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Rinat Ofer Supervisor: Amit Keren - Physics Department · PDF file 2018. 5. 8. · Rinat Ofer. Supervisor: Amit Keren. Outline . y. Motivation. y. Magnetic resonance for spin 3/2 nuclei

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  • 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.

  • MotivationMotivation The parent compounds of the cuprates superconductors are AFM 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 6.9 0

    100

    200

    300

    400

    AF

    Te m

    pe ra

    tu re

    [K ]

    Doping value - y

    Tc

    Superconducting

    OrthorhombicTetragonal

    TN

    0

    20

    40

    60

    80

    100

    120

    140

    160

    180

    200

    Doping Value

    Tetragonal Orthorhombic

    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 problem There is no clear correlation or anti-correlation between the dopant atoms and charge inhomogeneity.

  • Plan of operationPlan of operation Magnetic 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 shift the 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

    ( ) , , ,ij i j

    VV r V i j x y z x x ∂

    ⇒ ≡ = ∂ ∂

    nucleus theofspin The - ,, zyx III

    The EFG (Electric Field Gradient):

    -

    +

    -

    +

    -

    -

    + ++ +

    From the environment:

    From the nucleus:

    zz

    yyxx zzq V

    VV V

    − =∝ ην ( )2 2 2 236

    q z x yI I I I

    υ η⎡ ⎤= − + −⎢ ⎥⎣ ⎦H

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

    The quadrupole Hamiltonian:

  • NMRNMR Strong 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 -1/2 1/2 3/2

    Zeeman +quadrupole

  • Pure NQRPure NQR No permanent magnetic field

    For a spin 3/2 nucleus: 2

    1 3NQR q

    f ην= +h

    νq

    and η cannot be determined separately.

    ( )2 2 2 23 6 q

    z x yI I I I υ

    η⎡ ⎤= − + −⎢ ⎥⎣ ⎦H

  • Technical aspects of Technical aspects of NMRNMR\\NQRNQR

  • YY11 BaBa22 CuCu33 OOyy Phase diagram

    6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 0

    100

    200

    300

    400

    AF

    Te m

    pe ra

    tu re

    [K ]

    Doping value - y

    TC

    Superconducting

    OrthorhombicTetragonal TN

    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

    b a

    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/f 2

    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=6 b

    Cu(2)2

    Cu(1)2

    Oxygen atom Oxygen 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

    1 3NQR q

    f ην= +h zz

    yyxx zzq V

    VV V

    − =∝ ην

    η=0

    η≠0

  • NMR ResultsNMR Results For 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

    ni ts

    ) (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

    ( )112 2

    2

    ( , )s ( , )( , , , ) ( , ) sinin 2 3

    sin 3

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

    η λ θ φ γ

    η

    ⎛ ⎞⎟⎜ ⎟⎜ ⎟⎜ ⎟⎟⎜⎝ ⎠

    ⎛ ⎞⎟⎜ ⎟⎜∝ ⎟⎜ ⎟⎟⎝ ⎠++ ⎜

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

    12

    ( , )( , ) 2 3

    p H θ φω θ φ λ

    η 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 γ η 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 3 p H

    λ θ φω θ φ γ η

    = +

  • Nutation raw data

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

    ec ho

    in te

    ns ity

    [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

    ni ts

    )

    I/f 2

    (a rb

    . U ni

    ts )

    Nutation spectroscopyFerquency sweep y=7 (d)

    22MHz 31.5MHz

    η=0 (a)y=7

    65Cu(2)

    63Cu(2)4

    0.2 0.4 0.

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