Exploring the phase diagram of 3D artificial spin-ice

Abstract

Artificial spin-ices consist of lithographic arrays of single-domain magnetic nanowires organised into frustrated lattices. These geometries are usually two-dimensional, allowing a direct exploration of physics associated with frustration, topology and emergence. Recently, three-dimensional geometries have been realised, in which transport of emergent monopoles can be directly visualised upon the surface. Here we carry out an exploration of the three-dimensional artificial spin-ice phase diagram, whereby dipoles are placed within a diamond-bond lattice geometry. We find a rich phase diagram, consisting of a double-charged monopole crystal, a single-charged monopole crystal and conventional spin-ice with pinch points associated with a Coulomb phase. In experimental demagnetised systems, broken symmetry forces formation of ferromagnetic stripes upon the surface, forbidding the lower energy double-charged monopole crystal. Instead, we observe crystallites of single magnetic charge, superimposed upon an ice background. The crystallites are found to form due to the distribution of magnetic charge around the 3D vertex, which locally favours monopole formation.

Tailoring magnon modes by extending square, kagome, and trigonal spin ice lattices vertically via interlayer coupling of trilayer nanomagnets

“…Among the ASI structures studied are square, kagome, tetragonal, tetris, pinwheel, and shatki lattices [50][51][52][53][54][55][56][57], as well as plaquettes of coupled NMs [58,59]. Recently, focus has been directed towards extending MCs beyond the plane to 3D nanostructures [60,61] which present rich magnetization states and spin-wave behavior not seen in 2D lattices, and has been the subject of recent work on structures such as scaffolds [62], tetrapods [63][64][65], gyroids [66], and nanovolcanoes [67], among other exciting work [68][69][70][71][72][73]. However, fabricating complex 3D structures is currently time-consuming and incompatible with industrial fabrication equipment.…”

Ultrastrong magnon-magnon coupling and chiral spin-texture control in a dipolar 3D multilayered artificial spin-vortex ice

“…Recent technological advances enable sophisticated fabrication and characterisation of 3D magnetic nanostructures, but questions remain on how to precisely control such systems. Artificial spin systems have made impressive forays into the third dimension, led by the likes of Ladak et al [24][25][26][27][28][29] , Donnelly et al [30][31][32][33][34] , and Fernández-Pacheco et al 35,36 alongside others [37][38][39] , though these remain exchangecoupled rather than dipolar. Three-dimensional magnonic crystals have also been explored, with excellent studies by Gubbiotti et al 40,41 and Barman et al 28,29 amongst others [42][43][44] .…”

“…However, these increased system design freedoms are accompanied by a requirement of far more challenging nanofabrication and measurement approaches. Three-dimensional systems typically demand complex patterning techniques such as two-photon lithography 26,27 or focused electron beam-induced deposition 23,35 , and specialist measurement methods such as X-ray tomography 34 . These issues serve to restrict progress on studying three-dimensional magnetic systems and the new physics they offer.…”

“…While limited in system design freedom relative to 'true' 3D lithography approaches 26,27,33,35 , the system microstate space is greatly expanded relative to conventional 2D nanomagnetic structures. Each nanoisland layer may assume four distinct states (two macrospin and two vortex, termed 'artificial spin-vortex ice' 45 ) and the state of each magnetic layer may be independently addressed via global magnetic field as the layers have different thicknesses (20 and 30 nm, respectively) giving a coercive field offset.…”