Rinat Ofer

Supervisor: Amit Keren

Outline Outline Motivation.

Magnetic resonance for spin 3/2 nuclei.

The YBCO compound.

Three experimental methods and their results.

Summary and conclusions.

MotivationMotivationThe parent compounds of the cuprates superconductors areAFM insulators. Superconductivity is achieved by chemical doping.For some of these compounds there are evidence of phase separation in the CuO planes.Some theoretical work predict charge inhomogeneity as a natural consequence of an impurity independent Hamiltonian.Key question:Is this phase separation an intrinsic property of the CuO planes and is it an essential part of the mechanism of HTSC? or is it a result of the chemical doping?

Evidence of Evidence of inhomogeneityinhomogeneity with with μμSRSR

This result supports the presence of some magnetic structure.Increasing the doping decreases the inhomogeneity.It seems that the structure is a remainder of the AF phase.

Low doping

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

OrthorhombicTetragonal

TN

0

20

40

60

80

100

120

140

160

180

200

Doping Value

TetragonalOrthorhombic

Tg

SCSC

Evidence of charge Evidence of charge inhomogeneityinhomogeneity with neutron with neutron scatteringscattering

H. A. Mook et al,

Phys. Rev. Lett., 88, 097004 (2002)

Neutron scattering on YBCO6.35

The charge distribution is measured indirectly by atoms that move in response to the charge.

Low doping

Evidence of Evidence of inhomogeneityinhomogeneity with with STMSTM

Surface

M. Vershinin et al,

Science, 303, 1995 (2004)

Real-space conductance maps of underdoped Bi2 Sr2 CaCu2 Oy at 100K (pseudogap phase), showing the spatial dependence of the density of states.

Theoretical workTheoretical work•A model for phase separation in

2D Hubbard model.

•For strong U

: The doping driven transition from microscopic coexistence of AFM and SC to pure SC phase is accompanied by phase separation.

M. Aichhorn et al,

Phys. Rev. B, 76, 224509 (2007)

The problemThe problemThere is no clear correlation or anti-correlation between the dopant atoms and charge inhomogeneity.

Plan of operationPlan of operationMagnetic resonance experiment:

charge distribution in the bulk and not just on the surface.

NQR measurements on the Cu nuclei, the charge distribution in the Cu-O planes.

The YBCO compound:narrow NQR resonance lines, distinguish between the different Cu resonance lines.

A nucleus under magnetic field :

Energy levels:

Transitions between the levels are forced by a rf magnetic field perpendicular to the static field.

A nucleus in solid additional interactions shiftthe energy levels.

We will focus on the quadrupole interaction.

NNuclear uclear MMagnetic agnetic RResonance esonance

0ˆH z

0 0 zH H Iμ γ= − ⋅ = −H

0 0Hω γ=0 , 1...,E H m m I I Iγ= − = − −h

The Quadrupole The Quadrupole EnergyEnergy

( ) , , ,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:

zz

yyxxzzq V

VVV

−=∝ ην ( )2 2 2 23

6q

z x yI I I Iυ

η⎡ ⎤= − + −⎢ ⎥⎣ ⎦H

ηη is a measure of charge is a measure of charge inhomogeneityinhomogeneity. .

The quadrupole Hamiltonian:

NMRNMRStrong H0 the quadrupole term is treated as a perturbation.

For spin 3/2 nuclei:

powder average NMR line

η and νq can be extracted from the line shape.

I

H0

η=0 η=1/2 η=1

-3/2-1/21/23/2

Zeeman +quadrupole

Pure NQRPure NQRNo permanent magnetic field

For a spin 3/2 nucleus:2

13NQR qf ην= +h

νq

and η cannot be determined separately.

( )2 2 2 236q

z x yI I I Iυ

η⎡ ⎤= − + −⎢ ⎥⎣ ⎦H

Technical aspects of Technical aspects of NMRNMR\\NQRNQR

YY11 BaBa22 CuCu33 OOyyPhase 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)

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

Orientation of the YBCO Orientation of the YBCO powderpowderBo

b a

c Vzz

ba

c

Vzz

Bo || c || Vzz ≡ z

In YBCO7 Vzz is in the c direction.

