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Register a new userInterplay between effective mass anisotropy and Pauli paramagnetic effects in a multiband superconductor--Application to Sr2RuO4--
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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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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.
Despite numerous studies the exact nature of the order parameter in superconducting Sr2RuO4 remains unresolved. We have extended previous small-angle neutron scattering studies of the vortex lattice in this material to a wider field range, higher temperatures, and with the field applied close to both the <100> and <110> basal plane directions. Measurements at high field were made possible by the use of both spin polarization and analysis to improve the signal-to-noise ratio. Rotating the field towards the basal plane causes a distortion of the square vortex lattice observed for H // <001>, and also a symmetry change to a distorted triangular symmetry for fields close to <100>. The vortex lattice distortion allows us to determine the intrinsic superconducting anisotropy between the c-axis and the Ru-O basal plane, yielding a value of ~60 at low temperature and low to intermediate fields. This greatly exceeds the upper critical field anisotropy of ~20 at low temperature, reminiscent of Pauli limiting. Indirect evidence for Pauli paramagnetic effects on the unpaired quasiparticles in the vortex cores are observed, but a direct detection lies below the measurement sensitivity. The superconducting anisotropy is found to be independent of temperature but increases for fields > 1 T, indicating multiband superconductvity in Sr2RuO4. Finally, the temperature dependence of the scattered intensity provides further support for gap nodes or deep minima in the superconducting gap.
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.
Motivated by recent experiments on heavy fermion materials CeCu$_2$Si$_2$ and UBe$_{13}$, we develop a framework to capture generic properties of multiband superconductors with strong Pauli paramagnetic effect (PPE). In contrast to the single band case, the upper critical field $H_{rm c2}$ can remain second order transition even for strong PPE cases. The expected first order transition is hidden inside $H_{rm c2}$ and becomes a crossover due to the interplay of multibandness. The present theory based on full self-consistent solutions of the microscopic Eilenberger theory explains several mysterious anomalies associated with the crossover and the empty vortex core state which is observed by recent STM experiment on CeCu$_2$Si$_2$.
The upper critical field Hc2(T) of the multiband superconductor KFe2As2 has been studied via low-temperature thermal expansion and magnetostriction measurements. We present compelling evidence for Pauli-limiting effects dominating Hc2(T) for H || a, as revealed by a crossover from second- to first-order phase transitions to the superconducting state in the magnetostriction measurements down to 50 mK. Corresponding features were absent for H || c. To our knowledge, this crossover constitutes the first confirmation of Pauli limiting of the Hc2(T) of a multiband superconductor. The results are supported by modeling Pauli limits for single-band and multiband cases.
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