1. Non-Fermi Liquid Behavior in Weak Itinerant Ferromagnet MnSi Nirmal Ghimire April 20, 2010 In Class Presentation Solid State Physics II Instructor: Elbio Dagotto

2.  Introduction  Fermi Liquid Theory  Non-Fermi Liquid System  Non-Fermi Liquid State in MnSi  Magnetic Ordering and Spin Structure  Conclusion Outline

3. Introduction There are two basic mechanism for the observed magnetic moments in magnetic materials Local magnetic momentsItinerant magnetic moments W. K. Heisenberg (1901-1976) E. C. Stoner (1899-1968) Cases of complete localization or complete ionization are hardly ever found Both phenomena exist side by side: A unified theory of solid state magnetism is needed

4. Introduction L. D. Landau (1908-1968) 1957: Fermi Liquid Theory Model for metallic state: Pauli exclusion principle + screening effect Successfully described some near or weak ferromagnetic d-electron metals MnSi, a weakly magnetic d-electron compound, also shows Non- Fermi Liquid (NFL) behavior

5.  Introduction  Fermi Liquid Theory  Non-Fermi Liquid System  Non-Fermi Liquid State in MnSi  Magnetic Ordering and Spin Structure  Conclusion Outline

6. Fermi-Liquid Theory Quasiparticle excitation of interacting Fermi system Fermi liquids have spin and obey Fermi statistics One to one correspondence of quasiparticle and free electron: Interaction of the quasiparticle Energy of the systemEnergy of N quasiparticles

7. Fermi-Liquid Theory Energy of a quasiparticle is: Energy of quasiparticle at T =0 Mean field effect of interaction with other quasi particles Scattering amplitude of two quasi particles Accounts for the deviation of density of states from the equilibrium value n Fermi (n- n Fermi )

8. Fermi Liquid Theory Total energy: Prediction: Electrical resistivity of CeCl 3 Specific heat of CeCl 3 Experimental confirmation

9. Non-Fermi Liquid System Physical Properties: Experimental confirmation

10.  Introduction  Fermi Liquid Theory  Non-Fermi Liquid System  Non-Fermi Liquid State in MnSi  Magnetic Ordering and Spin Structure  Conclusion Outline

11. Non-Fermi Liquid State in MnSi Structure of MnSi B20 Cubic structure with a =4.588 Å Lacks space inversion symmetry Consequence of the broken inversion symmetry Helical spin density wave

12. Non-Fermi Liquid State in MnSi Magnetic phase transition at T c =29. 1 from paramagnetic to helical magnetic structure Wavelength of spiral = 180 Å in ( 111) direction Magnetic phase diagram Magnetic properties: Curie-Weiss fit of susceptibility: Effective magnetic moment = 1.4 μ B Observation: spontaneous magnetic moment of 0.4 μ B at 0K. Weak itinerant ferromagnet

13. Non-Fermi Liquid State in MnSi Variation of resistivity with temperature Resistivity drops monotonically with decreasing temperature 5.55 Kbar 8.35 Kbar 14.3 Kbar 15.5 Kbar Peak position indicates the transition temperature Below p c =14.6 Kbar, there is quadratic behavior At p c, quadratic behavior collapses Above p c, temperature variation of resistivity is slower than quadratic

14. Non-Fermi Liquid State in MnSi Comparison between experiment and FFL Theory High T: FFL model in agreement with experiment Low T: T dependence deviates from experimental observation

15.  Introduction  Fermi Liquid Theory  Non-Fermi Liquid System  Non-Fermi Liquid State in MnSi  Magnetic Ordering and Spin Structure  Conclusion Outline

16. Magnetic Order in NFL State Magnetic Order in NFL State Results from Neutron Scattering experiment: Critical pressure = 14.6 Kbar Magnetic Ordering above critical pressure? Helical with same periodicity and long range order Unusual thing: Considerable degree of disorderness in the direction of magnetic propagation vector A broad angular distribution around : not expected to be favored by the crystal field in cubic symmetry There exists magnetic moment even above p c Partial magnetic ordering

17. Non-Trivial Spin Structure! Two Possible Scenarios for the partial magnetic ordering Breaking of helical structure into multi-domain state Unlocking of helix direction from and no strict directional order Result of polarized neutron scattering : partial order on local scale is not related to helical structure No experimental or theoretical support Any other possibility?

18. Non-Trivial Spin Structure! Quantum critical phenomena ? NFL resistivity emerges under pressure without quantum criticality Spin ordering other than plain pining of the helix or a multi-domain state A non-trivial spin structure!!

19. Conclusion MnSi, a weak itinerant ferromagnet, shows a behavior of resistivity which is not consistent with current model of itinerant ferromagnetism Temperature dependence of resistivity may lie in the novel form of magnetic ordering Currently, there is no theoretical account for the NFL resistivity and how it is related to the partial magnetic ordering. There is need of more experimental evidences.

20. Thank You