Effects of two-band superconductivity on the flux-line lattice in magnesium diboride

We present neutron scattering from the flux line lattice (FLL) in MgB2. Between 0.5 and 0.9 T the FLL undergoes a 30 degrees reorientation, and simultaneously the scattered intensity falls sharply consistent with the weaker superconducting pi band being suppressed with increasing field. We speculate that the pi and sigma bands favor different FLL orientations, and that the reorientation is driven by the suppression of the pi band. When the c axis of the crystal is rotated 45 degrees to the applied field the penetration depth anisotropy could be measured, and rises both as a function of applied field and temperature.     

Field distribution and flux-line depinning in MgB (2)

We report the first observation of the field distribution and flux-line lattice (FLL) depinning in the vortex-state (VS) of a type-II superconductor probed by conduction electron spin resonance (CESR). CESR was performed in MgB (2) (T(c) approximately 39 K) at 4.1 GHz (1455 Oe) and 9.5 GHz (3390 Oe). The field distribution, n(H), and a standard deviation of sigma approximately 14 Oe (at 28 K/4.1 GHz and at 7 K/9.5 GHz) were inferred, respectively, from the distortion and broadening of the CESR in the VS. For both frequencies, the FLL depinning temperature was determined.     

Field dependent coherence length in the superclean, high-kappa superconductor CeCoIn5

Using small-angle neutron scattering, we have studied the flux-line lattice (FLL) in the superclean, high-kappa superconductor CeCoIn5. The FLL undergoes a first-order symmetry and reorientation transition at approximately 0.55 T at 50 mK. In addition, the FLL form factor in this material is found to be independent of the applied magnetic field, in striking contrast to the exponential decrease usually observed in superconductors. This result is consistent with a strongly field-dependent coherence length, proportional to the vortex separation.     

Flux line lattice reorientation in the borocarbide superconductors with H parallel a

Small angle neutron scattering studies of the flux line lattice in LuNi2B2C and ErNi2B2C induced by a field parallel to the a axis reveal a first order flux line lattice reorientation transition. Below the transition the flux line lattice nearest neighbor direction is parallel to the b axis, and above the transition it is parallel to the c axis. This transition cannot be explained using nonlocal corrections to the London model. In addition, the anisotropy of the penetration depth lambda and the coherence length xi change at the transition.     

Observation of a new magnetic anomaly below the ferromagnetic Curie temperature in Yb14MnSb11

Yb14MnSb11 is an unusual ferromagnet with a Curie temperature of 52 +/- 1 K. Recent optical, Hall, magnetic, and thermodynamic measurements indicate that Yb14MnSb11 may be a rare example of an underscreened Kondo lattice. We report the first experimental observation of a new magnetic anomaly in this system at around 47 K, a few degrees below T(c). Systematic investigations of the ac and dc susceptibilities of Yb14MnSb11 single crystals reveal features associated with possible spin reorientation at this temperature. This new anomaly is extremely sensitive to the applied measurement field and is absent in temperature-dependent dc magnetization data for fields above 50 Oe. The origin of this could be due to decoupling of two distinct magnetic sublattices associated with MnSb4 tetrahedra.     

Observation of the flux line lattice in high Tc-superconductor Bi2.2Sr2CaCu2OX and Ti2Ba2CaCu2OX single crystals

The flux-line lattice (FLL) has been observed on the (001) face of high T_c Bi_2.2Sr₂CaCu₂O_X and Ti₂Ba₂CaCu₂O_X single cristals using the technique of decorating the sample with small ferromagnetic particles. Strong pinning of the Abrikosov vortices by plane defects along (100) and (010) planes has been found out on Bi_2.2Sr₂CaCu₂O_X. The triangular FLL with a long-range order has been observed on the perfect Ti₂Ba₂CaCu₂O_X single crystal. The penetration depth for a magnetic field parallel to (001) axis has been evaluated as ≤0.2μm at 4.2K for both materials.     

On the correlation between flux line lattice and crystal lattice

For pure type-II superconductors with κ slightly above 1/√2 it is shown that the preferential orientations of the flux-line lattice relative to the crystal lattice are related to the anisotropy of the coherence length.     

