π-phase magnetism in ferromagnet-superconductor superlattices

New 0π and ππ Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states with antiferromagnetic orientation of magnetizations in the neighboring layers of a ferromagnetic metal (FM) are predicted for FM/superconductor (FM/S) superlattices. Under certain conditions, the critical temperature T _c of these states is higher than for the known 00 and π0 LOFF states with ferromagnetic ordering of the FM layers. It is shown that the nonmonotonic behavior of T _c in the FM/S superlattices with S-layer thickness d _s less than the threshold value d _s ^π is due to the phase transition cascade 0π-ππ-0π At d _s >d _s ^π , the T _c oscillations are caused by the 00-π0-00 transitions. New logic elements based on the FM/S structures and combining the advantages of the superconducting and magnetic data-record channels in a single sample are proposed.     

Nonmonotonic behavior of the superconducting transition temperature in bimetallic ferromagnet-superconductor structures

For layered ferromagnet/superconductor (F/S) structures we develop a theory of the proximity effect. In contrast to previous approaches, this theory allows for a finite transmission coefficient of the interface between the two metals and competition between the diffusion and spin-wave types of quasiparticle motion in the ferromagnet’s strong exchange field. The superconductivity in F/S systems proves to be a superposition of BCS pairing with a constant-sign pair amplitude in the S-layers and Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) pairing with an oscillating wave function in the F-layers. We show that the oscillatory behavior of the superconducting transition temperature T _c is due to oscillations of the Cooper pair flux from the S-layer to the F-layer, which are the result of oscillations of the discontinuity (jump) of the pair amplitude at the F/S boundary as the thickness d _f of the F-layer increases. The presence of nonmagnetic impurities leads to heavy damping of the oscillations of the LOFF pair amplitude and rapid deterioration of the coherent coupling of the boundaries of the F-layer in which the T _s vs. d _f dependence reaches a plateau as d _f increases. In F/S superlattices, in contrast to F/S double-layer junctions, there are two forms of the LOFF state, the 0-phase and the π-phase, which differ in their symmetry with respect to the center of the F layer. This gives rise to additional oscillations in the T _c (d _f ) dependence due to the 0-π transitions. As the most vivid manifestation of LOFF states in F/S-systems, we predict the existence of recurrent and periodically recurrent superconductivities. We give a qualitative explanation of the different behavior of the superconducting transition temperature observed by different groups of experimenters dealing with the same ferromagnet-superconductor structures. Zh. éksp. Teor. Fiz. 113, 1708–1730 (May 1998)     

Superconducting probe of electronic correlations and exchange field based on the proximity effect in F/S nanostructures

The proximity effect and competition between the BCS and LOFF states are studied in the Cooper limit for thin F/S and F/S/F nanostructures, where F is a ferromagnet and S is a superconductor. The dependences of the critical temperature on the exchange field I, electron correlations λ _f, and the thickness d _f of the F layer are derived for F/S bilayers and F/S/F trilayers. In addition, two new π-phase superconducting states with electron-electron repulsion in the F layers of F/S/F trilayers are predicted. A two-dimensional LOFF state in F/S/F trilayers is possible only in the presence of a weak magnetic field and the appropriate parameters of the F and S layers. The absence of the suppression of three-dimensional superconductivity in short-period Gd/La superlattices is explained and the electron-electron coupling constant in gadolinium is predicted. A method of superconducting sounding spectroscopy based on the proximity effect is proposed for determining the symmetry of the order parameter, the magnitude and sign of electron correlations, and the exchange field in various nanomagnets F.     

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.     

Critical temperature of superconductor/ferromagnet bilayers

Superconductor/ferromagnet bilayers are known to exhibit nontrivial dependence of the critical temperature T _c on the thickness d _f of the ferromagnetic layer. We develop a general method for investigation of T _c as a function of the bilayer parameters. It is shown that interference of quasiparticles makes T _c (d _f ) a nonmonotonic function. The results are in good agreement with experiment. Our method also applies to multilayered structures.     

