INSTITUT MAX VON LAUE - PAUL LANGEVIN Penetration Depth Anisotropy in MgB 2 Powder Measured by...
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Transcript of INSTITUT MAX VON LAUE - PAUL LANGEVIN Penetration Depth Anisotropy in MgB 2 Powder Measured by...
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
INSTITUT MAX VON LAUE - PAUL LANGEVIN
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
INSTITUT MAX VON LAUE - PAUL LANGEVIN
D22
SANS: ‘Diffraction’ from the Vortex Lattice
Vortex Lattice
Vortex
Rocking Curve
INSTITUT MAX VON LAUE - PAUL LANGEVIN
D22
D22: “Probably the best SANS instrument in the world!”
40m
INSTITUT MAX VON LAUE - PAUL LANGEVIN
No in-plane anisotropy
Single band anisotropy
=c/ab= ab/c
Double band/gap anisotropy
=c/ab
=ab/c
Anisotropic Superconductivity in MgB2
INSTITUT MAX VON LAUE - PAUL LANGEVIN
= -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)
INSTITUT MAX VON LAUE - PAUL LANGEVIN
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
INSTITUT MAX VON LAUE - PAUL LANGEVIN
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.
INSTITUT MAX VON LAUE - PAUL LANGEVIN
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
INSTITUT MAX VON LAUE - PAUL LANGEVIN
Orientation effects about the field direction
INSTITUT MAX VON LAUE - PAUL LANGEVIN
Orientationuncorrelatedwith ellipse.Lattice pinnedto a-axis forexample
Orientationcorrelatedwith ellipse
Orientation effects perpendicular to the field direction
INSTITUT MAX VON LAUE - PAUL LANGEVIN
Modeling the powder data
INSTITUT MAX VON LAUE - PAUL LANGEVIN
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
INSTITUT MAX VON LAUE - PAUL LANGEVIN
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
INSTITUT MAX VON LAUE - PAUL LANGEVIN
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?