Competing Spin Phases in Geometrically Frustrated Magnetic Molecules

We identify a class of zero-dimensional classical and quantum Heisenberg spin systems exhibiting anomalous behavior in an external magnetic field $B$ similar to that found for the geometrically frustrated kagome lattice of classical spins. Our calculations for the isotropic Heisenberg model show the emergence of a pronounced minimum in the differential susceptibility $dM/dB$ at $B_{\mathrm{s}\mathrm{a}\mathrm{t}}/3$ as the temperature $T$ is raised from 0 K for structures based on corner-sharing triangles, specifically the octahedron, cuboctahedron, and icosidodecahedron. As the first experimental evidence we note that the giant Keplerate magnetic molecule $\{{\mathrm{M}\mathrm{o}}_{72}{\mathrm{F}\mathrm{e}}_{30}\}$ (${\mathrm{F}\mathrm{e}}^{3+}$ ions on the 30 vertices of an icosidodecahedron) exhibits this behavior. For low $T$ when $B\approx B_{\mathrm{s}\mathrm{a}\mathrm{t}}/3$ two competing families of spin configurations exist of which one behaves magnetically “stiff” leading to a reduction of $dM/dB$.

Figure 1

Total energy vs magnetic field for $T=0\mathrm{K}$ for the classical AF triangle, octahedron, cuboctahedron, and icosidodecahedron. The solid curve is given by Eq. (2). The dashed curves correspond to collinear structures discussed in the text.

Figure 2

Low-temperature ($k_{B}T/J_c={10}^{-2}$) simulational results for $dM/dB$ vs $B$ for classical spins on the octahedron, the cuboctahedron, and the icosidodecahedron.

Figure 3

Differential susceptibility $dM/dB$ versus $B$ for the classical Heisenberg model of $\{{\mathrm{M}\mathrm{o}}_{72}{\mathrm{F}\mathrm{e}}_{30}\}$ obtained by Monte Carlo simulations for temperatures given in the legend.

Figure 4

Experimental results (in arbitrary units) for a sample of $\{{\mathrm{M}\mathrm{o}}_{72}{\mathrm{F}\mathrm{e}}_{30}\}$ performed at 0.42 K using a pulsed-field technique. In the inset Monte Carlo results for 0.42 and 2.0 K are given.

Figure 5

Differential susceptibility $dM/dB$ versus $B/B_{\mathrm{s}\mathrm{a}\mathrm{t}}$ of the quantum Heisenberg cuboctahedron ($s=1$) for values of $k_{B}T/J$ shown in the legend.