Properties of crystals with magnetic point groups

5 Properties of crystals with magnetic point groups 

For magnetic crystals belonging to the type III (black and white) point groups 

A ferromagnetic material is one that possesses a magnetic moment M in the absence of a magnetic field. The magnetic induction is given by 

The magnetoelectric polarizability [X, ] of a crystalline material gives rise to a magnetic moment I (Tan axial vector, or T( 1 )ax) when the crystal is placed in an electric field E (Aa polar vector, or T( 1)). Its transpose [T/ ] describes the converse magnetoelectric effect in which the roles of Y and X are interchanged. To find the structure of K = [T, ], we look for IRs which have components of both xy z and Rx Ry Rz as bases. 

Example 15.5-1 Determine the structure of the matrix [Xy] for the type I magnetic point group 4mm (C4v) and the type III group 4mm with G = C4v and H = C2v. 

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