The Wilson ratio of a metal is the dimensionless ratio of the zero-
temperature magnetic susceptibility
In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ap ...
to the coefficient of the linear temperature term in the electronic
specific heat. The relative value of the Wilson ratio, compared to the Wilson ratio for the non-interacting
Fermi gas, can provide insight into the types of interactions present.
Applications
Fermi liquid theory
The Wilson ratio can be used to characterize
strongly correlated Fermi liquids. The
Fermi liquid theory explains the behaviour of metals at very low temperatures. Two important features of a metal which obey this theory are:
# At temperatures much below the
Fermi temperature
The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature.
In a Fermi ga ...
the specific heat is proportional to the temperature
# The
magnetic susceptibility
In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ap ...
is independent of temperature
Both of these quantities, however, are proportional to the electronic density of states at the Fermi energy. Their ratio is a dimensionless quantity called the Wilson (or the Sommerfeld-Wilson) ratio, defined as:
:
After substituting the values of ''χ''
P (Pauli susceptibility) and ''C''
elec (electronic contribution to specific heat), obtained using Sommerfeld theory, the value obtained for ''R''
w in the case of a
free electron gas is 1.
In the case of real Fermi-liquid metals, the ratio can differ significantly from 1. The difference arises due to electron-electron interactions within the system. These tend to change the
effective electronic mass, which affects both
specific heat and magnetic susceptibility. Whether or not this increase in both is given by the same multiplicative factor is shown by the Wilson ratio. In some cases, electron-electron interactions give rise to an additional increase in susceptibility.
The converse is also true, i.e. a deviation of the experimental value of ''R''
w from 1 may indicate strong electronic correlations.
[Fundamentals of the Physics of Solids - Volume 2 by Jenö Sólyom] Very high Wilson ratios (above 2) indicate nearness to ferromagnetism.
See also
*
Fermi liquid theory
*
Heavy fermion
*
Kadowaki-Woods ratio
*
Wiedemann–Franz law
References
Condensed matter physics
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