Vortex lattice studies in CeCoIn5 with H is orthogonal to c

We present small angle neutron scattering studies of the vortex lattice (VL) in CeCoIn5 with magnetic fields applied parallel (H) to the antinodal [100] and nodal [110] directions. For H is parallel to [100], a single VL orientation is observed, while a 90° reorientation transition is found for H is parallel to [110]. For both field orientations and VL configurations we find a distorted hexagonal VL with an anisotropy, Γ=2.0±0.05. The VL form factor shows strong Pauli paramagnetic effects similar to what have previously been reported for H is parallel to [001]. At high fields, above which the upper critical field (H(c2)) becomes a first-order transition, an increased disordering of the VL is observed.     

Anisotropy of Critical Fields in MgB2： Two-Band Ginzburg-Landau Theory for Layered Superconductors

The temperature dependence of the anisotropy parameter of upper critical field γHc2(T)=H_{c2}^||(T)/H_{c2}^{\bot}(T) and London penetration depth γ_λ(T)=λ_{\perp} (T)/λ_{\bot} (T) are calculated using two-band Ginzburg-Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γ_{H_{c2}}(T) is increased, while theLondon penetration depth anisotropy γλ(T) reveals n opposite behavior.Results of our calculations are in agreement with experimental datafor single crystal MgB₂ nd with other calculations. Results of an analysis of magnetic field H_c1 in a single vortex between superconducting layers are also presented.     

Magnetization processes in nanocrystalline gadolinium

The thermal decline in magnetization, M(T), at fixed magnetic field (H) under 'zero-field-cooled' (ZFC) and 'field-cooled' (FC) conditions, the time evolution of ZFC magnetization, M(ZFC)(t), at fixed temperature and field, M(H) hysteresis loops/isotherms, and ac susceptibility have been measured on polycrystalline Gd samples with average grain sizes of d = 12 and 18 nm. The irreversibility in magnetization, M(irr), occurring below a characteristic temperature that reduces with increasing H, is completely suppressed above a grain-size-dependent threshold field, H*. At low fields (H ≤ 100 Oe), M(irr)(T), like the coercive field, H(c)(T), exhibits a minimum at ～16 K and a broad peak at ～50 K before going to zero at T ? T(C) (Curie temperature). At fixed temperature (T < T(C)) and field (H ? H*), where M(irr) is finite, M(ZFC) has a logarithmic dependence on time. The magnetic viscosity (S) at H = 1 Oe and T ≤ 290 K is independent of the measurement time above ～2 ms but for t < 2 ms it is strongly time-dependent. S(T) peaks at T ? T(C) for H = 1 Oe. A magnetic field reduces the peak height and shifts the peak in S(T) to lower temperatures. All the above observations are put on a consistent theoretical footing within the framework of a model in which the intra-grain magnetizations overcome the energy barriers (brought about by the intra-grain and grain-boundary/interfacial magnetic anisotropies) by the thermal activation process. These field- and temperature-dependent energy barriers, that separate the high-energy metastable (ZFC) state from the stable minimum-energy (FC) state, are independent of time for t ? 2 ms and have a very broad distribution. We show that the shape anisotropy plays a decisive role in the magnetization reversal process, and that the magnetocrystalline and magnetostatic fluctuations, prevalent in the grain-boundary and interfacial regions, govern the approach-to-saturation of magnetization in nanocrystalline Gd.     

Structure, spin reorientation and M(o)ssbauer effect studies of Tb0.3Dy0.7(Fe1-xAlx)1.95 alloys

The effect of Al substitution for Fe on crystal structure, magnetostriction and spontaneous magnetostriction, anisotropy and spin reorientation of a series of polycrystalline Tb0.3Dy0.7(Fe1-xAlx)1.95 alloys (x = 0, 0.05, 0.1, 0.15, 0.20, 0.25, 0.30, 0.35) at room temperature and 77 K was investigated systematically. It was found that the primary phase of Tb0.3Dy0.7(Fe1-xAlx)1.95 is the MgCu2-type cubic Laves phase structure when x < 0.4 and the lattice constant a of Tb0.3Dy0.7(Fe1-xAlx)1.95 increases approximately and monotonically with the increase of x. The substitution of Al leads to the fact that the magnetostriction ( inceases slightly in a low magnetic field (H ≤ 40 kA/m), but decreases sharply and is easily close to saturation in a high applied field as x increases, showing that a small amount of Al substitution is beneficial to a decrease in the magnetocrystalline anisotropy. It was also found that the spontaneous magnetostriction (ζ)111 decreases greatly with x increasing. The analysis of the M(o)ssbauer spectra indicated that the easy magnetization direction in the {110} plane deviates slightly from the main axis of symmetry with the changes of composition and temperature, namely spin reorientation. A small amount of non-magnetic phase exists for x = 0.15 in Tb0.3Dy0.7(Fe1-xAlx)1.95 alloys and the alloys become paramagnetic for x > 0.15 at room temperture, but at 77 K the alloys still remain magnetic phase even for x = 0.2. At room temperature and 77 K, the hyperfine field decreases and the isomer shifts increase with Al concentration increasing.     

