Phase diagrams of pressure-tuned Heavy Fermion Systems G. Knebel, D. Aoki, R. Boursier, D. Braithwaite, J. Derr, Y. Haga, E. Hassinger, G. Lapertot, M.-A. Méasson, P.G. Niklowitz, A. Pourret, B. Salce, J. Flouquet DRFMC / SPSMS 1/5/5 1
outline Phase diagram of a Kondo lattice near the magnetic quantum critical point : interplay with superconductivity Experimental development : AC specific heat in DAC at low temperatures (see poster D. Braithwaite, B. Salce) Experimental results and discussion Pressure induced superconductivity in antiferromagnetic CeRhIn 5 High pressure phase diagram of antiferromagnetically ordered YbRh 2 Si 2 Conclusion and perspectives 2
Doniach diagram ground state properties of heavy fermion systems : competition : Kondo interaction RKKY interaction T K ~ N(E F ) -1 exp(-1/n(e F )J) T RKKY ~ N(E F )J 2, J ~ V fc 2 k B T k B T K k B T RKKY large electronic Grüneisen parameter in heavy fermion systems J ~ V fc 2 very sensitive to P µ eff, T N magnetic order µ eff T N J N(E F ) heavy fermion intermediate valent J c N(E F ) ~P c Ce 3+ (4f 1 ) magnetic J=5/2 Yb 2+ (4f 14 ) non-magnetic Ce 4+ (4f ) non-magnetic increasing pressure: Yb 3+ (4f 13 ) magnetic J=7/2 3
QCP : itinerant versus local scenarios spin fluctuations : SDW instability at the Fermi surface T T K local quantum criticality at QCP T CEF T N T K * T N Ce P MO P KL NFL screened moment itinerant f electron SC P c P V T I FL P Yb magnetic order small FS δ c large FS divergence of dynamical susceptibility at P c f electron itinerant, large FS, continuous e.g. (Ce,La)Ru 2 Si 2 CeNi 2 Ge 2, CeIn 3 (Hertz, Millis, Moriya) reconstruction of FS at P c anomalous E/T, H/T scaling laws e.g. Ce(Cu,Au) 6, YbRh 2 Si 2 (Si, Coleman ) 4
The heavy fermion AF CeIn 3 2 15 1 n 2. 1.6 T N 2 NFL T I CeIn 3 ρ = ρ +AT n 4 P (kbar) Bulk superconductivity only at critical point? Coexistence of SC and AFM? SC at QCP due to spin fluctuation? existence of QCP? weakly 1st order transition at P c phase separation in magneticsuperconducting volume near P c (NQR measurement, Kitaoka, Osaka) 5 AFM FL 1 T SC s 2 4 6 open symbols: Mathur et al. closed symbols: GK et al. P (kbar) T c Specific heat under high pressure with almost optimal pressure conditions! 5
ac-calorimetry under high pressure in diamond anvil cell 5 µm thermometer τ i =τ i (η,κ T,κ H ) In-situ P-variation at low temperatures sample heater P = P (1+cosωt) Au/Au.7at% Fe thermocouple soldered on sample pressure medium: Argon pressure by ruby fluorescence at T = 4 K heating by laser or laser diode ( 3 He cryostat) Bath, T κ B,τ s =C/κ B High sensitivity not quantitative (for details : poster D Braithwaite, B Salce) 6
Pressure induced superconductivity in CeRhIn 5 bulk superconducting phase diagram quantum critical point? 7
