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Magnetic Exchange in Disordered Materials

Magnetic Exchange in Disordered Materials. Jonathan Sobota Cornell University Mentor: Dr. Vladimir Dobrosavljevic Condensed Matter Theory. Background Information. Local magnetic moments are distributed throughout a nonmagnetic host metal

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Magnetic Exchange in Disordered Materials

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  1. Magnetic Exchange in Disordered Materials Jonathan Sobota Cornell University Mentor: Dr. Vladimir Dobrosavljevic Condensed Matter Theory

  2. Background Information • Local magnetic moments are distributed throughout a nonmagnetic host metal • RKKY interactions facilitate magnetic ordering and contribute to the magnetic / electric properties of the material • Modeling this system is important for modern technical applications • What happens when it is disordered?

  3. Effects of Disorder • The RKKY interactions can be described by a statistical distribution • As disorder increases, the average interaction strength goes to zero • Current theory predicts that the width of this distribution will stay the same as disorder increases. But this contradicts other theories of metals (Anderson Localization)

  4. Simulation of the System • FORTRAN program simulates the system by calculating electronic susceptibility  as a function of R, the distance between two moments (  is proportional to the interaction strength) • Ran the program hundreds of times to accumulate data for multiple levels of disorder

  5. [(R)]av vs R [(R)]av R

  6. [(R)]av vs R (cont) • We can see that the interaction strength goes to zero as disorder is increased: • But the average value does not tell us the whole story. What is the typical value of interaction strength? • For this, we look at the distributions…

  7. Distributions of  within a single level of disorder P() 

  8. Scaling and Combining the Distributions • We find that within each level of disorder, each histogram is proportional to exp(-R/) • We can therefore collapse the distributions to a single distribution by scaling by exp(R/) • By joining all the data from these scaled distributions, we can have a single, ‘master’ distribution for each level of disorder

  9. ‘Master’ distributions for various levels of disorder P() 

  10. Tails of Distributions on log-log Axes ln(P()) ln()

  11. Slope of tails of distributions vs. disorder Slope W

  12. What does all this tell us? • The width of the distribution decreases as disorder increases, so the typical value of interaction strength must decrease • The distributions are linear on log-log axes, which indicates long tails. Physically, this means long-range RKKY interactions are irrelevant • Since the slopes asymptotically approach some value, there may be a ‘universal’ distribution which describes very high disorder

  13. Acknowledgements • Research Mentor • Vladimir Dobrosavljevic • With assistance from: • Darko Tanaskovic • CIRL Staff • Gina LaFrazza, Stacy Vanderlaan, Carlos Villa, Dave Sheaffer, Pat Dixon • National High Magnetic Field Laboratory • National Science Foundation

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