Multipolar exchange interaction: Difference between revisions

Revision as of 21:44, 25 August 2015

Revision as of 21:47, 25 August 2015

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[[File:AFM multipole chain.png|thumb|frame|right|AFM ordering chains of different multipoles.<ref name="multipolar exchange"/>]]

Unlike magnetic spin ordering where the [[antiferromagnetism]] can be defined by flipping the magnetization axis of two neighbor sites from a [[ferromagnetic]] configuration, flipping of the magnetization axis of a multipole is usually meaningless. Taking a <math> T_{yz} </math> moment as an example, if one flips the z-axis by making a <math> \pi </math> rotation toward the y-axis, it just changes nothing. Therefore, a suggested definition<ref name="multipolar exchange"/> of antiferromagnetic multipolar ordering is to flip their phases by <math> \pi </math>, i.e. <math> T_{yz} \rightarrow e^{i\pi}T_{yz}=-T_{yz} </math>. In this regard, the antiferromagnetic spin ordering is just a special case of this definition, i.e. flipping the phase of a dipole momentsmoment is equivalent to flipping its magnetization axis. As for high rank multipoles, e.g. <math> T_{yz} </math>, it actually becomes a <math> \pi/2 </math> rotation and for <math> T_{3z^2-r^2} </math> it is even not any kind of rotation.

== Compute Coupling Constants ==