Vortex lattice structures in uniaxial superconductors

Abstract

The structure of the vortex lattice in anisotropic, unaxial superconductors in the domain ${H}_{c1}\ensuremath{\ll}H\ensuremath{\ll}{H}_{c2}$ is considered within the London approach. To first order in the small parameter ${\frac{(L}{\ensuremath{\lambda})}}^{2}$, where $L$ is the average intervortex spacing and $\ensuremath{\lambda}$ is the average penetration depth, there exists a continuum of different lattices with the same free energy for any direction of the magnetic induction $\mathbf{B}$ with respect to the crystal. It is shown that the degeneracy is removed if terms in the free energy of order ${\frac{(L}{\ensuremath{\lambda})}}^{4}$ are taken into account, yielding both a unique structure and a preferred orientation of the vortex lattice with respect to the direction of $\mathbf{B}$ within the crystal. Parameters of the primitive cell for this structure are obtained and evaluated for known values of the anisotropy of Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7}$. For the particular case of vortices parallel to the Cu-O planes the degeneracy remains exact (within the London approach), which should make this lattice more susceptible to disorder. The magnetization is shown to be almost parallel to the $\stackrel{^}{c}$ crystal direction for all orientations of the external field ${\mathbf{H}}_{0}$, except in a narrow domain where ${\mathbf{H}}_{0}$ is nearly normal to $\stackrel{^}{\mathbf{c}}$.