  We have modeled magneto-dielectric phase transitions in ABX$_3$-type layered
triangular lattice compounds. The model consists of a spin system (magnetic
transition) and a lattice system (dielectric transition). Magnetic exchange
interactions are supposed to change with a relative positionbetween two spins.
This assumption produces an effective coupling between the lattice and the
spin. Applying the nonequilibrium relaxation method, we have found that a
simultaneous magneto-dielectric phase transition occurs when energy scales of
the spin part and the lattice part coincide. An intermediate phase like the
partial disordered phase disappears. Both systems relax frustration of the
other system cooperatively and realize ordered states.
