Fig. 2. Thermodynamics of the dipolar Apamea lattice.

a, c, d Vertex-type populations plotted as a function of temperature for two-, three-, and four-nanomagnet vertices, respectively. Error bars, calculated from the standard deviation of the mean over every XMCD frame, are present but smaller than the size of the markers. b Magnetic moment and charge configurations extracted from a single frame within an XCMD image sequence recorded at 290 K. Red shapes are positive charges, blue are negative, open circles are Type A vertices, higher energy Type B vertices are shown by closed circles, and pluses denote Type b vertices. e Schematic of a geometrically useful pair of plaquettes in a low-energy configuration. Under the conditions that only Type I and Type α vertices may exist, this pair of plaquettes is impossible to fill with entirely Type A vertices. Specifically, at least two of six of the coordination 3 vertices must be Type B. One of the Type B vertices is colored purple to denote that its sign will be determined by an undrawn spin. The dotted arrows indicate spins which are shared by paired plaquettes, making the total number of spins per paired plaquette 10.