Magnetism and unconventional superconductivity in strongly correlated - - PowerPoint PPT Presentation

Magnetism and unconventional superconductivity in strongly correlated CeRhIn5 and CeCoIn5

jdt with Tuson Park

Los Alamos National Laboratory and

Department of Physics, Sungkyunkwan University

Outline:

• introduction
• CeRhIn5 – pressure and field tuning magnetism and unconventional

superconductivity

• relationship to quantum criticality, magnetism, unconventional

superconductivity in CeCoIn5

• summary

Concepts in Electron Correlations, Hvar

special thanks to: A. Bianchi, N. J. Curro, Z. Fisk, M. Kenzelmann, R. Movshovich, M. Nicklas, F. Ronning, J. L. Sarrao, V. A. Sidorov,

• O. Stockert, Y. Tokiwa and R. Urbano

the general problem

♦ as a function of a tuning parameter, magnetic

• rder driven toward T=0, where a dome of

superconductivity emerges that obscures the quantum critical point ♦ found in several strongly correlated systems, eg. CeIn3, CePd2Si2, cuprates, organics…. (N. D. Mathur

et al., Nature 394, 39 (1998); P. Monthoux et al., Nature 450, 1177 (2007) and references therein)

♦ raises fundamental questions:

• - Do magnetism and superconductivity coexist

microscopically? If so, what is the nature of the superconductivity?

• - Can the QCP be revealed?
• - Are fluctuations around the QCP responsible for

superconductivity? ♦ CeRhIn5: temperature-pressure phase diagram typical of the generic phase diagram and allows exploration of these issues ♦ CeCoIn5: no magnetic order but quantum critical with a dome of Tc(P); instructive for comparison to CeRhIn5

Tuning parameter SC dome

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1 2 3 4

SC

AFM+SC

T (K) P (GPa)

CeRhIn5

AFM TN Tc

?

structure and properties of CeMIn5

CeIn3 unit

Ce M: Co, Rh, Ir In

MIn2 unit ♦ CeMIn5: form in the tetragonal HoCoGa5-type structure that can be viewed as layers of distorted CeIn3 units and parallelepiped MIn2 units stacked sequentially along c-axis ♦ nominally isoelectronic with Ce3+ (4f1) ♦ exceptionally crystalline (RRR>400 and ρ0 ≤ 400nΩcm)

• CeRhIn5: TN=3.8 K; γ ≈ 450 mJ/molK2
• CeCoIn5: Tc=2.3 K; γ ≈ 250 - 1000 mJ/molK2
• CeIrIn5: Tc=0.4 K; γ ≈ 750 mJ/molK2

♦ degeneracy temperature of heavy quasiparticles TF≈ (Rln2)/γ ≈ 10K ≈ Tc ≈ TN: no perturbative small energy scale; and not Landau Fermi liquids; Tc/TF ⇒ ‘high-Tc’ superconductivity ♦ power laws in C/T, 1/T1 and κ below Tc ⇒ nodal SC in all

♦ electronic structure similar in CeCoIn5, CeIrIn5 and CeRhIn5; dHvA frequencies uniformly lower in CeRhIn5⇒ larger Fermi volume for M=Co, Ir ♦ for M=Co, Ir, good agreement with calculations for itinerant 4fs; about 60% f-character at EF; ‘localized’ 4f electrons in CeRhIn5

electronic structure of 115s

• H. Shishido et al., JPSJ 71, 162 (2002)

CeRhIn5

2 4 6 8 500 1000 1500

1.14 GPa << P1 1.61 GPa < P1 2.05 GPa > P1

Cel/T (mJ/mol-K2) T (K)

