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Register a new userPauli Paramagnetic Effects on Vortices in Superconducting TmNi2B2C
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Morten Ring Eskildsen
Publication date
2007
fields
Physics
and research's language is
English
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The magnetic field distribution around the vortices in TmNi2B2C in the paramagnetic phase was studied experimentally as well as theoretically. The vortex form factor, measured by small-angle neutron scattering, is found to be field independent up to 0.6 Hc2 followed by a sharp decrease at higher fields. The data are fitted well by solutions to the Eilenberger equations when paramagnetic effects due to the exchange interaction with the localized 4f Tm moments are included. The induced paramagnetic moments around the vortex cores act to maintain the field contrast probed by the form factor.
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From small-angle neutron scattering studies of the flux line lattice (FLL) in CeCoIn5, with magnetic field applied parallel to the crystal c-axis, we obtain the field- and temperature-dependence of the FLL form factor, which is a measure of the spatial variation of the field in the mixed state. We extend our earlier work [A.D. Bianchi et al. 2008 Science 319, 177] to temperatures up to 1250 mK. Over the entire temperature range, paramagnetism in the flux line cores results in an increase of the form factor with field. Near H_c2 the form factor decreases again, and our results indicate that this fall-off extends outside the proposed FFLO region. Instead, we attribute the decrease to a paramagnetic suppression of Cooper pairing. At higher temperatures, a gradual crossover towards more conventional mixed state behavior is observed.
We study theoretically the mixed state properties of a strong uniaxially-anisotropic type II superconductor with the Pauli paramagnetic effect, focusing on their behaviors when the magnetic field orientation is tilted from the conduction layer ab plane. On the basis of Eilenberger theory, we quantitatively estimate significant contributions of the Pauli paramagnetic effects on a variety of physical observables, including transverse and longitudinal components of the flux line lattice form factors, magnetization curves, Sommerfeld coefficient, field distributions and magnetic torques. We apply these studies to Sr_2_RuO_4_ and quantitatively explain several seemingly curious behaviors, including the H_c2_ suppression for the ab plane direction, the larger anisotropy ratio and intensity found by the spin-flip small angle neutron scattering, and the first order transition observed recently in magneto-caloric, specific heat and magnetization measurements in a coherent and consistent manner. Those lead us to conclude that Sr_2_RuO_4_ is either a spin-singlet or a spin-triplet pairing with the d-vector components in the ab plane.
A novel spin density wave (SDW) instability mechanism enhanced by vortices under fields is proposed to explain the high field and low temperature (HL) phase in CeCoIn$_5$. In the vortex state the strong Pauli effect and the nodal gap conspire to enhance the momentum resolved spectral weight exclusively along the nodal direction over the normal value, providing a favorable nesting condition for SDW with ${bf Q}=(2k_F, 2k_F, 0.5)$ only under high field ($H$). Observed mysteries of the field-induced SDW confined within $H_{c2}$ are understood consistently, such facts that ${bf Q}$ is directed to the nodal direction independent of $H$, SDW diminishes under tilting field from the $ab$ plane, and the SDW transition line in $(H,T)$ has a positive slope.
Superconducting phase transitions in strongly type-II superconductors in the Pauli paramagnetic limit are considered within the framework of the Gorkov-Ginzburg-Landau approach in the lowest Landau level approximation for both s and d-wave electron pairing. Simple analytical expressions for the quadratic and quartic coefficients in the order parameter expansion of the superconducting free energy are derived without relying on gradient or wavenumber expansions. The existence of a changeover from continuos to discontinuos superconducting phase transitions predicted to occur in the clean limit is shown to depend only on the dimensionality of the underlying electronic band structure. Such a changeover can take place in the quasi 2D regime below a critical value of a 3D-2D crossover parameter.
We investigate the mixed state properties in a type II multiband superconductor with uniaxial anisotropy under the Pauli paramagnetic effects. Eilenberger theory extended to a multiband superconductor is utilized to describe the detailed vortex lattice properties, such as the flux line form factors, the vortex lattice anisotropy and magnetic torques. We apply this theory to Sr$_2$RuO$_4$ to analyze those physical quantities obtained experimentally, focusing on the interplay between the strong two-dimensional anisotropy and the Pauli paramagnetic effects. This study allows us to understand the origin of the disparity between the vortex lattice anisotropy ($sim$60) and the $H_{rm c2}$ anisotropy ($sim$20). Among the three bands; $gamma$ with the effective mass anisotropy $sim$180, $alpha$ with $sim$120, and $beta$ with $sim$60, the last one is found to be the major band, responsible for various magnetic responses while the minor $gamma$ band plays an important role in the vortex formation. Namely, in a field orientation slightly tilted away from the two dimensional basal plane those two bands cooperatively form the optimal vortex anisotropy which exceeds that given by the effective mass formula with infinite anisotropy. This is observed by small angle neutron scattering experiments on Sr$_2$RuO$_4$. The pairing symmetry of Sr$_2$RuO$_4$ realized is either spin singlet or spin triplet with the d-vector strongly locked in the basal plane. The gap structure is that the major $beta$ band has a full gap and the minor $gamma$ band has a $d_{x^2-y^2}$ like gap.
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