Giant domain walls in a ferromagnet

Giant domain walls with a width of ∼7 μm are observed on the surface of a ferromagnet — an amorphous magnetically soft alloy. A magnetooptic investigation shows that the walls have a Néel structure in the subsurface region. The subsurface structure of these walls differs substantially from that of the narrower walls previously observed in iron, Permalloy, and amorphous materials. According to the theoretical model of Scheinfein and co-workers, which relates the width of an asymmetric Bloch wall in the bulk with the width at the surface, the width of the wall in the bulk is estimated to be 3–4 μm. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 8, 528–530 (25 October 1999)     

Sudden critical current drops induced in S/F structures

In the search for new physical properties of S/F structures, we have found that the superconductor critical current can be controlled by the domain state of the neighboring ferromagnet. The superconductor is a thin wire of thickness d_s ≈2ξ_S. Nb/Co and Nb/Py (Permalloy Ni₈₀Fe₂₀) bilayer structures were grown with a significant magnetic anisotropy. Critical current measurements of Nb/Co structures with ferromagnet thickness d_F > 30 nm show sudden drops in two very defined steps when the measurements are made along the hard axes direction (i.e. current track parallel to hard anisotropy axes direction). These drops disappear when they are made along the easy axis direction or when the ferromagnet thickness is below 30 nm. The drops are accompanied by vortex flux flow. In addition magnetorestistance measurements close to T_C show a sharp increase near saturation fields of the ferromagnet. Similar results are reproduced in Nb/Py bilayer structure with the ferromagnet thickness d_F ~ 50 nm along the easy anisotropy axes. These results are explained as being due to spontaneous vortex formation and flow induced by Bloch domain walls of the ferromagnet underneath. We argue these Bloch domain walls produce a 2D vortex-antivortex lattice structure.     

Experimental investigation of the role of the triplet pairing in the superconducting spin-valve effect

An important role of the morphology of a superconducting layer in the superconducting spin-valve effect has been established. The triplet pairing induced by the superconductor/ferromagnet proximity effect has been experimentally investigated for samples CoO_x/Py1/Cu/Py2/Cu/Pb (where Py = Ni_0.81Fe_0.19) with a smooth superconducting layer. The optimization of the parameters of this structure has demonstrated a complete switching between the normal and superconducting states with a change in the relative orientation of magnetizations of the ferromagnetic layers from the antiparallel to orthogonal orientation. A pure triplet contribution has been observed for the sample with a permalloy layer thickness at which the superconducting spin-valve effect vanishes. A direct comparison of the experimental data with the theoretical calculation of the temperature of the transition to the superconducting state has been performed for the first time.     

Spin polarized current controlled dynamics of domain walls in magnetic films with in-plane anisotropy

We study the dynamic properties of asymmetric vortex Bloch walls and classical 1D Néel walls controlled by a spin-polarized current in magnetic films with in-plane anisotropy. It is shown that fairly high velocities of domain walls (up to 100 m/s) can be obtained for the current density in the range j = 10⁶–10⁸ A/cm². The nonlinear dependence of the wall velocity on the film thickness and the linear dependence of the velocity on the current density and inverse damping parameter are found.     

Transition micromagnetic structures in the Bloch and Néel asymmetric domain walls containing singular points

A three-dimensional computer simulation of transition structures separated from each other by regions of vortex asymmetric domain walls of the Bloch and Néel types in magnetically uniaxial permalloy films with in-plane anisotropy has been performed. The structures without localized magnetostatic poles on the surface of the film with one or two singular points have been investigated. It has been shown that the singular points and the vortex formations being elements of the domain walls can be considered as topological structures. A method has been proposed for visualizing the topology of magnetic configurations, which is based on the numerical determination of spatial distributions of topological charges of two types.     

