1 / 48

Philipp Gegenwart Max-Planck Institute for Chemical Physics of Solids, Dresden, Germany

Experimental Tutorial on Quantum Criticality. First part. Philipp Gegenwart Max-Planck Institute for Chemical Physics of Solids, Dresden, Germany. Reviews on quantum criticality in strongly correlated electron systems: E.g. G.R. Stewart, Rev. Mod. Phys. 73, 797 (2001).

george
Download Presentation

Philipp Gegenwart Max-Planck Institute for Chemical Physics of Solids, Dresden, Germany

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. ExperimentalTutorialon Quantum Criticality First part Philipp Gegenwart Max-Planck Institute for Chemical Physics of Solids, Dresden, Germany • Reviews on quantum criticality in strongly correlated electron systems:E.g. • G.R. Stewart, Rev. Mod. Phys. 73, 797 (2001). • H. v. Löhneysen, A. Rosch, M. Vojta, P. Wölfle, cond-mat/0606317 • Outline of this talk: • Introduction • Quantum criticality in some antiferromagnetic HF systems(mainly those studied in Dresden) • Ferromagnetic quantum criticality Second part

  2. Collaborators T. Westerkamp, J.-G. Donath, F. Weickert, J. Custers, R. Küchler, Y. Tokiwa, T. Radu, J. Ferstl, C. Krellner, O. Trovarelli, C. Geibel, G. Sparn, S. Paschen, J.A. Mydosh, F. Steglich K. Neumaier1, E.-W. Scheidt2, G.R. Stewart3, A.P. Mackenzie4, R.S. Perry4,5,Y. Maeno5, K. Ishida5, E.D. Bauer6, J.L. Sarrao6, J. Sereni7, M. Garst8, Q. Si9, C. Pépin10 & P. Coleman11 1Walther Meissner Institute, Garching, Germany 2Augsburg University, Germany 3University of Florida, Gainesville FL, USA 4St. Andrews University, Scotland 5Kyoto University, Japan 6Los Alamos National Laboratory, USA 7CNEA Bariloche, Argentina 8University of Minnesota, Minneapolis, USA 9Rice University, Texas, USA 10CEA-Saclay, France 11Rutgers University, USA

  3. f-electron based Heavy Fermion systems T localized moments+conduction electrons T* ~ 5 – 50 K moments boundinspin singlets • Lattice of certain f-electrons (most Ce, Yb or U) in metallic environment • La3+: 4f0, Ce3+: 4f1 (J = 5/2), Yb3+: 4f13 (J = 7/2), Lu3+: 4f14 (6s25d1,l=3) • partially filled inner 4f/5f shells  localized magnetic moment • CEF splitting  effective S=1/2

  4. Microscopic model: Kondo effect (Jun Kondo ´63) J: hybridization between local moments and conduction el. AF coupling J < 0 local moment conduction el  TK: characteristic „Kondo“-temperature Kondo- minimum TK T5 lnT T < TK: formation of a bound state between local spin and conduction electron spin  local spin singlet

  5. Anderson Impurity Model cond.-el f-el hybridizationVsf on-site Coulombrepulsion Uff Formation of an (Abrikosov-Suhl) resonance at EF of width kBT*  extremely high N(EF)  heavy fermions

  6. Landau Fermi liquid Lev Landau ´57 1:1correspondence Excitations of system with strongly interacting electrons Freeelectron gas

  7. Magnetic instability in Heavy Fermion systems Fermi-surface: Doniach 1977

  8. Itinerant (conventional) scenario TK T TN NFL SDW FL g gc Moriya,Hertz, Millis, Lonzarich, … OP fluctuations in space and time AF: z=2 (deff = d+z) • Heavy quasiparticles stay intact at QCP, scattering off critical SDW  NFL • “unconventional” quantum criticality (Coleman, Pépin, Senthil, Si): • Internal structure of heavy quasiparticles important:  4f-electrons localize • Energy scales beyond those associated with slowing down of OP fluctuations

  9. CeCu6-xAux E/T 1/(q) S(q,)T0.75 0T0.75 T0.75 H/T CeCu6-xAux: xc=0.1 inelastic neutron scattering O. Stockert et al., PRL 80 (1998): critical fluctuations quasi-2D ! A. Schröder et al., Nature 407 (2000): non-Curie-Weiss behavior q-independent  local !!

