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The Loewdin orthogonalization procedure being the well-known technique,particularly in quantum chemistry, however, gives rise to novel effects missedin earlier studies. Making use of the technique of irreducible tensorialoperators we have developed a regular procedure for account of theorthogonalization effects. For illustration we address the emergence of aspecific magnetoelectric coupling for noncentrosymmetric 3d or 4f ions.

The L\"owdin orthogonalization and magnetoelectric coupling for noncentrosymmetric ions