Abstract
The multiferroicity driven by the conical spin state, exhibiting both spontaneous magnetization and ferroelectric polarization, offers a great promise for the effective mutual control of magnetism and ferroelectricity. To investigate this novel multiferroic state in detail, Monte Carlo simulation is performed on a three-dimensional spinel lattice with classical Heisenberg spins. The spin configuration is analyzed in the case of different lattice sizes and different exchange interactions, which presents the optimal conical spin structure approximately incommensurate with the lattice periodicity. Moreover, it is revealed that the spin frustration, which is controlled by the exchange interactions, can modulate the conical spin structure effectively, and thereby control the corresponding magnetoelectric behavior.