Multipolar exchange interaction: Difference between revisions

Revision as of 01:45, 22 September 2016

Revision as of 03:36, 22 September 2016

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=== Multi-exchange Description ===

Using the addition theorem of tensor operators, the product of a rank n tensor and a rank m tensor can generate a new tensor with rank n+m ~ |n-m|. Therefore, a high rank tensor can be expressed as the inverted circular product of low rank tensors. This convention is useful to interpret and reduce the high rank multipolar exchange terms as a "multi-exchange" process of dipoles (or pseudospins). For example, for the spherical harmonic tensor operators of <math> J=1 </math> case, we have

:<math> Y_{2}^{-2}=2Y_{1}^{-1}Y_{1}^{-1} </math>

:<math> Y_{2}^{-1}=\sqrt{2}(Y_{1}^{-1}Y_{1}^{0}+Y_{1}^{0}Y_{1}^{-1}) </math>