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From Kondo and Spin Glasses to Heavy Fermions, Hidden Order and Quantum Phase Transitions

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Title: From Kondo and Spin Glasses to Heavy Fermions, Hidden Order and Quantum Phase Transitions


1
From Kondo and Spin Glasses to Heavy Fermions,
Hidden Order and Quantum
Phase Transitions
  • A Series of Ten Lectures at XVI Training Course
    on Strongly Correlated Systems, October 2011
  • J. A. Mydosh
  • Kamerlingh Onnes Laboratory and Institute Lorentz
  • Leiden University
  • The Netherlands

2
Lecture schedule October 3 7, 2011
  • 1 Kondo effect
  • 2 Spin glasses
  • 3 Giant magnetoresistance
  • 4 Magnetoelectrics and multiferroics
  • 5 High temperature superconductivity
  • 6 Applications of superconductivity
  • 7 Heavy fermions
  • 8 Hidden order in URu2Si2
  • 9 Modern experimental methods in correlated
    electron systems
  • 10 Quantum phase transitions

Present basic experimental phenomena of the above
topics
Present basic experimental phenomena of the above
topics
3
Lecture schedule October 3 7, 2011
  • 1 Kondo effect
  • 2 Spin glasses
  • 3 Giant magnetoresistance
  • 4 Magnetoelectrics and multiferroics
  • 5 High temperature superconductivity
  • 6 Applications of superconductivity
  • 7 Heavy fermions
  • 8 Hidden order in URu2Si2
  • 9 Modern experimental methods in correlated
    electron systems
  • 10 Quantum phase transitions

Present basic experimental phenomena of the above
topics
Present basic experimental phenomena of the above
topics
4
1 The Kondo Effect Experimentally Driven
1930/34 Theoretically Explained 1965 as magnetic
impurities in non-magnetic metals.
  • Low temperature resistivity minimum in AuFe and
    CuFe alloys. Increased scattering.
  • Strange decrease of low temperature
    susceptibility, deviation from Curie-Weiss law.
    Disappearance of magnetism.
  • Broad maximum in specific heat. Accumulation of
    entropy. Not a phase transition but a crossover
    behavior!
  • Virtual bond state of impurity in metal. Magnetic
    or non-magnetic?
  • s d exchange model for Hsd S J s S
  • Kondos calculation (1965) using perturbation
    theory for ?.
  • Wilsons renormalization group method (1974) and
    ?(T)/C(T) ratio.
  • Bethe ansatz theory (1981) for ?, M and C
    thermodynamics.
  • Modern Kondo behavior Quantum dots, Kondo
    resonance lattice.

5
Interaction between localized impurity spin and
conduction electrons temperature
dependent. Many body physics, strongly correlated
electron phenomena yet Landau Fermi liquid.
Not a phase transition but crossover in
temperature
6
Kondo effect scattering of conduction electron
on a magnetic imputity via a spin-flip
(many-body) process.
Kondo cloud
7
Magnetic resistivity ??(T) ?mag(T) ?0
?total(T) - ?phon(T) AuFe alloys. Note
increasing ?0 and ?(max) as concentration is
increased
8
Concentration scaled magnetic resistivity ??(T)/c
vs lnT CuAuFe alloys. Note lnT dependences
(Kondo) and deviations from Matthiessens rule.
9
Now ??spin/c vs ln(T/TK) corrected for DMsR
Note decades of logarithmic behavior in T/TK and
low T ? 0 ??spin/c ?un1 (T/TK)2, i.e.,
Fermi liquid behavior of Kondo effect
10
Quantum dots mesoscopically fabricated,
tunneling of single electrons from contact
reservoir controlled by gate voltage
This is Kondo!
11
Schematic energy diagram of a dot with one
spin-degenerate energy level ?0 occupied by a
single electron U is the single-electron
charging energy, and GL and GR give the tunnel
couplings to the left and right leads.
S M Cronenwett et al., Science 281(1998) 540.
12
Quantized conductance vs temperature
Gate voltage is used to tune TK measurements at
50 to 1000 mK.
13
Kondo quantum dot universality when scaled with
TK
14
Inverse susceptibility (? M/H) scaled with the
concentration for CuMn with TK 10-3K
15
Inverse susceptibility and concentration scaled
inverse susceptibility (c/?i) for CuFe with TK
30K
XXXX
CuFe
16
Excess specific heat ?C/c on logarithmic
scale CuCr alloys with TK 1K
17
Place a 3d (4f) impurity in a noble
(non-magnetic) metal Virtual bound state (vbs)
model-See V.Shenoy lecture notes
18
e
e
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22
? - U - ?
down-spin
up-spin
23
U splits the up and down vbs, note different
DOS Net magnetic moment of non-half integral spin
? U ?
24
transition
25
( J V2/U antiferromagnetic)
26
1st order perturbation theory processes
? S(S1)
Spin disorder scattering
27
2nd order perturbation non-spin flip
28
Spin flip 2nd order perturbation
29
Calculation of the logarithmic T resistivity
behavior
30
Calculation of the resistivity minimum with
phonons added
31
Clean resistivity experiments on known
concentrations of magnetic impurities, AuFe with
TK 0.5 K.
32
Collection of Kondo temperatures
33
Wilson renormalization group method (1974) scale
transformation of Kondo Hamiltonian to be
diagonalized
Spherical wave packets localized around
impurity Shell parameter ? gt 1 E ?-n/2 for n
states Calculate via numerical iteration ?(T) as
a universal function and C(T) over entire
T-range Lim(T?0) ?(T)/C(T)/T
3R(gµB)2/(2?kB)2 Wilson ratio R 2 for Kondo, 1
for heavy fermions Determination of Kondo
temperature TK D2J?1/2exp-1/2J? where
J is exchange coupling and ? the host metal
density of states
K. Wilson, RMP 47(1975)773.
34
Bethe Ansatz (1980s) - Andrei et al., RMP 55,
331(1983).
  • Bethe ansatz method for finding exact solution
    of quantum many-body Kondo Hamiltonian in 1D.
  • Many body wave function is symmetrized product of
    one-body wave functions. Eigenvalue problem.
  • Allows for exact (diagonalization) solution of
    thermodynamic propertries ?, M and C as
    fct(T,H). Does not give the transport properties,
    e.g. ?(T,H).


1D Fermi surface
TK ltlt D
35
Impurity susceptibility ?i(T) Agrees with
experiment
Low T ?i is constant Fermi liquid C-W law at
high T with To TK
36
Impurity magnetization as fct(H) Agrees with
experiment
M H at low H M ? free moment at large H (Kondo
effect broken)
37
Specific heat vs log(T/TK) for different spin
values Agrees with experiment
Note reduced CiV as the impurity spin increases.
38
Kondo cloud - wave packet but what happens with a
Kondo lattice?
Never unambiguously found!
39
Kondo resonance - how to detect? Photoemission
spectroscopy (PES)
Still controversial
40
Kondo effect (? Kondo lattice) gives an
introduction to forthcoming topics, e.g., SG,
GMR, HF QPT.
  • 1 Kondo effect
  • 2 Spin glasses
  • 3 Giant magnetoresistance
  • 4 Magnetoelectrics and multiferroics
  • 5 High temperature superconductivity
  • 6 Applications of superconductivity
  • 7 Heavy fermions
  • 8 Hidden order in URu2Si2
  • 9 Modern experimental methods in correlated
    electron systems
  • 10 Quantum phase transitions

41
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42
Kondo resonance to be measured via PES
43
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44
??? To use ???
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