Néel lines in ferrimagnetic garnet epilayers with orthorhombic anisotropy and canted magnetization

Néel lines in (TbY)₃(FeAl)₅O₁₂ epitaxial layers with orthorhombic anisotropy and canted magnetization are optically observed by the presence of a kink of the wall plane. The intrinsically asymmetrical character of Bloch walls is demonstrated by wall widening experiments. It follows that wall kinking may either be a consequence of the anisotropy specific to the samples, and/or be the result of magnetostatic interactions. A relaxation type numerical computation of the Néel line configuration indicates that anisotropy is the main source of wall kinking, demagnetizing field effects contributing to an amplification of the kink. The structure of those Néel lines is shown to bear two characters, that of a half-circular line characteristic of samples with in-plane anisotropy and that of a splay line, well known in bubble materials. Further, the charge distribution appears basically dipolar and lines contract when the saturation magnetization increases. They are therefore magnetostatistically analogous to vertical Néel (most generally called Bloch) lines in garnet epilayers supporting bubbles.     

Effect of interfacial s-d scattering on transport in structures ferromagnet/insulator/ferromagnet

A two-band s-d model based on the Green function method has been developed for calculating the conductivity and tunnel magnetoresistance of ferromagnet/insulator/ferromagnet structures. It is shown that s-d scattering at the interface between the ferromagnet and the insulator in Fe/Al₂O₃/Fe increases the tunnel magnetoresistance. The spin polarization of the current decreases thereby and even becomes negative, which is mainly due to scattering of strongly localized d electrons to the s band, followed by tunnelling through the insulator.     

Estimate of the Degree of the Spin Polarization of a Ferromagnet from Data on the Superconductor/Ferromagnet Proximity Effect

The superconductor/ferromagnet proximity effect in the Pb/Co₂Cr_1–xFe _x Al bilayer systems has been studied. Thin films of the Heusler alloy Co₂Cr_1–xFe _x Al have been prepared at different substrate temperatures. It has been established using Andreev spectroscopy of point contacts that the degree of spin polarization of conduction electrons in the Heusler alloy is on the order of 30 and 70% for the films prepared at a substrate temperature of 300 and 600 K, respectively. It has been found that the dependence of the superconducting transition temperature on the thickness of the Pb layer at a fixed thickness of the Heusler layer is determined by the degree of spin polarization of the conduction band in the ferromagnetic layer.     

Peculiarities of the proximity effect in superconductor-multilayered ferromagnet structures with collinear magnetizations in ferromagnetic layers

The proximity effect is investigated theoretically in different superconducting structures including multilayered ferromagnet consisting of arbitrary number of metallic ferromagnet (F) layers. The in-plane exchange fields in the F-layers are supposed to be collinear. Different cases of the exchange fields ordering including the case of antiferromagnetic one. It is shown for the last case that the proximity effect (for the fixed thickness of the M-interlayer) increases with the growing number of the layers N and significantly depends on whether this number is odd or even. It is shown that under the condition of diffusive electron transport, the anomalous proximity effect is exhibited which is related with singlet component of the condensate Green’s function. Peculiarities of the proximity effect are analyzed for S-M, S-I-M-S, and S-M-S superconducting structures (S is a superconductor, I is an insulating layer). It is shown that when the M-structure consists of N seriously connected F₁-N-F₂-N links in which F layers are separated by normal metallic layers (N), for antiferro-magnetic ordering of the magnetization the exchange field induced enhancement of the critical current may occur.     

Dominant Majorana bound energy and critical current enhancement in ferromagnetic-superconducting topological insulator

Among the potential applications of topological insulators, we theoretically study the coexistence of proximity-induced ferromagnetic and superconducting orders in the surface states of a 3-dimensional topological insulator. The superconducting electron-hole excitations can be significantly affected by the magnetic order induced by a ferromagnet. In one hand, the surface state of the topological insulator, protected by the time-reversal symmetry, creates a spin-triplet and, on the other hand, magnetic order causes to renormalize the effective superconducting gap. We find Majorana mode energy along the ferromagnet/superconductor interface to sensitively depend on the magnitude of magnetization m _zfs from superconductor region, and its slope around perpendicular incidence is steep with very low dependency on m _zfs . The superconducting effective gap is renormalized by a factor η(m _zfs ), and Andreev bound state in ferromagnet-superconductor/ferromagnet/ferromagnet-superconductor (FS/F/FS) Josephson junction is more sensitive to the magnitude of magnetizations of FS and F regions. In particular, we show that the presence of m _zfs has a noticeable impact on the gap opening in Andreev bound state, which occurs in finite angle of incidence. This directly results in zero-energy Andreev state being dominant. By introducing the proper form of corresponding Dirac spinors for FS electron-hole states, we find that via the inclusion of m _zfs , the Josephson supercurrent is enhanced and exhibits almost abrupt crossover curve, featuring the dominant zero-energy Majorana bound states.     

