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 Yb 3 Pt 4 : A New Type of Quantum Critical System? Meigan Aronson, Marcus Bennett, Yuri Janssen, Moosung Kim, Keeseong Park, Y Yuen Yiu, Peter Khalifah Yi P Kh lif h Stony Brook University and Brookhaven National Laboratory St B k U i it d B kh N ti l L b t W Work at Stony Brook carried out under auspices of NSF DMR-0405961 k t St B k i d t d i f NSF DMR 0405961

Quantum Critical Points: Universal Organizing Scheme? Heavy Electron Intermetallics Heavy Electron Intermetallics Cuprates CePd 2 Si 2 AF AF SC Mathur 1998 Organic Conductors SmO 1-x F x FeAs Liu 2008 (Jaccard 2001) AF AF SC

Critical Phenomena near the Quantum Critical Point -what are the manifestations of quantum criticality and how much of the phase di diagram is affected? i ff t d? -what are the universality classes for quantum phase transitions? -how do quantum fluctuations affect the normal and superconducting state properties? ti ? Novel order near the Quantum Critical Point -textured electronic and magnetic phases -unconventional superconductivity

Quantum Critical Phase Diagram YbRh 2 Si 2 Fermi Liquid AF Gegenwart et al 2007 Q Quantum Critical Point t C iti l P i t 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~B QCP ) C~-TlogT (C(B)-C(0))/T= Φ (B/T n ) Fermi Liquid (B>B QCP ) ∆ C= γ T γ ~(m*/m) γ ~m*/m~(B-B QCP ) -1/2 B B B=B QCP : T FL =0 T 0 Complete Breakdown of Fermi Liquid Description as B B QCP

f- Electron Delocalization at QCP YbRh 2 Si 2 n=2e - /uc n=3e - /uc Paschen 2004 (Shishido 2005)

Crystal Structure of Yb 3 Pt 4 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 T N =2.4 K Yb 3+ /m 3 ) 7 mole-Y 1/ χ (10 Magnetic susceptibility χ : Magnetic susceptibility χ : -low anisotropy -H || a Curie Weiss behavior (20 K – 300 K) µ =4.55 µ B , θ =-3 K θ (20 K 300 K) 4 55 3 K - discontinuity in d χ /dT: Antiferromagnetic Transition T N =2.4 K

Heat Capacity θ D ~260 K Ordering anomaly: T N =2.4 K 63 K 63 K ~150 K 150 K Strong evidence for local moment paramagnet: 26 K - Crystal field scheme: doublet ground state C t l fi ld h d bl t d t t Tetragonal Site − ∆ S~ Rln 2 Symmetry Yb 3+

First Order Magnetic Transition T N,C (K) L(mJ/g) Yb 3 Pt 4 2.4 0.217 Cr Cr 311 311 21 21 CuO 212.6 36 First order transition: T N =2.4 K Gd 5 Ge 3 0.5 237 D Dy 90 5 90.5 312 312 L=0.217 mJ/g Tb 221.5 855 DyCo 2 140 1200

Electrical Resistivity Ordering anomaly near antiferromagnetic transition T N Ordering anomaly obeys Fisher-Langer relation d ρ /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 octahedron. Octahedra are staggered among layers. Order parameter is not mean-field like. Discontinuity at T N =2.45 K at most ~0.5 µ B /Yb.

