The cuprate phase diagram: insights from neutron scattering and electrical transport. Mun Chan University of Minnesota, Minneapolis

Transcription

1 The cuprate phase diagram: insights from neutron scattering and electrical transport Mun Chan University of Minnesota, Minneapolis

2 Acknowledgements Martin Greven, University of Minnesota CRYSTAL GROWTH C. Dorow, M. Veit, Y. Ge (UMN); X. Zhao (Jilin U., China) ELECTRICAL TRANSPORT N. Barišić (CEA-Saclay, France, Vienna University of Technology, Austria) W. Tabis, M. Veit,Y. Li (UMN) C. Proust (Toulouse, France) NEUTRON SCATTERING Y. Tang, C. Dorow, M. Veit (UMN) L. Mangin-Thro, Y. Sidis, P. Bourges (LLB, CEA-Saclay, France) D. L. Abernathy, A. D. Christianson (ORNL, USA) P. Steffens (ILL, Grenoble, France) J.T. Park (FRM-II, Garching, Germany)

3 Cuprate phase diagram Generic T* strange-metal pseudogap A F superconductor T c Fermi liquid o Insulating parent compound: localized spins with antiferromagnetic order o Fermi-liquid at very high doping

4 Structural transitions and competing phases o Why is high-t c a hard problem (experimentally)? Disorder (e.g. Sr substitution) and structural transitions Other ordering tendencies: Universal? Integral? tetragonal La x Sr 2-x CuO 4 (LSCO) ê orthorhombic strange-metal pseudogap A F ½ ½ Fermi liquid stripe 1 / stripe 2

5 The most studied cuprates courtesy Guichuan Yu CuO chains 2 x CuO 2 planes orthorhombic T max c = 93 K No chains 1 x CuO 2 plane orthorhombic T max c = 40 K No CuO 2 chains 1 x CuO layer tetragonal T c max = 98 K (the highest of the single- layered cuprates)

6 The most studied cuprates courtesy Guichuan Yu Hg1201 LSCO LBCO : La 2- x Ba x CuO 4

7 Part 1: electrical transport Mike Veit (senior, UMN) LNCMI- Toulouse, France BapRste Vignolle, Cyril Proust Vienna University of Technology, Austria N. Barišić Na>onal High Magne>c Field Lab Tallahassee and Los Alamos A. Sheckter R. McDonald cleaved crystals 1 mm Au pads+ag paste contacted and ready for pulse field 1 mm

8 Resistivity (strange-metal) o T- linear resistivity to very high temperatures N. J. Hussey Phys.: Condens. Matter. (2008) Y. Ando et al., PRL (2004)

9 Magnetoresistance and Kohler s rule MagneRc field Scaaering rate ResisRvity H ch 1 τ c 1 τ ρ cρ ρ(h ) ρ 0 ρ 0 = δρ " = F H % $ ' ρ 0 # ρ 0 & Indium with different impurity levels at the same temperature o Contingent on: - Only the amount of scattering changes - Single scattering mechanism - Constant number of carriers δr R 0 Kohler plot H R 0 J. L. Olsen Electron transport in metals (1962)

10 Violation of Kohler s rule o Violation of Boltzmann kinetics T* = 200 K YBCO T c = 90 K YBCO T c = 60 K Kohler plot M. Harris et al. PRL (1995)

11 Explanations for unconventional transport o Charge-spin separation (P. W. Anderson, Phys. Rev. Lett. 67, 2092 (1991)) o Anisotropic Umklapp scattering (N. E. Hussey et al. PRL (1996)) o Coupling to a bosonic mode - Spin fluctuations (P. Monthoux and D. Pines, PRB (1994)) - Charge fluctuations (C. Castellani et al. PRL (1995))

12 Electrical transport in the pseudogap o Electrical transport is ill-defined in the pseudogap phase o Fluctuations of superconductivity or nearby ordered states T c =80 K p ~ 0.11 T (K) ρ/ρ(400k) T c ~ 80 K T* ~ 29 0 K ~ ρ (mωcm) T ~91 ~ K T* *~ ~ 170 K 2 4 T 2 (10 4 K 2 ) T ~ 91 K dρ/dt 2 N. J. Hussey Phys.: Condens. Matter. (2008) 0 T** ~ 170 K T 2 (10 4 K 2 ) N. Barišić, MKC et al. PNAS (2013)

13 Electrical transport in the pseudogap o Clear separation of a linear and quadratic regimes ρ = AT n n Boltzmann kinetics? M.K. Chan et al. unpublished

14 Magnetoresistance o Clear separation of a linear and quadratic regimes p = 0.91; T c = 70 K ρ = AT n n Boltzmann kinetics? M.K. Chan et al. unpublished

15 Validity of Kohler s rule o Pulsed field measurements at LCNMI-Toulouse. 30 T. j // ab; H//c o δρ/ρ 0 =a H 2 T c = 70 K M.K. Chan et al. arxiv:

16 Validity of Kohler s rule o Pulsed field measurements at LCNMI-Toulouse. 30 T. j // ab; H//c o δρ/ρ 0 =a H 2 o Kohler s rule is valid in the pseudogap T c = 70 K M.K. Chan et al. arxiv:

