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Maybe this is not eactly the same situation, but some examples of magnetic structure described as a mixture of two irreps are given for orthoferrites in old Izyumov's book ("Neutron Diffraction of Magnetic Materials"), chapter 13, pg. 105: called "abnormal magnetic structures".
 
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To: [email protected] ([email protected]);
Subject: magnetic structure defined by 2 or more irreps;
12.07.2025, 13:49, "[email protected]" <[email protected]>:

Dear all,

I am looking for cases in the literature in which at least 2 different
irreducible representations are necessary to describe the magnetic
structure at the same atomic site.

Specifically, I mean that the atomic site must be the same in the
magnetic cell; that is not the case where the A site in the nuclear cell
is split into A1 and A2 sites in the magnetic cell, with different
irreps at A1 and A2.

Thanks in advance,
Alberto

,

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Maxim Lobanov
[email protected]
 
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