Field Tuning the Transition: C(T) Creation of critical endpoint: H||c H || a -suppression of ∆ C, L, S(T N ) -modest anisotropy for phase diagram d t i t f h di 1.2 K,1.52 T 1.2 K,3.5 T

Field Tuning the Transition : M(T) Ordering Transition: C(T) dM/dT dM/dT - Continuous magnetization M(T) C ti ti ti M(T) - Discontinuous dM/dT, grows as H H cep

Field Tuning the Transition: χ ac χ ac g 0 -6 m 3 /kg) ) H||a C(T) C(T) χ ’ (10 dM/dT χ ’ H < 0.4 T: cusp in χ ’ (T N ) = dM/dH (T N ) H 0 4 T i ’ (T ) dM/dH (T ) H > 0.4 T: Discontinuity in χ ’(T N ) Discontinuity in χ ’(T N ) grows as H H cep Discontin it in ’(T ) gro s as H H

The Field-Temperature Phase Diagram ? First Order phase line (H CEP <1.5 T, T CEP =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 T N =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) ρ ( ) y p ( ) cep =1.8 K Slope discontinuity in ρ (H) T N >T>T p Peak in ρ (H) T<T cep =1.8 K Spin disorder scattering: Implied peak in M(H) along 2 d order line.

The Field – Temperature Phase Diagram Quantum Ferromagnets PM PM AF H||a H||a (Belitz 2005) Critical Endpoint (H||a) : H cep =1.5 T, T cep =1.2 K Quantum Critical Point (H||a): H qcp =1.62 T Phase line becomes 2d order near QCP: generally expect 1 st order near Phase line becomes 2d order near QCP: generally expect 1 st order near (avoided) QCP.

Antiferromagnetic Fermi Liquid: H<H QCP ρ (T)= ρ 0 +AT 2 T<T FL ~T N

Paramagnetic Fermi Liquid: H>H QCP H QCP H>H QCP and T<T FL (H) ρ = ρ 0 +A(H)T 2 ρ ρ 0 +A(H)T

T=0 Magnetic Susceptibility Antiferromagnetic Fermi Liquid (H<HQCP): χ 0 =dM/dH ~ constant Paramagnetic Fermi Liquid (H>HQCP): χ 0 =dM/dH~1/H 2 Divergence not controlled by H QCP =1.6 T

Specific Heat Coefficient γ mol-K 2 ) tky )/T (J/m (C-C Schott ( C(T)= γ T + β T 3 + C Schottky + C crit 3 Yb 3 Pt 4 : Moderate heavy fermion Yb 3 Pt 4 : Moderate heavy fermion H>H QCP : γ ~ 0.1 – 0.15 J/molK 2 27 K< T o < 41 K No enhancement of γ for H~H QCP

Fermi Liquid Parameters H QCP Enhancement of A, χ 0 but NOT γ , χ 0 γ as H~H QCP QCP No divergence of quasiparticle mass at quantum critical point

H~H QCP : Enhanced T=0 Susceptibility 9 T H=0 γ ~ (m*/m) χ 0 / γ ~ (1/1+F 0 χ o ~ (m*/m) (1/1+F 0 a ) a ) : Yb Pt normal heavy electron compound F a small H>>H H>>H QCP : Yb 3 Pt 4 normal heavy electron compound, F 0 small a ) ~ 1/H 3 H~H QCP : Divergence of quasiparticle interactions 1/(1+F o

H~H QCP : Enhanced Quasiparticle Scattering Tsujii 2005 T jii 2005 Slope=-2.6 Yb 3 Pt 4 (H=0) 9T A ~ (m*/m) 2 (1/1+F 0 γ ~ (m*/m) a ) A/ γ 2 ~ (1/1+F 0 A/ γ a ) (1/1+F 0 ) H>>H QCP : normal heavy electron compound H H QCP H~H QCP : divergence of qp interactions

Interaction Driven Magnetic Order Magnetic Order: Fermi surface instability driven by quasiparticle interactions not by quasiparticle mass divergence. examples: Stoner ferromagnet, nesting driven antiferromagnet, 3 He 3 Local moment-type order? -M AF ~1 µ B /Yb M 1 /Yb - ∆ S(T N )~0.6 Rln2 -H/T scaling as T T N

Yb 3 Pt 4 : 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 QCP : Ordered state is strongly interacting Fermi liquid with T FL ~T N . H<H O d d t t i t l i t ti F i li id ith T T H>H QCP : 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.