Yb Pt : A New Type of Quantum Yb 3 Pt 4 : A New Type of Quantum - - PowerPoint PPT Presentation

Yb Pt : A New Type of Quantum Yb3Pt4: A New Type of Quantum Critical System?

Meigan Aronson, Marcus Bennett, Yuri Janssen, Moosung Kim, Keeseong Park, Y Yi P Kh lif h Yuen Yiu, Peter Khalifah

St B k U i it d B kh N ti l L b t Stony Brook University and Brookhaven National Laboratory

W k t St B k i d t d i f NSF DMR 0405961 Work at Stony Brook carried out under auspices of NSF DMR-0405961

Heavy Electron Intermetallics

Quantum Critical Points: Universal Organizing Scheme?

Heavy Electron Intermetallics Cuprates CePd2Si2 AF AF SC

Mathur 1998

SmO1-xFxFeAs Organic Conductors AF

Liu 2008 (Jaccard 2001)

AF SC

Critical Phenomena near the Quantum Critical Point

• what are the manifestations of quantum criticality and how much of the phase

di i ff t d? diagram is affected?

• what are the universality classes for quantum phase transitions?
• how do quantum fluctuations affect the normal and superconducting state

ti ? properties? Novel order near the Quantum Critical Point

• textured electronic and magnetic phases
• unconventional superconductivity

Quantum Critical Phase Diagram

YbRh2Si2 Fermi Liquid AF

Gegenwart et al 2007

Q t C iti l P i t Quantum Critical Point Magnetic order vanishes, continuously or discontinuously Other electronic temperat re scales become small or anish Other electronic temperature scales become small or vanish

Divergence of Quasiparticle Mass at QCP

Trovarelli et al 2000 Gegenwart et al 2007

Quantum critical behavior (B~BQCP) C~-TlogT (C(B)-C(0))/T= Φ(B/Tn) Fermi Liquid (B>BQCP) ∆C=γT γ~(m*/m) γ~m*/m~(B-BQCP)-1/2 B B T B=BQCP: TFL=0 Complete Breakdown of Fermi Liquid Description as B BQCP

f- Electron Delocalization at QCP

YbRh2Si2 n=2e-/uc n=3e-/uc

Paschen 2004 (Shishido 2005)

Crystal Structure of Yb3Pt4

Previously reported compound(Palenzona 1977) Orthorhombic Cmmm, one Yb site symmetry a=1.3555 nm b=1.3372 nm c=0.5654 nm Single crystals grown from Pb flux.

Antiferromagnetic Order TN=2.4 K

Yb3+/m3)

7 mole-Y

1/χ (10

Magnetic susceptibility χ: Magnetic susceptibility χ:

• low anisotropy
• H || a Curie Weiss behavior

(20 K 300 K) 4 55 θ 3 K (20 K – 300 K) µ=4.55 µB, θ =-3 K

• discontinuity in dχ/dT: Antiferromagnetic Transition TN=2.4 K

Heat Capacity

θD~260 K 150 K 63 K Ordering anomaly: TN=2.4 K 26 K ~150 K 63 K Strong evidence for local moment paramagnet: C t l fi ld h d bl t d t t Tetragonal Site Symmetry Yb3+

• Crystal field scheme: doublet ground state

− ∆S~ Rln 2

First Order Magnetic Transition

TN,C (K) L(mJ/g) Yb3Pt4 2.4 0.217 Cr 311 21

First order transition: TN=2.4 K

Cr 311 21 CuO 212.6 36 Gd5Ge3 0.5 237 D 90 5 312

L=0.217 mJ/g

Dy 90.5 312 Tb 221.5 855 DyCo2 140 1200

Electrical Resistivity

Ordering anomaly near antiferromagnetic transition TN Ordering anomaly obeys Fisher-Langer relation dρ/dT ~ C(T)

Magnetic Order: Neutron Diffraction

c T(K)

7 g of powdered single crystals, experiments carried out on BT-7 TAS at NCNR-NIST. AF structure: octahedra of 6 Yb moments, each pointing towards near neighbor in next

• ctahedron. Octahedra are staggered among layers.

Order parameter is not mean-field like. Discontinuity at TN=2.45 K at most ~0.5 µB/Yb.

Field Tuning the Transition: C(T)

H||c H||a

Creation of critical endpoint:

• suppression of ∆C, L, S(TN)

d t i t f h di

• modest anisotropy for phase diagram

1.2 K,1.52 T 1.2 K,3.5 T

Field Tuning the Transition : M(T)

Ordering Transition: C ti ti ti M(T)

C(T) dM/dT

• Continuous magnetization M(T)
• Discontinuous dM/dT, grows as H Hcep

dM/dT

Field Tuning the Transition: χac g χac

)

C(T)

0-6 m3/kg) H||a

C(T) dM/dT χ’

χ’ (10 H 0 4 T i ’ (T ) dM/dH (T ) H < 0.4 T: cusp in χ’ (TN) = dM/dH (TN) H > 0.4 T: Discontinuity in χ’(TN) Discontin it in ’(T ) gro s as H H Discontinuity in χ’(TN) grows as H Hcep

The Field-Temperature Phase Diagram

?

