Abstract
One of the most remarkable examples of emergent quasi-particles is that of the‘fractionalization’ of magnetic dipoles in the low energy configurations of materials knownas ‘spin ice’ into free and unconfined magnetic monopoles interacting via Coulomb’s1/r law (Castelnovo et al 2008 Nature 451 42–5). Recent experiments have shown that aCoulomb gas of magnetic charges really does exist at low temperature in these materialsand this discovery provides a new perspective on otherwise largely inaccessiblephenomenology. In this paper, after a review of the different spin ice models, we presentdetailed results describing the diffusive dynamics of monopole particles starting both fromthe dipolar spin ice model and directly from a Coulomb gas within the grand canonicalensemble. The diffusive quasi-particle dynamics of real spin ice materials within the‘quantum tunnelling’ regime is modelled with Metropolis dynamics, with theparticles constrained to move along an underlying network of oriented paths, whichare classical analogues of the Dirac strings connecting pairs of Dirac monopoles.
Highlights
Spin ice materials[1, 2] form part of a series of rare-earth oxide insulator R2M2O7 with space group F d3m where R3+ is a magnetic (Dy3+ and Ho3+) and M4+ a non-magnetic (Ti4+ or Sn4+) ion
We have simulated the dynamics of both the dipolar spin ice (DSI) model and a Coulomb gas of magnetic monopoles in the grand canonical ensemble occupying the sites of the diamond lattice, using a Metropolis Monte Carlo algorithm
A second point to notice is that the monopole density falls to zero at a noticeable higher temperature for the DSI than for the nearest neighbour spin ice (NNSI) model which must surely be related to the brutal slowing down of the dynamics compared with our analytical Arrhenius law calculation
Summary
Spin ice materials[1, 2] form part of a series of rare-earth oxide insulator R2M2O7 with space group F d3m where R3+ is a magnetic (Dy3+ and Ho3+) and M4+ a non-magnetic (Ti4+ or Sn4+) ion. The physics of spin ice is captured to a good approximation by an effective model with nearest neighbour ferromagnetic interactions between the moments which, together with the strong crystal field, gives rise to a frustrated ferromagnetic system:. The nearest neighbour spin ice (NNSI) Hamiltonian maps onto an Ising antiferromagnet for the pseudo spins [7, 8] (see equation (2)); a model first derived by Anderson to describe spinel materials [9]. A consequence of such constraints in this and in Figure 1: Pyrochlore lattice: The spins are located on the corner of every tetrahedra and are fixed along their local [111] axis represented by the dashed lines. In order to see the emergence of true magnetic quasi-particles one has to go beyond the NNSI through the inclusion of dipolar interactions, as is considered
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