Correlation Between the Correlation Between the Critical Temperatures of Critical Temperatures of

Cuprates Superconductors Cuprates Superconductors and their Magnetic and their Magnetic

InteractionsInteractions

Rinat AssaRinat AssaAmit KerenAmit Keren

High Temperature SuperconductorsHigh Temperature Superconductors

The cuprates high The cuprates high TTCCsuperconductors are ceramic superconductors are ceramic compounds all having compounds all having CuOCuO22planes.planes.

At low doping levels the At low doping levels the origin of the magnetism lies origin of the magnetism lies in the CuOin the CuO22 planes.planes.

Superconductivity also Superconductivity also occurs in the planes.occurs in the planes.

Tg

TN

TC

Over doped

Under doped

Optimally doped

Temperature

Undoped

Schematic phase diagram

AFM SC

Previous workPrevious workFor all underdoped cuprates:For all underdoped cuprates:

Uemura: Uemura:

Kanigel et al:Kanigel et al:

Jf s is a magnetic energy scale per family in the SC state.

A. Kanigel et al, Phys. Rev. A. Kanigel et al, Phys. Rev. LettLett 8888,137003 (2002).,137003 (2002).

1 2 30

10

20

30

40

50

60

70

80

90

x=0.1 UD x=0.1 OD x=0.2 x=0.3 x=0.4 UD x=0.4 OD LSCO UD LSCO OD YBCO

Tc (

K)

UD=Under DopedOD=Over Doped

∝λ−2 ∝ns/m*

*1

2 mnT SC ∝∝ λ

SsfC nJT ⋅=

MotivationMotivation

Is Is JJffss unique for each family?unique for each family?

Showing , namely, Showing , namely, m*m* or or JJssff = const, by performing = const, by performing NQR measurements on YBCO.NQR measurements on YBCO.

Is Is TTCCmaxmax correlated with the Ncorrelated with the Nééel temperature el temperature TTNN of the of the parent antiferromagnetic compound?parent antiferromagnetic compound?

μμSR measurements on the CLBLCO family.SR measurements on the CLBLCO family.

SC nT ∝

YY11BaBa22CuCu33OOyyPhase diagram

6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.90

100

200

300

400

AF

Tem

pera

ture

[K]

Doping value - y

TC

Superconducting

OrthorhombicTetragonalTN

0

20

40

60

80

100

120

140

160

180

200

Unit cell

O -Cu -Y -Ba -b

a

c

YBCO6 YBCO7

planes

chains

Cu(2)

Cu(1)

These samples are unique in that they contain a single Cu63 isotope and not two.

Orientation of the YBCO powderOrientation of the YBCO powderBo

b a

c Vzz

ba

c

Vzz

Bo || c || Vzz ≡ z

• For better signal intensities the YBCO powder was oriented.

Nuclear Quadruple Resonance (NQR)Nuclear Quadruple Resonance (NQR)

( ) , , ,iji j

VV r V i j x y zx x∂

⇒ ≡ =∂ ∂

nucleus theofspin The - ,, zyx III

The EFG (Electric Field Gradient):

-

+

-

+

-

-

+ ++ +

From the environment:

From the nucleus:

To obtain the NQR Hamiltonian we must couple To obtain the NQR Hamiltonian we must couple V(rV(r) and I .) and I .Every spin Hamiltonian contains even powers of I.Every spin Hamiltonian contains even powers of I.The simplest coupling to write is The simplest coupling to write is

i ji j

VH I Ix x∂

∝∂ ∂

The NQR HamiltonianThe NQR Hamiltonian

2 2 2 2ˆ ˆ ˆ ˆ ˆ3 ( ) 6

qq z x yH I I I I

νη⎡ ⎤= − + −⎣ ⎦

For a spin 3/2 nucleus: 21

3NQR qf ην= +

Choosing directions wisely leaves: Vxx , Vyy , and Vzz.

Since Vxx+Vyy+Vzz=0 (Laplace)only two parameters remain:

zz

yyxxzzq V

VVV

−=∝ ην

fNQR is determined by the EFG.A change in fNQR indicates a change in the surrounding charges.

Technical aspects of NQRTechnical aspects of NQR

The impedance and the The impedance and the resonance frequency of the resonance frequency of the circuit can be changed by the circuit can be changed by the capacitors.capacitors.

One of the capacitors is One of the capacitors is automatically controlled by a automatically controlled by a motor. motor.