  10. Grüneisen ratio analysis T NFL AF FL  = p, x, B • Resolution: < 0.01Ål/l = 10-10 (l = 5 mm)for T  20 mK, B  20 Tesla Thermal expansion = –1/V∂S/∂p  = V-1 dV/dT Specific heat: C/T= ∂S/∂T Itinerant theory:  ~ Tz ~ T-1(L. Zhu, M. Garst, A. Rosch, Q. Si, PRL 2003)

  11. Experimental classification: unconventional CeCu6-xAux YbRh2Si2 … conventional CeNi2Ge2 CeIn3-xSnx CeCu2Si2 CeCoIn5 …

  12. CeNi2Ge2: very clean system close to zero-field QCP TK = 30 K, paramagnetic ground state P. Gegenwart, F. Kromer, M. Lang, G. Sparn, C. Geibel, F. Steglich, Phys. Rev. Lett. 82, 1293 (1999) See also: F.M. Grosche, P. Agarwal, S.R. Julian, N.J. Wilson, R.K.W. Haselwimmer, S.J.S. Lister, N.D. Mathur, F.V. Carter, S.S. Saxena, G.G. Lonzarich, J. Phys. Cond. Matt. 12 (2000) L533–L540

  13. CeNi2Ge2: thermal expansion In accordance with prediction of itinerant theory ~ aT1/2+b ~ aT1/2+bT R. Küchler, N. Oeschler, P. Gegenwart, T. Cichorek, K. Neumaier, O. Tegus, C. Geibel, J.A. Mydosh, F. Steglich, L. Zhu, Q. Si, Phys. Rev. Lett. 91, 066405 (2003)

  14. CeNi2Ge2: specific heat   for T  0 R. Küchler et al., PRL 91, 066405 (2003). T. Cichorek et al., Acta. Phys. Pol. B34, 371 (2003).

  15. CeNi2Ge2: Grüneisen ratio critical components: cr=(T)−bT Ccr=C(T)−T cr = Vmol/T cr/Ccr • cr(T)~T−1/(z) • prediction:  = ½, z = 2  x = 1 • observations in accordance with itinerant scenario INS: no hints for 2D critical fluct. Remaining problem: QCP not identified (would require negative pressure) cr ~ 1/Txwith x=1 (−0.1 / +0.05)

  16. Cubic CeIn3-xSnx N.D. Mathur et al., Nature 394 (1998) • Increase of J by Sn substitution • Volume change subdominant • TN can be traced down to 20 mK ! CeIn3 R. Küchler, P. Gegenwart, J. Custers, O. Stockert, N. Caroca-Canales, C. Geibel, J. Sereni, F. Steglich, PRL 96, 256403 (2006)

  17. CeIn3-xSnx • Thermodynamics in accordance with 3D-SDW scenario • Electrical resistivity: (T) = 0+ A’T, however: large 0 ! R. Küchler, P. Gegenwart, J. Custers, O. Stockert, N. Caroca-Canales, C. Geibel, J. Sereni, F. Steglich, PRL 96, 256403 (2006)

  18. CeCu6-xMx C/T ~ log T (universal!) H.v. Löhneysen et al., PRL 1994, 1996 A. Rosch et al., PRL 1997 O. Stockert et al., PRL 1998 2D-SDW scenario ? • A. Schröder et al., Nature 2000 • E/T scaling in “(q,) • (q) ~ {T(q)}0.75 for all q • locally critical scenario could we disprove 2D-SDW scenario thermodynamically?

  19. CeCu6-xAgx QCP AF E.-W. Scheidt et al., Physica B 321, 133 (2002).

  20. CeCu5.8Ag0.2 R. Küchler, P. Gegenwart, K. Heuser, E.-W. Scheidt, G.R. Stewart and F. Steglich, Phys. Rev. Lett. 93, 096402 (2004).

