Nirmal Ghimire
April 20, 2010
In Class Presentation
Solid State Physics II
Instructor: Elbio Dagotto

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

Introduction
There are two basic mechanism for the observed magnetic moments in magnetic materials
Local magnetic moments q c q s

1
Itinerant magnetic moments q c q s

1
W. K. Heisenberg
(1901-1976)
Cases of complete localization or complete ionization are hardly ever found
E. C. Stoner
(1899-1968)
Both phenomena exist side by side: A unified theory of solid state magnetism is needed

Introduction
1957: Fermi Liquid Theory
L. D. Landau
(1908-1968)
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

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

Fermi-Liquid Theory
•
• Quasiparticle excitation of interacting Fermi system
Fermi liquids have spin and obey Fermi statistics
2
One to one correspondence of quasiparticle and free electron:
Interaction of the quasiparticle
Energy of the system Energy of N quasiparticles

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
)

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

Non-Fermi Liquid System
Physical Properties:
Experimental confirmation

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

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

Non-Fermi Liquid State in MnSi
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
Magnetic phase diagram
•
•
Magnetic phase transition at T c
=29.
1 from paramagnetic to helical magnetic structure
Wavelength of spiral = 180 Å in ( 111) direction

Non-Fermi Liquid State in MnSi
Variation of resistivity with temperature
8.35
Kbar
•Resistivity drops monotonically with decreasing temperature
•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
14.3
Kbar
8.35
Kbar
5.55
Kbar
15.5
Kbar

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

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

Magnetic Order in NFL State
Results from Neutron Scattering experiment:
There exists magnetic moment even above p c
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 <110> : not expected to be favored by the crystal field in cubic symmetry

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
<111> 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?

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!!

Conclusion
• MnSi , a weak itinerant ferromagnet
T
3 , 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.