2 4 6 8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

1.14 GPa 1.40 GPa 1.61 GPa 2.05 GPa S (Rln2) T (K) CeRhIn5

♦ below ~ 8K, electronic entropy independent of ground state ⇒ different orders from same electronic degrees of freedom ♦ CeRhIn5: antiferromagnetic member of the 115s that include the unconventional heavy- fermion superconductors CeCoIn5 and CeIrIn5 ♦ exceptionally ‘clean’, with RRR ~ 500 and ρ0 ≤ 100nΩcm ♦ antiferromagnetic with TN=3.8 K, above which γ ≈ 450 mJ/molK2, and below which is an ordered moment M0≈ 0.8μB, slightly reduced from the full Ce moment expected in its CEF doublet state

M0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1 2 3 4

♦ below P1, magnetism and superconductivity; only superconductivity above P1 where TN=Tc; maximum Tc where TN extrapolates to T=0

0.0 0.5 1.0 1.5

SC

AFM+SC

T (K) P (GPa) P1 CeRhIn5 AFM TN Tc

M0

?

• T. Park et al., Nature 440, 65 (2006)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1 2 3 4 0.0 0.5 1.0 1.5

SC

AFM+SC

T (K) P (GPa) P1 CeRhIn5 AFM TN Tc

M0

?

• S. Kawasaki et al., PRL 91, 137001 (2003)

magnetism and superconductivity in CeRhIn5

♦ nuclear spin-lattice relaxation – a microscopic probe of magnetism and superconductivity ♦ at P < P1, clear signature of antiferromagnetism, followed by superconductivity; below Tc, 1/T1∝ T3, expected for a gap with line nodes; dxy symmetry from in-plane, field-angle specific heat, and no polar nodes

• T. Park et al., PRL (in press)

P=1.47 GPa < P1

♦ at P=2.1 GPa, no evidence for magnetic order above 150 mK, but extrapolated TN(P) gives TN ≈ 1K; 1/T1∝ T3 below Tc; magnetism & T-linear T1 disappear for P > P1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1 2 3 4 0.0 0.5 1.0 1.5

SC

AFM+SC

T (K) P (GPa) P1 CeRhIn5 AFM TN Tc

M0

?

1 2 3 4

10

2

10

3

Tc

γ(0) γΝ

0 T

1.1 T

C / T (mJ mol

• 1 K
• 2)

T (K) TN

P=1.4 GPa < P1

evolution of superconductivity with pressure

• T. Park et al., PNAS 105, 6825 (2008)

♦ below P1, 1/T1T = const. at the lowest temperatures – residual low-energy excitations reflected as well in finite γ(0) ♦ above P1, γ(0) becomes small and T-linear 1/T1 absent ⇒ both due to magnetism coexisting with nodal superconductivity; as P→P1, γN increases ⇒ itinerant charge carriers become more massive ♦ below P1, ΔC/γNTc ~ const ⇒ SC from heavy itinerant component reflected in γN ♦ above P1, ΔC/γNTc jumps and comparable to that in CeCoIn5 at P=0

1.0 1.5 2.0 2.5 200 400 γ (mJ mol

• 1K
• 2)

T (K) P1 CeRhIn5

γN γ0

CeRhIn

5

P1

(γN = γ(Tc))

emergence of magnetic order above P1

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1 2 3 4 0.0 0.5 1.0 1.5

SC

AFM+SC

T (K) P (GPa) P1 CeRhIn5 AFM TN Tc

M0

?

♦ at 2.1 GPa, where only superconductivity in H=0, magnetism ‘hidden’ by superconductivity emerges in the superconducting state when H ≥ 55 kOe; TN weakly increasing with H, as at P<P1 and S(TN) ∝ H ∝ areal density of vortices; similar results at P=1.8 and 1.9 GPa ♦ no evidence for field-induced magnetism at 2.3 GPa; once superconductivity suppressed, C/T diverges as T→0

• T. Park et al., Nature 440, 65 (2006);
• G. Knebel et al., PRB 74, 020501 (2006)

P2

120100 80 60 40 20 0 1.5 2.0 2.5

AFM

3.0 2.0

H ( k O e ) T (K) P ( G P a )