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.     

Proximity effect in the finite and incommensurate ferromagnet/superconductor systems

The original theory of a proximity effect is proposed for the bi- and tri-layered system ferromagnetic metal/superconductor (F/S) in dirty limit. The F₁/S/F₂ trilayer is examined more closely. The distinctions in materials, in thicknesses of F layers (d_f1 and d_f2), in parameters interfaces, and in local environments of layers are considered among the causes of incommensurability of trilayer. The peculiar T_c(d_f1, d_f2) interference pattern is predicted for the F₁/S/F₂ systems. The reentrant superconductivity and possibility of the better observability of the spin-valve regime are discussed.     

The proximity effect for weak itinerant ferromagnets

The Curie temperature T_c of a proximity sample composed of a thin film of a weak itinerant ferromagnet of thickness d_f in contact with a thick film of an enhanced parmagnetic metal is calculated using the Hubbard model in the Hartree-Fock approximation. The sample is paramagnetic for values of d_f less than a critical thickness d_f⁰ of the order of the coherence length. The shape of the curve of T_c vs. d_f for d_f > d_f⁰ depends on whether the bulk ferromagnet exhibits a Curie-Weiss or a Pauli susceptibility above the bulk Curie temperature. The letter is concluded by comments on the experimental situation.     

Dependence on interatomic distance of exchange coupling in rare-earth Al2 compounds

The effect of pressure on the Curie temperature of the heavy rare-earth dialuminides has been measured up to 3.5 kbar. The derivatives dT_c/d_p are 0.00(4), 0.09, 0.21, 0.39, 0.60 and 0.71 K/kbar respectively for TmAl₂ ErAl₂, HoAl₂, DyAl₂, TbAl₂ and GdAl₂ thus indicating a clear positive correlation between dT_c/dp and the de Gennes factor G. The results are discussed in terms of the RKKY model. However, the phenomenological parameter D/d, where D is the nearest-neighbour R-R distance and d the diameter of the 4f orbital, is used to reflect the non-δ-function character of the sf-coupling parameter Г. The experimental values of Г²D² and T_p/G are found to decrease linearly with increasing D/d. This is in keeping with the RKKY proportionality of $\text{T}{}_{\mathrm{c}}\text{?T}{}_{\mathrm{p}}$ to Γ²E^?1_FG. For GdAl₂, TbAl₂ and DyAl₂ the quantity $\text{?}\text{(}\text{d}\text{T}{}_{\mathrm{c}}\text{d}\text{p}\text{)}\text{k}{}_{\mathrm{l}}\text{(}\text{D}\text{d}\text{)}\text{G}$ coincides within the error limits with the slope of the T_p/G vs D/d plot.     

Quantum theory of radiation-pressure induced electrical currents: I. Free electrons

The maximum superconducting transition temperatures,T _c , of noncrystalline (Ti, Zr and Hf)-(3d metal) alloys are reported. The alloys have been produced by low temperature implantation of the 3d metals. The systematic behavior ofT _c as a function of 3d element content is discussed in comparison with metallic glasses and vapor-quenched films. A correlation between the recently observedd-band splitting in metallic glasses and superconducting behavior is pointed out.     

Effect of pressure and magnetic field on bilayer La1.25Sr1.75Mn2O7 single crystal

We report the temperature dependence of susceptibility for various pressures, magnetic fields and constant magnetic field of 5 T with various pressures on La_2−2xSr_1+2xMn₂O₇ single crystal to understand the effectiveness of pressure and magnetic field in altering the magnetic properties. We find that the Curie temperature, T_c, increases under pressure (dT_c/dP=10.9 K/GPa) and it indicates the enhancement of ferromagnetic phase under pressure up to 2 GPa. The magnetic field dependence of T_c is about 26 K for 3 T. The combined effect of pressure and constant magnetic field (5 T) shows dT_c/dP=11.3 K/GPa and the peak structure is suppressed and broadened. The application of magnetic field of 5 T realizes 3D spin ordered state below T_c at atmospheric pressure. Both peak structure in χ_c and 3D spin ordered state are suppressed, and changes to 2D-like spin ordered state by increase of pressure. These results reveal that the pressure and the magnetic field are more competitive in altering the magnetic properties of bilayer manganite La_1.25Sr_1.75Mn₂O₇ single crystal.     

