# Spin operators in the ZFS-PAS

1. Jun 3, 2012

### theflamer14

Hi guys,

My question is regarding defining spin operators in the zero field splitting principal axis system. I am currently working on a S = 2 spin system, and know how to define the Sx, Sy, and Sz spin matrices. My question is, how do I rotate them to the zfs-PAS? Some papers I came across simply leave it at etc. $\hat{S}$$_{x}$. I found a web page that uses:

R$_{r}$(θ) = e$^{i σ_{r} θ/2 }$

r = x,y,z

(can't post the website because this is my first post! :P )

But it is for spin 1/2 systems. Also, it uses only one angle, $\theta$. However, in my Zeeman Hamiltonian, I have my magnetic field, $\vec{B}$, specified by the polar angles ($\theta$ and $\varphi$) of the vertices of a truncated icosahedron (buckeyball). So is there a need to incorporate both the angles into converting a normal spin operator, ex. ${S}_{x}$, into $\hat{S}$$_{x}$? Any help in helping me understand/visualize is appreciated.

Regards,

Kiran

Last edited: Jun 3, 2012