Magnetostatic interactions on a square lattice

Abstract

The metastable zero field magnetic states of elongated Permalloy islands on square lattices of different geometries are investigated by means of magnetic force microscopy and numerical calculations. Keeping the island shape L / w = 10 fixed while varying the interparticle distances a, it is demonstrated that the relative frequencies of observed magnetic configuration at remanence strongly depend on the packing density of an array and the magnetic history ͑i.e., in which direction the array has been saturated before measurement͒. From 16 possible arrangements, only two are experimentally observed. For small L / a, a mixture of configurations, i.e., a spin ice, is found in agreement with previous studies, while for large L / a, an onion state unexpectedly prevails independent of the direction of the previously applied field. The results are discussed within the framework of potential theory and general stray field interaction. The relative frequencies of metastable states as well as the absence of the true ground state are in good agreement with theory.

Magnetic monopole and string excitations in two-dimensional spin ice

“…As experimentally shown in Ref. [8], this metastable state is a very real possibility when magnetic fields are applied. In this case only the topology of type (b) of Fig.…”

“…[8,9]. We would like to remark that although this is the ground state, its thermal equilibration in experiments seems to be very difficult [8,9,10]. Once the system is naturally frustrated, in the two-in/two-out configuration, the effective magnetic charge Q i,j M (number of spins pointing inward minus the number of spins pointing outward on each vertex (i, j)) is zero everywhere.…”

“…The same ground state was also reported in Refs. [8,9]. We would like to remark that although this is the ground state, its thermal equilibration in experiments seems to be very difficult [8,9,10].…”

“…Our aim in this paper is to study spin ice materials, but in two spatial dimensions. Such structures have been artificially produced in a geometrically frustrated lattice of nanoscale ferromagnetic islands [7,8,9]. Here, we examine the excitations ("magnetic monopoles") and how they interact in this 2d system.…”

Magneto-optical Kerr effect studies of square artificial spin ice

“…A wide range of interesting behavior 2,3 can be observed in these artificial frustrated magnets by tuning the geometry of square [4][5][6][7] , triangular 8,9 , hexagonal (and kagome) [10][11][12][13][14][15][16][17][18][19][20] and brickwork lattices, as well as isolated clusters 21 . In particular, the local moment behavior of these systems has shown that they are good realizations of ice models, and a range of studies have examined monopole excitations and drawn upon close analogies with the pyrochlore spin ice materials.…”