Effect of long- and short-range interactions on the thermodynamics of dipolar spin ice

Abstract

The thermodynamic properties of dipolar spin ice on square, honeycomb and shakti lattices in the long-range and shortrange dipole interaction models are studied. Exact solutions for the density of states, temperature dependencies of heat capacity, and entropy are obtained for these lattices with a finite number of point dipoles by means of complete enumeration. The magnetic susceptibility and average size of the largest low-energy cluster are calculated for square spin ice by means of Wang-Landau and Metropolis methods. We show that the long-range interaction leads to a blurring of the energy spectrum for all considered lattices. The inclusion of the long-range interaction leads to a significant change in the thermodynamic behaviour. An additional peak of heat capacity appears in the case of the honeycomb lattice. The critical temperature shifts in the direction of low or high temperatures; the direction depends on the lattice geometry. The critical temperature of the phase transition of square spin ice in the long-range model with frustrated ground states is obtained with the Wang-Landau and Metropolis methods independently.

Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices

“…The existence of clusters of a low-energy phase, cluster formation, the emergence of a "percolation cluster," i.e., the processes of merging into one large cluster the connection of clusters (domains) of the ground state with thermodynamics, were discussed for artificial superspin ice in Refs. [29,30], and for macrospin glass in Ref. [71].…”

“…For example, for systems with a finite number of Ising dipoles on some lattices, not all states obeying the ice rule are ground states. In particular, it is easy to verify that the configuration of dipoles of square dipole ice with long-range dipole interaction is all "up" and all "to the right" is not a configuration of the ground state, although it satisfies the ice rule-at each node, "two inward, two out" [29].…”

“…The study of the thermodynamic states of bulk spin ice to investigate the phenomenon of frustration and to study in detail the configurations of bulk magnets is associated with well-known experimental difficulties. Therefore, researchers often prefer two-dimensional (2D) analogs for studying the statistical mechanics of Ising-like frustrated spin systems on lattices with specific geometry, including those not observed in nature [29][30][31].…”

Influence of cutoff dipole interaction radius and dilution on phase transition in kagome artificial spin ice

“…Each magnetic island (macrospin) in artificial spin ice usually have a form anisotropy (for example length, width, and thickness of 220 nm × 80 nm × 25 nm in [3] or 63 nm × 26 nm × 6 nm in [15] or even 1000 nm × 75 nm × 10 nm in [13]), which limits the degree of freedom of the island magnetic moment and causes it to align along the long axis, at the same time remaining single-domain. In this work, the artificial spin ice model with dipole-dipole interaction described in the previous study [16,17] also in [18,19] is investigated. According to this model, each macrospin is represented by a point dipole, the magnetic moment of which have the Ising-like behavior.…”

Dipolar Cairo lattice: Geometrical frustration and short-range correlations

“…Artificial spin ice systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], initially introduced as two-dimensional analogues to pyrochlore spin ice [17], enabled the direct visualization of the consequences of geometrical frustration using appropriate magnetic imaging techniques. In particular, the introduction of artificial spin ices that exhibit thermally induced moment fluctuations paved the way to explore the statistical physics of geometrical frustration [3][4][5][6], emergent magnetic monopoles and macroscopic spin ice degeneracy [18,19], in addition to first attempts in achieving artificial spin glasses [20].…”