Free energy and torque for superconductors with different anisotropies of H(c2) and lambda

The free energy is evaluated for a uniaxial superconductor with the anisotropy of the upper critical field, gamma(H)=H(c2,a)/H(c2,c), different from the anisotropy of the penetration depth gamma(lambda)=lambda(c)/lambda(a). With increasing difference between gamma(H) and gamma(lambda), the equilibrium orientation of the crystal relative to the applied field may shift from theta=pi/2 (theta is the angle between the field and the c axis) to lower angles and reach theta=0 for large enough gamma(H). These effects are expected to take place in MgB2.     

Magnetic flux distribution in the bulk of the pure type-II superconductor niobium measured with positive muons

The spin precession of positive muons in ultra-pure Nb single crystals of high perfection, cooled down in transverse magnetic fields 0.68B _c2≤B _appl≤0.84B _c2 (B _c2=upper critical field) from temperatures well above the superconducting transition temperatureT _c=9.25 K, has been investigated in the temperature range 2.6 K≤T≤8.0 K. The experiments confirm the periodic fieldB(r) of triangular flux-line lattices as calculated from numerical solutions of the microscopic BCS-Gor'kov theory. The observed broadening of the van Hove singularities in the field distribution is discussed in terms of the combined effects of muon diffusion and random perturbations of the flux-line lattice.     

Weak Ferromagnetism and Field-Induced Spin Reorientation in K2V3O8

Magnetization and neutron diffraction studies of the 2D S = 1/2 antiferromagnet, K2V3O8, indicate an ordered state exhibiting weak ferromagnetism and field-induced spin reorientations. Of particular interest is the behavior in a basal plane magnetic field where a unique spin reorientation is observed in which the spins rotate from the easy c axis to the basal plane while remaining normal to the applied field. The experimental observations are well described by a two spin exchange model incorporating Heisenberg and Dzyaloshinskii-Moriya interactions with an additional c-axis anisotropy.     

Doping dependent evolution of magnetism and superconductivity in Eu(1-x)K(x)Fe2As2 (x = 0-1) and temperature dependence of the lower critical field H(c1)

We have synthesized polycrystalline samples of Eu(1-x)K(x)Fe2As2 (x = 0-1) and carried out systematic characterization using x-ray diffraction, ac and dc magnetic susceptibility, and electrical resistivity measurements. A clear signature of the coexistence of a superconducting transition (T(c) = 5.5 K) with spin density wave (SDW) ordering is observed in our underdoped sample with x = 0.15. The SDW transition disappears completely for the x = 0.3 sample and superconductivity arises below 20 K. The superconducting transition temperature Tc increases with increase in the K content and a maximum Tc = 33 K is reached for x = 0.5, beyond which it decreases again. The doping dependent Tx phase diagram is extracted from the magnetic and electrical transport data. It is found that magnetic ordering of Eu moments coexists with the superconductivity up to x = 0.6. The isothermal magnetization data taken at 2 K for the doped samples suggest the 2+ valence state of the Eu ions. We also present the temperature dependence of the lower critical field H(c1) of the superconducting polycrystalline samples. The values of H(c1)(0) obtained for x = 0.3, 0.5, and 0.7 after taking the demagnetization factor into account are 202, 330, and 212 Oe, respectively. The London penetration depth λ(T) calculated from the lower critical field does not show exponential dependence at low temperature, as would be expected for a fully gapped clean s-wave superconductor. In contrast, it shows a T2 power law feature up to T = 0.3Tc, as observed in Ba(1-x)K(x)Fe2As2 and BaFe(2-x)Co(x)As2.     

