Magnetic monopoles in spin ice
Spin ice is the name given to a class of magnetic materials that have a property called frustration, which occurs due to the lattice geometry - the way the atoms are arranged inside the crystal. These compounds have the general formula A2B2O7 where A is a rare-earth atom and B is transition metal. A widely studied example of spin ice is dysprosium titinate, Dy2Ti2O7.
The name comes from an analogy with common water ice - the spin directions map onto the positions of the hydrogens. In water ice, four hydrogen atoms surround an oxygen atom in a tetrahedral arrangment, and two of the hydrogens are closer to the central oxygen than the other two. By contrast, in spin ice we have two spins pointing towards the centre of the tetrahedra, and two pointing away. This is the lowest energy state of the system, but since there are many many configurations in which this state can be realised, we say that the ground state is highly degenerate.
The spins are coupled ferromagnetically with long-range dipolar interactions between spins leading to this '2-in/2-out' ground state. As we lower the temperature of the system, we find that the entropy does not tend to zero, showing that there is a degree of inherent randomness associated with the ground state. This is realised via the flipping of spins, all the way down to the lowest temperatures.
When a spin flip occurs, and the state of our tetraherdra is defined by 3 spins pointing in (out) and one spin pointing in (out), the state is excited. This is associated with a divergence of the magnetic field, and interpreted as a magnetic monopole excitation.
magnetic monopoles in spin ice whats ever?
You say "This is associated with a divergence of the magnetic field". You measure \grad \cdot B \ne 0, when a spin flip occurs?