CeRhIn 5 at ambient pressure HoCoGa 5 structure tetragonal with layers of CeIn 3 and RhIn 2 stacked sequentially in c direction «quasi 2D layered» structure, 2D Fermi sheets AF, T N = 3.8 K, helical spiral along c, q M = (1/2, 1/2,.297) m =.75 µ B (.84 µ B for CEF doublet-local moment) SC under pressure T s (CeRhIn 5 ) = 1 T s (CeIn 3 ), but T N max ~T c max 8
Pressure temperature phase diagram 5 4 CeRhIn 5 1. no change in magnetism under pressure when SC detected by resistivity 3 2 1 AF SC...5 1. 1.5 2. 2.5 P (GPa).75.5.25 M Q (µ B /Ce) coexistence of AF and SC for P < 2 GPa from NQR measurements (Kitaoka, Osaka) no sign of AF order for P >2 GPa existence of a QCP in CeRhIn5? Specific heat under high pressure with almost optimal pressure conditions! Llobet et al. PRB 69, 4223 (24) 9
CeRhIn 5 : AFM and SC under pressure by ac calorimetry 2.5 C/T (J mole -1 K -2 ) 2 1.5 1.5 CeRhIn 5 5 1 15 2.5 2 in high pressure cell : CeRhIn 5 C/T (J mole -1 K -2 ) 2 1.5 1.5 CeRhIn 5 C/T (a.u.) 1.5 1.5 P (GPa).65 1 2 3 4 1 1.5 2 2.5 3 3.5 4 4.5 1
CeRhIn 5 : magnetic transition 2 P (GPa) T c T N CeRhIn 5 Broadening of magnetic transition, intrinsic! C/T (a.u.) 1.5 1.5 1.9 1.85 1.6 1.38 1.7 appearance of SC near 1.9 GPa disappearance of magnetic transition near 2 GPa.65 1 1.5 2 2.5 3 3.5 4 4.5 (pressure tuning in-situ) 11
Ac calorimetry under high pressure 2.5 2 P (GPa) 2.55 CeRhIn 5 C/T (a.u.) 1.5 1.5 2.1 1.9 1.85 1.6 1.38 1.7.65 1 1.5 2 2.5 3 3.5 4 4.5 sharp superconducting transition for P > 2 GPa 12
superconductivity C/T (a.u.) 2.5 2 1.5 CeRhIn 5 P (GPa) 2.43 2.72 3. 3.38 3.5 1.5 1.4 1.6 1.8 2 2.2 2.4 1.5 CeRhIn 5 C/γT c ~const SC anomaly directly linked to effective mass m* C/C(T c ) (a.u.) 1.5 P c hidden magnetic QCP at 2.5 GPa? 2 2.5 3 3.5 P (GPa) 13
CeRhIn 5 : phase diagram 5 4 CeRhIn 5 3 P c * 2 AF 1 AF + SC..5 1. 1.5 2. 2.5 3. 3.5 4. P (GPa) SC clear AF anomaly C(T) broadening of AF in C(T) SC only very close to P c in C(T) absence of SC anomaly in C(T) sharp SC anomaly no signature of AF below T c 14
Bulk superconducting phase diagram? 4 No magnetic QCP at H=! CeRhIn 5 Hierarchy of transition on cooling: 3 2 AFM P c * P c H > H c2 P<P c : PM AF SC experimentally observed P>P c : PM SC AF never observed in HFS 1 AF + SC SC free energy of SC lower than AF 1.5 2. 2.5 3. P (GPa) 1st order transition AF SC (see also neutron scattering) inhomogeneous or ungapped SC below P c? phase separation in AFM + PM/SC (observed in CeIn 3 by NQR)? But : new effect in field expected CeCoIn 5 near H c2 () 15
Quantum criticality in YbRh 2 Si 2 Suppression of AF order in a magnetic field High pressure phase diagram: - resistivity - specific heat - resonant X-ray scattering 16
Quantum criticality in YbRh 2 Si 2 Yb based heavy fermion system with very low T N ~ 7mK m~.2 µ B field induced QCP local criticality divergence of m* ESR signal Trovarelli et al. PRL 85, 626 (2) Gegenwart et al. PRL 89, 5642 (22) 17
Resistivity (T,H) under high pressure 1 ρ (µωcm) 5 2.3 GPa 1.3 GPa.2 GPa Argon loaded DAC.5 1 1.5 16 A (µωcm/k 2 ) 25 2 15 1 YbRh 2 Si 2 H =.5.4.3.2 T A (K) ρ (µωcm) 12 8 4 7 GPa 6 GPa 4.8 GPa 5 2 4 6.1.2.4.6.8 1 1.2 1.4 p (GPa) 18