Our NQR system does an Our NQR system does an automatic frequency sweep in automatic frequency sweep in a wide range of frequencies a wide range of frequencies (~3MHz), while delivering (~3MHz), while delivering 1KW of power.1KW of power.

Motor

C1

C2R

L

NQR Raw dataNQR Raw data

26 28 30 32 26 28 30 32 26 28 30 32 26 28 30 32

I/f2

Y=6.4

Y=6.448

Y=6.555

Y=6.678

f (MHz)

Y=6.729

Y=6.773

Y=6.85

Y=7

One can see the importance of enrichment, without it lines would overlap.

Schematic illustration of the Cu site with locally Schematic illustration of the Cu site with locally different oxygen different oxygen coordinationscoordinations

c

a

Y=6

b

Cu(2)

Cu(1)2

Y=7

O(2)

O(4)

O(1)

Cu(2)

Cu(1)4

Y=6.5

Cu(2)

Cu(1)3

Oxygen atomOxygen vacancy

Copper atom

NQR ResultsNQR Results

27 28 29 30 31 32

6.4

6.5

6.6

6.7

6.8

6.9

7.0

y

f (MHz)

3 different Cu(2) lines, for 3 different Cu(2) lines, for the 3 different ionic the 3 different ionic environments:environments:

31MHz: Cu(2) with full 31MHz: Cu(2) with full chain.chain.

29MHz: Cu(2) with chain 29MHz: Cu(2) with chain half full, Cu(1) with half full, Cu(1) with corrdinationcorrdination 3.3.

27.5MHz: conducting 27.5MHz: conducting Cu(2) with empty chains.Cu(2) with empty chains.

YY11BaBa22CuCu33OOyy

NQR ResultsNQR Results

27 28 29 30 3120

30

40

50

60

70

80

90

T C (k

)

f (MHz)

When plotting TWhen plotting TCCvs. the NQR vs. the NQR frequency frequency →→three lines with a three lines with a common slopecommon slopedTdTCC //dfdf==3838±±6 (K/MHz)6 (K/MHz)

This is the first Uemura plot obtained not through penetration depth measurements. It allows the separation of J (m*) from ns.

Following Following HaaseHaase et al:et al: J. Haase et al, Phys. Rev. B 69, 094504 (2004).

3 main contributions to the EFG of the Cu(2) nucleus:3 main contributions to the EFG of the Cu(2) nucleus:I.I. The 3d hole concentration on the copper ion. The 3d hole concentration on the copper ion. II.II. There is a virtual hopping of electrons from neighboring There is a virtual hopping of electrons from neighboring

oxygen ions to unoccupied 4d oxygen ions to unoccupied 4d orbitalsorbitals of Cu. of Cu. III.III. The electric field of distant ions.The electric field of distant ions.

→→ NQR frequencyNQR frequency

nd - is the number of Cu holes (8-4np) - is the number of electrons in the neighboring oxygen β2 - is the probability to jump to the Cu 4d orbital C - is related to the contribution of distant ions.

It is widely accepted that doping increases the hole It is widely accepted that doping increases the hole content only for the oxygen in the planes (content only for the oxygen in the planes (nnd d is a constant)is a constant)

2 (8 4 )d pf A n B n Cβ∝ ⋅ − ⋅ − +

According to According to HaaseHaase et al:et al:

From our results, for each ionicFrom our results, for each ionicenvironment:environment:

Therefore:Therefore:

From the Uemura relation:From the Uemura relation: 27 28 29 30 312030

40

50

60

70

80

90

T C (k

)

f (MHz)

SC nT ∝

Cf TΔ ∝

C f ST J n= ⋅

Our data for the YBCO family is consistent Our data for the YBCO family is consistent with a with a Jf independent of the oxygen doping.independent of the oxygen doping.

Snplane in the holes ofnumber ∝∝Δf

Conclusions of the first partConclusions of the first part

MotivationMotivation

Is Is TTCCmaxmax correlated with the Ncorrelated with the Nééel temperature el temperature TTNN of the of the parent antiferromagnetic compound?parent antiferromagnetic compound?

μμSR measurements on the CLBLCO familySR measurements on the CLBLCO family

The CLBLCO familyThe CLBLCO family

Tetragonal - no ordered Cu-O chains.

Stable throughout all parabolic TC curves.

allows TC to be kept constant and other parameters to be varied, with minimal structural changes.

