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

Holes density Temperature TN

• The undoped materials are antiferromagnetic Mott insulators.
• As doping increases, TN decreases, very fast.

AFM TC

• Above some doping level superconductivity emerges.
• At these doping levels, even the “normal” state is not normal.
• Superconductivity (SC) in these materials seems to be very

different from SC in metallic superconductors. SC

Normal state correlations

• Even above Tc the system is not a Fermi liquid (Pseudo gap).
• AFM excitations/correlations even at optimal doping (Spin gap).

Holes density Temperature TN TC T* T0 AFM SC

Glass phase

• Spin

Holes density Temperature TC TN TG

• At intermediate doping levels a spin-glass phase can be found.
• It was identified using NQR and mSR.

AFM SC SG T* T0

Motivation

Holes density Temperature TC TN TG

• 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. AFM SC SG T* T0

• 123 structure
• Overdoping is possible.
• Doping is x-independent.

6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 20 40 60 80 (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy

y

X=0.1 X=0.2 X=0.3 X=0.4 Tc(K)

The CLBLCO system

CLBLCO allows Tc (or doping) to be kept constant and other parameters to be varied, with minimal structural changes. CLBLCO was chosen due to its characteristics:

y x x x x

O Cu La Ba La Ca

3 25 . 75 . 1 1

) )( (

  

Work plan

• We plan to measure Tg and T c for many CLBLCO

samples, with different x and y values.

• Tg , the spin-glass transition temperature, will be

measured by mSR.

• We will look for correlations between these two

transition temperatures.

Principles of mSR

• 100% spin polarized muons.
• m life time : 2.2msec.
• Positron emitted in the

spin direction.

• Very sensitive to internal

magnetic fields: 0.1G – 1T

• Asymmetry = (F-B) Pz

m(t).

Beam Forward External Transverse Field (H) or 0 m e+ Time Time Time Transverse Field Zero Field Time

SR m Principles of

• High T Pz(t) is from nuclei.
• Sudden change in P(t) well

below Tc.

• There are two contributions.
• One amplitude grows, the
• ther decreases.
• There is recovery to 1/3.
• At base T, relaxation is over-dumped.

2 4 6 8 10 12 14 16 0.00 0.05 0.10 0.15 0.20 0.25

Tc=33.1K

T(K)= 40.2 7.4 3.8 3.0 2.1 0.37

Asymmetry TIME (msec)

SR data m Raw ZF

To understand this spin glass phase lets examine the base T data.

P B

lo c m



. ) cos( ) ( 3 2 3 1 ) (

2



  dB t B B B t P

z m

 

On the average

B (B) <B>



B B

2(B)

We expect dumped oscillations in Pz(t). We expect

. 3 1 ) ( lim 

 

t P

z t ) ( cos2  ) ( sin2 

If then .

SR in Zero Applied Field: Static Case m

2 2

( , ) cos sin cos( ) cos

z z

P t B t B B

m

       B

2 4 6 8 0.0 0.2 0.4 0.6 0.8 1.0

TIME (a.u.)

Pz(t) 0.0 0.2 0.4 0.6 0.8 1.0 0.10 0.15 0.20 0.25 Spin Glass Fe0.05TiS2 Tg=15.5K T=4K Asymmetry TIME (msec)

Theory Experiments

1 2 0.15 0.16 CLBLCO X=0.1 Tc=7.0K T=1.9 K Asymmetry TIME (msec)

Gaussian (B)

• The peek in B2(B) corresponds to a dip in Pz(t).
• The position of the dip is determined by the width of (B).
• The recovery of PZ(t) is to 1/3.

Demonstration

B B

2(B)

B B

2(B)

The situation is not possible in CLBLCO since (over dumped). We must have . Namely, as we must have

. / 1 ) (

2

B B    B

There is an abnormal amount of sites with zero field.

1/3

T(K)= 0.37 K

The case of CLBLCO

SC SC SC M M 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.

Towards a model

M M M

S C

• The field from the magnetic

phase penetrates into the superconducting regions.

• The staggered moments

decay on a very short length scale.

A model

m

. ) / exp( ) 1 ( ) (

/

B(r) r

r

      r

a

Muon polarization in a sample with random magnetic centers. The position of S(0) is random. Muon-electron spin interaction is dipolar.

