Investigating the mechanism of High Temperature Superconductivity by Oxygen Isotope Substitution Eran Amit Amit Keren Technion- Israel Institute of Technology
Doping Meisner CuO 2 Spin Glass Magnetic Field Vortices Pseudo gap AFM Phonons Superconductivity How can we study a complex system? Apply a perturbation and check what happens.
Outline: Cuprates- a complicated system... What is the source of critical doping variations? CLBLCO NMR Results Conclusions Oxygen Isotope Effect on the Néel temperature. The Isotope Effect µsr Results Conclusions CLBLCO: is it all about disorder? Impurities in CLBLCO
Cuprates http://www.fis.unipr.it/~derenzi S. Chakravarty et al. PRB 63, 094503 Lee, Nagaosa, and Wen, Rev. Mod. Phys 78, 17 (2006)
The CLBLCO Compound (Ca x La 1-x )(Ba 1.75-x La 0.25+x )Cu 3 O y y controls the total charge (doping). x controls the charge location. The total cation charge does not change with x. There s a 30% difference in T C max between the families. Critical Doping levels x=0.1 (black) O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5
The CLBLCO Compound T C, T g, T N [K] 400 300 200 80 60 40 20 0 6.4 6.6 6.8 7.0 7.2 y Stretching each family data by a factor of K(x) creates identical critical doping levels. Is there a physical explanation? R.Ofer et al. PRB 74, 220508 (2006)
Previous Results- CLBLCO XAS- Cu XAS- O Cu NMR BVS calculations - Cu S. Sanna et al. EPL 86, 67007 (2009) O. Chmaissem, Y. Eckstein and C. G. Kuper, PRB 63, 174510 (2001) A. Keren, A. Kanigel and G.Bazalitsky, PRB 74, 172506 (2006)
The Experimental Method Oxygen 17 NMR 17 O nucleus has a quadrupole moment. It is sensitive to both electric and magnetic field distributions. H=H Zeeman +H Quadrupole (EFG) In the doping process holes are induced in the planar oxygen orbitals. 17 O has a relatively small spectral width.
The Enrichment System The Enrichment process: Samples are put in the furnace. The furnace is sealed and vacuumed. Gas containing the desired isotope - either 18 O or 17 O - is released into the tube with the sample. The furnace is heated to allow the isotope to diffuse into the sample. Isotope 16 O 17 O 18 O Natural abundance 99.76% 0.038% 0.21%
Nuclear Quadrupole Resonance E E θ ν Q
Nuclear Quadrupole Resonance E E θ ν Q The Quadrupole Frequency measures the Charge Distribution around the nucleus
Nuclear Magnetic Resonance E I 5 2 Zeeman E Quadrupole E H 0 h h HZeeman H H I 0 1 HQuadrupole 1 3I I I I 2 2 2 2 6 Q z x y NMR Spectrum: Q
17 O NMR of CLBLCO- Raw Data 3 2 1 2 1 3 The parameters x and y change the quadrupole frequency
17 O NMR of CLBLCO The contributions to the planar oxygen ν Q : 1. Holes in the oxygen 2p σ orbital O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5 2. Holes in copper orbitals 3. Surrounding atoms (La, Ba, Ca) Planar oxygen in CLBLCO We compare samples with different doping levels. ν Q measures the number of planar oxygen 2p σ holes J. Haase et al. PRB 69, 094504 (2004)
17 O NMR of CLBLCO
Results O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5 The ratio between the slopes is equal to K(x=0.1) over K(x=0.4) Eran Amit and Amit Keren PRB 82, 172509 (2010)
Results O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5 y N For y<y N the number of planar O 2p σ holes does not change y
Results O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5 The critical doping values are global and depend only on the number of 2p σ holes created by doping. y
CLBLCO Scaling Scaling: Dividing by T c max (x) Replacing T N with J The CLBLCO phase diagram is scaled with no adjustable parameter. The maximum T C is defined by the AFM coupling J
Summary: Critical doping variations We compared the number of 2p σ holes of CLBLCO samples with different x and y values using 17 O NMR. The critical doping values are global and depend only on the number of 2p σ holes created by doping. The CLBLCO phase diagram (with T C max difference of 30%) is scaled with no adjustable parameter. The maximum T C is defined by the AFM coupling J. Eran Amit and Amit Keren PRB 82, 172509 (2010)
The Isotope Effect THE main facts which a theory of superconductivity must explain are (1) a second-order phase transition at the critical temperature, T c, (5) the dependence of T c on isotopic mass, T c M=const. We present here a theory which accounts for all of these J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Phys. Rev. 108, 1175 1204 (1957). The Isotope Effect was one of the key experimental findings in the path to understanding conventional superconductivity
The Isotope Definition The Isotope Effect is the change in the critical temperature due to isotopic substitution: dlnt q dm T q m For a small effect: T T q q m m T q - the critical temperature. m - the element s mass. Δ the change caused by substitution.
