quantum criticality in Ce(Co , Rh)In 5 studied by low-temperature - PowerPoint PPT Presentation

qk exp. setup Motiv ation results Concl. quantum criticality in Ce(Co , Rh)In 5 studied by low-temperature thermal expansion J. G. Donath 1 F. Steglich 1 E. D. Bauer 2 J. L. Sarrao 2 P. Gegenwart 3 1 Max-Planck-Institute for Chemical Physics of Solids,  Dresden, Germany 2 Los Alamos National Laboratory, Los Alamos, New Mexico , USA 3 I. Physikalisches Institut, Universität Göttingen,  Göttingen, Germany Hvar – September th,  qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. Contents quantum criticality experimental setup motivation: materials results CeCoIn 5 − x Sn x CeRhIn 5 − x Sn x conclusion qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. specific heat and thermal expansion thermodynamic properties � ∂S temperature ◮ specific heat C p = T � ∂T p ◮ thermal expansion � ∂V NFL � � 1 � p = − 1 ∂S α = V ∂T V ∂p T ! α = α ( T ) , ( ∂S / ∂p ) T pointwise! MO LFL � � ◮ Grüneisen ratio Γ ∼ α / C = − 1 ∂E ∗ V E ∗ ∂p if single energy scale E ∗ dominates δ qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. specific heat and thermal expansion “nature” of qcp i. SDW type (“conventional QCP”) [Zhu et al. PRL  ,  ()] temperature AFM-QCP 3 D 2 D √ ( C / T ) cr ∼ − T − log T NFL √ ( α / T ) cr ∼ 1 / 1 / T T √ α cr ∼ T const MO LFL Γ cr ∼ 1 / T ii. local type (“unconventional QCP”) δ no T -dep. for α and C Γ cr ∼ 1 / T ǫ , ǫ < 1 qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. specific heat and thermal expansion “nature” of qcp i. SDW type (“conventional QCP”) [Zhu et al. PRL  ,  ()] temperature AFM-QCP 3 D 2 D √ ( C / T ) cr ∼ − T − log T NFL √ ( α / T ) cr ∼ 1 / 1 / T T √ α cr ∼ T const MO LFL Γ cr ∼ 1 / T ii. local type (“unconventional QCP”) δ no T -dep. for α and C Γ cr ∼ 1 / T ǫ , ǫ < 1 qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. quantum criticality experimental setup motivation: materials results CeCoIn 5 − x Sn x CeRhIn 5 − x Sn x conclusion qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. thermal expansion measuring cell ◮ capacitive method ◮ circular springs � parallel capacitor plates ◮ thermally decoupled with graphite elements � cell thermally stabilized ◮ relative resolution up to ∆ l / l = 10 − 11 ◮ dilution fridge: 0 . 02 � T � 6 K ◮ SC magnet: 0 � B � 20 T [Pott and Schefzyk, JPSI  ,  ()] qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. thermal expansion measuring cell 6cm [Pott and Schefzyk, JPSI  ,  ()] qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. quantum criticality experimental setup motivation: materials results CeCoIn 5 − x Sn x CeRhIn 5 − x Sn x conclusion qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. 115 systems ◮ tetragonal structure ◮ alternating layers of CeIn 3 and M In 2 � Fermi surface: 2 dimensional (cylindrical sheets along c ) ◮ large family of compounds � rich physics (SC, MO, NFL, . . . ) qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. 115 systems p, B = 0 T N 4 CeCoIn 5 T c ◮ HF SC with highest 3 T c = 2 . 3 K T (K) ◮ NFL at B c2 AFM 2 CeRhIn 5 SC 1 ◮ AFM at T c = 3 . 7 K SC ◮ SC for p > 1 . 6 GPa ? 0 ◮ NFL at p c 0 . 5 Co Co 0 . 5 Rh 0 . 5 Ir [Pagliuso et al. Physica B - ,  ()] qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 quantum criticality experimental setup motivation: materials results CeCoIn 5 − x Sn x CeRhIn 5 − x Sn x conclusion qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 CeCoIn 5 : phase diagram p, x = 0 ◮ complex SC phase for 0 < T � 2 . 3 K and 0 � B c2 � 5 T ◮ around 5 T : NFL - behavior in C, ρ , α , ... � reason for QCP still unclear � “hidden order (AFM)”, (SC QCP), ... [Paglione et al. PRL  ,  ()] qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 Sn doping: CeCoIn 5 − x Sn x why Sn -doping? ◮ separate B QCP from B c 2 � study origin of NFL qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 Sn doping: CeCoIn 5 − x Sn x p, B = 0 ◮ Sn (electron)-doping suppresses SC ◮ for x = 0 . 18 : T c = 0 , but no AFM order [Daniel et al. PRL  ,  ()] qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 CeCoIn 5 − x Sn x qc behavior: α and C p, x = 0 − 1/2 ~ T 20 CeCoIn 5 5 T // c − 1 ~ T 15 2 mol) − 2 ) − 6 K 1 ∆ C / T (J/K α / T (10 10 T * ~( const − T 1/2 ) 5 ~ log T a b 0 0 0.1 1 0.1 1 7 T (K) C / T : α / T : [A. Bianchi et al. PRL  ,  ()] [JGD et al. PRL  ,  ()] ◮ 2 D or 3 D ◮ 2 D: T > T ∗ , 3 D: T < T ∗ qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 CeCoIn 5 − x Sn x qc behavior: α and C p = 0 , B = B c2 ◮ diverging C for all concentrations at the upper critical field B c2 ◮ ( α / T ) cr ∼ 1 / T for T > T ∗ � 2 D √ ◮ α cr ∼ T for T < T ∗ � 3 D ◮ crossover temperature T ∗ increases with increasing x [Bauer et al. PRL ,  ()] qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 CeCoIn 5 − x Sn x qc behavior: α and C p = 0 , B = B c2 60 CeCoIn 5-x Sn x x 55 0.00 50 0.03 45 0.06 ◮ diverging C for all concentrations 0.09 40 0.12 at the upper critical field B c2 -2 ) -6 K 35 0.18 ◮ ( α / T ) cr ∼ 1 / T for T > T ∗ � 2 D �� / T (10 30 √ ◮ α cr ∼ T for T < T ∗ � 3 D 25 ◮ crossover temperature T ∗ 20 increases with increasing x 15 10 5 0 0.1 1 T (K) [JGD et al. PRL  ,  ()] qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 CeCoIn 5 − x Sn x qc behavior: α and C p = 0 , B = B c2 6 CeCoIn 5-x Sn x ◮ diverging C for all concentrations 5 at the upper critical field B c2 4 ◮ ( α / T ) cr ∼ 1 / T for T > T ∗ � 2 D -1 ) √ T* -6 K T for T < T ∗ � 3 D ◮ α cr ∼ 3 � (10 x 0.00 ◮ crossover temperature T ∗ 2 0.18 T* increases with increasing x 1 0 0 1 2 3 4 5 6 T (K) [JGD et al. PRL  ,  ()] qc in Ce(Co , Rh)In5 guido donath

qk exp. setup Motiv ation results Concl. CeCoIn5 CeRhIn5 CeCoIn 5 − x Sn x qc behavior: α and C p = 0 , B = B c2 ◮ disorder effect? ◮ intrinsic? � layered lattice structure � coupled planes � α and κ most sensitive ◮ Γ ∼ T − 0 . 65 [Bauer et al. PRB  ,  ()] qc in Ce(Co , Rh)In5 guido donath