Anomalous temperature dependence of the magnetoresistance in Co/Cu multilayers

An anomalous temperature dependence of magnetoresistance (MR) of Co/Cu multilayer films witha ～3 Å thick magnetic layer has been established experimentally. The temperature of the MR maximum T _max is shown to coincide with the Néel temperature. The variation of T _max with the Cu layer thickness follows an oscillatory pattern.     

Neutron investigations of the magnetic properties of Fe<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Mn<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>S under pressure up to 4.2 GPa

Fe _x Mn_1?x S belongs to the group of strong electron correlations compounds MnO. We present here experimental results for the antiferromagnetic iron–manganese sulfide system, based on X-ray and neutron diffraction studies. The neutron diffraction investigations were carried out at ambient conditions and at hydrostatic pressures up to 4.2 GPa in the temperature range from 65 to 300 K. Our results indicate that the Néel temperature of α-MnS increases up to room temperature by applying chemical (x _Fe) or weak hydrostatic pressure P. In Fe_0.27Mn_0.73S, the Néel temperature increases from 205(2) K (P = 0 GPa) to 280(2) K (P = 4.2 GPa) and the magnetization at 100 K decreases by a factor of 2.5 when the hydrostatic pressure increases from 0 to 4.2 GPa.     

Spontaneous symmetry breaking and a boundary value problem for the proximity effect in ferromagnet/superconductor nanostructures

A three-dimensional (3D) boundary value problem for the Eilenberger function has been microscopically derived. It is applicable for describing the proximity effect in ferromagnet/superconductor (F/S) nanostructures, where the superconductivity is the superposition of the BCS pairing with zero total momentum in the S layers and the pairing through the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) mechanism with nonzero 3D momentum of pairs k in the F layers. It has been shown that continuous matching at the F/S interface occurs only for the pair amplitudes with the same space symmetry. When two pairing types are simultaneously present, the processes of mutual transformations between LOFF and BCS pairs at the F/S interface occur as Umklapp processes through surface states. The phase diagrams of the surface states with the mixed BCS + LOFF pairing type have been analyzed. Superconductivity localized at the F/S interface has been predicted.     

Screening properties of multiply connected ferromagnet–superconductor hybrid structures

Superconducting phase transition temperature T _c of a ferromagnet/superconductor (SF) hybrid structure consisting of a hollow superconducting (S) cylinder (shell) with the central part (core) filled with a ferromagnetic (F) metal has been analyzed on the basis of linearized Usadel equations. It has been shown that the proximity effect between the S and F metals, as well as the exchange interaction, may induce an inhomogeneous superconducting state with Δ ~ exp(iLθ + ipz), which is characterized by nonzero circulation of phase L and wavenumber p describing the Larkin–Ovchinnikov–Fulde–Ferrell (LOFF) instability along the cylinder axis. The transitions between the states with different values of L and p, which are accompanied by a nonmonotonic dependence of superconducting transition temperature T _c and effective magnetic field penetration depth Λ into the SF structure on the characteristic size of the ferromagnetic region, have been investigated.     

Separate re-entrant superconductivity in asymmetric ferromagnet/superconductor/ferromagnet trilayers

The superconducting and magnetic states of asymmetric ferromagnet/superconductor/ferromagnet (F/S/F′) nanostructures have been investigated using the boundary value problem for the Eilenberger function. It has been shown that 0- and π-phase superconducting states of pure thin F/S/F′ trilayers are controlled by the magnitude and sign of electron correlations in the F and F′ layers, as well as by the competition between homogeneous Bardeen-Cooper-Schrieffer (BCS) pairing and inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) pairing. The LOFF-BCS-LOFF separate re-entrant superconductivity has been predicted for F/S/F′ trilayers. A continuous control of the pair-breaking factor in the Eilenberger function and transition to the state with re-entrant superconductivity is achieved by varying the thickness of the F′ layer. Sine-modulated 2D LOFF states in asymmetric F/S/F′ trilayers are possible not only for parallel, but also for antiparallel orientations of the magnetizations of the F and F′ layers; this fact significantly facilitates the experimental implementation of the predicted phenomena.     