IE in conventional SC The IE: Tq m For most conventional superconductors as explained by BCS theory: 0.5, 1 N(0) V e 1.13. The Cooper pairs are phonons mediated. TC Spring frequency: K m C. A. Reynolds et al., Phys. Rev. 84, 691 (1951)
Isotope Effect in Cuprates Bi 2 Sr 2 CaCu 2 O 8+δ Y 0.8 Ca 0.2 Ba 2 Cu 3 O 7 Y 0.84 Ca 0.16 Ba 2 Cu 3 O 7 Y 0.84 Ca 0.16 Ba 2 Cu 3 O 6 Y 1-y Pr y Ba 2 Cu 3 O 7 Y(Ba 1-y La y ) 2 Cu 3 O 7 YBa 2 (Cu 1-x Co x ) 3 O 7 YBa 2 Cu 3 O 7 YBa 2 Cu 4 O 8 Bi 2 Sr 2 CaCu 2 O 8+δ Y 1-y Ca y Ba 2 Cu 4 O 8 Y 0.8-y Pr 0.2 Ca y Ba 2 Cu 3 O 7 holes Why is there IE in Cuprates? D. J. Pringle et al., Phys. Rev. B 62, 12527 (2000)
IE in Cuprates: Theories Phonons BCS (1957), A. Bill (1996). Zero point motion D. S. Fisher (1988). T C N(0) V 1 * e * 1.13 EF 1 ln Polarons R. Khasanov (2008). Normal doping V. Z. Kresin (1994). t changes: m * e A m e Superfluid density M. Serbyn (2010). Exploring the AFM phase may improve our understanding of the SC phase.
CLBLCO advantage More accurate measurements can be performed. TN const y T N 1 Why is (Ca 0.1 La 0.9 )(Ba 1.65 La 0.35 )Cu 3 O y ideal for this experiment? R. Ofer et al., Phys. Rev. B 74, 220508(R) (2006)
Muon Spin Rotation Muon- A Lepton with a mass of 105.7 MeV, The charge is identical to a positron (or an electron). Spin-½, Life time-2.2 micro-seconds. Gyromagnetic ratio- 135.5*10 6 Hz/T. Decays into a positron (+ neutrino and anti-neutrino). The direction of the emitted positron: Muon spin Positron
Muon Spin Rotation A beam of polarized muons hits the sample. Each muon rotates and decays into a positron. Muon spin Positron
Muon Spin Rotation t P n P m a 1 2 Time Normal fraction Magnetic fraction Normal decay (t 2 ) 2 3 Normal decay Magnetic decay Non-magnetic phase (high T) Magnetic phase (low T) Oscillations at the Larmor frequency ω The muons polarization is: P t P e P ae a e cos t t 1t 2t ( ) ( (1 ) ( )) z n m
Choosing Order Parameter P n P m Larmor Frequency Normal fraction Magnetic fraction In order to increase the sensitivity we defined a new order parameter: Pinf P( T ) OP ( T ) P P(0) inf P t P e P ae a e cos t t 1t 2t ( ) ( (1 ) ( )) z n m
Results OP ( T ) Pinf P( T ) P P(0) inf P t P e P ae a e cos t t 1t 2t ( ) ( (1 ) ( )) z n m
Results There is no IE on T N : N 0.005 0.011 TN m N T N OP ( T ) Pinf P( T ) P P(0) inf P t P e P ae a e cos t t 1t 2t ( ) ( (1 ) ( )) z n m
OIE in Cuprates Temperature But maybe its because we should use the physical parameter The oxygen isotope effect changes with sample s doping: In the SC phase α>0; In the AFM phase α<0 In the SC phase Δn<0; In the AFM phase Δn<0 Holes x [a.u.] R. Khasanov et al., PRL 101, 077001 (2008) A change of about 1% in the number of planar holes between the isotopes may explain the effect.
