces. However different interdiffusion leads to the ~ -phase shift in accordance with experimental results for the Fe-Cr-Fe trilayers grown on an Fe whiskers. Distribution of magnetic moments on Fe atoms contains several distinct peaks but their position and relative area weakly depend on the alloying and interlayer exchange coupling in the superlattice. On the contrary, magnetic moments on Cr atoms are very sensitive to the intermixing and their behavior determines the strength and the phase of exchange coupling oscillations.     

Multilayer structures of the iron/chromium type with almost ideal interfaces in an external magnetic field

The magnetic phase diagram of the Fe/Cr/Fe three-layer structure with almost ideal interlayer boundaries was constructed. The effective interlayer interaction in this structure was described by the “half-angle coupling” model. Various system configurations were analyzed taking into account crystalline anisotropy, and the ground state of the system was determined. The behavior of the structure in an external magnetic field applied along easy and hard magnetic axes was studied. The magnetization curves M(H) characteristic of structures with various interface roughness parameter and interlayer exchange values were described and analyzed. The experimental situation is discussed.     

Effect of roughness, frustration, and antiferromagnetic order on magnetic coupling of Fe/Cr multilayers

The interplay between interfacial disorder and the antiferromagnetic order in Cr leads to complex behavior in Fe/Cr multilayers. Measurements of interlayer coupling are discussed for samples with different amounts of disorder ranging from optimally fabricated trilayers of Fe/Cr/Fe on Fe(0 0 1) whiskers, to trilayers with increasing degrees of interfacial roughness, and finally to superlattices of Fe/Cr. The coupling of ferromagnets through noble-metal spacer layers can be described by a model that consists of bilinear coupling averaged over thickness fluctuations and extrinsic biquadratic coupling induced by the thickness fluctuations. This, the conventional model, also describes much of the behavior observed for Fe/Cr multilayers. However, in this case, the antiferromagnetism in Cr leads to results not explained by the conventional model. For nearly ideal interfaces, the Fe–Cr coupling can induce order in Cr, modifying the temperature dependence of the interlayer coupling. In addition, interfacial disorder can frustrate the antiferromagnetic order in the Cr, leading to a variety of ordered states which have been observed by neutron scattering. Each of these ordered states, in turn modifies the interlayer coupling in unexpected ways. The different ways in which the systems minimize the frustration can explain the experimental results.     

Nuclear resonant magnetometry and its application to Fe/Cr multilayers

We introduce nuclear resonant magnetometry as a means to record the magnetization curve of isotopically enhanced regions of a sample. It is based on nuclear resonant scattering with circularly polarized synchrotron radiation and the use of a nuclear resonant reference sample. We apply this approach to study the interlayer coupling in Fe/Cr(100) multilayers and to obtain a layer-specific magnetization curve. Our measurements provide experimental evidence for the existence of a nontrivial interlayer-coupling angle in Fe/Cr/Fe.     

Understanding Cr segregation at the He bubble surface in Fe

Although Cr segregation at the free Fe surface is weak, noticeable segregation of Cr at the He bubble surface in Fe has recently been observed. To understand the driving force for Cr segregation, we have carried out first-principles density functional theory calculations on the energetics of solute Cr atoms at the He bubble surface, which was modeled by a Fe/He interface. We find that both the compressive stress produced by the He bubble and the direct interfacial interaction promote Cr segregation from inside the bulk to the bubble surface, along with reduced spin polarization. Electronic structure analyses show that at the Fe/He interface, Cr is more compressible than Fe due to having more empty e(g) orbitals and, accordingly, the Fe surface gets energetically more favorable for Cr than in the bulk. On the other hand, the segregation of Cr increases the charge density at the bubble surface, and thus hinders assimilation of further He atoms.     

Effect of vacancies on the spin density waves onset in Fe/Cr superlattices

The spin density wave’s onset in Cr based superlattices is considered within proximity of Fe interlayer boundaries and the effect of randomly located vacancies in Cr monolayers is examined. The study is performed for Fe/Cr, Fe/Cr/V superlattices with odd and even number of Cr monolayers. It is shown that the number of Cr monolayer determines the spin density wave’s nodes onset in the perfect Fe/Cr super lattices. Pinning of Cr magnetic moments on vacancies destroys this determination and leads to appearance or disappearance of nodes.     

Spin wave resonance study of exchange-coupled Ni80Fe20 double layers separated by thin interlayers of Cu, Cr and Pd

We have performed ferromagnetic resonance measurements on thin polycrystalline Ni₈₀Fe₂₀ (permalloy) double layers with interlayers of Cu, Cr and Pd. Furthermore, a mathematical model is presented, which allows a calculation of resonance fields in the parallel configuration. Comparison of the calculated and measured resonance field values yields an interlayer exchange coupling constant A₁₂ as a function of interlayer thickness d. We observe exponential dependencies of A₁₂ on d for Cr, Cu and Pd interlayers with the strongest decay for Cr. Additionally, we present FMR measurements and calculations for a Ni₈₀Fe₂₀/Cr/Co heterostructure layer system.     

Polarized neutron reflectometry of Fe/Cr/Gd superlattices

The magnetic structure of Fe/Cr/Gd superlattices is investigated using complementary methods of SQUID magnetometry and polarized neutron reflectometry. The complex magnetic behavior of the given system is caused by exchange interaction between the 3d (Fe) and 4f (Gd) layers of the ferromagnetic metals through the Cr antiferromagnetic spacer layer. It is found that a nonuniform profile of magnetization forms within the Gd layers under the influence of this interlayer interaction.     

