Shape of the magnetic resonance line in a thin film on the surface of an anisotropic superconductor

The shape of the EPR line in a thin (=λ/2, where λ is the London penetration depth of the magnetic field in the superconductor) paramagnetic film deposited on the surface of an anisotropic superconductor is calculated in an oblique magnetic field with allowance for the inhomogeneity of the local magnetic field of the Abrikosov vortex lattice. It is shown that, as the tilt angle of the external magnetic field is varied, the shape of the EPR line changes noticeably. This fact can give additional information about the superconductor parameters (the symmetry type of the vortex lattice and the anisotropy parameter of the superconductor). Fiz. Tverd. Tela (St. Petersburg) 41, 386–388 (March 1999)     

The magnetic field and energy of an Abrikosov vortex in an anisotropic London superconductor

The behavior of a straight Abrikosov vortex in an anisotropic uniaxial London superconductor is studied. Analytical expressions are derived that approximately describe the magnetic field in three regions: the asymptotic region, where the distance r from the vortex line is greater than λΓ (λ is the London length and Γ is the anisotropy constant), the intermediate region λ<r<λΓ, and the region r<λ. It is found that in the intermediate region with high anisotropy the component of the magnetic field along the vortex line changes sign for a certain interval of angles between the vortex line and the anisotropy axis. Because of this the interaction of parallel vortices whose plane is parallel to the anisotropy axis has a minimum and a maximum. This means that numerous metastable vortex lattices can exist. Additional terms in the vortex self-energy are obtained, and although they are smaller than the leading logarithmic term, they display a different dependence on the angle between the vortex line and the anisotropy axis. Zh. éksp. Teor. Fiz. 111, 954–963 (March 1997)     

Dynamic magnetic permeability of a thin, high-T c superconducting wafer

The field dependence of the vibrational contribution to the dynamic magnetic permeability μ _V(H) is calculated for a thin (of thickness d∼λ) high-T _c superconducting wafer in a magnetic field parallel to the surface. The resulting curves are plotted on the basis of an exact numerical analysis of the vortex structures both for the thermodynamic-equilibrium vortex lattice and in the presence of pinning forces and the Bean-Livingston surface barrier. It is shown that the μ _V(H) curves are highly sensitive to the size factor (d/λ) and exhibit abrupt changes corresponding to a change in the number of vortex rows. The equilibrium μ _V(H) curve is found to be similar in its general behavior and absolute value (obtained with allowance for the distribution of grain sizes and with appropriate values of λ and ϰ) to the experimental μ _V(H) curve plotted at nitrogen temperature for fine-grained YBa₂Cu₃O_x with grain diameters 〈D〉∼λ in an increasing magnetic field. It is established that the main cause of the experimentally observed irreversible behavior of the μ _V(H) curves during cyclic variation of the applied magnetic field is the existence of a surface barrier to the exit of vortices from the superconductor. The lower limit H _min(B) of stability of the mixed state in the presence of an ideal surface barrier in a thin, high-T _c superconducting wafer (d∼λ) is determined, along with the range of the vortex state (H _max-H _min) for a fixed number of vortices in micrometer-size grains of the investigated YBaCuO samples. Fiz. Tverd. Tela (St. Petersburg) 39, 1943–1947 (November 1997)     

Vorticity waves in problems of hydrodynamic stability

The known problem of flow transition near a circular cylinder at Re = 40 from a symmetrical form to the Karman vortex street can be considered as the problem of vortex wave development and intensification. Development of three bundles of vortex waves of low intensity is observed in a wake of a cylinder; these bundles are easily visualized as the structures of relative vorticity $ \bar \Omega $ \bar \Omega = Ω(t ₁) − Ω(t ₀): difference of vorticity Ω at two time moments, t ₀ being fixed. In the field of $ \bar \Omega $ \bar \Omega the alternating structure of quadrupoles is characterized by linear parameter l = h/d: the ratio of the width of the central bundle of vortex waves to the distance between the centers of quadrupoles of a “single sign”. When l = 0.281 is achieved, which coincides with the value of the same parameter of a stable Karman street, the transition from symmetrical streamlining by viscous incompressible liquid to the vortex street occurs.     