6.8 6.9 7.0 7.1 7.2 7.30

20

40

60

80

(CaxLa1-x)(Ba1.75-xLa0.25+x)Cu3Oy

y

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

T c(K

)

μμSRSR

• 100% spin polarized muons

• Muon life time : 2.2μsec

• Positron emitted preferentially in the muon spin direction

p

π

μνμ e+

μμSRSR

)()()()(

)(tNtNtNtN

tAFB

FB

+−

=

F

B

t

A(t)

NB(t)

NF(t)t

μμSR raw data for CLBLCOSR raw data for CLBLCO

There are 2 contributions to Az:

( ) )cos(expexp2

exp1

22

tT

tAtAtAA LRmnZ ωλ ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ−=

An – the amplitude of the nuclear frozen moments.Am – the amplitude of the magnetic phase.ALR – the amplitude of long range magnetic order.

0 2 4 6 8 10 120.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

x=0.4y=6.607

T=213.4(5)K T=251.7(4)K T=270.92(2)K T=280.87(4)K T=300.8(2)K T=350.2(1)K

Asy

mm

etry

Time

Measuring TMeasuring Tgg/T/TNN

As the temperature As the temperature decreases, decreases, AAmm the electronic the electronic magnetic part increases, at magnetic part increases, at the expense of the expense of AAnn..

the transition temperature is the transition temperature is the temperature at which:the temperature at which:

AAmm=A=Ammmaxmax/2/2

200 220 240 260 280 300 320 340 360

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Am

T (K)

TN=285

X=0.4Y=6.607

( ) )cos(expexp2

exp1

22

tT

tAtAtAA LRmnZ ωλ ⎟⎟⎠

⎞⎜⎜⎝

⎛ −+−+⎟⎟

⎠

⎞⎜⎜⎝

⎛ Δ−=

Scaling relation in the superconducting Scaling relation in the superconducting phase for CLBLCOphase for CLBLCO

-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

0.0

0.2

0.4

0.6

0.8

1.0

T c/T

cmax

K(x)*Δy-0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

0.0

0.2

0.4

0.6

0.8

1.00.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

T c/T

cmax

K(x)*Δy

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

T g/T

cmax

yxKyTTT cccΔ⇒

⇒)(

/ max

yxKy

TTT cggΔ⇒

⇒

)(

/ max

6.82 6.90 6.98 7.06 7.14 7.220

20

40

60

80

y

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

T c(K

)

6.93 6.94 6.95 6.96 6.97 6.98 6.99 7.00 7.01 7.020123456789

101112

x=0.3

x=0.1,0.2

x=0.4T g(K

)

y

A. Kanigel et al, Phys. Rev. Lett 88,137003 (2002).

( )

( )

sc f s m

sg f m

T J n p

T J f p

= Δ

= Δwhere•Jsf is a family dependent magnetic energy scale•f is a function of doping only

max

max

/ ( ) / (0)

/ ( ) / (0)c c s m s

g c m s

T T n p n

T T f p n

= Δ

= Δthen

with no family index.

InterpretationInterpretation

If

There is a common energy scale for magnetism and superconductivity

-0.15 -0.10 -0.05 0.00 0.05 0.10

0.0

0.2

0.4

0.6

0.8

1.00

5

10

15 CLBLCOx=0.1x=0.2x=0.3x=0.4 LSCO1

YCBCO Bi-2212 LSCO2

YBCO

(a)

T c/T

cmax

Δpm=K(sample)Δy

Tg/Tcmax=-0.15-2.5Δpm

(b)

T g/T

cmax

(x10

-2)

6.80 6.85 6.90 6.95 7.00 7.05 7.10 7.15 7.20 7.250

20

40

60

80

y

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

T c(K

)

6.93 6.94 6.95 6.96 6.97 6.98 6.99 7.00 7.01 7.020123456789

101112

x=0.3

x=0.1,0.2

x=0.4T g

(K)

y

Without the y scaling one might reach the opposite conclusion.

ProblemProblemTg of high Tcmax family is lower than Tg of low Tcmax family.

0.10

0.15

0.20

0.25

0 2 4 6 8 10

0.15

0.20

0.25

0 2 4 6 8 10 12

Asy

mm

etry

x=0.4y=6.607TN=285350

300

280270250

213

T(k)(a)

x=0.1y=6.61TN=378

398

380

375

374360

300

T(k) (b)

x=0.4y=6.424TN=420

426

422

420

418

413393

303

T(k) (c)

Time (μsec)

x=0.1y=6.427TN=379

381

379

378

377375

303

T(k) (d)

The family with higher The family with higher TTCCmaxmax has a higher has a higher TTNN at at very low doping very low doping

μμSR results: Phase diagram of CLBLCOSR results: Phase diagram of CLBLCO

•• However, while However, while TTccmaxmax changes by 30%, changes by 30%, TTNN changes by 10%.changes by 10%.

