Qimiao Si

1
Heavy fermion metals Global phase diagram, local
quantum criticality, and experiments

• Qimiao Si
• Rice University

KIAS, Oct 29, 2005
2
S. Paschen P. Gegenwart R. Küchler T.
Lühmann S. Wirth N. OeschlerT. Cichorek K.
Neumaier O. Tegus O. Trovarelli C. Geibel J.
A. MydoshF. Steglich P. Coleman
Lijun Zhu, Stefan Kirchner, Tae-Ho Park, Eugene
Pivovarov, (Rice University) Silvio Rabello,
J. L. Smith Kevin Ingersent (Univ.
of Florida) Daniel Grempel
(CEA-Saclay) Jianxin Zhu (Los Alamos)
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Quantum Critical Point

• QCP existence itself is conceptually simple
• but, can be elusive
• (required parameter tuning beyond practical
  range,
• order hidden, too many competing phases,
• 1st order along the physical axis, etc.)
• and, the nature of the QCP seems to be
  exceedingly rich.

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Materials (possibly) showing Quantum Criticality

• Insulating Ising magnet
• LiHoF4 transverse field Ising model
• Heavy fermion magnetic metals
• Simple magnetic metals
• Cr1-xVx, Sr3Ru2O7, MnSi (1st order, but )
• High Tc superconductors (?)
• Mott transition
• V2O3, QCP? (magnetic ordering intervenes at
  low T!)
• cold atoms 2nd order?
• Frustrated magnets (?)
• Field-driven BEC of magnons

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Materials (possibly) showing Quantum Criticality

• Metal-insulator transition in 3D SiP,
• Many theoretical questions remain
• (Finkelstein scaling theory? local
  moments?...)
• MIT in 2DEG of Si-MOSFETs, ... (?)
• Phase diagram?
• (Experiments seeing a genuine metal phase?)
• Superconductor-insulator transitions in films
• Phase diagram?
• (Intermediate metal?)
• QH-QH and QH-Insulator transitions
• 2nd order?

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Early part of the heavy fermion field

• Heavy electron mass
• Unconventional superconductivity
• Kondo screening ? Kondo resonances ?
• Fermi liquid of heavy quasiparticles

On the theory front Single-impurity
Anderson, Wilson, Nozières, Andrei, Wiegmann,
Coleman, Read Newns, Lattice
Varma, Doniach, Auerbach Levin, Millis Lee,
Rice Ueda,
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Past decade of the heavy fermion field

• Non-Fermi Liquid Behavior
• Quantum Criticality

New focus, perhaps due to cross-fertilization
w/ high Tc other correlated systems
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Heavy fermions near a magnetic QCP
H. v. Löhneysen et al, PRL 1994
CeCu6-xAux
TN
AF Metal
TN
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Heavy fermions near a magnetic QCP
N. Mathur et al, Nature 1998
CePd2Si2
H. v. Löhneysen et al, PRL 1994
CeCu6-xAux
TN
TN
AF Metal
Supercond.
AF Metal
Linear resistivity
YbRh2Si2
TN
J. Custers et al, Nature 2003
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• Heavy fermions near a magnetic QCP
• YbRh2Si
• easy-plane spin-anisotropy TK0 25 K
• Ce(Cu1-xAux )6
• Ising anisotropy TK0 6 K

• CePd2Si2, CeIn3 (first order?--NQR),
• CeNi2Ge2, CeCu2Si2
• YbAgGe frustrated (hexagonal) lattice
• CeMIn5,
• URu2Si2 (?)