Field-dependent diamagnetic transition in magnetic superconductor Sm1.85Ce0.15CuO4-y

The magnetic penetration depth of single crystal Sm(1.85)Ce(0.15)CuO(4-y) was measured down to 0.4 K in dc fields up to 7 kOe. For insulating Sm2CuO4, Sm3+ spins order at the Ne el temperature, T(N)=6 K, independent of the applied field. Superconducting Sm(1.85)Ce(0.15)CuO(4-y) (T(c) approximately 23 K) shows a sharp increase in diamagnetic screening below T(*)(H) which varied from 4.0 K (H=0) to 0.5 K (H=7 kOe) for a field along the c axis. If the field was aligned parallel to the conducting planes, T(*) remained unchanged. The unusual field dependence of T(*) indicates a spin-freezing transition that dramatically increases the superfluid density.     

Specific heat and anisotropic superconducting and normal-state magnetization of HoNi2B2C

The magnetization of single-crystal HoNi₂B₂C has been measured as a function of applied field (H) and temperature in order to probe the interplay between superconductivity and magnetism in this complex layered system. The normal-state magnetic susceptibility of HoNi₂B₂C is highly anisotropic with a Curie-Weiss-like temperature dependence for H applied perpendicular to the c-axis and with a much weaker temperature dependence for H applied parallel to the c-axis, indicating that the Ho⁺³ magnetic moments lie predominately in the tetragonal a−b plane below 20 K. High-field magnetization (2000 Oe), low-field magnetization (20 Oe) and zero-field specific heat all give an antiferromagnetic ordering temperature of T_N=5.0 K. Remarkably, in 20 Oe applied field both superconductivity (T_c=8.0 K) and antiferromagnetism (T_N=5.0 K) clearly make themselves manifest in the magnetization data. From these magnetization data a phase diagram in the H−T plane was constructed for both directions of applied field. This phase diagram shows a non-monotonic temperature dependence of H_c2 with a deep minimum at T_N=5 K. The high-field magnetization data for H applied perpendicular to the c-axis also reveal a cascade of three phase transitions for T < 5 K and H < 15 000 Oe, contributing to the rich H versus T phase diagram for HoNi₂B₂C at low temperatures.     

Anisotropic superconducting properties of FeSe0.5Te0.5 single crystals

We investigated the anisotropic electrical transport and magnetic properties of FeSe$_{0.5}$Te$_{0.5}$ single crystals grown by the self-flux method. The in-plane resistivity shows a metallic-like temperature dependence, while the out-of-plane resistivity shows a broad hump with a maximum at around 64 K. The magnetization loops for $H/\!/c$-axis and $H/\!/ab$-plane are also different, for example, there is a typical second peak for $H/\!/c$-axis. The in-plane critical current density is larger than the out-of-plane one. The coherence length and penetration depth were estimated by the Ginzburg-Landau theory. The anisotropic parameter $\gamma $ depends on the applied magnetic field and the temperature. The coupling of superconducting FeSe(Te) layers and the flux pinning mechanism relevant to anisotropy are also discussed.     

Anisotropy of penetration depth in superconducting tin

Microwave resonance technique at 3000 MHz has been used to carry out measurements of the temperature variation of penetration depth in single crystals of pure tin. Several samples of known crystallographic orientations have been studied, and the anisotropy of penetration depth obtained. The results clearly show non-tensorial anisotropy of penetration depth, and hence provide a direct experimental evidence for non-local relation between the current density and associated magnetic field in a type I superconductor.     

Vortex fluctuations in underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) crystals

Vortex thermal fluctuations in heavily underdoped Bi(2)Sr(2)CaCu(2)O(8+delta) (T(c)=69.4 K) are studied using Josephson plasma resonance. From the zero-field data, we obtain the c-axis penetration depth lambda(L,c)(0)=230+/-10 micrometer and the anisotropy ratio gamma(T). The low plasma frequency allows us to study phase correlations over the whole vortex solid state and to extract a wandering length r(w) of vortex pancakes. The temperature dependence of r(w) as well as its increase with dc magnetic field is explained by the renormalization of the vortex line tension by the fluctuations, suggesting that this softening is responsible for the dissociation of the vortices at the first order transition.