Geometric Frustration of Colloidal Dimers on a Honeycomb Magnetic Lattice

Abstract

We study the phase behavior and the collective dynamics of interacting paramagnetic colloids assembled above a honeycomb lattice of triangular shaped magnetic minima. A frustrated colloidal molecular crystal is realized when filling these potential minima with exactly two particles per pinning site. External in-plane rotating fields are used to anneal the system into different phases, including long range ordered stripes, random fully packed loops, labyrinth and disordered states. At a higher amplitude of the annealing field, the dimer lattice displays a two-step melting transition where the initially immobile dimers perform first localized rotations and later break up by exchanging particles across consecutive lattice minima. DOI: 10.1103/PhysRevLett.116.038303 Geometric frustration arises when the spatial arrangement of the system elements prevents simultaneous minimization of all interaction energies, and features at low temperature a highly degenerate ground state [1]. Effects of such phenomenon manifest in disparate systems, from classical magnets [2,3] [7][8][9]. Recent experiments with size-tuneable microgel particles [10] have shown that strongly confined colloids represent a versatile model to investigate geometrically frustrated states. In contrast to lattices of interacting nanoscale islands such as artificial spin ice [11,12], colloids feature time and length scales that are accessible via simple light microscopy, combined with the possibility to control in situ the pair interaction via external fields.Above a periodic potential, microscopic particles can be arranged into colloidal molecular crystals [13], i.e., lattices of doublets, triplets, or larger clusters characterized by internal rotational degrees of freedom [14]. While colloidal molecular crystals are excellent models to study geometric frustration effects due to competing orientational order and lattice constraints [15][16][17][18], the focus of these experiments has been placed mainly on the melting scenario of trimer systems on a triangular lattice [13]. On this lattice, trimers can be arranged only in one of two orientational states, while dimers present a richer phase behavior due to the larger number of possible configurations between pairs [17]. The lattice covering by dimer particles is also a fascinating problem in statistical mechanics [19], which has been recently the subject of renewed theoretical interest [20,21], in addition to being present in different processes like melting [18], self-assembly [22], and molecular adsorption on a crystalline surface [23].This Letter investigates the colloidal ordering and dynamics of interacting microscopic dimers self-assembled above a honeycomb magnetic lattice. Each dimer is composed of a pair of paramagnetic colloids confined in a triangular shaped magnetic minimum. An external precessing field sets the dimers into rotational motion, annealing the lattice to a minimum energy state. Depending on the field parameters, the resulting dimer arrangement can be mapped to a long range striped...

Emergent geometric frustration of artificial magnetic skyrmion crystals

“…The system reveals a rich phase behavior when skyrmion-current interactions compete with structural confinement strength. In contrast to lattices of interacting nanoscale particles/islands such as artificial spin ice [43,44], or colloids [71,72,105], the spin-torque reconfigurability of the proposed skyrmion ices makes them compatible with standard spintronic devices such as magnetic tunnel junctions and thus straightforwardly integrable to the existing semiconductor manufacturing processes.…”

“…It has been shown numerically that both the colloid and vortex ice systems can produce not only the same spin ice rules observed for nanomagnet ices, but also the ice-rule-obeying ground states not yet observed in nanomagnet ices [58,60]. A colloidal version of an artificial spin ice system has been realized using interacting paramagnetic colloids [71,72] …”

Living islands of driven two-dimensional magnetic colloids on the disordered substrate

“…Using an external field, we can control and track the motion of colloidal particles, and thereby probing the microscopic rheological properties and viscous elastic responses of the biological cells. But an external field will cause an equilibrium system into a non-equilibrium moving state, and thus there will exhibit a series of unusual phenomena, such as self-assembly [5,6,10,30], clustering [7][8][9][10][31][32][33][34][35], swarming [36,37], phase separation [25,38,39], odd rheological and phase behaviors [8,40,41].…”

“…The living clusters and living crystals are shown to form in the low density active colloids [7], and there will exhibit non-equilibrium stripes either in the direction of the driving force or in the transverse direction, depending on the pinning strength [26]. It is pointed out that adjusting the short-range attraction between colloidal particles could control the structure and growth of kinetic clusters [44], and the long-range repulsion between the colloidal particles as well as the attraction between colloidal particles and pinning centers in the substrate will lead to rich phase behaviors [32]. This provides a way to manipulate the active particles by changing the boundaries [33] and the environments [15,34,45].…”

Statistical analysis of phase formation in 2D colloidal systems

“…Of particular interest are studies of frustration [6], network formation [7][8][9][10][11][12], crystallization [13][14][15][16][17] or the glass transition [18][19][20]. The beauty of microscopy in this context is that the structures are imaged in real space and can be directly visualized.…”