[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The artificial magnetic honeycomb lattice is expected to manifest a broad and tunable range of novel magnetic phenomena associated with the geometric frustration at the magnetic bar vertices. The theoretically predicted phase diagram of the magnetic honeycomb lattice has four unique magnetic vertex configurations, completely dependent on temperature. The system will transition from a paramagnetic gas state to a spin ice state to a magnetic charge-ordered state, manifested as pairs of vortex loops with opposite chirality, as the temperature of the system is reduced. At low enough temperature, the magnetic correlation is expected to develop into the spin solid state configuration with net zero entropy density and magnetization, with an lternating distribution of magnetic vortex loops of opposite chirality repeating across the lattice. Current efforts to experimentally access the lower energy phases have been unsuccessful due to the huge inter-elemental energy between the large ([about]1 m long) bars produced using lithography. For the first time, we have fabricated macroscopicsized samples of permalloy (N[subscript i 0.8]F[subscript e 0.2]) or tin-neodymium (SnNd) honeycomb lattices with ultra-small, connected bar elements by utilizing the self-assembly properties of the diblock copolymer PS-b-P4VP for the template. This new technique produces bar elements of [approximanetly equal to] 12-18 nm in length, reducing the inter-elemental energy by several orders of magnitude (from [approximanetly equal to] 10[subscript 4] K to [approximanetly equal to]12 K), allowing our system to access the lower energy states. We have performed detailed magnetic, electrical, and neutron scattering experiments to observe these predicted phase transitions in our connected honeycomb lattice of permalloy. Numerical modeling of the polarized neutron reectometry measurements, omplimented by the results from micromagnetic simulations and magnetic measurements, provided detailed information on the temperature dependent evolution of spin correlation in the system. We found that our magnetic honeycomb lattice tends to develop the spin solid state configuration for very low temperatures. Small-angle neutron scattering results indicate that the system manifests a non-unique magnetic state, showing a coexistence of both the long-range ordered and the short-range magnetic charge ordered states at an intermediate temperature of T [approximanetly equal to] 175 K, contrary to the previous theoretical reports. Electrical measurements on the magnetic honeycomb have led to a patent for a new magnetic, diode-type electronic device that exhibits strong unidirectional electrical transport behavior characterized by an asymmetric colossal enhancement in differential conductivity. Experimental observations from the Nd-based antiferromagnetic artificial honeycomb lattice presented evidences to the development of an unconventional solid state described by interpenetrating Wigner crystals of magnetic charges. The SnNd honeycomb system produces highly unusual diamagnetic behavior and a magnetic field induced two-step switching in differential conductivity as a function of current bias.
Localization and duality for ABJM latitude Wilson loops