Dipolar Interaction and Magnetic Ordering Ground State in Mn₁₂ Molecular Magnet

Here a direct calculation of the dipolar interaction in a single crystal Mn₁₂, with all of Mn ions summed, shows that a transition between ferromagnetic and antiferromagnetic ground states takes place where the dimension along the a(b) axis versus the dimension along the c axis reaches a certain critical value. It is shown that the ground state is dependent upon the shape of the specimen. The reason of the shape dependence of ordering is that dipolar interaction is of long-range nature and the sign of dipolar interaction is dependent on the direction.