17 Doping dependence of Kohler s rule o In-house measurements : H = 9 Tesla o Kohler s rule valid throughout pseudogap n regime where ρ ~ T 2 o Kohler s rule broken in the strange-metal regime: ρ ~ T 1

18 Temperature dependence of MR a, a orb (T 2 ) a (T -1 ) (a) δρ ( Hτ ) 2 T 4 ρ 0 δρ = a! H 2 ρ 0 HgUD70a HgUD70b HgUD81 T** T** T* a orb (T 2 ) T (K) ρ a (mω.cm) (b) YBCO6.5 YBCO6.6 T** T (K) (c) YBCO6.5 YBCO T 2 (K 2 )

19 Temperature dependence of MR a, a orb (T 2 ) a (T -1 ) (a) δρ ρ 0 Hτ δρ = a! H 2 ρ 0 HgUD70a HgUD70b HgUD81 ( ) 2 T 4 + ρ ( 1 τ ) T 2 T** T** T* a orb (T 2 ) T (K) ρ a (mω.cm) (b) YBCO6.5 YBCO6.6 T** T (K) (c) YBCO6.5 YBCO T 2 (K 2 ) = Kohler s rule

20 Implications ρ = AT n n T* T** o Only one Fermi-liquid-like scattering rate o Constant carrier density o Stable Fermi surface between T c and T**

21 Implications pseudogap superconducting ρ = AT n n T* T** A. Kanigel et al. Nat. Phys (2006) o Pseudogap is not fluctuarng superconducrvity o Stable Fermi arc in the pseudogap supported by more recent ARPES results in oprmally doped Bi- compounds: T. Kondo et al. PRL (2013)

22 The case of YBCO 1- D CuO chains chain CuO 2 planes // chain Adapted from Y. Ando et al. PRL (2002) o CuO chains contribute to the electrical transport : measurements in twinned crystals naturally violate Kohler s rule o Chains shouldn t contribute to the electrical transport transverse to them

23 Transport perpendicular to CuO chains ρ 1 τ T 2 δρ ρ 0 τ 2 T 4 Kohler s rule valid T c = 56 K T c = 56 K T c = 62 K T c = 62 K a (T -1 ) Adapted from Y. Ando et al. PRL (2002)

24 Transport perpendicular to CuO chains ρ 1 τ = b + ct 2 δρ ρ 0 τ 2 = 1 ( b + ct 2 ) 2 Kohler s rule not valid T c = 56 K T c = 56 K T c = 62 K T c = 62 K a (T -1 ) Adapted from Y. Ando et al. PRL (2002)

25 Magnetic phase diagram and residual resistivity o 3D AF! incommensurate SDW D. Haug et al. New Jour. of Phys. (2010 ) Y 2 Ba 3 CuO 6+y Y. Ando et al. PRL (2002) Y 2 Ba 3 CuO 6+y p=0.1 SDW D. LeBoeuf et al. PRB (2011)

26 Magnetic phase diagram and residual resistivity o 3D AF! diagonal incommensurate!parallel incommensurate Local moment physics K. Yamada et al. PRB (1998) M. Kofu et al. PRL (2009) B=0 T B=60 T o Large residual resistivity is an indicator of carrier localization at low temperatures and quasielastic magnetic ordering G. S. Boebinger et al. PRL (1996)

27 Magnetic phase diagram and residual resistivity o 3D AF! diagonal incommensurate!parallel incommensurate Hg1201 p = Local moment physics K. Yamada et al. PRB (1998) M. Kofu et al. PRL (2009) o p MI (LSCO).17 o p MI (YBCO).10 o p MI (Hg1201) < o Quantum oscillations in p=0.09 (N. Barišić et al. Nature Phys. (2013))

28 Part 2: Inelastic Neutron scattering

29 Part 2: Inelastic Neutron scattering LLB, CEA-Saclay, France Philippe Bourges Yvan Sidis Lucille Mangin- Thro FRM-II, Garching, Germany Jitae Park Yang Tang (UMN) ILL, Grenoble, France Paul Steffens ORNL, Oakridge Andrew ChrisRanson ORNL, Oakridge Doug Abernathy

30 Magnetic phase diagram o 3D AF! diagonal incommensurate!parallel incommensurate K (rlu) K (rlu) Local moment physics K (rlu) é (½, ½) H (rlu) O.J. Lipscombe et. al, PRL (2009)

31 Magnetic phase diagram o 3D AF! diagonal incommensurate!parallel incommensurate STRIPES J. M. Tranquada et al. Nature (2004) Local moment physics Stripe- ordered La 5/3 Sr 1/3 CoO 4 δ (rlu) A. T. Boothroyd et al. Nature (2011)

32 Magnetic phase diagram o 3D AF! diagonal incommensurate!parallel incommensurate o 3D AF! anisotropic incommensurate!? Y 2 Ba 3 CuO 6+y FluctuaRng stripes? M. Fujita et al. Physica C (2012)

33 Preparing a neutron sample Hg1201 T* superconducrvity Each neutron sample: o ~ 40 growths o ~30 crystals, ranging from 20 mg 100 mg each o 2 3 months anneal o 2 g total mass

34 Antiferromagnetic Fluctuations energy d! σ dωde = 2(γr!)! k! πg!!! F(!)! k! χ!! (!, ω)! 1 exp!( ω/k! T) 53 mev F(!) = Form!Factor!!!!!"#!(!!/!!!)!=!Bose!factor! H ½ K!χ!!!, ω = Imaginary!magnetic!!!!!!!!!!!!!!!!!!!!!!!!!!!susceptibility! k i,!k f!=!incident!and!final!momenta!

