Ignoring Your Neighbors: Moment Correlations Dominated by Indirect or Distant Interactions in an Ordered Nanomagnet Array

We have studied the moment correlations within triangular lattice arrays of single-domain coaligned nanoscale ferromagnetic islands. Independent variation of lattice spacing along and perpendicular to the island axis tunes the magnetostatic interactions between islands through a broad range of relative strengths. For certain lattice parameters, the sign of the correlations between near-neighbor island moments is opposite to that favored by the pairwise interaction. This finding, supported by analysis of the total correlation in terms of direct and convoluted indirect contributions across multiple pairwise interactions, indicates that indirect interactions and/or those mediated by further neighbors can be tuned to be dominant, with implications for the wide range of systems composed of interacting nanomagnets.

Figure 1

(a) Schematic of triangular lattice arrays. The near-neighbor pair types are labeled $C_1$, $C_2$, $C_3$, and $C_4$. (b) MFM image of a section of one triangular lattice array ($x=680\mathrm{nm}$, $d/x=0.4$). Black and white halves represent the north and south poles, respectively, of each ferromagnetic island. The scale bar is $1\mu \mathrm{m}$.

Figure 2

(a)–(d) Correlation values $\mathrm{sgn}(J_t)C_t$ as a function of $x$ for fixed $d/x$ ratios 0.4, 0.8, 1, and 1.2, respectively. (e)–(h) Interaction energies $J_t$ as a function of $x$ for fixed $d/x$ ratios 0.4, 0.8, 1, and 1.2, respectively, as simulated by OOMMF software (in units of ${10}^{-19}\mathrm{J}$).

Figure 3

(a)–(c) Correlation values $\mathrm{sgn}(J_1)C_1$, $\mathrm{sgn}(J_2)C_2$, and $\mathrm{sgn}(J_3)C_3$ as a function of $d$ for fixed $x$ distance. Each contains 5 groups of patterns with fixed $x$ (400, 480, 560, 680, and 880 nm). (d)–(f) Interaction energies $J_1$, $J_2$, and $J_3$ as a function of $d$ for fixed $x$, as simulated by OOMMF software (in units of ${10}^{-19}\mathrm{J}$).

Figure 4

Tests of the ansatz (in units of ${10}^{-19}\mathrm{J}$) that further-neighbor and indirect interactions are important in determining $C_1$ and $C_2$. The data funnel through the origin in both plots. The fanout away from the origin may be attributable to different effective temperatures in different lattices.