Deviations from the extended London model at high magnetic fields in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$

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Deviations from the extended London model at high magnetic fields in ${YBa}_{2} {Cu}_{3} O_{7}$

E. Campillo, M. Bartkowiak, R. Riyat, E. Jellyman, A. S. Cameron, A. T. Holmes, O. Prokhnenko, W.-D. Stein, A. Erb, E. M. Forgan, and E. Blackburn

Phys. Rev. B 105, 184508 – Published 11 May 2022

Abstract

We report on the evolution with the magnetic field and the temperature of the vortex lattice (VL) in fully oxygenated ${YBa}_{2} {Cu}_{3} O_{7}$ as studied by time-of-flight small-angle neutron scattering. Using the High Field Magnet/Extreme Environment Diractometer beamline at Helmholtz-Zentrum Berlin, we have obtained data up to 25.9 T—much higher than data available previously. Our VL structure results are consistent with the progressive suppression by the field of the superconductivity along the crystallographic $b$ (CuO chain) direction and an accompanying shift of the nodal directions as the field is increased. The intensity of the diffracted signal reveals the spatial variation of magnetization caused by the VL (the “form factor”). Instead of a rapid falloff with the field, as seen in superconductors with smaller upper critical fields, we find that the form factor is almost constant with the field above $\sim 12$ T. We speculate that this is due to Pauli paramagnetic effects.

Received 3 March 2022
Accepted 21 April 2022

DOI:https://doi.org/10.1103/PhysRevB.105.184508

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Superconducting order parameter Superconductivity Vortex lattices

High-temperature superconductors

Neutron scattering

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

E. Campillo ^1,*, M. Bartkowiak ², R. Riyat³, E. Jellyman³, A. S. Cameron⁴, A. T. Holmes ⁵, O. Prokhnenko ², W.-D. Stein², A. Erb⁶, E. M. Forgan³, and E. Blackburn ¹

¹Division of Synchrotron Radiation Research, Lund University, SE-22100 Lund, Sweden
²Helmholtz-Zentrum Berlin für Materialien und Energie, Hahn-Meitner-Platz 1, D-14109 Berlin, Germany
³School of Physics and Astronomy, University of Birmingham, Birmingham B15 2TT, United Kingdom
⁴Institut für Festkörperphysik und Materialphysik, Technische Universität Dresden, D-01069 Dresden, Germany
⁵European Spallation Source ERIC, P.O. Box 176, SE-221 00 Lund, Sweden
⁶Walther Meissner Institut, BAdW, D-85748 Garching, Germany

^*emma.campillo@sljus.lu.se

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Vol. 105, Iss. 18 — 1 May 2022

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Figure 1
A vortex lattice diffraction pattern at 23 T and 3 K. The opening angle $ν$ is used to describe the structure of the vortex lattice. The plotted signal is a measure of the counts per pixel summed along $q_{z}$ divided by the product of the incident beam intensity and the square of the neutron wavelength.
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Figure 2
(a) The evolution of the vortex lattice structure with the magnetic field at 3 K. The circular points are from this study while the filled square points are from a previous study [12] up to 11 T, and the open squares are included from Ref. [13]. (b) Variation of the opening angle with temperature at 25 and 25.9 T with two single points at 19 and 23 T. The diamond and circular points are from a previous study [13] and are provided for reference.
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Figure 3
(a) The vortex lattice form factor as a function of the magnetic field. The circular points are the new data reported here; the square points are drawn from Refs. [12, 13]. The dashed line is a fit to the solid square points using an extended London model specified in the main text. (b) The temperature dependence of the vortex lattice form factor. The triangular and square points are from this work and the diamond and circular points from Ref. [13] are included for comparison. The solid line is discussed in the main text. Our data in this panel were taken in the second experiment, and the values of the form factor have been multiplied by a normalization constant of 1.5 to account for a loss in intensity observed due to a change in the detector between our first and second experiments. This normalization constant has been confirmed by a third experiment performed at the same facility with a 15% Ca-doped YBCO sample.
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Figure 4
Schematic representation of the variation of a $d + s$ superconducting order parameter around a cylindrical Fermi surface. In YBCO, such an admixture must arise because of the crystal structure and it has the same orthorhombic symmetry. It is seen that the nodal positions lie nearer the direction of weaker superconductivity. This will be the a direction at low fields and we propose that it is the b direction at high fields.
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Figure 5
Form factors versus field using several different theoretical approaches. Solid circles: The exact solution of the GL equations [22] (at a large value of $κ = 100$ ). Empty circles: The numerical solution of the Eilenberger equations. Dashed line: The Hao-Clem variational solution of the GL equations. Solid line: London model with exponential cutoff (the Brandt model). The form factors are calculated (a) for $T = 0.1 T_{c}$ using results from Ref. [24] and (b) for $T = 0.5 T_{c}$ using results from Ref. [23]. This is an updated version of the comparisons of GL solutions in Ref. [38].
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Figure 6
The $q_{z}$ width of the diffraction spots at the base temperature versus the field above 8 T. The empty square points are from a previous study [13]. The dashed line indicates the expected instrumental resolution for HFM/EXED.
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Deviations from the extended London model at high magnetic fields in ${YBa}_{2} {Cu}_{3} O_{7}$

E. Campillo, M. Bartkowiak, R. Riyat, E. Jellyman, A. S. Cameron, A. T. Holmes, O. Prokhnenko, W.-D. Stein, A. Erb, E. M. Forgan, and E. Blackburn

Phys. Rev. B 105, 184508 – Published 11 May 2022

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Physical Review B

covering condensed matter and materials physics

Deviations from the extended London model at high magnetic fields in YBa2Cu3O7

E. Campillo, M. Bartkowiak, R. Riyat, E. Jellyman, A. S. Cameron, A. T. Holmes, O. Prokhnenko, W.-D. Stein, A. Erb, E. M. Forgan, and E. Blackburn

Phys. Rev. B 105, 184508 – Published 11 May 2022

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Deviations from the extended London model at high magnetic fields in ${YBa}_{2} {Cu}_{3} O_{7}$