  The light curves of magnetic, chemically peculiar stars typically show
periodic variability due to surface spots that in most cases can be modeled by
low-order harmonic expansion. However, high-precision satellite photometry
reveals tiny complex features in the light curves of some of these stars that
are difficult to explain as caused by a surface phenomenon under reasonable
assumptions. These features might originate from light extinction in corotating
magnetospheric clouds supported by a complex magnetic field dominated by
higher-order multipoles. We aim to understand the photometric signatures of
corotating magnetospheres that are governed by higher-order multipoles. We
determined the location of magnetospheric clouds from the minima of the
effective potential along the magnetic field lines for different orders of
multipoles and their combination. From the derived magnetospheric density
distribution, we calculated light curves accounting for absorption and
subsequent emission of light. For axisymmetric multipoles, the rigidly rotating
magnetosphere model is able to explain the observed tiny features in the light
curves only when the higher-order multipoles dominate the magnetic field not
only at the stellar surface, but even at the Kepler radius. However, even a
relatively weak nonaxisymmetric component leads to warping of equilibrium
surfaces. This introduces structures that can explain the tiny features
observed in the light curves of chemically peculiar stars. The light emission
contributes to the light variability only if a significant fraction of light is
absorbed in the magnetosphere.