η is a measure of charge homogeneity in the CuO2 planes.

NQR lines for YBCO NQR lines for YBCO

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.

63Cu

65Cu

27 28 29 30 31 32

6.4

6.5

6.6

6.7

6.8

6.9

7.0

y

f (MHz)

Site assignmentSite assignment

3 different Cu(2) lines, for the 3 different ionic environments:31MHz: Cu(2) with full chain.29MHz: Cu(2) with chain half full, Cu(1) with coordination 3.27.5MHz: conducting Cu(2) with empty chains.

Y=7

O(2)

O(4)

O(1)

Cu(2)4

Cu(1)4

Y=6.5

Cu(2)3

Cu(1)3

c

a

Y=6b

Cu(2)2

Cu(1)2

Oxygen atomOxygen vacancy

Copper atom

For YBCO7 Vzz

is in the c

direction of the lattice.η determines the homogeneity of the charge distribution in the

CuO planes:

Our Main motivation; finding Our Main motivation; finding ηη

2

13NQR qf ην= +h

zz

yyxxzzq V

VVV

−=∝ ην

η=0

η≠0

NMR ResultsNMR ResultsFor lower doping levels, the satellites disappear

η cannot be extracted.

4.9 5.0 5.1 5.2 5.3 7.5 7.6 7.7 7.8

(a)

Field (Tesla)

y=7

x5

(b)

y=6.85

(c)

y=6.77

I (a

rb. U

nits

)(d)

y=6.68

Measuring the NQR signal as a function of tp.

The intensity of the signal after a time t:

where:

Fourier transform over tp gives the frequency:

NutationNutation SpectroscopySpectroscopy

( )1122

2

( , )s ( , )( , , , ) ( , ) sinin2 3

sin3

p r QpH tI t H t tλ θ φθ φ η λ θ φ γ ωη

λ θ φ γη

⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎟⎜⎝ ⎠

⎛ ⎞⎟⎜ ⎟⎜∝ ⎟⎜ ⎟⎟⎝ ⎠++ ⎜

( )( )2 2 2 2( , ) 9 6 cos 2 sin 4 cosλ θ θ θη φ ηφ η= + + +

12

( , )( , )2 3

p Hθ φω θ φ λη

γ=+

tp tr

acquisition

G. S. Harbison et al.

, Z. Naturforch. 45A, 575 (1990).

NutationNutation SpectroscopySpectroscopy

A. J. Vega, Israel Journal of Chemistry 32, 195 (1992)

Three singularities:

Theoretical I(ωp)for different η:

The location of the singularities is independent of the EFG orientation.

1 1 12 2 2

2 3 3, , 2 3 2 3 2 3

H H Hη η ηγ γ γη η η

− +

+ + +

The The nutationnutation probeprobe

• Small sample in a long coil to improve the homogeneity H1

.

• A current monitor - perform all measurements with the same H1

.

2 1( , )( , )

2 3p Hλ θ φω θ φ γ

η=

+

Nutation raw data

0 30 60 90 120 150 0 50 100 150 200 250 300

echo

inte

nsity

[a.u

]

tp [μsec]

YBCO7 31.5MHz

FT

ωp [KHz]

NutationNutation ResultsResults

0.2 0.4 0.6 0.8 1.0 1.227 28 29 30 31 32

η=1

I (a

rb. U

nits

)

I/f2 (

arb.

Uni

ts)

Nutation spectroscopyFerquency sweepy=7 (d)

22MHz 31.5MHz

η=0(a)y=7

65Cu(2)

63Cu(2)4

0.2 0.4 0.6 0.8 1.0 1.227 28 29 30 31 32

η≅1 η=0y=7 (d)

22MHz 31.5MHz

η≅0

y=6.73 (e)

31.0MHz 29.3MHz

η≅0

y=6.68 (f)

ωp/γH1

30.8MHz 29.2MHz 28.1MHz

y=6.73Enriched

Cu(2)3

Cu(2)4

(a)y=7

65Cu(2)

63Cu(2)4

(c)

I (a

rb. U

nits

)

(b)

y=6.68Enriched

I/f2 (

arb.

