Common energy scale for magnetism and superconductivity in the - PowerPoint PPT Presentation

Common energy scale for magnetism and superconductivity in the cuprates. Amit Kanigel Amit Keren Collaborators A. Knizhnik -Technion J. Lord-ISIS A. Amato-PSI

Phase diagram of the cuprates • Above some doping level superconductivity emerges. • The undoped materials are antiferromagnetic Mott insulators. •At these doping levels, even the “normal” state is not normal. • As doping increases, T N decreases, very fast. • Superconductivity (SC) in these materials seems to be very different from SC in metallic superconductors. T N Temperature T C AFM SC Holes density

Normal state correlations • Even above Tc the system is not a Fermi liquid (Pseudo gap). • AFM excitations/correlations even at optimal doping (Spin gap). T * T N Temperature T 0 T C AFM SC Holes density

Spin - Glass phase • At intermediate doping levels a spin-glass phase can be found. • It was identified using NQR and m SR. T * T N Temperature T 0 T C T G AFM SC SG Holes density

Motivation • Despite the AFM Correlations there is NO EXPERIMENTAL EVIDENCE for a connection between AFM and superconductivity. • The place to look for correlations between MAGNETISM and SUPERCONDUCTIVITY is the spin-glass phase. T * T N Temperature T 0 T C T G AFM SC SG Holes density

The CLBLCO system ( Ca La )( Ba La ) Cu O    x 1 x 1 . 75 x 0 . 25 x 3 y CLBLCO was chosen due to its characteristics: (Ca x La 1-x )(Ba 1.75-x La 0.25+x )Cu 3 O y • 123 structure 80 X=0.1 X=0.2 • Overdoping is possible. X=0.3 60 X=0.4 • Doping is x- independent. T c (K) 40 20 0 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 y CLBLCO allows T c (or doping) to be kept constant and other parameters to be varied, with minimal structural changes.

Work plan • We plan to measure T g and T c for many CLBLCO samples, with different x and y values. • T g , the spin-glass transition temperature, will be measured by m SR. • We will look for correlations between these two transition temperatures.

Principles of m SR • 100% spin polarized muons. • m life time : 2.2 m sec. • Positron emitted in the spin direction. • Very sensitive to internal magnetic fields: 0.1G – 1T

m Principles of SR External Transverse Field (H) or 0 Forward Beam e + m Time Time Transverse Zero Field Field Time Time • Asymmetry = (F-B)  P z m (t).

m Raw ZF SR data • High T P z (t) is from nuclei. T c =33.1K 0.25 T(K)= 40.2 • Sudden change in P(t) well 7.4 0.20 below T c . 3.8 3.0 Asymmetry 0.15 • There are two contributions. 2.1 0.37 0.10 • One amplitude grows, the 0.05 other decreases. 0.00 • There is recovery to 1/3. 0 2 4 6 8 10 12 14 16 TIME ( m sec) • At base T, relaxation is over-dumped. To understand this spin glass phase lets examine the base T data.

m SR in Zero Applied Field: Static Case      2 2 ( , ) B cos sin cos( ) P t B t m z B B    z lo c cos P B m cos 2  sin 2  ( ) ( ) 1 2      2 On the average ( ) ( ) cos( ) . P t B B B t dB m z 3 3 If then . 2  (B)  (B)  B <B> B B We expect dumped oscillations in P z (t). 1  We expect lim P ( t ) .   t z 3

Demonstration 1.0 Theory 0.8 Gaussian  (B) Experiments 0.6 P z (t) 0.25 0.4 Spin Glass 0.20 Asymmetry 0.2 Fe 0.05 TiS2 T g =15.5K T=4K 0.0 0.15 0 2 4 6 8 0.16 TIME (a.u.) CLBLCO X=0.1 0.10 Asymmetry Tc=7.0K T=1.9 K 0.0 0.2 0.4 0.6 0.8 1.0 TIME ( m sec) 0.15 0 1 2 TIME ( m sec) • The peek in B 2  (B) corresponds to a dip in P z (t). • The position of the dip is determined by the width of  (B). • The recovery of P Z (t) is to 1/3.

The case of CLBLCO 2  (B) The situation B B T(K)= 0.37 K is not possible in CLBLCO since (over dumped). 1/3 2  (B) We must have . B B  B   2 ( ) 1 / . B 0 B Namely, as we must have There is an abnormal amount of sites with zero field.

Towards a model M SC SC M SC M • If there was a macroscopic phase with zero field, it would be seen as an increase in the tail , to a value larger than 1/3. • We can put an upper limit on size of such a phase.

M M M A model • The field from the magnetic phase penetrates into the superconducting regions. • The staggered moments decay on a very short S C length scale.

Numerical Simulations Muon polarization in a sample with random magnetic centers. S(0) S(0) m The position of S (0) is random.       r / a ( r ) ( 1 ) exp( r / ) B(r) . Muon-electron spin interaction is dipolar.

