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Zero Field ESR

Zero Field ESR A Novel Technique of Measuring the Magnetic Penetration Depth of Superconductors and Application to High Tc YBa 2 Cu 3 O 7- d. Outline. Short ESR introduction ESR in superconductors with magnetic ions l extraction method Results. ESR. Free spin system of S levels.

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Zero Field ESR

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  1. Zero Field ESR A Novel Technique of Measuring the Magnetic Penetration Depth of Superconductors and Application to High Tc YBa2Cu3O 7-d UBC Superconductivity

  2. Outline • Short ESR introduction • ESR in superconductors with magnetic ions • l extraction method • Results UBC Superconductivity

  3. ESR Free spin system of S levels Without an external magnetic field all the levels are degenerate. When a magnetic field is applied the degeneracy is lifted => Zeeman levels An AC magnetic field perpendicular to the main spin axis can be described as a combination of the ladder operators and . UBC Superconductivity

  4. Magnetic ions in a crystal • The levels aren’t degenerate even in the absence of an external magnetic field. Initial splitting is caused by the crystal field environment – the “fine structure”. • The fine structure can be described by an “effective spin Hamiltonian.” UBC Superconductivity

  5. Hamiltonian • The effective spin Hamiltonian is an expansion in spherical harmonics of the crystal field in the magnetic ion site. • Each term in the expansion can be written as a “Stevens operator” the operator equivalent of the spherical harmonics. where is a function of and of the order q . UBC Superconductivity

  6. Microwave Field - Perturbation In addition to the fine structure we apply a small oscillating magnetic field - a time dependent perturbation to the fine structure:g – coupling constant h – applied field in the x direction - Bohr magneton UBC Superconductivity

  7. Perturbation theory • The perturbation will create transitions between the energy levels of the magnetic ion. • The transition rate (according to Fermi’s Golden rule) is: UBC Superconductivity

  8. The Spectrum Normalized c” Frequency UBC Superconductivity

  9. ESR through microwave spectroscopy • Assuming (superconducting state)and (the case for small paramagnetic contribution) The real part of the impedance, , is approximately: UBC Superconductivity

  10. lExtraction • The spectrum of lc’’(w) is measured by the experiment. • The spectrum of c’’(w) can be calculated theoretically. • The comparison yields l. UBC Superconductivity

  11. Results Surface resistance Rs(W) Frequency(GHz) UBC Superconductivity

  12. (1/2 m0l)c”(10-15W/Hz) Frequency(GHz) UBC Superconductivity

  13. YBCO unit cell: Chains along the b-axis UBC Superconductivity

  14. Oxygen Ordering F Band G Band UBC Superconductivity

  15. G Band fitting Normalized c” Frequency(Hz) UBC Superconductivity

  16. F Band fitting Normalized c” Frequency(Hz) UBC Superconductivity

  17. G+F Band fitting Normalized c” Frequency(Hz) UBC Superconductivity

  18. Optimally doped sample -results Transitions Crystal field parameters UBC Superconductivity

  19. Fitted a-axis spectrum UBC Superconductivity

  20. Fitted b-axis spectrum UBC Superconductivity

  21. Overdoped Results Transitions CF parameters UBC Superconductivity

  22. Penetration Depth UBC Superconductivity

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