Local Quantum Criticality and non

Report
Heavy fermion metals: Global
phase diagram, local quantum
criticality, and experiments
Qimiao Si
Rice University
KIAS, Oct 29, 2005
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)
S. Paschen
T. Lühmann
T. Cichorek
O. Trovarelli
F. Steglich
P. Gegenwart
S. Wirth
K. Neumaier
C. Geibel
P. Coleman
R. Küchler
N. Oeschler
O. Tegus
J. A. Mydosh
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.
Materials (possibly) showing Quantum Criticality
•
Insulating Ising magnet
–
LiHoF4: transverse field Ising model
•
Heavy fermion magnetic metals
•
‘‘Simple’’ magnetic metals
–
•
•
High Tc superconductors (?)
Mott transition
–
–
•
•
Cr1-xVx, Sr3Ru2O7, MnSi (1st order, but …) …
V2O3, …: QCP? (magnetic ordering intervenes at low T!)
cold atoms: 2nd order?
Frustrated magnets (?)
Field-driven BEC of magnons
Materials (possibly) showing Quantum Criticality
• Metal-insulator transition in 3D Si:P, …
– 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?
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, …
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
Heavy fermions near a magnetic QCP:
CeCu6-xAux
H. v. Löhneysen
et al, PRL 1994
TN
AF Metal
TN
Heavy fermions near a magnetic QCP:
CeCu6-xAux
H. v. Löhneysen
et al, PRL 1994
N. Mathur et al,
Nature 1998
CePd2Si2
TN
TN
AF Metal
AF Metal
Supercond.
Linear
resistivity
YbRh2Si2
TN
J. Custers et al,
Nature 2003
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 (?)
Kondo Lattice Model
I: RKKY interaction; AF
G=Innn/Inn etc.
Kondo Lattice Model
I: RKKY interaction; AF
G=Innn/Inn etc.
Bandwidth W
Kondo coupling JK
Kondo Lattice Model
I: RKKY interaction; AF
G=Innn/Inn etc.
Bandwidth W
Kondo coupling JK
Fixed I and W with I<<W, varying G and JK
Kondo lattices
Bandwidth W
G
Kondo coupling JK
Local moment magnetism, Irkky
G ~ frustration, reduced
dimensionality, etc.
JK
JK >>W>>Irkky
G
JK
JK >>W>>Irkky
• xNsite tightly bound local singlets
(cf. If x were =1, Kondo insulator)
• (1-x)Nsite lone moments:
JK >>W>>Irkky
• xNsite tightly bound local singlets
(cf. If x were =1, Kondo insulator)
• (1-x)Nsite lone moments:
– projection:
– (1-x)Nsite holes with U=∞
JK >>W>>Irkky
• xNsite tightly bound local singlets
(cf. If x were =1, Kondo insulator)
• (1-x)Nsite lone moments:
– projection:
– (1-x)Nsite holes with U=∞
• Luttinger’s theorem:
(1-x) holes/site in the Fermi surface
(1+x) electrons/site
---- Large Fermi surface!
JK >>W>>Irkky
G
paramagnet, w/
Kondo screening
PML
JK
Local moment magnetism, Irkky
JK<<Irkky<<W
G
JK
JK<<Irkky<<W
• With Ising anisotropy, the magnetic spectrum of the
local moment component is gapped.
• JK is irrelevant!
JK<<Irkky<<W
• 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
JK<<Irkky<<W
Néel, without
Kondo screening
G
AFS
JK
QS, J.-X. Zhu, & D. Grempel, cond-mat /0506207
Global phase diagram
G
I
II PML
AFS
AFL
JK
QS, J.-X. Zhu, & D. Grempel,
cond-mat /0506207
Type II transition
Hertz fixed point for T=0 SDW transition
Type I transition
Second order if
Destruction of Kondo screening at the magnetic QCP
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
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)
Nature of the phases
• T2 resistivity on both sides of the QCP
TN
Nature of the phases (cont’d)
• 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)