P1 P2

M O SC N M

H = k O e p l a n e T = 0.5 K plane 1.0

~P2 ~P2

field-induced criticality in CeRhIn5

♦ line of field-induced, second-

• rder magnetic transitions

connecting P1 and P2 inside the SC state; line separates a phase of coexisting magnetic order (MO) and superconductivity (SC) from a purely unconventional superconducting state ♦ diverging cyclotron mass and specific heat at P2 ⇒ QCP at P2 ♦ small-to-large Fermi surface and magnetic- nonmagnetic boundary at P2

(H. Shishido et al., JPSJ 74, 1103 (2005)); CeCoIn5-like above P2

♦ not expected at a conventional QCP ♦ new branches in interval ∼ P1 < P < ∼ P2 ; what happens at P1?

• T. Park et al., Nature

440, 65 (2006)

connecting P1 and P2

• T. Park et al., PNAS 105, 6825 (2008)

~P1 ~P2

♦ from slope of Bc2 (T) near Tc, (1/Bc2’)1/2 ∝ vF ∝ 1/m* ♦ m* (~ γN) increasingly heavy as P approaches P1 but jumps by ~ 2x upon crossing P1, not seen in high field dHvA ♦ diverging high field m* at P2 from dHvA and jump in zero-field m* at P1; consistent with T- P-H phase diagram – line of criticality accompanied by Fermi-surface reconstruction, with P1 the H=0 limit of P2 <P1 >P1

P1 P2

nature of the quantum criticality in CeRhIn5

♦ highest Tc and highest scattering rate coincident near P2 ♦ absolute resistivity at P2 for ρab and ρc ≈ chemically disordered CeCoIn5, where disorder scattering kills SC (J.

Paglione et al., Nature Phys. 3, 703 (2007)) ⇒ not disorder

scattering in CeRhIn5 vs P but scattering from fluctuations at P2 favors superconductivity ♦ unusual sublinear Tε,ε ≈ 0.85, resistivity from 0.25 to ~15K emanating from P2; expect ε =1 to 3/2 in conventional criticality ♦ unexpected decrease in anisotropy centered on P2 and extending from ~300 K to Tc ⇒ isotropic, i.e. local, nature of criticality; in FL regime ρab/ρc ≈ 0.2 ≈ m*a/m*c ~ 0.18 in CeCoIn5 with ‘large’ Fermi volume

• T. Park et al.,

CeRhIn5 near P2: CeCoIn5 at P=0

♦ H-T phase diagram for CeRhIn5 near P2 very similar to that of CeCoIn5 whose quantum critical point is avoided by superconductivity at P= 0 ♦ divergence of T2 coefficient resistivity (A ∝ ΔH-n with n ≈ 0.5) as H → Hc2(0) present but weaker than in CeCoIn5 (n ≈1.4); a reflection of differences in criticality? CeCoIn5 – conventional Hertz-Millis-Moriya criticality in only bosonic degrees of freedom vs. CeRhIn5 – isotropic ⇒ critical bosonic and fermionic degrees of freedom

• J. Paglione et al., PRL 91, 246405 (2003)
• T. Park et al.,

1 2 3 5 10 15

10 12 14 20 40 60

H (T) T (K) SC FL

NFL

CeRhIn5 2.35 GPa

A (μΩcm K

• 2)

H (T)

A=A0(H-HC2)

• n

Hc2(0)

CeCoIn5 P=0

magnetic fluctuations in CeCoIn5

♦ no long range static order for H=0, but above Tc, Lorentzian response in magnetic excitation spectrum at Q = (½,½,½) ♦ in the superconducting state, spin excitations sharply peaked at E0 = 0.60 meV, with a relaxation rate ħΓ < 0.07 meV; develops by removing spectral weight from low-energy ♦ large fluctuating moment ≈ 0.6μB, only slightly smaller than the static moment in CeRhIn5 ♦ emergence of dynamic spin correlations below ~15K in quantum critical state, where ρ ∝ T and -cotΘH ∝ T2 ♦ spin resonance in cuprates, with E0/2Δ ≈ 0.6 -- compared to E0/2Δ ≈ 0.5 in CeCoIn5, and similar power laws in transport properties ♦ not unique to CeCoIn5; spin gap below Tc also in CeCu2Si2, with energy scale ~ 0.2 meV and correspondingly lower Tc

