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The structure of an isolated single vortex and the vortex lattice, and themagnetization in a $d$-wave superconductor are investigated within aphenomenological Ginzburg-Landau (GL) model including the mixture of the$d_{x^2-y^2}$-wave and $d_{xy}$-wave symmetry. The isolated single vortexstructure in a week magnetic field is studied both numerically andasymptotically. Near the upper critical field $H_{c2}$, the vortex latticestructure and the magnetization are calculated analytically.Comment: 14 pages, REVTeX, 2 EPS figures, Journal of Physics: Condensed Matter  (in press

The effects of mixing on vortex structures and magnetization