35 Antiferromagnetic Fluctuations energy d! σ dωde = 2(γr!)! k! πg!!! F(!)! k! χ!! (!, ω)! 1 exp!( ω/k! T) 53 mev F(!) = Form!Factor!!!!!"#!(!!/!!!)!=!Bose!factor!!χ!!!, ω = Imaginary!magnetic!!!!!!!!!!!!!!!!!!!!!!!!!!!susceptibility! k i,!k f!=!incident!and!final!momenta! ½ H Convert to susceprbility K

36 Antiferromagnetic spectrum energy ½ K H

37 Antiferromagnetic spectrum o Constant energy images: reveals the Q-structure: commensurate at low energies, ring-like at high energies T << T c [110] [100] energy 53 mev ½ K H

38 Antiferromagnetic spectrum o Constant energy images: reveals the Q-structure: commensurate at low energies, ring-like at high energies T << T c [110] [100] energy ½ K H M.K. Chan et al. arxiv:

39 Antiferromagnetic spectrum o Constant energy images: reveals the Q-structure: commensurate at low energies, ring-like at high energies T << T c [110] [100] M.K. Chan et al. arxiv:

40 Antiferromagnetic spectrum o Y - shaped dispersion with 27 mev gap M.K. Chan et al. arxiv: M. Fujita et al. Physica C (2012)

41 Compare to LSCO o Gaped vs ungaped o Low energy commensurate vs incommensurate dispersion o Stripe correlations, if present would have to be very weak FWHM O. J. Lipscombe, et al. PRL (2009)

42 Doping dependence T c = 55 K; p T c = 71 K; p T c = 88 K; p T = 5 K M. K. Chan et al. unpublished

43 Doping dependence T c = 55 K; p T c = 71 K; p T c = 88 K; p T = 5 K UD55 UD71 UD88 5 K o Magnetic weight decreases with increasing doping M. K. Chan et al. unpublished

44 What is the magnetic phase diagram? Stripe 1 / Stripe 2 T* UD55 UD71 UD88 5 K SuperconducRvity Onset Hg1201 YBCO SDW LSCO P. Bourges Physica B (1995); M. Kofu et al. PRL (1999); D. Haug et al. New Jour. of Phys. (2010 )

45 No static magnetism PANDA: FRMII T c = 45 K 3 K 300 K 0.1 μ B2 /Cu 2+ o No commensurate or diagonal elastic response of the same size as in LSCO or YBCO

46 Neutron: Conclusion 1 o Low energy commensurate fluctuations: weak or absent stripe correlations o No static local magnetism in the most underdoped Hg1201 sample studied (p = 0.058

47 Change across T* (pseudogap) T c = 55 K; p T c = 71 K; p T c = 88 K; p T = 5 K T > T* 410 K 350 K 250 K

48 Onset of AF fluctuations T c = 55 K; p T c T* 42 mev 5K 70 K 410 K T c = 71 K; p K 220 K 350 K 70 K

49 Onset of AF fluctuations T c = 55 K; p T c T* 42 mev 5K 70 K 410 K T c = 71 K; p K 220 K 350 K 70 K Y. Li. et al. PRB (2011)

50 Neutron: Conclusion 2 o Low energy commensurate fluctuations: weak or absent stripe correlations o No static local magnetism in the most underdoped Hg1201 sample studied (p = 0.058) : supported by resonance and a spin gap o Majority of fluctuation weight onsets at the pseudogap temperature T*

51 Conclusions Hg1201: highest Tc, lower disorder, simple tetragonal structure ρ = AT n n Pseudogap characterized by: o Fermi-liquid like electrical transport with a largely stable Fermi-surface (w.r.t. temperature) o Onset of commensurate magnetic fluctuations o No incommensurate AF ordering B. Fauqué et al. PRL (2006) Y. Li. et al. PRB (2011) N. Barišić, MKC et al. PNAS (2013) q=0 loop current order

52 Cuprate phase diagram controlled by AF fluctuations ρ = AT n n W. Tabis et al. arxiv: Short- ranged CDW observed in Hg1201 Ghiringhelli et al., Science (2012) Chang et al., Nature Phys. (2012)

53 Cuprate phase diagram controlled by AF fluctuations ρ = AT n n Y. Wang & A. Chubukov arxiv: M. A. Metlitski & S. Sachdev, PRB (2010). o Recent and old theorercal proposals based on spin fluctuarons o the hot spots (connected by q AF ) near the anr- nodes o Nodal quasiparrcles are Fermi- liquid like