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Kondo Lattice Model
I RKKY interaction AF
GInnn/Inn etc.
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Kondo Lattice Model
I RKKY interaction AF
GInnn/Inn etc.
Bandwidth W
Kondo coupling JK
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Kondo Lattice Model
I RKKY interaction AF
GInnn/Inn etc.
Bandwidth W
Kondo coupling JK
Fixed I and W with IltltW, varying G and JK
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• Kondo lattices

G frustration, reduced dimensionality, etc.
Bandwidth W
G
Kondo coupling JK
Local moment magnetism, Irkky
JK
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JK gtgtWgtgtIrkky
G
JK
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JK gtgtWgtgtIrkky

• xNsite tightly bound local singlets
• (cf. If x were 1, Kondo insulator)
• (1-x)Nsite lone moments

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JK gtgtWgtgtIrkky

• xNsite tightly bound local singlets
• (cf. If x were 1, Kondo insulator)
• (1-x)Nsite lone moments
• projection
• (1-x)Nsite holes with U8

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JK gtgtWgtgtIrkky

• xNsite tightly bound local singlets
• (cf. If x were 1, Kondo insulator)
• (1-x)Nsite lone moments
• projection
• (1-x)Nsite holes with U8
• Luttingers theorem
• (1-x) holes/site in the Fermi surface
• (1x) electrons/site ----
  Large Fermi surface!

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JK gtgtWgtgtIrkky
paramagnet, w/ Kondo screening
G
PML
JK
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JKltltIrkkyltltW
G
Local moment magnetism, Irkky
JK
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JKltltIrkkyltltW

• With Ising anisotropy, the magnetic spectrum of
  the local moment component is gapped.
• JK is irrelevant!

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JKltltIrkkyltltW

• With Ising anisotropy, the magnetic spectrum of
  the local moment component is gapped.
• JK is irrelevant!
• Local moments stay charge neutral, and do not
  contribute to the electronic excitations.
• Fermi surface is small

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JKltltIrkkyltltW
Néel, without Kondo screening
G
AFS
JK
QS, J.-X. Zhu, D. Grempel, cond-mat /0506207
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Global phase diagram
G
I
PML
II
AFS
AFL
JK
QS, J.-X. Zhu, D. Grempel, cond-mat /0506207
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Type II transition
Hertz fixed point for T0 SDW transition
Type I transition
Second order if
Destruction of Kondo screening at the magnetic QCP
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Local Quantum Critical Point

• Fluctuations of the magnetic order parameter are
  slow at the magnetic QCP
• The slow magnetic fluctuations decohere the Kondo
  screening
• Kondo effect is critical, which is in addition to
  the critical fluctuations of magnetic order
  parameter

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Local Quantum Critical Point
Destruction of Kondo effect (Eloc ? 0) at the
QCP

• Anomalous spin dynamics

QS, S. Rabello, K. Ingersent, J. L. Smith,
Nature 413, 804 (2001)
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Nature of the phases

• T2 resistivity on both sides of the QCP

TN
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Nature of the phases (contd)

• Small Fermi surface in the AF metal phase

CeRh2Si2
TN
TN
S. Araki, R. Settai, T. C. Kobayashi, H. Harima,
Y. Onuki, Phys Rev. B 64, 224417 (2001)
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In what sense is the QCP local?

• Localization of f-electrons
• Reconstruction of the Fermi surface across ?QCP
• m ? 8 over the entire Fermi surface as ? ? ?QCP
• Anomalous spin dynamics.
• Destruction of Kondo effect
• Non-Fermi liquid excitations part of the
  quantum-critical spectrum.

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CeCu6-xAux (xc0.01)
TN
AF Metal
TN
H. v. Löhneysen et al, PRL 1994
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Dynamical and Static Susceptibilities in
CeCu5.9Au0.1

• E/T scaling
• Fractional exponent a0.75

• a0.75 everywhere in q.

1/c(q)
q0
. . .
qQ
T0.75
E/T
INS _at_ qQ
INS and M/H

• A. Schröder et al., Nature 00 PRL 98 O.
  Stockert, H. v. Löhneysen,
• A. Rosch, N. Pyka, M. Loewenhaupt, PRL 98

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Dynamics of the quantum critical CeCu5.9Au0.1

• Frequency and temperature dependences of the
  dynamical spin susceptibility
• an anomalous exponent ? lt 1
• ?/T scaling
• implying non-Gaussian fixed
  point
• The anomalous exponent ? is seen essentially
  everywhere in the momentum space

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O. Stockert, H. v. Löhneysen, A. Rosch, N. Pyka,
M. Loewenhaupt, Phys. Rev. Lett. 98
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Ce(Ru1-xRhx)2Si2 (xc0.04)
TN
H. Kadowaki, Y. Tabata, M. Sato, N. Aso, S.
Raymond, S. Kawarazaki, cond-mat/0504386
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Ce(Ru1-xRhx)2Si2
C/T?0-a T1/2
?0350mJ/K2 for x0
TN
H. Kadowaki, Y. Tabata, M. Sato, N. Aso, S.
Raymond, S. Kawarazaki, cond-mat/0504386
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In what sense is the QCP local?

