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Calculation of Impurity-Averaged Properties of Kondo Systems

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)

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Calculation of Impurity-Averaged Properties of Kondo Systems

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  1. Calculation of Impurity-Averaged Properties of Kondo Systems Jesse Gregory (Kenyon College and U. of F.) Kevin Ingersent (U. of F.)

  2. 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

  3. 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

  4. 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

  5. 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!!!

  6. 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)

  7. Averaging an Arbitrary Property over a Probability Distribution • General Program Info • Fortran • NAG Schemes • Program divisions (within main loop) • Data collation • Interpolation • Integration

  8. 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)

  9. Probability Schemes • See Overhead

  10. Graphs and Explanation • Graphs on Overhead • What is a critical J value? • Where do we see its effect in the physical model?

  11. Future Extensions • Problems we experienced • Interpolation at low temperatures • Critical J Problem • Remedies • Split Interpolation • Other Properties

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