Magnetic properties and hydrostatic pressure effect on the curie temperature of (Co,Mn)2B amorphous alloys

The temperature dependence of magnetization and magnetic susceptibility and hydrostatic pressure effect on the Surie temperature (dT_c/dP) are measured for (Co_1-xMn_x)₂B (0?x?0.4) amorphous alloys and the results are compared with those of crystalline compounds with the same composition. The Curie temperature decreases linearly with an increasing Mn content but magnetization shows a maximum around x=0.15. The reciprocal magnetic susceptibility of all the prepared alloys obeys the Curie-Weiss law above T_c. The magnitude of the negative value of dT_c/dP decreases linearly with increasing x from about 1.1 K/kbar (x=0) to zero (x=0.4), the composition dependence of which is opposite to that of the crystalline compound. The composition dependence of the average magnetic moment per transition metal atom and the Curie temperature and dT_c/dP are analysed on the basis of the local environment and the pair order interaction mode, respectively.     

Phonon spectrum softening near temperatures of superconducting and structural transitions in HTSC ceramic “1-2-3”

Anomalous behavior of the Mössbauer factorf for iron and tin impurity atoms in the ceramic of the 1-2-3 composition indicates a phonon softening nearT _c andT _t≈190 K.     

Phase transitions in hybrid SFS structures with thin superconducting layers

Features of a phase transition between 0 and π states in superconductor/ferromagnet/superconductor (SFS) Josephson structures with thin superconducting layers and a ferromagnetic barrier are studied experimentally and theoretically. The dependence of the critical temperature T_c of a transition of the hybrid structure to a superconducting state on the thickness of superconducting layers d_s is analyzed by a local method involving measurements of the nonlinear microwave response of the system by a near-field probe. An anomalous increase in the measured temperature T_c at the reduction of the thickness d_s is detected and is attributed to the 0-π transition.     

Elastic properties, thermal expansion coefficients and electronic structures of Ti0.75X0.25C carbides

Elastic properties, thermal expansion coefficients and electronic structures of Ti_0.75X_0.25C carbides (X=W, Mo, Ta, Nb, V, Hf, Zr, Cr and Al) were systematically investigated using ab initio density functional theory (DFT) calculations. The calculated elastic moduli, electronic structures and thermal expansion coefficients α(T) of pure TiC are in good agreement with experimental data and other DFT calculations. Based on a phenomenological formula, the trends of elastic properties and ductile/brittle behavior of Ti_0.75X_0.25C were analyzed. It was found that alloying elements W, Mo, Ta, Nb, V and Hf can increase elastic moduli, while Zr, Cr and Al reduce moduli. The nearly free electron model and Debye approximation were applied in the evaluation of α(T). The anharmonic effect was taken into account by including volume-dependent elastic moduli and Debye temperature. Results show that alloying additions of 3d V, 4d Zr and Mo slightly reduce α(T), while 3d Cr increases α(T), Al, 4d Nb, 5d Hf and W almost keep α(T) unchanged in Ti_0.75X_0.25C at high temperatures. The electronic structures of Ti_0.75X_0.25C were calculated and analyzed, and the electronic density of states was used to interpret variations of elastic properties and ductile/brittle behavior induced by alloying additions.     

