Abstract
We show that two $g$-wave components of the order parameter are induced by the internal orbital motion of $d$-wave pairing electrons in the presence of a magnetic field without assuming additional pairing interactions. Near a $d$-wave vortex center, the $g$-wave components with a relative phase $\ensuremath{\pi}/2$ have an opposite winding number with respect to the dominant $d$-wave component. The spatial dependence of the magnetically induced $g$-wave components is the same as that of an induced $s$-wave component by spatial variation of the $d$-wave component and each $g$-wave component has a fourfold symmetry. Therefore, the vortex has an eight-lobe profile.
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