Hidden Order and Nexus between Quantum Criticality and Phase Formation :

The Case of URu2Si2

J. A. Mydosh

Max Planck Institute for Chemical Physics of Solids, Dresden

andKamerlingh Onnes Laboratory, Leiden University

Main Collaborators

M. Jaime

N. Harrison NHMFL-LANL

K. H. Kim*

H. Amitsuka Hokkaido Univ.

Haung Ying Kai Amsterdam/Leiden

*Seoul National University

Outline

• Introduction to URu2Si2 and Hidden Order (HO)• Pressure Tuning : Neutron Diffraction and NMR• Theories, Models and Conjectures over HO• Destruction of HO with Field : Magnetization and

Transport Properties – Phase Diagram• Effects of Rh-doping• Simplified Phase Diagram – only Phase II• Nexus between Quantum Criticality and Phase

Formation• Characterization of Phase II via C(T,H) and MCE

Introduction

ThCr2Si2 bct - type ( I4/mmm )

U

SiRu

a = 4.127 (Å)c = 9.570 (Å)

URu2Si2

Coexistence of HO with SC

0

100

200

300

400

500

1 10 100 1000

ρ(µ

Ω c

m)

T (K)

I // a

I // c

To ~ 17.5 K

Tc ~ 1.2 K

T.T.M. Palstra et al.(1985)W. Schlabitz et al.(1986) M.B. Maple et al.(1986)

Magnetic susceptibility

0

2

4

6

8

10

12

0 100 200 300 400

χ(1

0 -3

emu

/ mol

)

T (K)

URu2Si2

H // c

H // a

To

µzeff ~ 2.2 µB

Specific heat vs. magnetic Bragg-peak intensity

µord ~ 0.01 - 0.04 µB

ξc ~ 100 Åξ ~ 300 Å

To

Tc

URu2Si2

C5f

/ T

(mJ/

K2 m

ol)

0

100

200

300

400

500

T (K)

Inte

nsity

(arb

.uni

t)

0

1

0 5 10 15 20 25

Q = (1,0,0)

MasonFåkHonma

Type-I AF

Smag ~ 0.2 R ln 2

Pseudo-gap in URu2Si2 measured through optical conductivity, D. A. Bonn et al. PRL (1988)

Zone-center gap in URu2Si2 measured through neutron scattering, C. Broholm et al. PRL (1987) &

PRB (1991)

Similarity between optics and neutrons suggests magnetic excitations are strongly coupled to charge excitations

Magnetization as function of temperature, C. Pfleiderer et al. to be published (2005)

2.1 10-3

2.13 10-3

2.16 10-3

13 14 15 16 17 18 19 20 21

1T6T12T

M/B

(µB/U

-ato

m te

sla)

T(K)

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0 20 40 60 80 100

0.1T1.0 T6.0 T12 T

M/B

(µB/U

-ato

m te

sla)

T(K)

c-axisab-plane

• Neutron scattering under hydrostatic pressure

H. Amitsuka, M. Sato, N.Metoki, M. Yokoyama, K. Kuwahara, T. Sakakibara, H. Morimoto, S. Kawarazaki, Y. Miyako, and JAMPRL 83 (1999) 5114

29Si NMR in Aligned Powder

Si1

Si2

U

(110)

Matsuda, et al., PRL 87 (2001) 87203NMR, under pressure [P-induced IAF]

Γ 2 (Η,θ,Τ ) = α 2 Μ 2 (Η,θ,Τ ) + λ2(Τ )

Temperature (K)0 5 10 15 20

λ (G

)

0

5

10

15URu2Si2

s = 1/2 Mean Field

H _|_ cH || c

Bernal et al., PRL 87 (2001) 196402Ambient Pressure [Internal Field]

Γ

OAF?

Orbital Antiferromagnet

U Is the internal field

also isotropic at Ru sites?