Uni

ts)

fNQR (MHz)

Ferquency sweep Nutation spectroscopy

Cu(2)2

Cu(2)3 Cu(2)4

22 MHz - Cu(1)

31.5MHz - Cu(2)

NutationNutation ResultsResultsFor YBCO7: Cu(2) η=0

Cu(1) η=1

For lower doping:η≈0

for all different Cu(2) environments.

Not sensitive to the EFG orientation.

Angle dependant NQRAngle dependant NQR

0 50 100 150 200 250 300 350

0.0

0.2

0.4

0.6

0.8

1.0

η=0 η=0.4 η=0.6 η=0.8 η=1

Inte

nsity

[a.u

]

θ[degree]

H1θ

c

For η=0, θ=0ϰNQR

and ϰ rf

commute no spin transitions.

For η>0,ϰNQR and ϰrf do not commute even for θ=0

signal even for θ=0.

( )2 2 2 2

1

1 1

36

cos( )

sin cos , sin sin , cos

qNQR z x y

rf

I I I I

H I t

H H

υ

γ ωθ φ θ φ θ

η⎡ ⎤= − + −⎢ ⎥⎣ ⎦= ⋅

⎡ ⎤= ⎣ ⎦

H

H

S. Levy and A. Keren, Journal of Magnetic Resonance 167, 317 (2004)

The ADNQR probeThe ADNQR probe

• Spherical coil to improve the homogeneity of the rf field.

• Connection to a motor for an automated rotation of the sample. (ability to measure at low temperatures).

ADNQR resultsADNQR results

0 40 80 120 160 2000.0

0.3

0.6

0.9

1.2y=6.678Enriched

(d)

f(MHz) η30.8 0(0.15)29.2 0.55(6)28.1 0.60(6)

Cu(2)4

Cu(2)2/3

0.0

0.3

0.6

0.9

1.2

1.5

Angle (θ)

Nor

mal

ized

Inte

nsity

ADNQR(c)y=7

f(MHz) η32 0(0.15)31.55 0(0.15)31 0.65(2)

Cu(2)3

Cu(2)4

27 28 29 30 31 32

(b)y=6.678Enriched

Cu(2)2

Cu(2)3 Cu(2)4

f (MHz)

I/f2 (

arb.

Uni

ts)

Ferquency sweep

(a)y=7

65Cu(2)

63Cu(2)4

63Cu(2)3

InterpretationInterpretation

An alternative explanation for the YBCO6.68 with oxygen deficiency in the chain:

Rotation of Vzz

from the c

direction:

When Vzz⊥c:

ϰNQR

and ϰrf

do not commute even for η=0.

( )2 2 2 2

1

1 1

36

cos( )

sin cos , cos , sin sin

qNQR z x y

rf

I I I I

H I t

H H

υ

γ ωθ φ θ θ φ

η⎡ ⎤= − + −⎢ ⎥⎣ ⎦= ⋅

⎡ ⎤= ⎣ ⎦

H

H

The ADNQR assumes Vzz//c.

This in true for YBCO7, what about lower doping?

SummarySummaryYBCO7 - η=0, the CuO2 plane is charge homogeneous.

For lower doping:

NMR – η cannot be determined

Nutation – η=0 for all different Cu(2) environments.

Not sensitive to the EFG orientation.

ADNQR: – For Cu(2) neighboring a full chain - η=0

For Cu(2) next to an oxygen deficiency in the chain –there is a rotation of Vzz

from the c

direction.

ConclusionConclusionAny charge inhomogeneity in the CuO2 planes is found only in conjunction with oxygen deficiency in the chains.

In other words,

if there is a phase separation in the planes in the YBCO compound, it is correlated with the O dopant atoms.