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The exchange interaction is investigated theoretically for electrons confinedto a 2-D sample placed in a linearly varying magnetic field perpendicular tothe plane. Unusual and interesting behavior is predicted: starting from zero,as one adds electrons to the system, its size will increase continuously butwill then collapse. However this collapse will be reversed as the numbercrosses another critical value, which we estimate here. For electron parameterstypical for 2DEG's, the instability could be observable at sufficiently lowelectron densities. A Hartree Fock equation is derived and investigated. Wealso show that in an appropriate asymptotic limit an approximate localpotential can be derived. One key lesson is that the exchange interaction islarge and cannot be reasonably excluded from any valid theoreticalinvestigation.

Instability induced by exchange forces in a 2-D electron gas in a magnetic field with uniform gradient