1. Vortex Lattice Anisotropy in Magnesium Diboride Morten Ring Eskildsen Department of Physics University of Notre Dame

2. R. Cubitt and C. D. Dewhurst Institut Laue Langevin, Grenoble, France N. Jenkins, M. Kugler, G. Levy, S. Tanaka and Ø. Fischer DPMC, University of Geneva, Switzerland J. Jun, S. M. Kazakov and J. Karpinski Solid State Physics Laboratory, ETHZ, Zürich, Switzerland This work was supported by the Swiss National Science Foundation, MaNEP and the Swiss Federal Office BBW. Collaborators

3. VL Anisotropy in Uniaxial Superconductors L. J. Campbell, M. M. Doria and V. G. Kogan, Phys. Rev. B 38, 2439 (1988). Rotating applied field away from axis distorts vortex lattice. Vortices in unit cell lies on ellipse. Distortion determined by anisotropy of penetration depth and coherence length

4. MgB 2 : A Two-Band Superconductor H. J. Choi et al., Nature 418, 758 (2002).  -band  -band J. Nagamatsu et al., Nature 410, 63 (2001).

5. Vortex Lattice Imaging by SANS The reciprocal lattice is directly observed in diffraction patterns measured on 2D detector. VL distortion due to uniaxial anisotropy? VL reflectivity determined by superconducting penetration depth and coherence length. Measurements done at d22 at Institut Laue Langevin (ILL).

6. Form Factor Measurements Measurement of absolute scattered intensity allows determination of characteristic lengthscales.

7. Vortex Lattice Anisotropy MgB 2 is uniaxial superconductor. Measurements done with field rotated away from c axis. VL anisotropy reflects . 2 K, 0.5 T

8. Field & Temperature Dependence of  Anisotropy increases with both field and temperature. Increase with field due to suppresseion of  -band and is expected to saturate at  =  H ~ 6. Increase with temperature due to thermally mixing of  and  bands. Temperature dependence in good agreement with theoretical prediction.

9. A Couple of Problems… Anisotropy found by STS with H  c is smaller than SANS extrapolation. SANS results on MgB 2 powder gives upper limit on  = 1.4 at 0.5 T/2 K, well below result for single crystals. NMR at 2 T and 5 K indicates  close to 1 (W. Halpering, Northwestern). R. Cubitt et al., Phys. Rev. Lett. 90, 157002 (2003).

10. …More Problems: A Vortex Lattice Reorientation Transition Low field orientation with VL-planes perpendicular to a-axis. Reorientation quantified by angular split of the two degenerate domain orientations. At 60  split the VL is aligned parallel to a-axis, and a single domain is re- formed. As field is rotated away from c axis the transition field remains essentially unchanged, but transition becomes 1 st order.

11. VL Anisotropy above Reorientation Trans. Above reorientation transition Bragg peaks no longer lies on an ellipse! May be effect of slight misalignment between crystalline axes and field rotation axis. VL anisotropy drops to ~1 (no anisotropy) above reorientation transition. VL anisotropy no longer reflects  !?!

12. Summary Two-band superconductivity in MgB 2 is now well established, with the smaller gap associated with the 3D  -band and the larger gap with the 2D  -band. SANS form factor measurements show a suppression of superconductivity in the  - band with increasing field, in quantitative agreement with results obtained by STS. The supression of the  -band leads to structural changes of the VL: 1. With H || c, the VL undergoes a 30 o reorientation in the field range 0.5 - 0.9 T. 2. Below the reorientation transition, the VL anisotropy was determined as a function of field and temperature and found to increases with both temperature and field. We believe that this reflects a changing penetration depth anisotropy. 3. Above reorientation transition the VL is rhombic and isotropic, and apparently no longer influenced by penetration dept anisotropy!