In what sense is the QCP local?
• Localization of f-electrons
– Reconstruction of the Fermi surface across QCP
– m*  ∞ over the entire Fermi surface as   QCP
• Anomalous spin dynamics.
• Destruction of Kondo effect
– Non-Fermi liquid excitations part of the quantum-critical
spectrum.
CeCu6-xAux
(xc≈0.01)
TN
AF Metal
TN
H. v. Löhneysen
et al, PRL 1994
Dynamical and Static Susceptibilities in CeCu5.9Au0.1
• E/T scaling
• a=0.75 `everywhere’ in q.
•Fractional exponent a=0.75
1/c(q)
q=0
..
q=Q
T0.75
INS @ q=Q
E/T
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
Dynamics of the quantum critical CeCu5.9Au0.1
• Frequency and temperature dependences of the
dynamical spin susceptibility:
– an anomalous exponent a < 1
– /T scaling
implying non-Gaussian fixed point
• The anomalous exponent a is seen essentially
`everywhere’ in the momentum space
O. Stockert, H. v. Löhneysen, A. Rosch, N. Pyka,
& M. Loewenhaupt, Phys. Rev. Lett. ’98
Ce(Ru1-xRhx)2Si2
(xc≈0.04)
c Q (T )
c  Q,  , T ) 
1 - i/Q (T )
TN
H. Kadowaki, Y. Tabata, M. Sato, N. Aso, S. Raymond,
& S. Kawarazaki, cond-mat/0504386
Ce(Ru1-xRhx)2Si2
C/T=0-a T1/2
0=350mJ/K2 for x=0
TN
H. Kadowaki, Y. Tabata, M. Sato, N. Aso, S. Raymond,
& S. Kawarazaki, cond-mat/0504386
In what sense is the QCP local?
• Localization of f-electrons
– Reconstruction of the Fermi surface across QCP
– m*  ∞ 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.
Hall Effect in YbRh2Si2:
probing the Fermi-surface change
Linear
resistivity
TN
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)
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)
Hall Effect in YbRh2Si2
Hall Effect in YbRh2Si2
Hall Effect in YbRh2Si2
• Finite T crossover
width  T0.5±0.1
• T=0 (extrapolation):
sharp jump @ QCP
S. Paschen, T. Lühmann, S. Wirth, P.Gegenwart, O.Trovarelli, C. Geibel,
F. Steglich, P.Coleman, & QS, Nature 432, 881 (2004)
Hall Effect in YbRh2Si2
• Finite T crossover
width  T0.5±0.1
• T=0 (extrapolation):
sharp jump @ QCP
S. Paschen, T. Lühmann, S. Wirth, P.Gegenwart, O.Trovarelli, C. Geibel,
F. Steglich, P.Coleman, & QS, Nature 432, 881 (2004)
dHvA in CeRhIn5
_
H. Shishido, R. Settai, H. Harima, & Y. Onuki, JPSJ 74, 1103 (2005)
Divergence of the Grüneisen Ratio
 1x
T
with
x 1/z
L. Zhu, M. Garst, A. Rosch,
and QS, Phys. Rev. Lett. ’03
Divergence of the Grüneisen Ratio
160
 1x
T
T
CeNi2 Ge2
80

Grüneisen Ratio
-80
with
x 1/z
L. Zhu, M. Garst, A. Rosch,
and QS, Phys. Rev. Lett. ’03
R. Küchler et al.,
Phys. Rev. Lett. ’03
YbRh2 Si 2
-160
0
Magnetic
2
4
T(K)
Paramagnetic
p
Grüneisen exponent in Ge-doped YbRh2Si2
• LQCP:
XY case
xloc ≈ 0.66 to 2nd order in ε-expansion for the
• Cf. AF-SDW: x = 1 / z = 1
R. Küchler et al., Phys. Rev. Lett. ’03
Spin-glass QCP in heavy fermions?
G
I
paramagnet, w/
Kondo screening
II
SG, without
Kondo screening
• Type I: interacting f.p.
JK
– UPdxCu5-x (?): /T scaling (M. Aronson et al ’95; D. MacLaughlin et al)
– Sc1-xUxPd3 (?): /T scaling (P. Dai et al’04)
• Type II: Gaussian f.p.
– Fluctuation of the spin glass order parameter
(Sachdev et al, ’95; Sengupta and Georges ‘95)
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)
SUMMARY
• Global phase diagram of the magnetic heavy fermion metals
• Two types of quantum critical metals
– T=0 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?

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