The spin ice compounds Dy 2 Ti 2 O 7 and Ho 2 Ti 2 O 7 are highly unusual magnets that epitomize a set of concepts of great interest in modern condensed matter physics: Their low-energy physics exhibits an emergent gauge field and their excitations are magnetic monopoles that arise from the fractionalization of the microscopic magnetic spin degrees of freedom.

In particular, we analyse a two dimensional spin-ice model; we nd that the topological transition is strongly a ected by geometrical constraints in the shape of the sample, and that in the case where the dimension perpendicular to the eld is much smaller than the longitudinal one, i.e. in the quasi-1D spin-ice-ladder limit, it splits into a series of rst-order phase transitions characterised.

Kagome spin-ice system means frustration In the HoAgGe crystals, the magnetic moments (spins) of the holmium atoms form a so-called two-dimensional Kagome pattern.

Specific examples include a monopole crystal phase for spin ice and the charge ordered KII phase of artificial kagome ice (3). Recent experiments have shown evidence of this fragmentation in three dimensions, in the frustrated pyrochlore magnet Nd2Zr2O7 (4), in artificial kagome ice (5) and in the layered quasi-two-dimensional magnet Dy3Mg2Sb3O14 (6), and I shall comment on these exciting.

We present a numerical study of magnetic ordering in spin ice on kagome, a two-dimensional lattice of corner-sharing triangles. The magnet has six ground states and the ordering occurs in two stages, as one might expect for a six-state clock model. In spin ice with short-range interactions up to second neighbors, there is an intermediate critical phase separated from the paramagnetic and.

An artificial spin-ice material is a geometrically frustrated lattice of nanoscale ferromagnetic islands used to create a two-dimensional model, analogue to spin ice, in which the physics of frustration can be directly visualized and investigated at finite temperature. Main results.

Fig. 1 Thermally activated two-dimensional artificial square ice with height offsets between nanomagnets. (A) Tilted-sample scanning electron microscopy (SEM) image of an artificial square ice with an introduced height offset h, which can be varied from sample to sample, until the competing interactions J 1 and J 2 are equalized and an extensive spin ice degeneracy is achieved.

Here we study the statistical properties of two-dimensional spin ice in its ground state by the Monte Carlo simulation method. Using a new sampling algorithm, we show that the short-range ice rule in two dimensions gives rise to long-range but not dipole-like correlations, to non-Gaussian probability density function for magnetization and to non-extensive conditional entropy (entropy with.