Fermionic entropy of the vortex state in d-wave superconductors

In d-wave superconductors the electronic entropy associated with an isolated vortex diverges logarithmically with the size of the system even at low temperatures. In the vortex array the entropy per vortex per layer, S _V , is much larger than k _B and depends on the distribution of the velocity field v _s around the vortex. If there is a first-order transition upon a change of the velocity distribution, then there will be a big entropy jump ΔS _V ∼k _B at the transition. This entropy jump comes from the electronic degrees of freedom on the vortex background, which is modified by the vortex transition. This can explain the big jump in the entropy observed in the so-called vortex-melting transition [A. Junod, M. Roulin, J-Y. Genoud et al., Physica C, to be published], in which the vortex array and thus the velocity field are redistributed. The possibility of the Berezinskii-Kosterlitz-Thouless transition in the 3-dimensional d-wave superconductor due to the fermionic bound states in the vortex background is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 6, 465–469 (25 March 1997) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Oscillation galvanomagnetic effect in double-layer metal films

A semiclassical approximation has been used to analyze theoretically the dependence of the conductivity σ (resistivity ρ) of a double-layer film consisting of plane-parallel single-crystal metal layers of different thickness d_j ≠ d_n and grade l_j ≠ l_n on the layer thickness ratio d_2,1 = d₂/d₁ and on the magnitude of the magnetic field normal to the layer interface. A general expression (for any d_2,1) and asymptotic expressions (for thick and thin (compared to the electron free path l_j) metal layers in a weak and a strong magnetic field) for the conductivity of a double-layer specimen have been obtained. A nonmonotonic relation between the conductivity of a double-layer film and the layer thickness ratio at weak magnetic fields has been predicted which is sensitive to the character of the interaction of charge carriers with the conductor boundaries. At strong magnetic fields, ρ becomes an oscillating function of magnetic field (layer thickness). A detailed numerical analysis of the resistivity of a double-layer film on the layer thickness ratio and on the magnetic field strength has been performed for arbitrary values of the parameters that describe the character of the interaction of charge carriers with the specimen boundaries. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 26–33, July, 2007.     

Structure of the Abrikosov vortex lattice in a thin superconducting film in a parallel magnetic field

The structure of a vortex lattice in thin (d<λ, where d is the film thickness and λ is the London penetration depth) superconducting films is investigated in a magnetic field parallel to the film surface. It is shown that the stable configuration has the form of discrete vortex rows whose number changes discretely with an increase in the applied magnetic field. The entry fields H _c1 ^(N) (d) for vortex rows are calculated for N=1, 2. It is shown that the structural transition in the vortex ensemble is a second-order phase transition. A simpler method (as compared to the Monte Carlo technique) is proposed for calculating the vortex lattice parameters.     

Shape of a magnetic resonance line in a thin film on the surface of anisotropic superconductor with irregularly distributed Abrikosov’s vortices

The form of an electron paramagnetic resonance (EPR) in a thin paramagnetic film (λ/10, λ-London’s depth of magnetic field penetration into superconductor) overlying the surface of an anisotropic superconductor is calculated taking into account the local magnetic field non-uniformity of an irregular Abrikosov’s vortex lattice. It is shown that the form of EPR is noticeably varied with the degree of irregularity of the superconductor vortex lattice. It is suggested that an inclusion of this circumstance into consideration may essentially change the conclusions made on the lattice type and parameters of this superconductor, which are typically derived from the analysis of the EPR form. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 49–52, January, 2007.     