  21. CeCu5.8Ag0.2 Incompatible with itinerant scenario! R. Küchler et al., Phys. Rev. Lett. 93, 096402 (2004)

  22. YbRh2Si2: a clean system very close to a QCP P. Gegenwart et al., PRL 89, 056402 (2002).

  23. YbRh2(Si0.95Ge0.05)2 =Bc C/T ~ T-1/3 0(b) J. Custers et al., Nature 424, 524 (2003)

  24. Stronger than logarithmic mass divergence T NFL 1 AF FL  2 • stronger than logarithmic mass divergence incompatible with itinerant theory • T/b scaling 0 YbRh2(Si.95Ge.05)2 ~b1/3 b= J. Custers et al., Nature 424, 524 (2003)

  25. Thermal expansion and Grüneisen ratio R. Küchler et al., PRL 91, 066405 (2003) Prediction: cr(T) ~ T−1/(z) (L. Zhu, M. Garst, A. Rosch, Q. Si, PRL 2003)  = ½, z=2 (AF)  x = 1  = ½, z=3 (FM)  x = ⅔

  26. AF and FM critical fluctuations B // c P. Gegenwart, J. Custers, Y. Tokiwa, C. Geibel, F. Steglich, Phys. Rev. Lett. 94, 076402 (2005).

  27. Pauli-susceptibility P. Gegenwart et al., PRL 2005

  28. 29Si – NMR on YbRh2Si2 K. Ishida et al. Phys. Rev. Lett 89, 107202 (2002): Knight shift K ~ ’(q=0) ~ bulk Saturation in FL state at B > Bc Spin-lattice relaxation rate 1/T1T ~ q-average of ’’(q,) At B > 0.15 T: Koringa –relation S  1/T1TK2 holds with dominating q=0 fluct. B  0.15 T: disparate behavior  Competing AF (q0) and FM (q=0) fluctuations  ’’(q,) has a two component spectrum

  29. Comparison: YbRh2Si2vs CeCu5.9Au0.1 q CeCu5.9Au0.1 q Q q YbRh2Si2 q 0 Q Spin-Ising symmetry Easy-plane symmetry YRS AF and FM quantum critical fluct.

  30. Hall effect evolution P. Coleman, C. Pépin, Q. Si, R. Ramazashvili, J. Phys. Condes. Matter 13 R723 (2001). S. Paschen et al., Nature 432 (2004) 881: Large change of H though tiny ordered! SDW: continuous evolution of H

  31. Thermodynamic evidence for multiple energy scales at QCP Fermi surface change  clear signatures in thermodynamics Multipleenergy scales at QCP P. Gegenwart et al., cond-mat/0604571.

  32. Conclusions of part 1 • There exist HF systems which display itinerant (conventional) quantum critical behavior: CeNi2Ge2, CeIn3-xSnx, … YbRh2Si2: incompatible with itinerant scenario: • Stronger than logarithmic mass divergence • Grüneisen ratio divergence ~ T0.7 • Hall effect change • Multiple energy scales vanish at quantum critical point QC fluctuations have a very strong FM component: • Divergence of bulk susceptibility • Highly enhanced SW ratio, small Korringa ratio, A/02scaling • Relation to spin anisotropy (easy-plane)?

  33. Metallic ferromagnetic QCPs ? Itinerant ferromagnets: QPT becomes generically first-order at low-T Experiments on ZrZn2, MnSi, UGe2, … M. Uhlarz, C. Pfleiderer, S.M. Hayden, PRL ´04 D. Belitz and T.R. Kirkpatrick, PRL ´99 • New route towards FM quantum criticality: metamagnetic QC(E)P e.g. in URu2Si2, Sr3Ru2O7, … • What happens if disorder broadens the first-order QPT?

