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We calculate the ground-state of a two-dimensional electron gas in ashort-period lateral potential in magnetic field, with the Coulombelectron-electron interaction included in the Hartree-Fock approximation. For asufficiently short period the dominant Coulomb effects are determined by theexchange interaction. We find numerical solutions of the self-consistentequations that have hysteresis properties when the magnetic field is tilted andincreased, such that the perpendicular component is always constant. Thisbehavior is a result of the interplay of the exchange interaction with theenergy dispersion and the spin splitting. We suggest that hysteresis effects ofthis type could be observable in magneto-transport and magnetizationexperiments on quantum-wire and quantum-dot superlattices.Comment: 3 pages, 3 figures, Revtex, to appear in Phys. Rev.

Hysteresis effect due to the exchange Coulomb interaction in short-period superlattices in tilted magnetic fields