Shape- and orientation-dependence of surface barriers in single crystalline d-wave Bi_2Sr_2CaCu_2O_8+delta

TL;DR

This study investigates how the shape and orientation of a single crystal of Bi_2Sr_2CaCu_2O_8+delta influence the magnetic field at which vortices first enter, revealing effects of geometry and crystal alignment on surface barriers.

Contribution

It provides experimental evidence on the dependence of surface barriers on crystal shape and orientation, and compares results with theoretical geometric barrier calculations.

Findings

H_p varies with aspect ratio as predicted by geometric barrier theory.

Square shape significantly enhances the first flux entry field.

Minor orientation-dependent effects observed at low temperatures.

Abstract

Magneto-optical imaging and Hall-probe array magnetometry are used to measure the field of first flux entry, H_p, into the same Bi_2Sr_2CaCu_2O_8+delta single crystal cut to different crystal thickness-to-width ratios (d/w), and for two angles alpha between the edges and the principal in-plane crystalline (a,b) axes. At all temperatures, the variation with aspect ratio of H_p is qualitatively well described by calculations for the so-called geometric barrier [E.H. Brandt, Phys. Rev. B 60, 11939 (1999)]. However, the magnitude of H_p is strongly enhanced due to the square shape of the crystal. In the intermediate temperature regime (T < ~ 50 K) in which the Bean-Livingston barrier limits vortex entry, there is some evidence for a tiny crystal-orientation dependent enhancement when the sample edges are at an angle of 45 deg; with respect to the crystalline axes, rather than parallel to them.