Giant magnetoresistance in ferromagnet/superconductor superlattices

We show magnetoresistance in excess of 1000% in trilayers containing highly spin-polarized La0.7Ca0.3MnO3 and high-Tc superconducting YBa2Cu3O7. This large magnetoresistance is reminiscent of the giant magnetoresistance (GMR) in metallic superlattices but with much larger values, and originates at spin imbalance due to the injection of spin-polarized carriers. Furthermore, in contrast to ordinary GMR, the magnetoresistance is intimately related to the superconductivity in the YBa2Cu3O7 layer and vanishes in the normal state. This result, aside from its fundamental importance, may be of interest for the design of novel spintronic devices based on ferromagnet/superconductor structures.     

Recent experimental results on the superconductor/ferromagnet proximity effect

The recent experimental results on the proximity effect in heterostructures composed of superconducting and ferromagnetic thin films are reviewed. First, the experimental observation and investigation of the spin screening effect, i.e., a spin polarization in the V layer developing in the superconducting state under the influence of a spin polarization of conduction electrons in the ferromagnetic layer are discussed. This effect was predicted theoretically by Bergeret et al. [F. S. Bergeret, A. F. Volkov, and K. B. Efetov, EPL 66, 111 (2004); Phys. Rev. B 69, 174504 (2004)]. Then, the progress concerning the experimental realization of the superconducting spin switch device based on the superconductor/ferromagnet proximity effect is presented.     

Triplet pairing states with equal spins in ferromagnet/superconductor heterojunctions for noncollinear magnetizations

Four-component Bogoliubov-de Gennes equations are applied to study tunneling conductance spectra of ferromagnet/ferromagnet/d-wave superconductor (F₁/F₂/d-wave S) tunnel junctions and to find out signs of spin-triplet pairing correlations induced in the proximity structure. The pairing correlations with equal spins arises from the novel Andreev reflection (AR), which requires at least three factors: the usual AR at the F₂/S interface, spin flip in the F₂ layer, and superconducting coherence kept up in the F₂ layer. Effects of angle α between magnetizations of the two F layers, polarizations of the F₁ and F₂ layers, the thickness of the F₂ layer, and the orientation of the d-wave S crystal on the tunneling conductance are investigated. A conversion from a zero-bias conductance dip at α = 0 to a zero-bias conductance peak at a certain value of α can be seen as a sign of generated spin-triplet correlations.     

Static properties of asymmetric vortex-like domain walls in magnetically uniaxial thick films

The structure and energy of asymmetric vortex-like Bloch and Néel walls in a magnetically uniaxial film with an easy magnetization axis lying in the film plane are investigated by numerically minimizing the total energy within the rigorous micromagnetic approach and the two-dimensional model of the magnetization distribution. The calculations are performed over wide ranges of film thicknesses b (up to b = 1 μm) and magnetic parameters of the films. It is established that the asymmetric vortex-like domain walls are the most universal wall structures in the films under consideration. In magnetically uniaxial films, unlike in magnetically multiaxial films, the asymmetric Bloch walls are always stable.     

Magnetic properties of Pb<Subscript>2</Subscript>Fe<Subscript>2</Subscript>Ge<Subscript>2</Subscript>O<Subscript>9</Subscript> single crystals

Single crystals of Pb₂Fe₂Ge₂O₉ have been grown. They were subjected to X-ray diffraction, magnetic, neutron diffraction, Mössbauer and spin resonance studies. It has been established that Pb₂Fe₂Ge₂O₉ is a weak ferromagnet with a Néel temperature T _N = 46 K, and the exchange and spin-flop transition fields have been estimated. It has been demonstrated that the weak ferromagnetic moment is actually the result of the single-ion anisotropy axes for the magnetic moments of different magnetic sublattices being not collinear.