NMR OF SUPERDCONDUCTORS
These are materials which exhibit zero electrical resistivity.
They exhibit this zero electrical resistivity below a temperature
critical temperature and below a critical field Hc.
Depending on critical temperature
1 :these are pure metals have low values of
some examples :
In 1930 a no of alloys were found which exhibit higher
and higher critical fields
some examples :
These are ceramic materials with layers of copper oxide
spaced by layers containing Ba and other atoms
currently known is 130k in Mercury Based
Here mainly concentrating on high Tc superconductors
Phase Diagram of high Tc Superconductors
The cuprates exhibit a wide range of unusual
behaviour depending on the temperature and the level
of doping. This includes antiferromagnetic ordering
(green region), a so
gap" phase (blue),
superconductivity (red) and anomalous metallic
behaviour above the superconducting transition
(black line) at "optimal" doping
If we observe the
high Tc Superconductors all of them
have copper oxide planes.
Even a decade and a half after the discovery of the high
superconductors Containing copper oxide plane ,these
materials continue to puzzle to condesed Matter theorists.
The challenge is not to predict a reasonable formula that
predicts high value of
in cuprates. But it have to explain
the complex phase diagram exhibited these materials.
Depending on doping concentration, no of copper planes
present in the structure we have variation in value of Tc for
the same material.
what is unique about the cuprates
In order to explain these we consider the
Landu Fermi Liquid Theory
In this the properties of single electrons are changed by
interactions with other electrons to form quasiparticles the
properties of the material can then be understood in terms
of weak residual interactions between quasi particles.
A common feature of all superconductors both low and high
temperature is that electrons some how overcome the coulomb
repulsion force to form cooper pairs.
Based on Landu Fermi Liquid Theory electrons don’t
obey paulis exclusion principle, condense into a
In LTSC interaction between electron and phonon is responsible
for pairing. They are in S
wave state(they are in antiferomagnetic
alignment in superconducting state)
In cuprates it has been shown that the superconducting order
parameter (gap) has a d
wave symmetry, quite different that
most conventional, low
Tc superconductors which have a s
symmetry. Early experiments recent penetration depth, specific
heat and Raman experiments at the CSR have shown the gap
symmetry in the cuprates is d
we have ferromagnetic and paranmagnetic interaction In
superconducting state and short range antiferromagnetic
HTSC are insulators and have antiferromagnetic interaction with out
doping. Depending on doping they turned into semiconductors and then
to superconductors(i.e. antiferromagnetic interaction is decreasing
while going to superconducting phase)
for ex ,if we take
is an insulator,
after removing oxygen
Conduction process in HTSC is explained by the process “hopping”
Oxygen vacancies creates holes and these holes hops from one copper
site to other by hopping process. This process does not ocuur in
antifrromagnetic state, so in order to have superconductivity electrons
must interact in such a way not to have complete antiferromagnetism.
Therefore the conductivity in HTSC seems to be by
the interactions between electrons through lattice phonons, and
by the Holes created by the oxygen
And the occurance of antiferromagnetic correlation in the copper
oxides seems to support the notion that superconductivity in
these compounds may be due to magnetic interactions.
Experiments indicate that the layered cuprates display
Short range AF spin correlations at any doping and at all
These short range correlations are responsible for NMR
In this NMR experiments we observe the copper and oxygen
In order to obtain the equations for relaxation rates
consider magnetic properties of lightly doped mott insulators
assuming spin carrying quasiparticles in these systems are
fermions with spin ½ which form a large fermisurface.
(Based on landu fermi liquid model,electron interactions and
In order to incorporate the short range AF
fluctuations into the spinon picture, seperate the
spinons close to the Fermisurface and constructe
quasispins from the spinons far from it.
Assuming only lowest order appromation in the
interaction between quasispins and spinons,not
going to higher drder in pertubation
Relaxation Time in NMR Experiments
The magnetis moment of the nucleus at site n interacts with
the surrounding spins :
hyper fine interaction constant and is small,so this
interaction can be treated as a small perturbation.
The nuclear relaxation rate is related to the spin susceptibility
by the relation
The frequency w of NMR EXPT is very low, so relaxation
time is a very effective probe of low energy spin excitatrions.
Using the assumption that the spin of copper nucleus interacts only
with the spin on copper site and the spin of the oxygen nucleus with
spins on adjacent copper sites.
We get relaxation rate at the oxygen site :
v(Єf) is spinion density of states
Copper relaxation rate:
(1/T1T)= 0.16 k
We get NMR relaxation rate for two AF correlation lengths as
l both the theoritical and
a experiments gave the same
Information we get from this NMR study
The modifications of magnetic properties induced by substitutions or defects in the planes,
which do not modify appreciably the charge transfer have been studied.
The spatial dependence of the spin susceptibility
chi ' (r) of the pure material can be
directly probed through the study of the modifications of the NMR spectra of various nuclei
(89Y, 17O, 63Cu) induced by such localised magnetic impurities.
Large qualitative differences between the underdoped and slightly overdoped YBCO are
evidenced from 17O NMR line broadening in Ni substituted YBCO. This allows us to
propose a quite powerful method for studying the q and T dependence of the static
magnetic susceptibility .
gap in the AF excitations at the AF wave vector is detected by NMR.
The impurity magnetic state also directly reflects the occurence of electronic
correlations in the metallic state. The case of Zn will be examined in some detail.
89Y NMR has revealed that the substitution of this 3d^10 non magnetic atom on a
Cu site induces a Curie like contribution to the local susceptibility on the near
The effective induced moment decreases with hole doping and becomes rather
weak, but is still present for optimal doping. Combination of magnetic
susceptibility and NMR data in Zn and Ni substituted YBCO allows to confirm that
the decrease of Tc is not due to magnetic pair breaking, but rather to pair
breaking of d
wave superconductivity by strong carrier scattering. However the
large scattering due to Zn, has to be associated with its peculiar electronic state.
(J. Bobroff et al, Phys. Rev. Letters 78, 3757 (1997
V. Mahajan, H. Alloul, G. Collin and J. F. Marucco, Physical
Review Letters 72, 3100 (1994).).
Physics world Feb 2000
Physics world Dec 1999
Proceedings of high tc superconductors :world scientific
Some Abstracts, some information from net