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We consider a neutral particle with permanent magnetic dipole moment in anelastic medium with the presence of a uniform distribution of screwdislocations interacting with a radial electric field. We show that the uniformdistribution of dislocations plays the role of an effective uniform magneticfield, and obtain a spectrum of energy which depends on the Aharonov-Cashergeometric phase [Y. Aharonov and A. Casher, Phys. Rev. Lett. 53, 319 (1984)].Moreover, from the dependence of energy levels on the Aharonov-Casher geometricphase, we calculate the persistent spin currents in this elastic Landau system.

Persistent spin currents in an elastic Landau system