Temperature-dependent magnetism in artificial honeycomb lattice of connected elements

Artificial magnetic honeycomb lattices are expected to exhibit a broad and tunable range of novel magnetic phenomena that would be difficult to achieve in natural materials, such as long-range spin ice, entropy-driven magnetic charge-ordered states, and spin order due to the spin chirality. Eventually, the spin correlation is expected to develop into a unique spin-solid-state-density ground state, manifested by the distribution of the pairs of vortex states of opposite chirality. Here we report the creation of an artificial permalloy honeycomb lattice of ultrasmall connecting bonds, with a typical size of $\simeq 12$ nm. Detailed magnetic and neutron-scattering measurements on the newly fabricated honeycomb lattice demonstrate the evolution of magnetic correlation as a function of temperature. At low enough temperature, neutron-scattering measurements and micromagnetic simulation suggest the development of a loop state of vortex configuration in this system.

Figure 1

Schematic description of spin configuration on a two-dimensional honeycomb lattice vertex and the atomic force micrograph. (a)–(c) Typical two-out, one-in and all-out spin arrangements on a vertex of a two-dimensional artificial magnetic honeycomb lattice resulting in net magnetic charges of $\pm Q$ and $\pm 3Q$, respectively. (d) Theoretical researches suggest that, at sufficiently low temperature, magnetic charges at the vertexes of an artificial honeycomb lattice can arrange themselves to create a spin solid state, manifested by the periodic arrangement of pairs of chiral vortex states. (e) A full-size atomic force micrograph of artificial honeycomb lattice, derived from a diblock porous template combined with reactive ion etching. The bond length, width, and lattice separation are approximately 12 nm, 5 nm, and 26 nm, respectively. (f) Atomic force micrograph of a typical metallic honeycomb lattice fabricated using the method described in the text and the Supplemental Material.

Figure 2

In-plane magnetic measurements and polarized off-specular neutron reflectometry data. (a) Here we show $M$ vs $T$ data in zero-field-cooled (ZFC) and field-cooled (FC) measurements at characteristic fields. $M$ vs $T$ measurements in different fields not only exhibit strong temperature dependence but also reveal multiple ordering regimes as functions of field and temperature (also see inset). (b) Spin-solid-state configuration, used to simulate the off-specular polarized reflectometry profile [(d), right]. (c) Off-specular neutron-reflectometry data recorded with spin-up incident polarization at $T=300$ and 5 K, respectively. Here, the $x$ axis indicates the in-plane correlation while the $y$ axis indicates the out-of-plane correlation. The specular reflection at room temperature, indicating a paramagnetic state, is replaced by a broad diffuse scattering extending along the $x$ axis, primarily due to the development of the spin solid phase. (d) Numerically simulated off-specular neutron-reflectometry profiles for paramagnetic [weakly ferromagnetic (FM)] honeycomb film (left) and the spin solid state (right) are consistent with the experimental data. Compared to the off-specular data where a very weak intensity is observed, specular reflection is strong in the FM case (left). Unlike the FM case, the simulated profile using the spin solid state [as shown in (b)] exhibits bands of broad scattering along the horizontal axis (right) with almost negligible specular intensity. The error bar represents one standard deviation in the experimental data.

Figure 3

Magnetic measurements in an applied magnetic field and micromagnetic simulation results of permalloy honeycomb lattice. (a) $M$ vs $H$ measurements at two different temperatures. Magnetic field was applied in plane to the sample. The error bar represents one standard deviation in the experimental data. (b) Experimental data are compared with micromagnetic simulation. Near zero field, the artificial honeycomb lattice exhibits two-in and one-out spin-ice structure. As the field is reduced, a pair of chiral vortices arises, as indicated by the arrows. (c) The magnetic hysteresis loop obtained from the micromagnetic simulation agrees well with the experimental data. The micromagnetic simulation was performed using a $0.2\times 0.2$ ${\mathrm{nm}}^2$ mesh size, with magnetic field applied in plane to the lattice.