I have measured via MOKE the reduced remanence, Mr/Ms, of a Permalloy thin film with well-defined uniaxial anisotropy (induced by a field applied during deposition) as a function of applied field angle. The result is a pretty polar plot (https://www.dropbox.com/s/29x7w2gyhbvdd8v/UApolar.png) which fits well to abs(cos(theta)), with theta=0 being the easy axis.
I would like to know where to begin in deriving this functionality. I think I can start from the Stoner-Wohlfarth/coherent rotation model although I know my sample does not follow such a reversal mechanism for all field angles.
What I've done so far is write my free energy terms for uniaxial anisotropy and Zeeman energy. I see in a couple of my favorite resources (O'Handley's "Modern Magnetic Materials" pg. 319 and http://iopscience.iop.org/0143-0807/29/3/008) that the next step is to apply my equilibrium conditions (take derivatives wrt angle between H and M) to come up with some relations that allow you to analytically play with applied field as a function of magnetization.
It is here that I've hit a brick wall. Am I on the right track?
You're doing it right. But the explanation of this dependence is much easier.
Almost any magnetometer (MOKE in particular) measures the projection of the magnetic moment of the external field. Ie M * cos (alpha). For a uniform magnetization reversal of magnetization in zero field is directed along the easy axis, i.e. rotated by an angle theta relative to the axis of the field. Thus You always measure M * cos (theta).
See for example https://www.researchgate.net/publication/257919787_Magnetic_anisotropy_in_Fe_films_deposited_on_SiO2_Si(001)_and_Si(001)_substrates?ev=prf_pub
Article Magnetic anisotropy in Fe films deposited on SiO2 /Si(001) a...
Hi Sergey,
Thank you for your answer! It does make perfect sense, however, I was hoping to develop the cosine relationship from somewhere, like coherent rotation model or from the free energy expression of uniaxial anisotropy. This is because I am proposing a teaching experiment based on the MOKE.
Also thank you for including your publication. I found it very helpful in answering my next question: how to do the same for four-fold anisotropy!
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Physical Phenomena
- Luminescence