INSTITUT MAX VON LAUE - PAUL LANGEVIN

Penetration Depth Anisotropy in MgB2 Powder Measured by Small-

Angle Neutron Scattering

by Bob Cubitt & Charles Dewhurst

Institut Laue LangevinGrenobleFrance

In collaboration with:

S. J. Levett - ISIS, Rutherford Laboratory, UK

M. R. Eskildsen - University of Notre Dame, USA

S. L. Bud’ko, N. E. Anderson, P. C. Canfield- Ames Laboratory, USA

J. Jun, S. M. Kazakov, J. Karpinski- ETH Zurich, Switzerland

MgB2 Single Crystals provided by:

MgB2 Powder provided by:

INSTITUT MAX VON LAUE - PAUL LANGEVIN

Summary: Penetration Depth Anisotropy in MgB2 Powder

• Neutrons and the Vortex Lattice

– Small Angle Neutron Scattering

• Anisotropic superconductivity in MgB2

• Modeling diffraction from the VL in powder grains

• Results: – Field dependent penetration depth anisotropy

– Discrepancy between powder and single crystal data

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D22

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

0.0

2.0x105

4.0x105

6.0x105

8.0x105

1.0x106

1.2x106

Inte

nsity

[A.U

.]Sample Angle [Degrees]

SANS: ‘Diffraction’ from the Vortex Lattice

Vortex Lattice

Vortex

Diffraction from the Vortex Lattice

Rocking Curve

• Neutrons, with their magnetic moment can diffract from the internal field modulation

e.g. B=1T

a0 = 490Å, d=425Å (hex)

n10Å 0.68º

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D22

SANS: ‘Diffraction’ from the Vortex Lattice

Vortex Lattice

Vortex

Rocking Curve

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D22

D22: “Probably the best SANS instrument in the world!”

40m

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No in-plane anisotropy

Single band anisotropy

=c/ab= ab/c

Double band/gap anisotropy

=c/ab

=ab/c

Anisotropic Superconductivity in MgB2

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= -band anisotropy at T=0K

= mean anisotropy of all bands at T=0K

double gap:c/ab= ab/c only at Tc

ab/c=Bc2(B//ab)/Bc2(B//c)

c/ab distorts vortex lattice

Anisotropy in a two-band superconductor: MgB2

P. Miranovic et al., J. Phys. Soc. Japan, 72, 221 (2003)

V. G. Kogan, PRB 66, 020509 (2002)

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Anisotropy distorts the VL: Measurement of by SANS

• = 1.63(6)@ 2K, 0.4T

• i.e very different to H ~ 6

222

22

cossin

Inverted Campbell formula

= 0o = 40o = 60o = 70o

YX

=X/Y

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It’s all been done on crystals: Why bother measuring MgB2 powder?

History:

• It took a while for quality MgB2 crystals to become available.• In the absence of crystals why not measure a powder-diffraction measurement of the VL.

• could extract • could get an idea of the anisotropy

• First experiment demonstrated that only tiny quantities of MgB2 were necessary in order to observe the VL with neutrons (98g!).

Some considerations:

• Since the scattering is so strong, quantity of sample should be minimal in order to avoid multiple scattering.• High background scattering from the powder grains.• Assume grains are randomly oriented.• Assume relationship between ellipse axis ratio and anisotropy holds.• Assume each grain is a single crystallite.

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Measuring the anisotropy with a powder sample

Real space Reciprocal space

Hc

a

•Still need to perform a rocking curve

•Ring is the sum of the intensityfrom all orientations of crystallites

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Orientation effects about the field direction

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Orientationuncorrelatedwith ellipse.Lattice pinnedto a-axis forexample

Orientationcorrelatedwith ellipse

Orientation effects perpendicular to the field direction

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Modeling the powder data

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Single crystal

Powder

=1.60(5)

=1.55(5)

=2.7(2)

=1.71(5)

0.4T

0.7T

Single crystal and powder data

INSTITUT MAX VON LAUE - PAUL LANGEVIN

Why does -powder not rise?

• Grains>1.5m (neutrons). If crystallites<<1.5m thencurrent ellipses cannot follow different orientations of crystallites so anisotropy is washed out.

• Have we misinterpreted the higher field (above reorientation) single crystal data?

grain

crystallite

c-axis

-anisotropy determined from single crystal and powder data

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FWHM rocking curve width

B(T)

w(d

eg

)

Correlation length along B

d/s

in(w

) (

m)

B(T)

Finite size of flux lattice along B at least 1.5m

Finite length of flux-lattice along B due to grain size

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Summary:

• determined from single crystal and powder data

• Discrepancy in between crystal and powder data at higher fields possibly due to:

• Averaging effect due to multiple randomly oriented crystallites within a single powder grain?

• Do we need to reinterpret the distorted (elliptical) VL and apparent above the reorientation transition?