  34. Layered perovskite ruthenates Srn+1RunO3n+1 n=1: unconventional superconductor n=2: strongly enhanced paramagnet (SWR = 10) metamagnetic transition! n=3: itinerant el. Ferromagnet (Tc = 105 K) n=: itinerant el. Ferromagnet (Tc = 160 K)

  35. 1 4 0 0 1 2 0 0 ] K m 1 0 0 0 [ e r u 8 0 0 t a r QCEP @ 8 T // c-axis e p 6 0 0 m e T 4 0 0 8 2 0 0 ] 7 a l s 0 e t 0 [ 6 2 0 d l e 4 0 a i n F g l 6 0 e f r o 5 m 8 0 a b [ d e 1 0 0 g r e e s ] Field angle phase diagram on “second-generation” samples(RRR ~ 80) S.A. Grigera et al. PRB 67, 214427 (2003) Evidence for QC fluctuations: Diverging A(H) at Hc (S.A. Grigera et al, Science 2001)

  36. Thermal expansion Calculation for itinerant metamagnetic QCEP P. Gegenwart, F. Weickert, M. Garst, R.S. Perry, Y. Maeno,Phys. Rev. Lett. 96, 136402 (2006)

  37. Behavior consistent with 2D QCEP scenario P. Gegenwart, F. Weickert, M. Garst, R.S. Perry, Y. Maeno, Phys. Rev. Lett. 96, 136402 (2006)

  38. Thermal expansion on Sr3Ru2O7 Compatible with underlying2D QCEP at Hc = 7.85 T =0 marks accumulation points of entropy

  39. Fine-structure near 8 Tesla 0.2 0.4 0.5 0.7 0.8 1.0 1.1 1.3 Dominant elastic scattering  Formation of domains! T (K) 2.1 0.1 0.3 r(mWcm) 1.6 0.6 0.9 1.2 1.2 6.5 7.0 7.5 8.0 8.5 9.0 B (T) S.A. Grigera, P. Gegenwart, R.A. Borzi, F. Weickert, A.J. Schofield, R.S. Perry, T. Tayama, T. Sakakibara, Y. Maeno, A.G. Green and A.P. Mackenzie, SCIENCE 306 (2004), 1154.

  40. Thermodynamic analysis of fine-structure • No clear phase transitions • Signatures of quantum criticality survive in QC regime • also: 1/(T1T)~1/T @7.9T down to 0.3K!! (Ishida group) • 3) First-order transitions haveslopes pointing away from bounded state • Clausius-Clapyeron: • Enhanced entropy in bounded regime!

  41. Conclusion Sr3Ru2O7 liquid two-phase gas • Quantum criticality in accordance with itinerant scenario for metamagentic quantum critical end point (d=2) • Fine-structure close to 8 Tesla due to domain formation • Formation of symmetry-broken phase (Pomeranchuk instability)? Unlikely because of enhanced entropy • Real-spacephase separation?(C. Honerkamp, PRB 2005)

  42. QCEP Smeared Ferromagnetic Quantum Phase Transition Theoretical prediction: FM QPT generically first order at T = 0 [D. Belitz et al, PRL 1999] Sharp QPT can be destroyed by disorder exponential tail [T. Vojta, PRL 2003] [M. Uhlarz et al, PRL 2004 ]

  43. Ce Pd,Rh c The Alloy CePd1-xRhx • Orthorhombic CrB structure • CePd is ferromagnetic with TC = 6.6 K • CeRh has an intermediate valent ground state • High T measurements suggested quantum critical point (dotted red line) • Detailed low T investigation: tail

  44. AC Susceptibility in the Tail Region Crossover transition for x > 0.6 indicated by sharp cusps in cAC‘ down to mK temperatures Frequency dependence at low frequencies and high sensitivity on tiny magnetic DC fields no long range order c‘(T) in DC field Maxima of c‘(T) in phase diagram

  45. Spin Glass-like Behavior • Frequency shift (e.g. x=0.85: DTC/[TCD log(n)] of 5%) • Spin glass-like behavior No maximum in specific heat but NFL behavior for x ≥ 0.85

  46. Grüneisen parameter shows no divergence

  47. ”Kondo Cluster Glass“ • Strong increase of TK for x ≥ 0.6 indicated by Weiss temperature qP, evolution of entropy and lattice parameters Possible reason for spin glass-like state: Variation of TK for Ce ions depending on Rh or Pd nearest neighbors leading distribution of local Kondo temperatures ”Kondo cluster glass“

  48. Conclusion & Outlook • Classification of different types of QCPs in HF systems (conventionalvsunconventional) • Importance of frustration in the spin interaction? • Role of disorder? – e.g.: smearing of sharp 1st order trans.

More Related