• Localization of f-electrons
• Reconstruction of the Fermi surface across ?QCP
• m ? 8 over the entire Fermi surface as ? ? ?QCP
• Anomalous spin dynamics everywhere in q.
• Destruction of Kondo effect
• Non-Fermi liquid excitations part of the
  quantum-critical spectrum.

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Hall Effect in YbRh2Si2 probing the
Fermi-surface change
Linear resistivity
TN
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Hall Effect in YbRh2Si2

• S. Paschen, T. Lühmann, S. Wirth, P.Gegenwart,
  O.Trovarelli, C. Geibel,
• F. Steglich, P.Coleman, QS, Nature 432,
  881 (2004)

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Hall Effect in YbRh2Si2

• S. Paschen, T. Lühmann, S. Wirth, P.Gegenwart,
  O.Trovarelli, C. Geibel,
• F. Steglich, P.Coleman, QS, Nature 432,
  881 (2004)

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Hall Effect in YbRh2Si2
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Hall Effect in YbRh2Si2
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Hall Effect in YbRh2Si2

• Finite T crossover
• width ? T0.50.1
• T0 (extrapolation)
• sharp jump _at_ QCP

S. Paschen, T. Lühmann, S. Wirth, P.Gegenwart,
O.Trovarelli, C. Geibel, F. Steglich,
P.Coleman, QS, Nature 432, 881 (2004)
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Hall Effect in YbRh2Si2

• Finite T crossover
• width ? T0.50.1
• T0 (extrapolation)
• sharp jump _at_ QCP

S. Paschen, T. Lühmann, S. Wirth, P.Gegenwart,
O.Trovarelli, C. Geibel, F. Steglich,
P.Coleman, QS, Nature 432, 881 (2004)
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dHvA in CeRhIn5
_
H. Shishido, R. Settai, H. Harima, Y. Onuki,
JPSJ 74, 1103 (2005)
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Divergence of the Grüneisen Ratio
with

• L. Zhu, M. Garst, A. Rosch,
• and QS, Phys. Rev. Lett. 03

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Divergence of the Grüneisen Ratio
with

• L. Zhu, M. Garst, A. Rosch,
• and QS, Phys. Rev. Lett. 03
• R. Küchler et al.,
• Phys. Rev. Lett. 03

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Grüneisen exponent in Ge-doped YbRh2Si2

• LQCP xloc 0.66 to 2nd order in
  e-expansion for the XY case
• Cf. AF-SDW x 1 / ?z 1
• R. Küchler et al., Phys. Rev. Lett. 03

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Spin-glass QCP in heavy fermions?
G
I
paramagnet, w/ Kondo screening
II
SG, without Kondo screening
JK

• Type I interacting f.p.
• UPdxCu5-x (?) ?/T scaling (M. Aronson et al
  95 D. MacLaughlin et al)
• Sc1-xUxPd3 (?) ?/T scaling (P. Dai et al04)
• Type II Gaussian f.p.
• Fluctuation of the spin glass order parameter
• (Sachdev et al, 95 Sengupta and Georges 95)

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Spin-glass QCP in heavy fermions?
S. Wilson, P. Dai et al, Phys. Rev. Lett. 05
D. Gajewski, R. Chau, and M. B. Maple, Phys.
Rev. B (00)
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SUMMARY

• Global phase diagram of the magnetic heavy
  fermion metals
• Two types of quantum critical metals
• T0 SDW transition (Gaussian)
• Locally quantum-critical destruction of Kondo
  effect exactly at the magnetic QCP (interacting)
• Evidence from magnetic dynamics, Fermi surface
  evolution, and thermodynamic ratio.
• Relevance to other strongly correlated metals?