Magnetism and unconventional superconductivity in strongly correlated - PowerPoint PPT Presentation

Magnetism and unconventional superconductivity in strongly correlated CeRhIn 5 and CeCoIn 5 jdt with Tuson Park Los Alamos National Laboratory and Department of Physics, Sungkyunkwan University Outline: • introduction • CeRhIn 5 – pressure and field tuning magnetism and unconventional superconductivity • relationship to quantum criticality, magnetism, unconventional superconductivity in CeCoIn 5 • summary 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 Concepts in Electron Correlations, Hvar

the general problem ♦ as a function of a tuning parameter, magnetic order driven toward T=0, where a dome of superconductivity emerges that obscures the quantum critical point ♦ found in several strongly correlated systems, eg. SC dome CeIn 3 , CePd 2 Si 2 , 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: Tuning parameter -- Do magnetism and superconductivity coexist microscopically? If so, what is the nature of the 4 superconductivity? CeRhIn 5 TN -- Can the QCP be revealed? AFM 3 -- Are fluctuations around the QCP responsible for Tc superconductivity? T (K) 2 ♦ CeRhIn 5 : temperature-pressure phase diagram SC 1 typical of the generic phase diagram and allows ? exploration of these issues AFM+SC ♦ CeCoIn 5 : no magnetic order but quantum 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 critical with a dome of T c (P); instructive for P (GPa) comparison to CeRhIn 5

structure and properties of CeMIn 5 CeIn 3 unit ♦ CeMIn 5 : form in the tetragonal HoCoGa 5 -type structure that can be viewed as layers of distorted CeIn 3 units and MIn 2 unit parallelepiped MIn 2 units stacked sequentially along c-axis ♦ nominally isoelectronic with Ce 3+ (4f 1 ) ♦ exceptionally crystalline (RRR>400 and ρ 0 ≤ 400n Ω cm) • CeRhIn 5 : T N =3.8 K; γ ≈ 450 mJ/molK 2 • CeCoIn 5 : T c =2.3 K; γ ≈ 250 - 1000 mJ/molK 2 • CeIrIn 5 : T c =0.4 K; γ ≈ 750 mJ/molK 2 Ce ♦ power laws in C/T, 1/T 1 and κ below T c ⇒ nodal SC in all In ♦ degeneracy temperature of heavy quasiparticles T F ≈ (Rln2)/ γ ≈ 10K ≈ T c ≈ T N : no perturbative small energy scale; and not M: Co, Rh, Ir Landau Fermi liquids; T c /T F ⇒ ‘high-T c ’ superconductivity

electronic structure of 115s ♦ electronic structure similar in CeCoIn 5 , CeIrIn 5 and CeRhIn 5 ; dHvA frequencies uniformly lower in CeRhIn 5 ⇒ larger Fermi volume for M=Co, Ir ♦ for M=Co, Ir, good agreement with calculations for itinerant 4fs; about 60% f-character at E F ; ‘localized’ 4f electrons in CeRhIn 5 H. Shishido et al., JPSJ 71 , 162 (2002)

CeRhIn 5 ♦ CeRhIn 5 : antiferromagnetic member of the 4 1.5 CeRhIn 5 TN 115s that include the unconventional heavy- fermion superconductors CeCoIn 5 and CeIrIn 5 AFM 3 P1 1.0 ♦ exceptionally ‘clean’, with RRR ~ 500 and ρ 0 Tc ≤ 100n Ω cm M 0 T (K) 2 M0 ♦ antiferromagnetic with T N =3.8 K, above which SC 0.5 γ ≈ 450 mJ/molK 2 , and below which is an ordered 1 moment M 0 ≈ 0.8 μ B , slightly reduced from the ? AFM+SC full Ce moment expected in its CEF doublet state 0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 P (GPa) ♦ below P1, magnetism and superconductivity; only superconductivity above P1 where T N =T c ; maximum T c where T N extrapolates to T=0 0.7 1.14 GPa << P1 CeRhIn 5 0.6 1500 1.61 GPa < P1 ♦ below ~ 8K, 2.05 GPa > P1 Cel/T (mJ/mol-K2 ) 0.5 electronic entropy 0.4 S (R ln 2) 1000 independent of ground 0.3 state ⇒ different orders 1.14 GPa 1.40 GPa 0.2 500 from same electronic 1.61 GPa 0.1 2.05 GPa degrees of freedom 0.0 0 0 2 4 6 8 0 2 4 6 8 T (K) T (K) T. Park et al., Nature 440 , 65 (2006)

magnetism and superconductivity in CeRhIn 5 4 1.5 ♦ nuclear spin-lattice relaxation – a microscopic CeRhIn 5 TN probe of magnetism and superconductivity AFM 3 P1 ♦ at P < P1, clear signature of antiferromagnetism, 1.0 Tc followed by superconductivity; below T c , 1/T 1 ∝ T (K) 2 M0 T 3 , expected for a gap with line nodes; d xy symmetry from in-plane, field-angle specific heat, SC 0.5 1 and no polar nodes ? AFM+SC 0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 P (GPa) P=1.47 GPa < P1 S. Kawasaki et al., PRL 91 , 137001 (2003) ♦ at P=2.1 GPa, no evidence for magnetic order above 150 mK, but extrapolated T N (P) gives T N ≈ 1K; 1/T 1 ∝ T 3 below T c ; magnetism & T-linear T 1 disappear for P > P1 T. Park et al., PRL (in press)