•• The scaling relation no longer holds in the nonThe scaling relation no longer holds in the non

superconducting samples.superconducting samples.

370 380 390 400 410 420 430 44050

55

60

65

70

75

80

85

90

x=0.1

x=0.3

T Cm

ax

TN

x=0.4TTCCmaxmax is a monotonic is a monotonic

function of function of TTNN in a in a

system with minimal system with minimal

structural changes.structural changes.

Problem solvedProblem solved

TheoryTheory

TTNN is determined by is determined by JJ while various anisotropies (while various anisotropies (αα‘‘s) s) enter logarithmically.enter logarithmically.

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅+⋅+⋅= ∑∑∑

⊥

⊥+⊥++j

ji

iiji

zi

zixy

iii SSSSSSJH

δδ

δδ

δδ αα

,,,

( )⎪⎭⎪⎬⎫

⎪⎩

⎪⎨⎧

≈

παπαπ

/4ln4

ln2

20

0

eff

effN

M

MJT ⊥⊥+= ααα zz xyeffz – coordination numberM0 - sublattice magnetization

spacingsneighbor nearest the- , 1, jxy ⊥⊥

In order for the energy scale In order for the energy scale JJffss, which is common to , which is common to TTgg and and TTc c in the in the superconducting region, to be exactly superconducting region, to be exactly JJff of the AFM, one needs the of the AFM, one needs the alpha's to changes between different families. alpha's to changes between different families.

We can predict how these alphas must change.We can predict how these alphas must change.

We write: We write:

Calibrate C using YBCO (Calibrate C using YBCO (nnss(0)=(0)=0.08, 0.08, TTCCmaxmax =90, =90, J=100meV)J=100meV) C=0.8.C=0.8.

Assume for all CLBLCO families.Assume for all CLBLCO families.

Use the Eq. for Use the Eq. for TTNN to obtain the to obtain the αα’’ss..

We obtain:We obtain:

This is a prediction for future experiments (muon rotation frequThis is a prediction for future experiments (muon rotation frequency vs. T )ency vs. T )

sfcfsf nCJTCJJ ==

max that so

)0(

max

CnTJ cf =

0.0 0.1 0.2 0.3 0.4 0.50.010

0.015

0.020

0.025

0.030

αef

f

x

Conclusions of the second partConclusions of the second part

TTccmaxmax is a monotonic function of is a monotonic function of TTNN..However, the magnetic energy scale However, the magnetic energy scale JJssff that enters inthat enters in

is not necessarily the AFM is not necessarily the AFM JJ. The anisotropies . The anisotropies αα’’ss might might be important for be important for TcTc..

JJffss could still be the AFM could still be the AFM JJ if the if the αα’’ss change.change.

sc f sT J n=

SummarySummary

For the YBCO family we confirmed that For the YBCO family we confirmed that JJssff is a constant for all is a constant for all doping values in the superconducting dome. doping values in the superconducting dome.

TTCCmaxmax is a monotonic function of is a monotonic function of TTNN. However, . However, TTNN a prioria priori has has a magnetic energy scale of its own.a magnetic energy scale of its own.

TTNN, T, Tgg, and , and TTcc could all be proportional to the AFM could all be proportional to the AFM JJ if the if the αα’’ssvaried between families.varied between families.

AcknowledgmentsAcknowledgments

Galina Galina BazalitskyBazalitsky

Leonid Leonid IominIomin

Larisa Larisa PatalgenPatalgen

Arkadi Arkadi KnizhnikKnizhnik

Oren Shafir, Eva Sagi, Oshri Peleg, Meni Shay, Ariel Maniv, Lior Shkedy,Shahar Levy, Amit Kanigel

Correlation Between the Critical Temperatures of Cuprates Superconductors and their Magnetic InteractionsHigh Temperature SuperconductorsPrevious workMotivationY1Ba2Cu3OyOrientation of the YBCO powderNuclear Quadruple Resonance (NQR)The NQR HamiltonianTechnical aspects of NQRNQR Raw dataSchematic illustration of the Cu site with locally different oxygen coordinations NQR ResultsNQR ResultsConclusions of the first part The CLBLCO familymSRmSRmSR raw data for CLBLCOMeasuring Tg/TNScaling relation in the superconducting phase for CLBLCOmSR results: Phase diagram of CLBLCOProblem solvedTheoryConclusions of the second partSummaryAcknowledgments