U-U Bond Current Direction

Resultant Magnetic Field

Hidden Order Unique Enough to Stimulate New Ideas:

crystal fields Niewenhuys ’86quant. spin fluctuation Sikkema et al. ’96duality: loc./itin. Okuno, Miyake ’98spin-orbital cancellation Yamagami ’99fragile AF order Bernhoeft et al. ’02

Dipolar order with small g values

S

µ=gµBS

quadrupole Miyako et al. ’91 triple spin Barzykin, Gor’kov ’93quadrupole (Γ4) Santini, Amoretti ’94quadrupole (Γ5) H. A., Sakakibara ’94structural distortion Barzykin, Gor’kov ’95U dimer Kasuya ’97d-wave SDW Ikeda, Ohhashi ’98quadrupole (Γ5) Shimizu, Ohkawa ’99bond order - OAF Chandra et al. ’01unconventional SDW Virosztek, Maki, Dóra

’02

Non-dipolar order

?

Hidden Order Unique Enough to Stimulate New Ideas:

Landau-Pomeranchuk Varma ’03/’05Valency transition Gor’kov ’04Octupolar Kiss & Fazekas ’05SDW Mineev & Zhitomir. ’05 Falicov-Kimble Zlatic ’05Itinerant quadrupole Harrison et al. ’05Itinerancy & HO Tripathi & (PC)2 ’05

Non-translational-symmetry breaking

30 32 34 36 38 40 42

0.001

0.002

0.003

0.004

0.005

0.006

Mag

netiz

atio

n (a

.u.)

B (T)

0.46 K

1.55 K

4.00 K

5.00 K

5.50 K5.75 K6.00 K7.00 K8.00 K

11.00 K

30 32 34 36 38 40 42

0.001

0.002

0.003

0.004

0.005

0.006

Mag

netiz

atio

n (a

.u.)

B (T)

0.46 K

1.55 K

4.00 K

5.00 K

5.50 K5.75 K6.00 K7.00 K8.00 K

11.00 K

0.46 K

1.55 K

4.00 K

5.00 K

5.50 K5.75 K6.00 K7.00 K8.00 K

11.00 K

Switching to the Metamagnetic Transition in URu2Si2

N. Harrison, M. Jaime, and JAM, PRL 90(2003)

What happens as T is lowered?

χ exhibits divergence for T > 6 K as for CeRu2Si2,

Sr3Ru2O7 and UPt3

CAN FIELD-INDUCED QCP INSTIGATE NEW PHASES?

H decreasing

THEN SUDDENLY crossover splits for T < 6 K (T-stabilitycrucial for discovery)

Transitions consistentwith specific heat

measurements [Jaime et al. PRL 89, 287201(2002)]

0 5 10 15 20 25 30 35 40 45

0

0.5

URu2Si2

360

ρ xx (µ

Ωcm

) 360

1.62.545

678910111214

18

I//ab, H//c

20 K

Fig 1 Kim Harrison and Mydosh

0

µ0H (T)

ρxx for URu2Si2 ρxy for URu2Si2

FS change

Curvature change?

Hall Effect Results for URu2Si2 in Pulsed Magnet

Multiple phases nearby a QCP: H decreasing

30 31 32 33 34 35 36 37 38 39 40

0

40

40

0.591.0 1.5 2.3 3 4

5

URu2Si2

ρ (µ

Ωcm

)

0

6

8

10

12 K

µ0H (T)

Phase transitions observed as extremities in dρ/dBand dρ/dT confirmed in M, C and sound velocity vs

30 32 34 36 38 40 42 440

2

4

6

8

10

12

14

16

FermiLiquid (IV)

ρmax

µ0H (T)

URu2Si2

IIIT

(K)

HiddenOrder (I)

II

V

T*

Multiple phases nearby a QCP: H decreasing

30 32 34 36 38 40 42 440

2

4

6

8

10

12

14

16

FermiLiquid (IV)

ρmax

µ0Η (T)

URu2Si2

IIIT

(K)

HiddenOrder (I)

II

V

T*

0 2 4 6 8 10 12 14 16 18 200

10

20

30

40

50

0

10

20

30

40

50

38.9

39.5

42

44.5

37.736.6 50

0

T (K)

38.4

50

0

35.7

0

ρ (µ

Ω c

m)

