Magnetic monopole and string excitations in two-dimensional spin ice

Abstract

We study the magnetic excitations of a square lattice spin-ice recently produced in an artificial form, as an array of nanoscale magnets. Our analysis, based upon the dipolar interaction between the nanomagnetic islands, correctly reproduces the ground-state observed experimentally. In addition, we find magnetic monopole-like excitations effectively interacting by means of the usual Coulombic plus a linear confining potential, the latter being related to a string-like excitation binding the monopoles pairs, what indicates that the fractionalization of magnetic dipoles may not be so easy in two dimensions. These findings contrast this material with the three-dimensional analogue, where such monopoles experience only the Coulombic interaction. We discuss, however, two entropic effects that affect the monopole interactions: firstly, the string configurational entropy may loose the string tension and then, free magnetic monopoles should also be found in lower dimensional spin ices; secondly, in contrast to the string configurational entropy, an entropically driven Coulomb force, which increases with temperature, has the opposite effect of confining the magnetic defects.

Broken vertex symmetry and finite zero-point entropy in the artificial square ice ground state

“…This results in a twofold degenerate ground state in the square ice 14 , as experimentally observed in ref. 7 and in a small intensive entropy, S = k B ln(2), as expected from Ising models, such that the entropy per island vanishes in the thermodynamic limit.…”

Realizing three-dimensional artificial spin ice by stacking planar nano-arrays

“…Indeed, as shown in Fig. 5(a), the tension σ of the Dirac string grows with increasing |h − h * | in the ordered states [32,40] (see supplementary materials for details). Interestingly, the tension is finite even when h = h * due to the long-range part of the dipolar interactions.…”

Defect Dynamics in Artificial Colloidal Ice: Real-Time Observation, Manipulation, and Logic Gate

“…Since VðlÞ scales with the coupling constant, it follows that Q; κ ∼ ω ∼ H 2 . By fitting this potential, we obtain the ratio Q=κ ¼ 0.0290 AE 0.0014a 2 between the Coulombic and line tension contribution, which is 1 order of magnitude lower than the corresponding one found for ASI [21].…”

“…Artificial spin ice systems (ASI) are lattices of interacting nanoscale ferromagnetic islands, recently introduced as a versatile model to investigate geometrically frustrated states [9,10], including the role of disorder [11,12], thermalization [13][14][15], and the excitation dynamics [16][17][18][19][20]. In opposition to bulk spin ice such as pyrochlore compounds, ASI allow us to directly visualize the spin textures and to tailor the spatial arrangement of the system elements.An intriguing aspect in ASI, which is attracting much theoretical interest, is the dynamics of defects [21][22][23][24][25][26][27][28]. The interactions between pairs of defects is one of the distinctive features between three dimensional (3D) and two dimensional (2D) spin ice.…”

“…An intriguing aspect in ASI, which is attracting much theoretical interest, is the dynamics of defects [21][22][23][24][25][26][27][28]. The interactions between pairs of defects is one of the distinctive features between three dimensional (3D) and two dimensional (2D) spin ice.…”