Numerical Simulations

S(0) S(0)

1 2 3 4

(a)

2 4 6 8 10 12 14 0.00 0.25 0.50 0.75 1.00 Pz(t) Time(msec)

50 100 150 200 1 2 3

p=35% p=15%



<B>

(b)

(|B|)B

2 (a.u.)

B(Gauss)

2 4 6 8 10 12 14 0.00 0.25 0.50 0.75 1.00 Pz(t) Time(msec)

Dumped oscillations at high p. Over dumped oscillations at low p. p = magnetic concentration

Simulation Results

We fit the data to

). , ( ) exp( ) , ( t P A t A t T A

n m

     ) , ( t P 

is determined at high T.

SR data m Raw ZF

0.00 0.05 0.10 0.15 0.20 0.25 Time(msec) T(K)= 40.2 7.4 3.8 2.1 0.37 Asymmetry

• At low T the magnetic amplitude saturates.
• The spin glass temperature Tg is the T where Am=Am

max/2.

g

T Determination of

5 10 15 20 0.00 0.05 0.10 0.15 0.20 0.25

x=0.3 y=6.965 Tc=21.7 y=6.994 Tc=29.8 y=7.005 Tc=37.4

8.0 5.5 Tg=3.2 Am T(K)

Tg decreases as doping increases.

6.93 6.94 6.95 6.96 6.97 6.98 6.99 7.00 7.01 7.02 1 2 3 4 5 6 7 8 9 10 11 12 x=0.3 x=0.1,0.2 x=0.4

Tg(K) y

y

O

3

)Cu

+x 0.25

La

x

• 1.75

)(Ba

x

• 1

La

x

• vs. x and y in (Ca

g

T

Scaling

6.8 6.9 7.0 7.1 7.2 7.3 20 40 60 80 (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3O6+y y

X=0.1 X=0.2 X=0.3 X=0.4

Tc(K)

6.8 6.9 7.0 7.1 7.2 7.3 0.0 0.2 0.4 0.6 0.8 1.0 Tc/Tc

max

y

max

/

C C C

T T T 

• 0.2
• 0.1

0.0 0.1 0.2 0.0 0.2 0.4 0.6 0.8 1.0 Tc/Tc

max

K(x)*y

( ) y K x y  

6.90 6.95 7.00 7.05 1 2 3 4 5 6 7 8 9 10 11 12

X=0.2,0.1 X=0.3 X=0.4

Tg (K) y 6.90 6.95 7.00 7.05 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 Tg/Tc

max

y

max

/

g g C

T T T 

• 0.25
• 0.20
• 0.15

0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 Tg/Tc

max

K(x)y

( ) y K x y  

Other compounds

• 0.15
• 0.10
• 0.05

0.00 0.05 0.10 0.0 0.2 0.4 0.6 0.8 1.0 5 10 15

CLBLCO x=0.1 x=0.2 x=0.3 x=0.4 LSCO

1

YCBCO Bi-2212 LSCO

2

YBCO

(a) Tc/Tc

max

pm=K(sample)´Doping

Tg/T

c max=-0.15-2.5pm

(b) Tg/Tc

max (x10

• 2)

For La2-xSrxCuO4

0.16.

m

p x   

Data from: Niedermayer et. al. PRL ,80, 3843 (98). Panagopoulos et. al. PRB, 66, 64501 (02). Sanna, unpublished.

Zn doping

(Panagopoulos La2-xSrxCu1-yZnyO4)

0.05 0.10 0.15 0.20 0.25 10 20 30 40 50 y=0.02 y=0.01 y=0.00 Tc p 0.05 0.10 0.15 0.20 2 4 6 8 10 12 y=0.02 y=0.01 y=0.00 Tg p

• 0.10
• 0.05

0.00 0.05 0.10 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.5

Tc/Tc

max

K*y y=0.02 y=0.01 y=0.00 Tg/Tc

max

In this case the scaling transformation of Tc does not apply for Tg.

y x K y T T T T T T

c g g c c c

    ) ( / /

max max

• The vertical axis is dimensionless.
• We scaled using a single energy scale, , both and .
• Both the Magnetism and the Superconductivity are governed

by the same energy scale.

Single energy scale.

max C

T

C

T

• The vertical axis represents energy.
• The horizontal axis represents density.

