By the fabrication of periodically arranged nanomagnetic systems it is possible to engineer novel physical properties by realizing artificial lattice geometries that are not accessible via natural crystallization or chemical synthesis. This has been accomplished with great success in two dimensions in the fields of artificial spin ice and magnetic logic devices, to name just two. Although first proposals have been made to advance into three dimensions (3D), established nanofabrication pathways based on electron beam lithography have not been adapted to obtain free-form 3D nanostructures. Here we demonstrate the direct-write fabrication of freestanding ferromagnetic 3D nano-architectures. By employing micro-Hall sensing, we have determined the magnetic stray field generated by our free-form structures in an externally applied magnetic field and we have performed micromagnetic and macro-spin simulations to deduce the spatial magnetization profiles in the structures and analyze their switching behavior. Furthermore we show that the magnetic 3D elements can be combined with other 3D elements of different chemical composition and intrinsic material properties.

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 $dM/dB$.

The observation of hysteresis effects in single molecule magnets like ${\mathrm{Mn}}_{12}$-acetate has initiated ideas of future applications in storage technology. The appearance of a hysteresis loop in such compounds is an outcome of their magnetic anisotropy. In this Letter we report that magnetic hysteresis occurs in a spin system without any anisotropy, specifically where spins mounted on the vertices of an icosahedron are coupled by antiferromagnetic isotropic nearest-neighbor Heisenberg interaction giving rise to geometric frustration. At $T=0$ this system undergoes a first-order metamagnetic phase transition at a critical field $B_{\mathrm{c}}$ between two distinct families of ground state configurations. The metastable phase of the system is characterized by a temperature and field dependent survival probability distribution.