Nonradiative decay from 5d states of rare earths in crystals

Nonradiative decay from 4f^n?1 5d states was investigated for trivalent rare earths in Y₃Al₅O₁₂. The rates of both 5d→4f and 5d→5d transitions were determined from measurements of the lifetimes and intensities of 5d fluorescence from Ce³⁺ and Pr³⁺. Because of the stronger ion-lattice coupling, nonradiative decay rates for transitions involving 5d states are much faster than those between 4f states. Decay rates are dependent upon the temperature and the energy gap to the next-lower level. The temperature dependences of the 5d fluorescence lifetimes from 77 to 700°K are reported.     

Quasi-particle transport in vortex state of nodal superconductors

The quasi-classical approach has proved very useful for studying the vortex state of nodal superconductors like d-wave superconductors in high T_c cuprates. After a brief introduction, we review our work on the thermal conductivity tensor in d-wave superconductors and f-wave superconductors.     

Vehicular traffic through a self-similar sequence of traffic lights

We study the dynamical behavior of vehicular traffic through a sequence of traffic lights positioned self-similarly on a highway, where all traffic lights turn on and off simultaneously with cycle time T_s. The signals are positioned self-similarly by Cantor set. The nonlinear-map model of vehicular traffic controlled by self-similar signals is presented. The vehicle exhibits the complex behavior with varying cycle time. The tour time is much lower such that signals are positioned periodically with the same interval. The arrival time T(x) at position x scales as (T(x)-x)∝x^d_f, where d_f is the fractal dimension of Cantor set. The landscape in the plot of T(x)−x against cycle time T_s shows a self-affine fractal with roughness exponent α=1−d_f.     

Surface states and tunneling spectroscopy of high-Tcsuperconductors

Recent studies of high- T_csuperconductors have clarified new aspects of tunneling spectroscopy. The unconventional pairing states, i.e. d-wave symmetry in these materials have been established through various measurements. Differently from isotropic s-wave superconductors, d-wave pairing states have an internal phase of the pair potential. The internal phase modifies the surface states due to the interference effect of the quasiparticles. Along these lines, a novel formula of tunneling spectroscopy has been presented that fully takes into account of the anisotropy of the pair potential. The most essential difference of this formula from conventional ones is that it suggests the phase-sensitive capability of tunneling spectroscopy. The formula suggests that the symmetry of the pair potential is determined by the orientational dependence measurements of tunneling spectroscopy. Along these lines, several experiments have been performed on high-T_c superconductors. The observation of the zero-bias conductance peaks (ZBCP) on Y Ba₂Cu₃O_7 − δstrongly suggests the d_{x² − y²}-wave pairing states of hole-doped high-T_c superconductors. On the other hand, the absence of ZBCP on (electron-doped)Nd_1.85Ce_0.15CuO_4 − δindicates that the pair potential of this material is a nodeless state. In this paper, recent developments of tunneling spectroscopy for anisotropic superconductors are reviewed both on theoretical and experimental aspects.     

High-temperature VUV spectroscopy of KYF4 crystals doped with Nd3+, Er3+ and Tm3+ ions

Thermal quenching of 5d-4f luminescence from Nd³⁺, Er³⁺ and Tm³⁺ ions doped into KYF₄ crystals has been investigated in the temperature range up to ∼750 K where this luminescence is completely quenched. The obtained temperatures of thermal quenching (T_q) are ∼270, 495, 450 K for Nd³⁺, Er³⁺, Tm³⁺, respectively. At high temperatures, thermal quenching of 5d-4f luminescence from Nd³⁺ and Er³⁺ is accompanied by the appearance of 4f-4f luminescence from the lower-energy 4f levels. It has been shown that the dominating mechanism of thermal quenching for Nd³⁺ and Er³⁺ ions is thermally stimulated non-radiative transitions (intersystem crossing) from the 5d states to lower-energy 4f levels, namely ²G(2)_9/2 and ²F(2)_7/2, respectively, whereas for the Tm³⁺ ion, thermally stimulated ionization of 5d electrons to the conduction band states is responsible for thermal quenching of 5d-4f luminescence. The energy gap between the lowest Tm³⁺ 5d level and the bottom of the KYF₄ conduction band has been estimated to be 0.66 eV.