Summary: The Isotope Effect in Cuprates We compared the Néel temperature of samples with 16 O and 18 O using µsr. The isotope coefficient was found to be 0.005 0.011 Isotope substitution does not change the magnetic excitations. The isotope effect in cuprates can be explained by a change in the doping efficiency. In order to use isotope experiments to understand the mechanism of superconductivity, precise measurements should be performed on materials where T C does not depend on doping. N
Impurities in CLBLCO (Ca x La 1-x )(Ba 1.75-x La 0.25+x )Cu 3 O y y controls the total charge (doping). x controls the charge location. The total cation charge does not change with x. There s a 30% difference in T C max between the families. Could it be that it's all about impurities? O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5
17 O NMR of CLBLCO (Ca x La 1-x )(Ba 1.75-x La 0.25+x )Cu 3 O y There are three oxygen cites in CLBLCO: Planar oxygen- O 2,3 Bridging oxygen- O 1 Chain oxygen- O 4 - has a wider peak O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5 The widths of NMR signals are similar for all families. E. Oldfield et al., Phys. Rev. B 40, 6842 (1989)
Quadrupole frequency as inhomogeneity measurement Ratio of peaks width Charge inhomogeneity The quadrupole frequency distribution The widths of NMR signals are similar for all families.
Quadrupole frequency as inhomogeneity measurement NMR does not show any difference in crystal quality of the different CLBLCO families. Impurities cannot explain the big difference in T c max of the families. O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5
Summary: Small Effects in the Cuprates Phase Diagram Charge Distribution Meisner Hole Density Isotopic Mass Magnetic Field Vortices AFM Phonons Pseudo gap Superconductivity The hole effect can be misinterpreted as some more exotic mechanism
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Copper Measurements http://www.chemcomp.com It is very difficult to distinguish between the different contributions. Planar Oxygen Planar Copper Cu O 3d x y 2p Cu 3d z 2 O Cu II Cu 2p z 4s 2 2 O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25 )
17 O NMR of CLBLCO Comparing samples of different families: The typical length changes, but the symmetries of the electronic wavefunctions do not change. O Cu (Ca x La 1-x ) (Ba 1.75-x La 0.25+x ) 0.5 x=0.4 x=0.1 a 0.1 Planar oxygen in CLBLCO a 0.4 a 0.4 Ca n 3 Q x p Cu O 3d x y 2p 2 2 ν Q measures the number of planar oxygen 2p σ holes
The NMR Field Sweep Method We measure at a constant frequency and change the external magnetic field. For each field we integrate the real part of the spectrum. The theoretical line is: 5 2 1 1 iso Q iso Q 2 2 2 iso Q iso Q 3 m 0 0 2, S H f W m d e d e 2 iso Q cos d d f H, m,,,,,, f 0 0 1 2 1 2 1 f H, m,, Q,,, H 1 iso q 3cos 1 sin cos 2 m 2 2 2 2 where S(H,f) is the intensity at external field H and frequency f.