Simulation Results p = magnetic concentration 1.00 p=15% 4 0.75 3 0.50 P z (t) 0.25 2 0.00 0 2 4 6 8 10 12 14 Time( m sec) 1 2 (a.u.) (a) 0  (|B|)B 1.00 3 p=35% 0.75 P z (t) 0.50 2 0.25  0.00 1 0 2 4 6 8 10 12 14 Time( m sec) (b) <B> 0 0 50 100 150 200 B(Gauss) Dumped oscillations at high p . Over dumped oscillations at low p .

m Raw ZF SR data T(K)= 0.25 40.2 7.4 0.20 3.8 2.1 Asymmetry 0.37 0.15 0.10 0.05 0.00 Time( m sec)      A ( T , t ) A exp( t ) A P ( , t ). We fit the data to m n P  is determined at high T. ( , t )

Determination of T g 0.25 x=0.3 y=6.965 T c =21.7 0.20 y=6.994 T c =29.8 y=7.005 T c =37.4 0.15 A m 0.10 0.05 T g =3.2 5.5 8.0 0.00 0 5 10 15 20 T(K) • At low T the magnetic amplitude saturates. • The spin glass temperature T g is the T where A m =A m max /2.

vs. x and y in (Ca La )(Ba La )Cu O T g x 1 - x 1.75 - x 0.25 +x 3 y 12 11 10 9 8 7 T g (K) 6 5 4 3 x=0.1,0.2 2 x=0.3 x=0.4 1 0 6.93 6.94 6.95 6.96 6.97 6.98 6.99 7.00 7.01 7.02 y T g decreases as doping increases.

Scaling (Ca x La 1-x )(Ba 1.75-x La 0.25+x )Cu 3 O 6+y 1.0 80 X=0.1 X=0.2 0.8 60 X=0.3 X=0.4  max 0.6 max T T / T T c (K) 40 T c /T c C C C 0.4 20 0.2 0 0.0 6.8 6.9 7.0 7.1 7.2 7.3 6.8 6.9 7.0 7.1 7.2 7.3 y y 1.0 0.8   0.6 max y K x ( ) y T c /T c 0.4 0.2 0.0 -0.2 -0.1 0.0 0.1 0.2 K(x)*  y

12 0.16 X=0.3 X=0.2,0.1 11 X=0.4 10 0.14 9 0.12 8 max 7 0.10  T g (K) T g /T c 6 max T T / T 5 0.08 g g C 4 0.06 3 2 0.04 1 0 0.02 6.90 6.95 7.00 7.05 6.90 6.95 7.00 7.05 y y 0.16 0.14 0.12 max   0.10 T g /T c y K x ( ) y 0.08 0.06 0.04 0.02 -0.25 -0.20 -0.15 K(x)  y

Other compounds CLBLCO max =-0.15-2.5  p m c 15 T g /T x=0.1 -2 ) max (x10 For La 2-x Sr x CuO 4 x=0.2 x=0.3 x=0.4    10 p x 0.16. 1 T g /T c LSCO m YCBCO Bi-2212 5 2 LSCO YBCO (b) 0 (a) 1.0 0.8 max 0.6 T c /T c 0.4 Data from: 0.2 0.0 Niedermayer et. al. PRL ,80, 3843 (98). -0.15 -0.10 -0.05 0.00 0.05 0.10  p m = K(sample) ´ Doping Panagopoulos et. al. PRB, 66, 64501 (02). Sanna, unpublished.

Zn doping (Panagopoulos La 2-x Sr x Cu 1-y Zn y O 4 ) 0.5 12 y=0.02 y=0.02 0.4 10 y=0.01 y=0.01 y=0.00 y=0.00 8 0.3 T g 6 max T g /T c 0.2 4  max / T T T c c c  2 max T T / T 0.1 g g c   y K ( x ) y 0 0.05 0.10 0.15 0.20 p 0.0 1.0 50 y=0.02 0.8 40 y=0.01 y=0.00 max 0.6 30 T c /T c T c 0.4 20 0.2 10 0.0 0 -0.10 -0.05 0.00 0.05 0.10 0.05 0.10 0.15 0.20 0.25 K*  y p In this case the scaling transformation of T c does not apply for T g .

Single energy scale. Before Scaling • The vertical axis represents energy. • The horizontal axis represents density. After Scaling • The vertical axis is dimensionless. max • We scaled using a single energy scale, , both and . T T T C C g • Both the Magnetism and the Superconductivity are governed by the same energy scale.

Additional background before interpretation n • The Uemura relation:   s T c * m  • is common to all HTSC.

  m Penetration depth determination with transverse field m SR T c =77K 0.4 B (a) 0.2 0.0 m 1 m 2 -0.2 T=80K -0.4 B (b) -1  0.2 Asymmetry 0.0 -0.2 m 1 m 2 T=70K -0.4 B (c) -1  0.2 0.0 -0.2 T=10K m 1 m 2 -0.4 0 2 4 6 8 TIME ( m sec)

Uemura relations for the CLBLCO system • We determine the muon relaxation rate which is proportional to  2 . (Ca x La 1-x )(Ba 1.75-x La 0.25+x )Cu 3 O 6+y 80 70 60 50 x=0.1 T c (K) x=0.2 40 x=0.3 x=0.4 30 20 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 -1 )   -2  ( m sec Equal T c means also equal  and equal n s /m *

   • Using the London equation we know: 2 n s  • The results show that: T n C s • According to simple valence sums, the holes density in the CLBLCO system is independent of x (the Ca content). • We can have samples with equal Tc, but different doping. (Ca x La 1-x )(Ba 1.75-x La 0.25+x )Cu 3 O y 80 X=0.1 X=0.2 X=0.3 60 X=0.4 T c (K) 40 20 0 6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 y • Not all the doped holes contribute to the superfluid density! • This is the origin of the scaling factor K.