Magnetostriction in the vicinity of spin-reorientation phase transitions in singlecrystal DyFe11Ti

The field, temperature, and angular dependences of longitudinal λ_‖ and transverse λ_⊥ magnetostriction in single-crystal DyFe₁₁Ti are investigated. Tensometric measurements were made in the temperature range from 78 to 300 K in magnetic fields up to 12 kOe. Measurements of the magnetostriction of single-crystal DyFe₁₁Ti, YFe₁₁Ti, and LuFe₁₁Ti imply that the sublattice of 3d transition metals makes only a small contribution to the magnetostriction in compounds RFe₁₁Ti, and that the primary contribution to the magnetostriction of these compounds comes from the rare-earth metal sublattice. The primary microscopic mechanism for magnetostriction is single-ion magnetostriction caused by the interaction of the anisotropic orbital electron cloud around the Dy³⁺ magnetic ion with the crystal field of the lattice. Fiz. Tverd. Tela (St. Petersburg) 41, 1647–1649 (September 1999)     

Concerning the shift of nonlinear optical resonances in a magnetic field

The shift of components of the magnetic hyperfine structure (MHS) of a vibrational-rotational molecular transition in a weak magnetic field is explored. The numerical data are given for the methane transition at λ=3.39 μm [theF ₂ ⁽²⁾ component of theP(7) line of thev ₃ band]. The shift of the line contour due to the magnetic field is found when the MHS components overlap.     

Magnetostriction of the spin-Peierls compound CuGeO3

The longitudinal and transverse magnetostriction λ of the spin-Peierls compound CuGeO₃ in the b-c plane is measured in magnetic fields up to 20 T both above and below the transition temperature T _sp=14.3K. It is found that for a given crystallographic direction the value of magnetostriction is weakly dependent on the magnetic field direction. In the uniform U phase at T⩾T _sp, λ is negative and approximately equal in the b and c directions, while in the dimerized D phase at T<T _sp, λ is positive and λ _b >λ _c . At low temperatures, λ increases sharply at the magnetic-field-induced transition from the dimerized to the magnetic M phase. The experimental data allow estimation of the stress derivatives of the antiferromagnetic intrachain exchange interaction parameter and of the stress dependence of the critical field of the D-Mphase transition. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 156–159 (10 August 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

Structure property correlations in superconducting Ti-Nb alloys

Titanium-rich transition metal alloys are metastable in their quenched boc β phase. The instability is relieved by low temperature structural transformations. We have investigated this in a series of Ti-Nb alloys, through the measurements of electrical resistivity (ρ), superconducting transition temperature and upper critical field. Supporting structural evidence has been obtained from transmission electron microscopy (tem) and x-ray studies. It is shown that both ρ and dρ/dT can be used as useful indices of this instability. The enhanced value of resistivity on account of the instability results in the enhancement of upper critical field as shown from dH _c2/dT measurements.     

Magnetism and superconductivity in ErNi2B2C

We have performed a series of neutron diffraction experiments from the magnetic order and the vortex lattice in single crystal ErNi₂B₂C. The incommensurate magnetic structure develops additional even harmonics below the ‘ferromagnetic’ ordering temperature, T _F of 2.3 K. This feature and the existence of rods of diffuse scattering suggest the development of ferromagnetic microdomain walls. The magnetic structure is very sensitive to the application of a magnetic field with changes in modulation vector and harmonic content. Studies of the vortex lattice show the presence of a 45° reorientation transition and a distorted hexagonal to square transition as a function of applied field. Further distortions of the vortex lattice occur at T _N, but no changes are seen at T _F.     

μSR study of RNi5 intermetallics where R=La,Gd or Tb

Zero-field μSR studies of some hexagonal intermetallic compounds are described. Our LaNI₅ data provide information on the muon localisation site. This site could be one of the deuterium sites deduced from neutron diffraction. A comparison of the temperature dependence of the exponential damping rate, λ(T), of our samples shows that λ(T) is strongly influenced by crystal field effects. The TbNi₅ spectra exhibit two components forT<60 K. We discuss the possible explanations of this result. We see a μSR signal below the magnetic phase transition in GdNi₅. This makes the study of the spin-lattice relaxation rate possible in the ordered magnetic state.     

