Zero Field ESR

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

2
Outline

• Short ESR introduction
• ESR in superconductors with magnetic ions
• l extraction method
• Results

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 gt Zeeman levels
An AC magnetic field perpendicular to the main
spin axis can be described as a combination of
the ladder operators and .
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Magnetic ions in a crystal

• The levels arent 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.

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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 .
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Microwave Field - Perturbation

• In addition to the fine structure we apply a
  small oscillating magnetic field - a time
  dependent perturbation to the fine structureg
  coupling constant
• h applied field in the x direction - Bohr
  magneton

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Perturbation theory

• The perturbation will create transitions between
  the energy levels of the magnetic ion.
• The transition rate (according to Fermis Golden
  rule) is

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The Spectrum
Normalized c
Frequency
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ESR through microwave spectroscopy

• Assuming (superconducting state)and
  (the case for small paramagnetic
  contribution) The real part of the impedance,
  , is approximately

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l Extraction

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

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Results
Surface resistance Rs(W)
Frequency(GHz)
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(1/2 m0l)c(10-15W/Hz)
Frequency(GHz)
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YBCO unit cell Chains along the b-axis
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Oxygen Ordering
G Band
F Band
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G Band fitting
Normalized c
Frequency(Hz)
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F Band fitting
Normalized c
Frequency(Hz)
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GF Band fitting
Normalized c
Frequency(Hz)
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Optimally doped sample -results
Transitions
Crystal field parameters
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Fitted a-axis spectrum
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Fitted b-axis spectrum
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Overdoped Results
Transitions
CF parameters
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Penetration Depth