Calculation of Impurity-Averaged
Properties of Kondo Systems
Jesse Gregory (Kenyon College and U. of F.)
Kevin Ingersent (U. of F.)
Background Info/Importance of
Magnetic Impurities
What is a magnetic impurity?
 Important effect on physical properties of
host materials (Kondo effect)
 Impurities provide a unique signature

Real Applications

J. Bobroff et al (Phys. Rev. Lett. 1999)
“Spinless Impurities in High-Tc Cuprates”
 nonmagnetic
impurities disrupting spins of native
copper atoms

Heavy-fermion system
 polycrystalline
sample in an external magnetic field
Specifics (Defining Parameters)
Energy of interaction b/w impurity and host
electrons
 Two parameters J and V
 E = J(Selec·Simp) + V(Nelec - 1)
 J and V vary because of impurity’s position in
crystal or orientation in B-field

Why Modeling is not Easy

Real systems are in disorder
 Impurities
of varying J’s and V’s
Many ways to model contribution of a single
impurity
 We must model the contribution of many
impurities!!!

Averaging an Arbitrary Property
over a Probability Distribution

Given impurity of parameters J and V
–
Series of data sets
–

Temperature dependence for a single J and V combination
Given a probability function
 P(J,V)
Need to interpolate data to arbitrary J and V
 Then calculate the average:

–
X(T) = dJ dV P(J,V)·X(J,V,T)
Averaging an Arbitrary Property
over a Probability Distribution

General Program Info
Fortran
 NAG Schemes
 Program divisions (within main loop)

–
–
–
Data collation
Interpolation
Integration
The Program in Action

Our focus: Thermodynamic properties of
high Tc superconductors
–
–

C (Specific Heat Capacity)
 (Magnetic Susceptibility)
Calculations for a single impurity:
–
Numerical renormalization group method
 (Gonzalez-Buxton
and Ingersent, Phys. Rev. 1998)
Probability Schemes

See Overhead
Graphs and Explanation
Graphs on Overhead
 What is a critical J value?
 Where do we see its effect in the physical
model?

Future Extensions

Problems we experienced
–
Interpolation at low temperatures
 Critical

Remedies
–

J Problem
Split Interpolation
Other Properties