1. INSTITUT MAX VON LAUE - PAUL LANGEVIN Penetration Depth Anisotropy in MgB 2 Powder Measured by Small-Angle Neutron Scattering by Bob Cubitt & Charles Dewhurst Institut Laue Langevin Grenoble France 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 MgB 2 Single Crystals provided by: MgB 2 Powder provided by:

2. INSTITUT MAX VON LAUE - PAUL LANGEVIN Summary: Penetration Depth Anisotropy in MgB 2 Powder Neutrons and the Vortex Lattice – Small Angle Neutron Scattering Anisotropic superconductivity in MgB 2 Modeling diffraction from the VL in powder grains Results: – Field dependent penetration depth anisotropy  – Discrepancy between powder and single crystal data

3. INSTITUT MAX VON LAUE - PAUL LANGEVIN D22 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 a 0 = 490 Å, d=425Å (hex) n   10Å   0.68º

4. INSTITUT MAX VON LAUE - PAUL LANGEVIN D22 SANS: ‘Diffraction’ from the Vortex Lattice Vortex Lattice Vortex Rocking Curve

5. INSTITUT MAX VON LAUE - PAUL LANGEVIN D22 D22: “Probably the best SANS instrument in the world!” 40m

6. 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 MgB 2

7. 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 T c  ab /  c =B c2 (B//ab)/B c2 (B//c) c / ab distorts vortex lattice Anisotropy in a two-band superconductor: MgB 2 P. Miranovic et al., J. Phys. Soc. Japan, 72, 221 (2003) V. G. Kogan, PRB 66, 020509 (2002)

8. 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 Inverted Campbell formula  = 0 o  = 40 o  = 60 o  = 70 o Y X  = X/Y

9. INSTITUT MAX VON LAUE - PAUL LANGEVIN It’s all been done on crystals: Why bother measuring MgB 2 powder? History: It took a while for quality MgB 2 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 MgB 2 were necessary in order to observe the VL with neutrons (98  g!). 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.

10. INSTITUT MAX VON LAUE - PAUL LANGEVIN Measuring the anisotropy with a powder sample Real space Reciprocal space H c   a Still need to perform a rocking curve Ring is the sum of the intensity from all orientations of crystallites

11. INSTITUT MAX VON LAUE - PAUL LANGEVIN Orientation effects about the field direction

12. INSTITUT MAX VON LAUE - PAUL LANGEVIN Orientation uncorrelated with ellipse. Lattice pinned to a-axis for example Orientation correlated with ellipse Orientation effects perpendicular to the field direction

13. INSTITUT MAX VON LAUE - PAUL LANGEVIN Modeling the powder data

14. 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

15. INSTITUT MAX VON LAUE - PAUL LANGEVIN Why does  -powder not rise? Grains>1.5  m (neutrons). If crystallites<<1.5  m then current 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

16. INSTITUT MAX VON LAUE - PAUL LANGEVIN FWHM rocking curve width B(T) w(deg) Correlation length along B d/sin(w) (  m) B(T) Finite size of flux lattice along B at least 1.5  m Finite length of flux-lattice along B due to grain size

17. 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?