URu2Si2

50

32.5T

Multiple new phases result from (1) multiple competing interactions and/or (2) close proximity of BM to Hidden Order phase

Metamagnetictransition

30 32 34 36 38 40 42 441.0

1.5

2.0

0

4

8

12

16

µ0H (T)

n

0

2

4

6

8

10

12

14

16

ρmax

ρ(µΩcm)

URu2Si2

FL (IV)III

T (K

)

HO (I)II

V

T*

06121824293339455155

A-1/2 (K

/µΩcm

-1/2)

Summary of Transport Results for URu2Si2

Metamagnetictransition

ρ=ρ0+ATn

~0.6K≤ T ≤ 3 K

HQCP~37 T !!

All the ”smoking guns”indicate

URu2Si2 :Another example of order created at quantum critical point ??

K.H.Kim, N.Harrison, M.Jaime, G.S.Boebinger and JAM. PRL 91, ‘03

Effects of Rh-doping in URu2Si2

Quantum criticality occurs in absence of hidden order: so hidden order not responsible for quantum criticality

Phase diagram simplified on doping with Rh, yielding single field-induced phase (II) [without phase I (Hidden Order)] and clearer evidence for quantum critical point

(mag

netiz

atio

n in

pul

sed

field

s an

d tra

nspo

rt in

dc

field

s)

Nexus between quantum critical point, phase II and BM observed as a function of Rh, indicating causality link

K.H.Kim, N.Harrison, H.Amitsuka, G.A.Jorge, M.Jaimeand JAM, PRL 93(2004)

Quantum criticality and Phase II

Evidence for quantum criticality occurs at at low and high magnetic fields, pointing to single quantum critical point concealed inside phase II, with scaling: T* ∝ A-1/2 ∝ εF

Fits of A to (B-BM)α support divergence in m* at quantum critical point: formation of phase II leads to suppression of fluctuations

Phase II likely holds key to understanding magnetism, because it has 1/3rd of full saturated moment (neutrons should be able to detect large moment that is absent in Hidden Order phase): Ising moments imply broken translational symmetry likely

α ~ 1 α ~ 0.7

Metamagnetism and Quantum Criticality

H

T or ε non Fermi liquid

Paramagnetic Fermi liquid

Fully polarized f -electrons + Fermi liquid

Experimentally first order transition not seen in itinerant electron metamagnets CeRu2Si2 or UPt3 [Sakakibara et al. PRB 51,12030(1995)].

“Transition” from Fermi surface A to Fermi surface B

AB

Existence of Fermi liquid at BM nevertheless quite unthinkable ?

BM

Issue of Fermi surface change at antiferromagnetic QCP in antiferromagnetic heavy fermion systems

Metamagnetism expected to be first order (no symmetry change?)

Understanding Fermi surface topology holds the key to everything

Fermi Liquids and Quantum Criticality

Quantum critical point between two Fermi liquids: one with polarized f-electrons

H

T or ε non Fermi liquid

Paramagnetic Fermi liquid

Fully polarized f -electrons + Fermi liquid

Phase with 1/3rd saturated moment possibly analogous to to Q = 2/3c* ferrimagneticphase in UPd2Si2? [Honma et al.,J.Phys.Soc.Japan 67,1017(1998)]

New phase forms so as to avoid quantum critical point

ferrimagnetic?Phase II

A.V.Silhanek, N.Harrison, C.D.Batista, M.Jaime, A.Lacerda, H.Amitsuka and JAM, PRL 95(2005)

X = 0.04

T2 (K2)

C/T

X

Low T ~ 2 K

High T ~ 6 K

Summary of Progress

1) URu2Si2 exhibits quantum critical behaviour associated with itinerant electron metamagnetism

2) Quantum criticality is involved in creation of new phase(s) at high magnetic fields

3) New phases may also help us to understand Hidden Order parameter

4) Rh doping greatly simplifies the phase diagram with a single phaseII surrounded by two low temperature Fermi liquid phases

5) Phase II exhibits an enormous specific heat discontinuity indicative of a first order phase transition – tricritical points