Anisotropies of the lower and upper critical fields in MgB2_2 single crystals

The temperature dependence of the London penetration depth ($\lambda$) and coherence length ($\xi$) has been deduced from Hall probe magnetization measurements in high quality MgB$_2$ single crystals in the two main crystallographic directions. We show that, in contrast to conventional superconductors, MgB$_2$ is characterized by two different anisotropy parameters ($\Gamma_\lambda = \lambda_c/\lambda_{ab}$ and $\Gamma_\xi = \xi_{ab}/\xi_c$) which strongly differ at low temperature and merge at $T_c$. These results are in very good agreement with recent calculations in weakly coupled two bands suprerconductors (Phys. Rev. B, 66, 020509(R) (2002).Comment: 4 pages, 4 figure

Unconventional superconductivity in YNi2B2C

We use the semi-classical (Doppler shift) approximation to calculate magnetic field angle-dependent density of states and thermal conductivity kappa_zz for a superconductor with a quasi-two-dimensional Fermi surface and line nodes along k_x=0 and k_y=0. The results are shown to be in good quantitative agreement with experimental results obtained for YNi2B2C.Comment: 5 pages, 3 figure

Hc2 of anisotropy two-band superconductors by Ginzburg-Landau approach

The purpose of this research is to study the upper critical field (Hc2) of two-band superconductors by two-band Ginzburg - Landau approach. The analytical formula of Hc2 included anisotropy of order parameter and anisotropy of effective-mass are found . The parameters of the upper critical field in ab-plane and c-axis can be found by fitting to the experimental data . Finally, we can find the ratio of upper critical field that temperature dependent in the range of experimental result .Comment: 10 pages. accepted by Physica

Ginzburg-Landau theory of vortices in a multi-gap superconductor

The Ginzburg-Landau functional for a two-gap superconductor is derived within the weak-coupling BCS model. The two-gap Ginzburg-Landau theory is, then, applied to investigate various magnetic properties of MgB2 including an upturn temperature dependence of the transverse upper critical field and a core structure of an isolated vortex. Orientation of vortex lattice relative to crystallographic axes is studied for magnetic fields parallel to the c-axis. A peculiar 30-degree rotation of the vortex lattice with increasing strength of an applied field observed by neutron scattering is attributed to the multi-gap nature of superconductivity in MgB2.Comment: 11 page

11^{11}B NMR study of pure and lightly carbon doped MgB2_2 superconductors

We report a $^{11}$B NMR line shape and spin-lattice relaxation rate ($1/(T_1T)$) study of pure and lightly carbon doped MgB$_{2-x}$C$_{x}$ for $x=0$, 0.02, and 0.04, in the vortex state and in magnetic field of 23.5 kOe. We show that while pure MgB$_2$ exhibits the magnetic field distribution from superposition of the normal and the Abrikosov state, slight replacement of boron with carbon unveils the magnetic field distribution of the pure Abrikosov state. This indicates a considerable increase of $H_{c2}^c$ with carbon doping with respect to pure MgB$_2$. The spin-lattice relaxation rate $1/(T_1T)$ demonstrates clearly the presence of a coherence peak right below $T_c$ in pure MgB$_2$, followed by a typical BCS decrease on cooling. However, at temperatures lower than $\approx 10$K strong deviation from the BCS behavior is observed, probably from residual contribution of the vortex dynamics. In the carbon doped systems both the coherence peak and the BCS temperature dependence of $1/(T_1T)$ weaken, an effect attributed to the gradual shrinking of the $\sigma$ hole cylinders of the Fermi surface with electron doping.Comment: 8 pages, 6 figures, submitted to Phys. Rev.

MgB2 single crystals: high pressure growth and anisotropic properties

Single crystals of MgB2 with a size up to 1.5x0.9x0.2 mm3 have been grown with a high pressure cubic anvil technique. The crystal growth process is very peculiar and involves an intermediate nitride, namely MgNB9. Single crystals of BN and MgB2 grow simultaneously by a peritectic decomposition of MgNB9. Magnetic measurements in fields of 1-5 Oe show sharp transitions to the superconducting state at 37-38.6 K with width of ~0.5 K. The high quality of the crystals allowed the accurate determination of magnetic, transport and optical properties as well as scanning tunnelling spectroscopy (STS) and decoration studies. Investigations of crystals with torque magnetometry show that Hc2//c is very low (24 kOe at 15 K), while Hc2//ab increases up to 140 kOe at 15 K. The upper critical field anisotropy gamma = Hc2//ab/ Hc2//c was found to be temperature dependent (decreasing from 6 at 15 K to 2.8 at 35 K). The effective anisotropy gamma_eff, as calculated from reversible torque data near Tc, is field dependent (increasing roughly linearly from 2 in zero field to 3.7 in 10 kOe). The temperature and field dependence of the anisotropy can be related to the double gap structure of MgB2 with a large two-dimensional gap and small three-dimensional gap, the latter being rapidly suppressed in a magnetic field. Torque magnetometry investigations show a pronounced peak effect, indicating an order-disorder transition of vortex matter. Decoration experiments and STS visualise a hexagonal vortex lattice. STS spectra evidence two gaps (3 meV/6 meV) with direction dependent weight. Magneto-optic investigations with H//c show a clear signature of the smaller of the two gaps, disappearing in fields higher than Hc2//c.Comment: 17 pages pdf only, 15 figures integrated (higher resolution photographs available on request); submitted to Supercond. Sci. Technol. (Proceedings of Boromag conference

The Upper Critical Field Hc2 in Advanced Superconductors with Anisotropic Energy Spectrum

A brief review of works on the microscopic theory of determining the upper critical field in two-band isotropic and anisotropic superconductors is given. The research is based on a set of the Ginzburg-Landau equations for the order parameters in a magnetic field that are studied in terms of the classical approach to a superconducting system in a magnetic field. Two inequivalent energy bands with different topology of Fermi surface cavities overlapping on the Fermi surface are discussed. The cases of the direction of the external magnetic field H\to// the (ab) plane and H\to // the crystallographic c axis are studied. The equations for determining Hc2(ab) and Hc2(c) for a pure superconductor and a superconductor doped with electrons and holes are derived. The analytical solutions to these equations in the vicinity of the superconducting transition temperature (Tc - T<<Tc) and in the vicinity of zero (T<<Tc) are found. The temperature and impurity dependences of the upper critical fields Hc2(ab) and Hc2(c), as well as the anisotropy coefficient \gammaH, are studied. The resulting theory is applied to determine the dependences of the above magnetic characteristics of intermetallic compound MgB2. The theory agrees qualitatively with experimental data.Comment: 24 pages, 6 fi

Nonlocal effects in angular dependence of in-plane magnetization of tetragonal superconductors

The reversible magnetization M of Lu(Ni1-xCox)(2)B2C with x = 0 and 0.06 is measured in a broad temperature domain as a function of field orientation theta in the basal crystal plane. The data are interpreted within London theory extended for nonlocality of the current-field relation in superconductors. The dependence M (theta) diminishes on warming, vanishes at T* T*. The low-T sign is opposite to what is expected from the known angular dependence of the upper critical field and therefore cannot be attributed to the latter. Upon doping with Co, the effect disappears with decreasing mean-free path in agreement with theory.This article is published as Kogan, V. G., S. L. Bud’ko, P. C. Canfield, and P. Miranović. "Nonlocal effects in angular dependence of in-plane magnetization of tetragonal superconductors." Physical Review B 60, no. 18 (1999): R12577. DOI: 10.1103/PhysRevB.60.R12577. Copyright 1999 American Physical Society. Posted with permission