First Order phase line (HCEP<1.5 T, TCEP=1.2 K): p (

CEP

,

CEP

)

• Discontinuous: heat capacity C, χ’=dM/dH, dM/dT
• Continuous: Magnetization M, resistivity ρ

Beyond the critical endpoint: crossover or phase line(s) ?

Beyond the Critical Endpoint: C(H) Beyond the Critical Endpoint: C(H)

For TN=2.45 K > T > T

cep=1.2 K : discontinuity in C(H)

For T<T

cep=1.2 K : peak in C(H)

First order line continues as a second order line, emanating from critical endpoint.

Beyond the critical endpoint: ρ(H), M(H) y p ρ( ) ( )

TN>T>T

cep=1.8 K Slope discontinuity in ρ(H) p

T<T

cep=1.8 K

Peak in ρ(H) Spin disorder scattering: Implied peak in M(H) along 2d order line.

The Field – Temperature Phase Diagram PM

Quantum Ferromagnets

PM

H||a

AF

H||a

(Belitz 2005)

Critical Endpoint (H||a) : Hcep=1.5 T, T

cep=1.2 K

Quantum Critical Point (H||a): Hqcp=1.62 T Phase line becomes 2d order near QCP: generally expect 1st order near Phase line becomes 2d order near QCP: generally expect 1st order near (avoided) QCP.

Antiferromagnetic Fermi Liquid: H<HQCP

T<TFL~TN ρ(T)=ρ0+AT2

Paramagnetic Fermi Liquid: H>HQCP

HQCP

H>HQCP and T<TFL(H) ρ=ρ0+A(H)T2 ρ ρ0+A(H)T

T=0 Magnetic Susceptibility

Antiferromagnetic Fermi Liquid (H<HQCP): χ0=dM/dH ~ constant Paramagnetic Fermi Liquid (H>HQCP): χ0=dM/dH~1/H2 Divergence not controlled by HQCP=1.6 T

Specific Heat Coefficient γ

mol-K2)

tky )/T (J/m

(C-CSchott (

3

C(T)=γT + βT3 + CSchottky + Ccrit Yb3Pt4: Moderate heavy fermion Yb3Pt4: Moderate heavy fermion H>HQCP: γ~ 0.1 – 0.15 J/molK2 27 K< T

• < 41 K

No enhancement of γ for H~HQCP

Fermi Liquid Parameters

HQCP Enhancement of A, χ0 but NOT γ as H~HQCP , χ0 γ

QCP

No divergence of quasiparticle mass at quantum critical point

H~HQCP: Enhanced T=0 Susceptibility

H=0 9 T χo ~ (m*/m) (1/1+F0

a)

γ ~ (m*/m) χ0/γ ~ (1/1+F0

a)

H>>H : Yb Pt normal heavy electron compound F a small H>>HQCP: Yb3Pt4 normal heavy electron compound, F0 small H~HQCP: Divergence of quasiparticle interactions 1/(1+Fo

a) ~ 1/H3

H~HQCP: Enhanced Quasiparticle Scattering

T jii 2005 Tsujii 2005

Yb3Pt4 Slope=-2.6 (H=0) 9T A ~ (m*/m)2 (1/1+F0

a)

γ ~ (m*/m) A/γ2 ~ (1/1+F0

a)

A/γ (1/1+F0 ) H>>HQCP: normal heavy electron compound H H~HQCP: divergence of qp interactions HQCP

Interaction Driven Magnetic Order

Magnetic Order: Fermi surface instability driven by quasiparticle interactions not by quasiparticle mass divergence.

3

examples: Stoner ferromagnet, nesting driven antiferromagnet, 3He Local moment-type order? M 1 /Yb

• MAF~1 µB/Yb
• ∆S(TN)~0.6 Rln2
• H/T scaling as T TN

Yb3Pt4: A New Route to Quantum Criticality A New Route to Quantum Criticality

A Unique Antiferromagnetic Phase Diagram: First order magnetic transition suppressed by field, terminates in critical endpoint. At higher fields, line of second order transitions terminates in quantum critical point. Two Fermi Liquids: H<H O d d t t i t l i t ti F i li id ith T T H<HQCP: Ordered state is strongly interacting Fermi liquid with TFL~TN. H>HQCP: Paramagnetic Fermi Liquid with enhanced quasiparticle scattering and susceptibility in vicinity of critical endpoint. A New Route to Quantum Criticality Quasiparticle interactions but not quasiparticle mass diverge at QCP Quasiparticle interactions but not quasiparticle mass diverge at QCP. Interaction driven instability of Fermi surface.