Kramers Trimer Clusters and Time-Reversal Symmetry

  • Ion I. GeruEmail author
Part of the Springer Tracts in Modern Physics book series (STMP, volume 281)


In this chapter is shown that structural distortions of trihomonuclear Kramers clusters occur as a consequence of the time-reversal symmetry. These distortions are caused by the fact that the time-reversal operator \(\mathbf {T}\) is not a separate element of the magnetic point group \(G^{\prime }\), but forms a combined \(\mathbf {T}g\) element with other g elements of the original point group G. The order of the element g cannot be an odd number, otherwise it would lead to \(\mathbf {T}\in G^{\prime }\), which contradicts the definition of the group \(G^{\prime }\). Forbidden rotations by \(2\pi /3\) and \(2\pi /5\) in the group \(G^{\prime }\) lead to the fact that metal ions of homonuclear magnetic clusters in a magnetic ordered state cannot occupy the vertices of an equilateral triangle or those of a regular pentagon. The distortion of the regular triangle or pentagon occurs only if the time-reversal operator \(\mathbf {T}\) is taken into account. Hence these structural distortions are due to the time-reversal symmetry. There are presented and discussed experimental data concerning the anomalous behavior of chromium(II), iron(III), copper(II), vanadium(II) and cobalt(II) trihomonuclear clusters determined by their four-color symmetry.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Institute of ChemistryAcademy of Sciences of MoldovaChisinauMoldova

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