qimiao si rice university kias, oct 29, 2005 heavy fermion metals: global phase diagram, local...

Qimiao SiRice University

KIAS, Oct 29, 2005

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

S. Paschen P. Gegenwart R. KüchlerT. Lühmann S. Wirth N. OeschlerT. Cichorek K. Neumaier O. TegusO. 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)

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.

• 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

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?

Materials (possibly) showing Quantum Criticality

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-xAuxH. v. Löhneysen et al, PRL 1994

AF MetalTN

TN

Heavy fermions near a magnetic QCP:

CeCu6-xAux

YbRh2Si2

H. v. Löhneysen et al, PRL 1994

J. Custers et al, Nature 2003

CePd2Si2N. Mathur et al, Nature 1998

AF MetalTN

TN

TN

AF MetalSupercond.

Linearresistivity

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

Bandwidth W

Kondo coupling JK

I: RKKY interaction; AF

G=Innn/Inn etc.

Kondo Lattice Model

Bandwidth W

Kondo coupling JK

Fixed I and W with I<<W, varying G and JK

I: RKKY interaction; AF

G=Innn/Inn etc.

Kondo lattices

JK

G

G ~ frustration, reduceddimensionality, etc.

Loc

al m

omen

t mag

netis

m, I

rkky

Kon

do c

oupl

ing

J K

Bandwidth W

JK

G

JK >>W>>Irkky

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

G

PML

paramagnet, w/ Kondo screening

JK >>W>>Irkky

JK

G

JK<<Irkky<<WL

ocal

mom

ent m

agne

tism

, Irk

ky

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

G

AFS

QS, J.-X. Zhu, & D. Grempel, cond-mat /0506207

JK<<Irkky<<W

Néel, without Kondo screening

JK

G

AFS

PML

AFL

QS, J.-X. Zhu, & D. Grempel, cond-mat /0506207

I

II

Global phase diagram

Type I transition

Type II transitionHertz fixed point for T=0 SDW 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

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

• Anomalous spin dynamics

Destruction of Kondo effect (Eloc

* 0) at the QCP

Nature of the phases

TN

• T2 resistivity on both sides of the QCP

Nature of the phases (cont’d)

TN

• Small Fermi surface in the AF metal phase

TN

S. Araki, R. Settai, T. C. Kobayashi, H. Harima, & Y. Onuki, Phys Rev. B 64, 224417 (2001)

CeRh2Si2

• 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.

In what sense is the QCP local?

CeCu6-xAux (xc≈0.01)

H. v. Löhneysen et al, PRL 1994

AF Metal

TN

TN

Dynamical and Static Susceptibilities in CeCu5.9Au0.1

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

• E/T scaling

•Fractional exponent =0.75• =0.75 `everywhere’ in q.

INS @ q=Q E/T

q=Q

q=0

INS and M/H

T0.75

1/(q)

...

Dynamics of the quantum critical CeCu5.9Au0.1

• Frequency and temperature dependences of the dynamical spin susceptibility:– an anomalous exponent < 1 /T scaling

implying non-Gaussian fixed point

• The anomalous exponent is seen essentially `everywhere’ in the momentum space

O. Stockert, H. v. Löhneysen, A. Rosch, N. Pyka, & M. Loewenhaupt, Phys. Rev. Lett. ’98

TN

Ce(Ru1-xRhx)2Si2 (xc≈0.04)

)()(

),,T

TTQ

Q

Q

/i-1

H. Kadowaki, Y. Tabata, M. Sato, N. Aso, S. Raymond, & S. Kawarazaki, cond-mat/0504386

Ce(Ru1-xRhx)2Si2

H. Kadowaki, Y. Tabata, M. Sato, N. Aso, S. Raymond, & S. Kawarazaki, cond-mat/0504386

TN0=350mJ/K2 for x=0

C/T=0-a T1/2

• 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.

In what sense is the QCP local?

Hall Effect in YbRh2Si2: probing the Fermi-surface change

TN

Linear resistivity

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

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)

• Finite T crossover width T0.5±0.1

• T=0 (extrapolation): sharp jump @ QCP

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)

H. Shishido, R. Settai, H. Harima, & Y. Onuki, JPSJ 74, 1103 (2005)_

dHvA in CeRhIn5

Divergence of the Grüneisen Ratio

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

xT1

zx /1with

Divergence of the Grüneisen Ratio

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

R. Küchler et al., Phys. Rev. Lett. ’03

Magnetic Paramagnetic

T

0 2 4-160

-80

80

160

YbRh2Si2

Grüneisen Ratio

T(K)

CeNi2Ge2

p

xT1

zx /1with

• LQCP: xloc ≈ 0.66 to 2nd order in ε-expansion for the XY case

• Cf. AF-SDW: x = 1 / z = 1

R. Küchler et al., Phys. Rev. Lett. ’03

Grüneisen exponent in Ge-doped YbRh2Si2

Spin-glass QCP in heavy fermions?

JK

Gparamagnet, w/ Kondo screening

SG, without Kondo screening

• 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 al’04)

• Type II: Gaussian f.p. – Fluctuation of the spin glass order parameter

(Sachdev et al, ’95; Sengupta and Georges ‘95)

I

II

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?