Magnetic Monopoles: Investigating Spin-Ice Evidence

[stedwards]

(This is not really an advanced question, but one for physicists advanced in this science, which I am not.)

In fairly recent investigation, the signature of Dirac monopoles was observed in spin ice.

Say I possessed a consistent mathematical development allowing for both magnetic monopoles and a 4-vector electromagnetic potential cast in microscopic form. Classically, it works nicely, and the monopoles can be gauged-away in vacuum. I say this just for background; I'm not advancing a theory in these forums.

1) For solid state physicists, would it be more useful if I reformulated in macroscopic form?

2) I know virtually nothing about spin-ice. Should I be concerned over non-isotropic permeability and/or permittivity? I would far prefer not to use non-isotropic formulations if applicable to materials that have shown evidence of Dirac strings.

 

[radium]

How do you gauge away a magnetic monopole? I don't think that's possible since you cannot define vector potential globally and therefore have nontrivial topology. The definition of something being topologically nontrivial is that you cannot shrink it to a point, there is an obstruction which gives you a quantization conditions.

Monopole like objects occur in a lot of condensed matter systems. Some examples are in Weyl semimetals and in spin liquids (they are the vison excitation found originally in the toric code).

 

[stedwards]

How do you gauge away a magnetic monopole? I don't think that's possible since you cannot define vector potential globally and therefore have nontrivial topology. The definition of something being topologically nontrivial is that you cannot shrink it to a point, there is an obstruction which gives you a quantization conditions.

As I said, my stuff is classical, But could you expound on this?

Monopole like objects occur in a lot of condensed matter systems. Some examples are in Weyl semimetals and in spin liquids (they are the vison excitation found originally in the toric code).

Thanks for the response, by the way. Are Weyl semimetals and spin liquids best written in microscopic or macroscopic form?

 

[radium]

I have no idea what your background is, but I'll assume you know E&M and vector calculus.
The fact that a magnetic monopole cannot be gauged away is not just a quantum mechanical thing. It is a purely topological thing. Charges are topological objects.
You cannot write a vector potential for a magnetic monopole defined globally because of the singularity at the origin. Younusve to write them in different regions and then glue them together now. Look at Nakahara's geometry topology and physics.

I have no idea what you mean by microscopic or macroscopic form, but they come in mean field theory. In SLs you have an emergent gauge structure in MF due to the Hilbert space being over complete.