• O. Stockert et al., unpublished

CeCoIn5

• C. Stock et al., PRL 100, 087001 (2008)

T <Tc T >Tc Q= (½,½,½)

magnetism induced by Cd doping CeCoIn5

2 4 6 500 1000 1500 2000

1 2 3 4 5 6 7 0.0 0.1 0.2 0.3 0.4 0.5

x% 0.25 0.50 0.75 1.0 1.25 1.5 2.5

[C-Clatt]/T (mJ/mole-K2) T (K)

CeCo(In1-xCdx)5

x% 2.5 temperature (K) Smag(RLn2)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1 2 3 4 5

CeCo(In1-xCdx)5

TC TN

T(K) x% Cd

AFM SC P

Tc TN ♦ Cd substitution for In: induces a second transition that coexists with bulk superconductivity (L.Pham

et al., PRL 97, 056404 (2006));

S ~ 0.3Rln2 at phase boundary-- independent

• f ground state

♦ T-x phase diagram similar to T-P diagram of CeRhIn5 and reversible with pressure ♦ new transition: microscopic coexistence of large- moment (~0.7μB) antiferromagnetism for x=1% that nucleates initially near dopant sites (from NQR: R. Urbano

et al., PRL 99, 146404 (2007)

♦ commensurate order at (½,½,½) from neutrons ( M.

Nicklas et al., PRB 76, 052401(2007)); as expected from spin

excitation spectrum in undoped parent; growth of magnetic intensity arrested abruptly at Tc ⇒ strong coupling between AFM and SC orders

CeCoIn5 T2

field-induced magnetism in CeCoIn5: CeRhIn5 at P1<P<P2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 9.8 10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4

T2 Tc

T (K) H (T)

♦ CeCoIn5: Hc2 Pauli limited and 1st order in low-T, high-H limit ⇒ phase inside T2 that may be FFLO, now also magnetic by NMR (B.-L.

Young et al., PRL 98, 036402 (2007)) and neutrons:

field-induced Q=

(0.44,0.44, 0.5) [not the

expected (½, ½, ½)] and m0≈ 0.15μB

• T. Park et al.,

PRL, in press CeCoIn5 P1<P<P2

• A. Bianchi et al., PRL 91, 187004 (2003)

♦ field-induced magnetism in CeRhIn5 for P1 < P < P2 and extends into normal state; in contrast to CeCoIn5 where superconductivity is necessary for magnetic order

• M. Kenzelmann et al., Science 321, 1652 (2008)

♦ CeRhIn5: Hc2 also Pauli limited and 1st order near P2

summary summary

CeCoIn5 ♦ microscopic coexistence of magnetism (with doping) and nodal superconductivity ♦ unconventional superconductivity from an SDW-like quantum-critical state ♦ quantum-critical point avoided by the presence of superconductivity ♦ weak, field-induced incommensurate antiferromagnetism existing only in the superconducting phase ♦ magnetically mediated superconductivity CeRhIn5 ♦ microscopic coexistence of magnetism and nodal superconductivity (P<P1) ♦ unconventional superconductivity from isotropic (local) quantum criticality ♦ field-induced line of quantum-critical points inside the superconducting dome ♦ field-induced magnetic order in the superconducting state and extending into the normal phase ♦ superconductivity from magnetic and charge fluctuations? similarities but also differences between CeRhIn5 and CeCoIn5 that reflect extent of Kondo coupling of the 4f electron with its electronic environment and that span behaviors in several heavy-fermion systems; experimental and theoretical prototypes for understanding the relationship between magnetism and the pairing mechanism