Are Verdet Constants Temperature Dependent? The Verdet constant of a magneto-optical material shows up in the calculation of the rotation of polarized light in a medium submerged in a magnetic field.  The amount of rotation is given by
$$
\theta=VBd,
$$
where $\theta$ is the angle of rotation of linear polarized light, $V$ is the Verdet constant, $B$ is the magnetic field (assumed to be constant over the length of the crystal), and $d$ is the path length over which the magnetic field interacts with the light.
I was told that there should be a temperature dependence somewhere as well as a  dependence on the wavelength of the laser? Where do these dependencies fit in this equation?
 A: The Verdet constant is a coefficient which sums up the magneto-optical properties of the medium.  So, the temperature and wavelength dependence are wrapped up in it.  Fundamentals of Photonics by B.E.A. Saleh expresses the Verdet constant in terms of the wavelength as
$$
V\simeq-\frac{\pi\gamma}{\lambda n}
$$
where $\lambda$ is the wavelength of the light and $n$ is the index of refraction of the material, and $\gamma$ is called the magnetogyration coefficient.  The magnetogyration coefficient shows up in the equation of motion of the electrons in the material which is given by
$$
\mathbf{D}=\mathbf{\epsilon E}+i\epsilon_0\gamma\mathbf{B\times E}.
$$
So, $\gamma$ tells how strongly the electrons in the material are curved by the magnetic field when they are driven by the electric field of the light.  Determining $\gamma$ from solid state calculations is an arduous task, but the authors of this paper (unfortunately behind a paywall) say that "the effect is most likely associated with shifts in the band gap."  
In the same paper they measured the temperature dependence of the Verdet constant in three common magneto-optical glasses.  As you can see below the temperature dependence of all of them is on the order of $\sim10^{-4}$ of the static Verdet constant.


*

*For SF-57 they measure $V_0=11.5\ \frac{\text{deg}}{\text{cm}}$ and $\frac{dV}{dT}=1.26\cdot10^{-4}\ \frac{1}{\text{K}}$.  

*For SiO$_2$ they measure $V_0=2.1\ \frac{\text{deg}}{\text{cm}}$ and $\frac{dV}{dT}=0.69\cdot10^{-4}\ \frac{1}{\text{K}}$. 

*For BK-7 they measure  $V_0=2.3\ \frac{\text{deg}}{\text{cm}}$ and $\frac{dV}{dT}=0.63\cdot10^{-4}\ \frac{1}{\text{K}}$.

