Multipolar exchange interaction: Difference between revisions

Revision as of 16:57, 29 October 2015

Revision as of 18:16, 20 November 2015

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

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

If so, a quadrupole-quadrupole interaction (see next section) can be considered as a two steps dipole-dipole interaction. For example, <math> Y_{2_{i}}^{+2_{i}}Y_{2_{j}}^{-2_{j}}=4Y_{1_{i}}^{+1_{i}}Y_{1_{i}}^{+1_{i}}Y_{1_{j}}^{-1_{j}}Y_{1_{j}}^{-1_{j}} </math>, so the one step quadrupole transitontransition <math> Y_{2_{i}}^{+2_{i}} </math> on site <math> i </math> now becomes a two steps of dipole transition <math> Y_{1_{i}}^{+1_{i}}Y_{1_{i}}^{+1_{i}} </math>. Hence not only inter-site-exchange but also intra-site-exchange terms appear (so called multi-exchange). If <math> J </math> is even larger, one can expect more complicated intra-site-exchange terms would appear. However, one has to note that it is not a perturbation expansion but just a mathematical technique. The high rank terms are not necessarily smaller than low rank terms. In many systems, high rank terms are more important than low rank terms.<ref name="Review"/>

== Multipolar Exchange Interactions ==