evolution of superconductivity with pressure ♦ below P1, 1/T 1 T = const. at the lowest 4 1.5 temperatures – residual low-energy excitations CeRhIn 5 TN reflected as well in finite γ (0) AFM 3 P1 ♦ above P1, γ (0) becomes small and T-linear 1.0 Tc 1/T 1 absent ⇒ both due to magnetism T (K) 2 M0 coexisting with nodal superconductivity; as P → P1, γ N increases ⇒ itinerant charge carriers SC 0.5 1 become more massive ? ♦ below P1, Δ C/ γ N T c ~ const ⇒ SC AFM+SC 0 0.0 from heavy itinerant component 0.0 0.5 1.0 1.5 2.0 2.5 3.0 P (GPa) reflected in γ N ♦ above P1, Δ C/ γ N T c jumps and P1 P=1.4 GPa < P1 TN CeRhIn 5 comparable to that in CeCoIn 5 at 3 10 0 T -2 ) 400 -1 K P=0 1.1 T C / T (mJ mol -2 ) -1 K T c γ N γ (mJ mol 200 γΝ CeRhIn P1 γ 0 2 10 5 γ(0) 0 1.0 1.5 2.0 2.5 ( γ N = γ (T c )) 0 1 2 3 4 T (K) T (K) T. Park et al., PNAS 105 , 6825 (2008)

emergence of magnetic order above P1 4 1.5 CeRhIn 5 TN AFM 3 P1 1.0 Tc T (K) 2 M0 SC 0.5 1 ? AFM+SC 0 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 P (GPa) P2 ♦ at 2.1 GPa, where only superconductivity in H=0, magnetism ‘hidden’ by superconductivity emerges in the superconducting state when H ≥ 55 kOe; T N weakly increasing with H, as at P<P1 and S(T N ) ∝ 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)

field-induced criticality in CeRhIn 5 ♦ line of field-induced, second- H = ♦ small-to-large Fermi 0 k O e p l a n e order magnetic transitions surface and magnetic- 3.0 connecting P1 and P2 inside the SC nonmagnetic boundary at P2 P1 state; line separates a phase of (H. Shishido et al., JPSJ 74 , 1103 T (K) coexisting magnetic order (MO) and (2005)); CeCoIn 5 -like above P2 2.0 AFM superconductivity (SC) from a ♦ not expected at a SC purely unconventional conventional QCP 1.0 ♦ new branches in interval ∼ superconducting state P2 ) 120100 80 60 40 20 0 e O k 1.5 ( H P1 < P < ∼ P2 ; what happens 2.0 ♦ diverging cyclotron at P1? 2.5 P mass and specific heat M ( G O P a ) T = 0.5 K plane at P2 ⇒ QCP at P2 N M ~P2 ~P2 T. Park et al., Nature 440 , 65 (2006)

connecting P1 and P2 ~P1 ~P2 <P1 >P1 P2 P1 ♦ from slope of B c2 (T) near T c , (1/B c2 ’) 1/2 ∝ v F ∝ 1/m* ♦ m* (~ γ N ) 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, T. Park et al., PNAS 105 , 6825 (2008) with P1 the H=0 limit of P2

nature of the quantum criticality in CeRhIn 5 ♦ unexpected decrease in anisotropy ♦ unusual sublinear T ε , ε ≈ 0.85, centered on P2 and extending from ~300 K resistivity from 0.25 to ~15K emanating to T c ⇒ isotropic , i.e. local, nature of from P2; expect ε =1 to 3/2 in criticality ; in FL regime ρ ab / ρ c ≈ 0.2 ≈ conventional criticality m* a /m* c ~ 0.18 in CeCoIn 5 with ‘large’ Fermi volume ♦ highest T c and highest scattering rate coincident near P2 ♦ absolute resistivity at P2 for ρ ab and ρ c ≈ chemically disordered CeCoIn 5 , where disorder scattering kills SC (J. Paglione et al., Nature Phys. 3 , 703 (2007)) ⇒ not disorder scattering in CeRhIn 5 vs P but scattering from fluctuations at P2 favors superconductivity T. Park et al.,

CeRhIn 5 near P2: CeCoIn 5 at P=0 FL -n 15 A=A 0 (H-H C2 ) 60 -2 ) A ( μΩ cm K 40 H c2 (0) 20 10 H (T) 0 10 12 14 H (T) NFL CeCoIn 5 5 CeRhIn 5 P=0 SC 2.35 GPa 0 0 1 2 3 T. Park et al., J. Paglione et al., PRL 91 , 246405 (2003) T (K) ♦ H-T phase diagram for CeRhIn 5 near P2 very similar to that of CeCoIn 5 whose quantum critical point is avoided by superconductivity at P= 0 ♦ divergence of T 2 coefficient resistivity (A ∝ Δ H -n with n ≈ 0.5) as H → H c2 (0) present but weaker than in CeCoIn 5 (n ≈ 1.4); a reflection of differences in criticality? CeCoIn 5 – conventional Hertz-Millis-Moriya criticality in only bosonic degrees of freedom vs . CeRhIn 5 – isotropic ⇒ critical bosonic and fermionic degrees of freedom