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.     

An estimation of the magnetic disorder at Fe/Cr interfaces in coupled and non-coupled Fe/Cr multilayers

The antiferromagnetic coupling at the Fe/Cr interfaces, inferred from the orientation of the Cr magnetic moments, is used to estimate the magnetic disorder resulting from the interfacial roughness in Fe/Cr multilayers. A crossover from in-plane to out-of-plane orientation of Cr moments depends on the energy cost in either case: (i) to break the interfacial Fe–Cr antiferromagnetic coupling or (ii) having sites with frustrated Cr–Cr antiferromagnetic coupling in the Cr interlayers. A quantitative model of the magnetic frustration due to interfacial disorder in Fe/Cr multilayer systems is described. The step edge density, or terrace size, required to break the interfacial Fe–Cr coupling and destroy the Fe–Fe interlayer exchange coupling is estimated.     

Diagnostics of the atomic structure of multilayer metallic nanoheterostructures from reflectometry data: A new approach to low-contrast systems

A new method for determining the concentration profiles of chemical elements in multilayer metallic nanoheterostructures from X-ray reflectometry data has been developed as applied to low-contrast systems. The method is based on the solution of the Fredholm integral equation of the first kind, which relates the reflection coefficient and the concentration profile of the chemical elements involved in the composition of the sample. The ill-posed inverse problem of the determination of the concentration profile is solved by the regularization method. The efficiency of the proposed method is confirmed by model calculations performed for a four-layer Cr/Gd/Fe/Cr//Si structure with high-contrast Cr/Gd pairs and low-contrast Fe/Cr pairs. The experimental results on the determination of the concentration profile of the surface layer of the epitaxial thin Cr films and three-layer Cr/Fe/Cr structure deposited on the Al₂O₃ substrate are presented.     

Magnetisation and remagnetisation peculiarities of Fe/Cr multilayer films caused by instability of Cr layers magnetic structure

A model to describe the magnetic properties of Fe/Cr/Fe films with nanometer-thick layers of Fe and Cr is proposed. The model rests on the assumption that there exists a magnetic order of the linearly polarized spin-density wave type in a chromium interlayer with thicknesses even less than its wavelength. This only assumption proved to be enough to describe the following characteristics, experimentally observed, of the magnetic properties of the multilayer Fe/Cr films: the existence of short and long periods, dependences of their magnetic properties on the chromium layer thickness, noncollinear orientation of the magnetizations of neighboring iron layers, the existence of the magnetization curves beyond the hysteresis loops of magnetization.     

[Fe/Cr]多层膜及掺入Si中介层后的层间耦合和磁电阻效应

用真空蒸镀方法制备了［Ｆｅ／Ｃｒ］，［Ｆｅ／Ｃｒ／Ｓｉ］和［Ｆｅ／Ｓｉ］多层膜．研究了Ｃｒ层、Ｓｉ层和Ｃｒ＋Ｓｉ层厚度变化对层间耦合和磁电阻的影响．Ｆｅ层厚为２ｎｍ，Ｃｒ层厚度变化存在耦合振荡和巨磁电阻及其振荡．磁电阻值为１４.６％（４.２Ｋ）．在Ｃｒ层中加入一半Ｓｉ层或全部由Ｓｉ层替代，振荡消失，磁电阻减小到千分之几．根据掺Ｓｉ层后多层膜的电阻率变化，认为Ｓｉ加入使非磁层中自由电子数减少，随之极化效应也变弱，导致振荡消失，磁电阻大为降低 关键词：     

Origin of biquadratic coupling in Fe/Cr(100) superlattices

We investigate the magnetic properties of a (100) oriented [Fe(1.7 nm)/Cr(8.4 nm)](10) superlattice by means of perturbed angular correlation spectroscopy. The magnetic ordering in the Cr layers is obtained by measuring the magnetic hyperfine interaction at implanted 111Cd nuclear probes. We identify dynamic antiferromagnetic spin fluctuations in the Cr layers and show that it gives rise to the biquadratic interlayer coupling.     

Spin polarization in photoelectron spectroscopy from antiferromagnets: Cr films on Fe(1 1 0) from first principles

The spin- and angle-resolved photoelectron spectroscopy from ultrathin Cr films on Fe(1 1 0) is investigated by means of first-principles electronic structure and photoemission calculations. The antiferromagnetic ordering in the Cr films leads in dependence on film thickness to a rapidly decreasing and oscillating photoelectron spin polarization, in reasonable agreement with recent experiments (Dedkov (2007) [1]). The oscillation period is explained by quantum-well states in the Cr film and by a Fermi surface nesting vector. The importance of transition matrix elements is highlighted. The findings point to a noncollinear magnetic structure at the Fe/Cr interface.     

Applying angle resolved EXAFS spectroscopy to the study of layers and interfaces in metallic multilayer nanoheterostructures

A new technique is proposed for determining concentration profiles and local atomic structure at various depths in metallic multilayer films, using the dependence of the EXAFS spectra on the angle of incidence. The abilities of this technique are demonstrated via modelling calculations for the three-layered Cr/Fe/Cr system. The first experimental results for thin Cr films on sapphire substrates are obtained.