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

Herlach, D.; Majer, G.; Major, J.; Rosenkranz, J.; Schmolz, Manfred; Schwarz, Winfried H.; Seeger, A.; Templ, Wolfgang; Brandt, Ernst Helmut; Eßmann, U.; Fürderer, K.; Gladisch, M.

doi:10.1007/bf02395983

Cited by 30 publications

(15 citation statements)

References 16 publications

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“…Neglecting theh/τ life term in the ratio expression, we compute R φ = 1 when T = 0.04 K for B ext = 0.4 T. This B ext value corresponds approximately to B c2 for a high-quality niobium sample. 14 The theory for the form factor and resulting field map and field distribution discussed here is therefore expected to be valid down to 0.04 K for simple superconductors such as niobium when the VL is composed of equilateral triangles. The correlation function has the periodicity of the VL with respect to the center of mass of a Cooper pair, i.e., (r 1 + r 2 )/2.…”

Section: Physical Principles For the Description Of The Magnetizmentioning

confidence: 96%

“…However, it is only expected at really low temperature, i.e., for b = 0.0011;c = 0.01 c 0.10, in contrast to observation. 14 The D c (B Z ) shape near the minimum field is really different near T = 0 and T c0 . This difference remains to be seen experimentally.…”

Section: Numerical Analysis Of the Form Factor Field Map And Fmentioning

confidence: 96%

“…In terms of the free-energy expression given by Eq. (14), ∂F /∂B Z = −[a/(2B Z )](∂F /∂a) and therefore we need to evaluate a(∂/∂a)(u /a). This is done in Appendix B.…”

Section: Magnetizationmentioning

confidence: 99%

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Magnetic form factor, field map, and field distribution for a BCS type-II superconductor near itsBc2(T)phase boundary

Maisuradze

Yaouanc

2013

Phys. Rev. B

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We review the magnetic form factor deduced by Delrieu from Gorkov's equation for a Bardeen-Cooper-Schrieffer (BCS) type-II superconductor near its B c2 phase boundary, i.e., when its magnetization is small. A numerical study of the form factor, field map, and field distribution follows. The characteristics of the transition from the low-temperature BCS to the high-temperature Ginzburg-Landau vortex lattices is studied. The exotic shape of the component field distribution and the form factor at low temperature and as a function of the external field intensity are discussed. Our numerical work should be helpful for the analyzing of small-angle neutron scattering and muon spin rotation vortex-lattice data recorded for BCS superconductors and may be other superconductors in the clean limit.

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Section: Physical Principles For the Description Of The Magnetizmentioning

confidence: 96%

Section: Numerical Analysis Of the Form Factor Field Map And Fmentioning

confidence: 96%

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Magnetic form factor, field map, and field distribution for a BCS type-II superconductor near itsBc2(T)phase boundary

Maisuradze

Yaouanc

2013

Phys. Rev. B

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“…The 3D flux distribution inside the superconductor also can be probed by neutron depolarization (Weber 1974, Roest andRekveldt 1993). A further method which probes the field distribution of the FLL in the bulk is muon spin rotation (µSR) (Brandt and Seeger 1986, Pümpin et al 1988, Herlach et al 1990, Harshman et al 1989, Brandt 1988a,b, 1991c, Lee et al 1993, Cubitt et al 1993a, Weber et al 1993, Sonier et al 1994, Alves et al 1994, Song 1995, Riseman et al 1995, see also section 5.7.…”

Section: Observation Of the Flux-line Latticementioning

confidence: 99%

The flux-line lattice in superconductors

1995

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Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux φ 0 = h/2e. These tiny vortices of supercurrent tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-T c superconductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth λ: The shear modulus of the FLL is c 66 ∼ 1/λ 2 , and the tilt modulus c 44 (k) ∼ (1 + k 2 λ 2 ) −1 is dispersive and becomes very small for short distortion wavelength 2π/k ≪ λ. This softness is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may "melt" the FLL and cause thermally activated depinning of the flux lines or of the two-dimensional "pancake vortices" in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSC's as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

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“…In contrast, the experiments of Refs. [2,3] used energetic (∼ 4 MeV) µ + that stop at interstitial or bond sites in the bulk of the sample where they directly probe the local magnetic fields. The term "bulk" means that the stopping range of these faster muons is approximately 150 mg/cm 2 , which requires samples ∼ 1 mm thick.…”

Section: Introductionmentioning

confidence: 99%

Muon spin rotation studies of electronic excitations and magnetism in the vortex cores of superconductors

Sonier

2007

Rep. Prog. Phys.

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The focus of this article is on recent progress in muon spin rotation (µSR) studies of the vortex cores in type-II superconductors. By comparison of µSR measurements of the vortex-core size in a variety of materials with results from techniques that directly probe electronic states, the effect of delocalized quasiparticles on the spatial variation of field in a lattice of interacting vortices has been determined for both single-band and multi-band superconductors. These studies demonstrate the remarkable accuracy of what some still consider an exotic technique. In recent years µSR has also been used to search for magnetism in and around the vortex cores of high-temperature superconductors. As a local probe µSR is specially suited for detecting static or quasistatic magnetism having short-range or random spatial correlations. As discussed in this review, µSR experiments support a generic phase diagram of competing superconducting and magnetic order parameters, characterized by a quantum phase transition to a state where the competing order is spatially non-uniform.

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

Cited by 30 publications

References 16 publications

Magnetic form factor, field map, and field distribution for a BCS type-II superconductor near itsBc2(T)phase boundary

Magnetic form factor, field map, and field distribution for a BCS type-II superconductor near itsBc2(T)phase boundary

The flux-line lattice in superconductors

Muon spin rotation studies of electronic excitations and magnetism in the vortex cores of superconductors

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