Before Scaling After Scaling

g

T

• The Uemura relation:
• is common to all HTSC.

Additional background before interpretation

*

m n T

s c

 



m2 m1

m2 m1

 

m

m2 m1

Penetration depth determination with transverse field mSR

B B B

• 0.4
• 0.2

0.0 0.2 0.4 (a) T=80K

• 0.4
• 0.2

0.0 0.2



• 1

(b) T=70K

Asymmetry

2 4 6 8

• 0.4
• 0.2

0.0 0.2



• 1

(c) Tc=77K TIME (msec) T=10K

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

20 30 40 50 60 70 80

x=0.1 x=0.2 x=0.3 x=0.4

(CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3O6+y

Tc(K)

 (msec

• 1)  
• 2

Uemura relations for the CLBLCO system

Equal Tc means also equal  and equal ns/m*

• We determine the muon relaxation rate which is proportional to 2.

• Using the London equation we know:
• The results show that:
• 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.

2 s

n  

C s

T n 

• Not all the doped holes contribute to the superfluid density!
• This is the origin of the scaling factor K.

6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.25 20 40 60 80 (CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy

y

X=0.1 X=0.2 X=0.3 X=0.4 Tc(K)

Intermediate Conclusion

where Jf can vary between cuprates families.

( ).

c f s m

T J n p  ´ 

• 0.15
• 0.10
• 0.05

0.00 0.05 0.10 0.0 0.2 0.4 0.6 0.8 1.0 5 10 15

CLBLCO x=0.1 x=0.2 x=0.3 x=0.4 LSCO

1

YCBCO Bi-2212 LSCO

2

YBCO

(a) Tc/Tc

max

pm=K(sample)´Doping

Tg/T

max c =-0.15-2.5pm

(b) Tg/Tc

max (x10

• 2)

Therefore, and

max

(0)

c f s

T J n  (0)( 0.15 2.5 ).

g f s m

T J n p    

Tc and Tg have the same energy scale.

From experiment to theory

• We discuss models with both antifferomagnetic(AF) and

superconducting (SC) phases.

• The Hubbard model at half filling (zero doping) will give us the

Mott AF phase.

• Some believe superconductivity is also contained in this model.

 

    

   

ij i i i j i

n n U c h c c t H .) . (

• Altman and Auerbach derived an effective Hamiltonian by

solving the Hubbard model on 4 sites and keeping only low energy states.

• The effective model is a model of 4 interacting bosons.

 i a

t , Is the creation operator of a magnon triplet on site i.

 i

b

Is the creation operator of an hole pair on site i.

 

   

   

i ij j i b i i b b

c h b b J b b H .) . ( ) 2 ( m 

 

   

  

ij j ia t i i i t t

c h t t J t t H

    

 ) . (

In the range of parameters were pair binding is favorable

Theoretical prediction

t b

J J ~

t b

J J ~

U/t Different compounds can have different U and t.

AFM phase (condensate of t bosons at ) SC phase (condensate of b bosons at )

The model provides

c

m m 

c

m m 

The Uemura relation

n J T

b c 

And the relation

b t

J J ~

• In the AFM phase TN is governed by Jt .
• We make a nontrivial assumption that, although the lattice

is doped:

t g

J T 

Therefore, according to our data Jb is proportional to Jt . This is only slightly different from the AA prediction.

) ( p f J T

t g

 

s b c

n J T 

) ( ) (

max s s c c

n p n T T  

) ( ) (

max s b t c g

n p f J J T T  

Summery

• We found that at intermediate doping levels, there is a

microscopic phase separation in CLBLCO samples.

• We found a scaling relation between Tc and Tg.
• This scaling relation is found to be common to many

HTSC families.

• The scaling relation agrees with theoretical predictions.

Acknowledgements

Galina Bazalitsky Mordehai Ayalon Shmuel Hoida

• Dr. Leonid Iomin

Larisa Patalgen

• Dr. Michael Reisner

Rinat Assa, Ariel Maniv, Oshri Peleg, Eva Segal, Oren Shafir, Meni Shay, Lior Shkedy

Assa Auerbach and Ehud Altman

• Works on diluted AFM

showed that the long range AF

• rder survives up to a dilution

level of 40%.

• TN decreases monotonically

as the dilution is increased.