Investigation of Rb <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript> atomic lines in strong magnetic fields by fluorescence from a half-wave-thick cell

It has been experimentally demonstrated that the use of the effect of significant narrowing of the fluorescence spectrum from a nanocell that contains a column of atomic Rb vapor with a thickness of L = 0.5λ (where λ = 794 nm is the wavelength of laser radiation, whose frequency is resonant with the atomic transition of the D ₁ line of Rb) and the application of narrowband diode lasers allow the spectral separation and investigation of changes in probabilities of optical atomic transitions between levels of the hyperfine structure of the D ₁ line of ⁸⁷Rb and ⁸⁵Rb atoms in external magnetic fields of 10–2500 Gs (for example, for one of transitions, the probability increases ∼17 times). Small column thicknesses (∼390 nm) allow the application of permanent magnets, which facilitates significantly the creation of strong magnetic fields. Experimental results are in a good agreement with the theoretical values. The advantages of this method over other existing methods are noted. The results obtained show that a magnetometer with a local spatial resolution of ∼390 nm can be created based on a nanocell with the column thickness L = 0.5λ. This result is important for mapping strongly inhomogeneous magnetic fields.     

Thermodynamics of a vortex system in a thin superconducting film with radiation defects

The effect of radiation defects on the thermodynamics of a system of Pearl vortices in a thin superconducting film is examined. The scenario for a Kosterlitz-Thouless transition in this system is shown to depend on the defect concentration n _d . At low concentrations, the transition takes place continuously, while at high concentrations, a range of temperatures exists in which there are two metastable states. The concentrations of free vortices and of vortices captured by defects are calculated as functions of temperature for different defect concentrations n _d . A phase diagram is constructed for the vortex system in the n _d −T plane. Zh. éksp. Teor. Fiz. 116, 1081–1090 (September 1999)     

High contrast <Emphasis Type="Italic">D</Emphasis><Subscript>1</Subscript> line electromagnetically induced transparency in nanometric-thin rubidium vapor cell

The electromagnetically induced transparency (EIT) on the atomic D ₁ line of rubidium is studied using a nanometric-thin cell with atomic vapor column length in the range of L=400–800 nm. It is shown that the reduction of the cell thickness by four orders as compared with an ordinary cm-size cell still allows to form an EIT resonance for L=λ=794 nm with the contrast of up to 40%. Further reduction of thickness to L=λ/2 leads to significant reduction of EIT contrast, verifying that the key parameter for EIT in wavelength-scale-thickness cells is not the value of L itself but L/λ ratio. Remarkable distinctions of EIT formation in nanometric-thin and ordinary cells are demonstrated. Well-resolved splitting of the EIT resonance in a magnetic field for L=λ can be used for magnetometry with nanometric spatial resolution. The presented theoretical model well describes the observed results.     

Magnetostriction and magnetization of the intermetallic compounds R Fe2 ? x Co x ( R = Tb, Dy, Er) with compensated magnetic anisotropy

The compounds Tb_0.35Dy_0.45Er_0.2Fe_{2 − x} Co _x (0 ≤ x ≤ 2) are synthesized in both polycrystalline and single-crystal states. The composition of the new multicomponent alloys with compensated magnetic anisotropy is calculated in the framework of the single-ion magnetic anisotropy model with allowance for the data on the temperature dependences of the magnetic anisotropy constants for RFe₂ single crystals. The synthesized compounds are characterized using metallographic, chemical, X-ray diffraction, and thermomagnetic methods. A combined analysis of the magnetic and magnetoelastic properties is also carried out. It is established that the high magnetostriction characteristics of the rare-earth intermetallic compounds Tb_0.35Dy_0.45Er_0.2Fe_{2 − x} Co _x with a structure of Laves phases are observed in the region of the spin-reorientational phase transition whose temperature can be varied by properly choosing the Co content. It is found that, in the room-temperature region, the magnetic susceptibility (dλ/dH) of the composition with x = 1.3 reaches levels in excess of the value of dλ/dH for terphenol D due to the compensation of magnetic anisotropy. Original Russian Text ? I.S. Tereshina, S.A. Nikitin, G.A. Politova, A.A. Opalenko, E.A. Tereshina, I.V. Telegina, 2009, published in Fizika Tverdogo Tela, 2009, Vol. 51, No. 1, pp. 85–90.