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Posted on 02/05/2014

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Kirrily Rule

Magnetic monopoles in the pyrochlore structure

What does it look like?

Image generated by the VESTA (Visualisation for Electronic and STructural analysis) software http://jp-minerals.org/vesta/en/

The red atoms here are oxygen, and blue are the transition metal with the purple atoms representing the position of the rare earth atoms. Image generated by the VESTA (Visualisation for Electronic and STructural analysis) software http://jp-minerals.org/vesta/en/

What is it?

The pyrochlore crystal structure is a cubic that can be described by the spacegroup Fd-3m. The general formulae for these materials are A₂B₂O₆ and A₂B₂O₇ where the A and B species are typically either rare earth ions, or transition metal species. The A and B sites form an array of interlinked tetrahedra, which are 3 sided shapes consisting of triangles and it is this that often leads to exotic magnetic properties.

Dy₂Ti₂O₇ and Ho₂Ti₂O₇ are two such pyrochlore systems which have been called "spin-ice". This stems from the "2in-2out" magnetic spin structure which can be likened to the water-ice structure where for each oxygen ion, two protons (or hydrogens) must be in the near position and two in the far position. Dy₂Ti₂O₇ and Ho₂Ti₂O₇ are also part of a larger family of geometrically frustrated pyrochlores in which the magnetic "spins" cannot simultaneously satisfy their antiferromagnetic (antiparallel) spin arrangements with all of their neighbouring spins due to the geometric constraints, similar to Jarosite.

(left) The rare earth tetrahedra structure of the pyrochlore lattice can be used to understand the magnetism in these materials. (right) The “3in-1out” (red) and “1in-3out” (blue) “monopoles” can be seen joined by an infinitely thin Dirac string [Morris et al., Science 326, 411 (2009)].

(left) The rare earth tetrahedral pyrochlore structure can be used to understand the magnetism in these materials. (right) The "3in-1out" (red) and "1in-3out" (blue) "monopoles" can be seen joined by an infinitely thin Dirac string [Morris et al., Science 326, 411 (2009)].

Both Dy₂Ti₂O₇ and Ho₂Ti₂O₇ received a lot of attention in the media in 2009 due to the observation of the elusive magnetic monopoles as emergent quasi-particles. We all know that every magnet has a north and south pole and that if we cut these dipole magnets in half, we fail to separate the ends into monopoles, but instead create two new magnets each with a north and south pole. However due to the topology of the spin structure in Dy₂Ti₂O₇ and Ho₂Ti₂O₇, under certain applied field and low temperature sample conditions, magnetic monopoles could be formed within the structure. The application of a small magnetic field could flip one of the spins such that one tetrahedron was a "3in-1out" (south) pole and its neighbouring tetrahedron was a "1in-3out" (north) pole (eee Figure). It was shown that with no additional energy input, these two "monopoles" could move away from each other such that locally there appeared to be an isolated monopole. In actual fact these two monopoles were connected by an extremely long, tensionless Dirac string. However the sensational news of observing a "magnetic monopole" for the first time became a hot topic on news websites around the world – even being mentioned in "The Big Bang Theory".

Where did the structure come from?

This crystal structure was taken from van de Velde et al., Powder Diffraction 5 (4), pp. 229-31 (1990) and displays the pyrochlore structure for the related Tb₂Ti₂O₇ material. Each of the A₂Ti₂O₇ materials (A = rare earth) forms a cubic structure with a lattice parameter close to 10 Å.