Ac specific heat under high pressure C/T (a.u.).5.4.3.2 p (GPa) 11.6 11.1 1.8 1.5 1.3 1.2 9.6 9.3 C/T (a.u.) 7 6 5 4 3 4.6 GPa.1 2 6.3 GPa YbRh 2 Si 2 2 3 4 5 1.6.8 1 1.2 1.4 (E Hassinger, A Pourret, stages DEA 5, 4) 19
Phase diagram From resistivity and specific heat : 4 3 2 1 YbRh 2 Si 2 3 6 9 12 p (GPa) qualitatively different from usual Ce Kondo lattice! ( compare to Plessel et al, RPB 23 ) T K /T K Ce Yb localisation of 4f orbitals Yb (.25 Å); Ce (.37Å) Yb ~.1 Ce for the same T K : (1-n f ) Yb << (1-n f ) Ce spin fluctuation but also valence fluctuations important Yb 2+ Yb 3+ + 5d P key point: determination of valence 2
Valence transition (collaboration with C. Dallera, M. Grioni et al, ESRF, ID26) Resonant inelastic X ray scattering (ESRF) direct probe of the valence of Yb due to measurements at Yb L 3 edge: excitation: Yb 2p 3/2 Yb 5d decay : 2p 5 4f N εd 3d 9 4f N εd temperature dependence (P=): pressure dependence (T = 3 K): 3 K YbRh 2 Si 2 hν IN = 8.9375 kev 1 K hν IN = 8.933 kev 1.51 1.52 1.53 1.54 Energy transfer (ev) 3 K 1 K 3 K 1 K 3+ 2+ YbRh 2 Si 2 hν IN = 8.937 kev 1 K 3 K 8.93 8.94 8.95 Energy (kev) Yb Lα 1 RXES 2+ 3+ 1.5 GPa 4.6 GPa 8.5 GPa 13 GPa 1.51 1.52 1.53 1.54 1.55 Energy transfer (ev) 1.52 1.53 1.54 Energy transfer (ev) 21
(p T ) phase diagram 4 3 YbRh 2 Si 2 p < 3 GPa: T N increase with pressure large planar magnetic anisotropy small moment : 1-3 µ B at p= closeness to QCP (P c ~ -.5 GPa) 2 1 3 6 9 12 p (GPa) 4 < p < 8.5 GPa: T N decrease with pressure drastic change in magnetoresistance p > 8.5 GPa: from Mössbauer spectroscopy: magnetic anisotropy changed at 9 GPa from planar to axial: term B 2 (P) changes sign large moment (Mössbauer) like usual Ce Kondo lattice v Yb ~ 3 (almost pure Yb 3+, from RIXS) B 2 planar axial 3. v YB 2.9 5 1 P (GPa) 2.8 5 1 P (GPa) 22
Conclusions Behaviour on real system at the «QCP» much more rich! CeRhIn 5 : 1 st order transition AF - SC under pressure P < P c * : inhomogeneous SC state, phase separation AF - PM/SC? P > P c * : Pure unconventional d-wave SC, possibility for QCP for H ~H c2 YbRh 2 Si 2: Very rich high pressure phase diagram no simple electron hole analogy P > 8.5 GPa usual Kondo lattice behaviour 23
perspectives normal state : description of anomalous RE by comparison to Ce magnetic furtivness: tiny ordered moment TEP(P) gap, valence, and magnetism (SmS, SmB 6 ) superconductivity : precise determination of SC, M boundary (UGe 2, URu 2 Si 2, CeIn 3 ) field dependences of SC, AF boundaries (CeRhIn 5 ) new examples: quadrupolar fluctuations in PrOs 4 Sb 12 superconducting Yb compounds near P c instrumentation : -improvement of reliability - extension ac-calorimetry to H, T << 1K (P in-situ) - ac calorimetry (P fixed), H < 18T, T min < 1 mk 24
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