Transcript From Kondo and Spin Glasses to Heavy Fermions, Hidden

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
Lecture schedule October 3 – 7, 2011
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#1
#2
#3
#4
#5
#6
#7
#8
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#10
Kondo effect
Spin glasses
Giant magnetoresistance
Magnetoelectrics and multiferroics
High temperature superconductivity
Applications of superconductivity
Heavy fermions
Hidden order in URu2Si2
Modern experimental methods in correlated electron systems
Quantum phase transitions
Present
Present basic
basic experimental
experimental phenomena
phenomena of
of the
the above
above topics
topics
Lecture schedule October 3 – 7, 2011
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#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
Kondo effect
Spin glasses
Giant magnetoresistance
Magnetoelectrics and multiferroics
High temperature superconductivity
Applications of superconductivity
Heavy fermions
Hidden order in URu2Si2
Modern experimental methods in correlated electron systems
Quantum phase transitions
Present
Present basic
basic experimental
experimental phenomena
phenomena of
of the
the above
above topics
topics
#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 Ĥsd = Σ J s · S
Kondo’s calculation (1965) using perturbation theory for ρ.
Wilson’s renormalization group method (1974) and χ(T)/C(T) ratio.
Bethe ansatz theory (1981) for χ, M and C: thermodynamics.
Modern Kondo behavior: Quantum dots, Kondo resonance & lattice.
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
Kondo effect: scattering of conduction electron on a
magnetic imputity via a spin-flip (many-body) process.
Kondo cloud
Magnetic resistivity Δρ(T) = ρmag(T) + ρ0 = ρtotal(T) - ρphon(T)
AuFe alloys. Note increasing ρ0 and ρ(max) as concentration is increased
Concentration scaled magnetic resistivity Δρ(T)/c vs lnT
CuAuFe alloys. Note lnT dependences (Kondo) and deviations from
Matthiessen’s rule.
Now Δρspin/c vs ln(T/TK) corrected for DM’sR
Note decades of logarithmic behavior in T/TK and low T  0 Δρspin/c =
ρun[1 – (T/TK)2], i.e., Fermi liquid behavior of Kondo effect
Quantum dots – mesoscopically fabricated, tunneling of single
electrons from contact reservoir controlled by gate voltage
This is Kondo!
Schematic energy diagram of a dot with one spin-degenerate energy level Ɛ0
occupied by a single electron; U is the single-electron charging energy, and ΓL
and ΓR give the tunnel couplings to the left and right leads.
S M Cronenwett et al., Science 281(1998) 540.
Quantized conductance vs temperature
Gate voltage is used to tune TK; measurements at 50 to 1000 mK.
Kondo – quantum dot universality when scaled with TK
Inverse susceptibility (χ = M/H) scaled with the
concentration for CuMn with TK = 10-3K
Inverse susceptibility and concentration scaled
inverse susceptibility (c/χi) for CuFe with TK = 30K
XXXX
CuFe
Excess specific heat ΔC/c on logarithmic scale
CuCr alloys with TK = 1K
Place a 3d (4f) impurity in a noble (non-magnetic) metal
Virtual bound state (vbs) model-See V.Shenoy lecture notes
e
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up-spin
-U-

down-spin
U splits the up and down vbs’, note different DOS’
Net magnetic moment of non-half integral spin
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U

transition”
( J = V2/U; antiferromagnetic)
1st order perturbation theory processes
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S(S+1)
Spin disorder scattering
2nd order perturbation non-spin flip
Spin flip 2nd order perturbation
Calculation of the logarithmic – T resistivity behavior
Calculation of the resistivity minimum with phonons added
Clean resistivity experiments on known concentrations
of magnetic impurities, AuFe with TK = 0.5 K.
Collection of Kondo temperatures
Wilson renormalization group method (1974): scale
transformation of Kondo Hamiltonian to be diagonalized
Spherical wave packets localized around
impurity
Shell parameter Λ > 1; E ~ Λ-n/2 for n states
Calculate via numerical iteration χ(T) as a
universal function and C(T) over entire Trange
Lim(T0): χ(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 = D|2Jρ|1/2exp{-1/2Jρ}
where J is exchange coupling and ρ the host
metal density of states
K. Wilson, RMP 47(1975)773.
Bethe Ansatz (1980’s) - 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: χ, M and C as fct(T,H). Does not give the
transport properties, e.g. ρ(T,H).
“1D” Fermi surface
TK << D
Impurity susceptibility χi(T)
Agrees with experiment
Low T χi is constant: Fermi liquid; C-W law at high T with To ≈ TK
Impurity magnetization as fct(H) Agrees with experiment
M ~ H at low H; M  free moment at large H (Kondo effect broken)
Specific heat vs log(T/TK) for different spin values
Agrees with experiment
Note reduced CiV as the impurity spin increases.
Kondo cloud - wave packet but what happens with a
Kondo lattice?
Never unambiguously found!
Kondo resonance - how to detect?
Photoemission spectroscopy (PES)
Still controversial
Kondo effect ( Kondo lattice) gives an introduction to
forthcoming topics, e.g., SG, GMR, HF; QPT.
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#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
Kondo effect
Spin glasses
Giant magnetoresistance
Magnetoelectrics and multiferroics
High temperature superconductivity
Applications of superconductivity
Heavy fermions
Hidden order in URu2Si2
Modern experimental methods in correlated electron systems
Quantum phase transitions
Kondo resonance to be measured via PES
??? To use ???