ENgineering FrustratiOn in aRtificial Colloidal icEs: degeneracy, exotic lattices and 3D states

Project Information

ENFORCE

Grant agreement ID: 811234

DOI

10.3030/811234

Project closed

EC signature date 18 February 2019

Start date 1 January 2020

End date 30 June 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 850 298,00

EU contribution

€ 1 850 298,00

Coordinated by

UNIVERSITAT DE BARCELONA
Spain

Periodic Reporting for period 3 - ENFORCE (ENgineering FrustratiOn in aRtificial Colloidal icEs:degeneracy, exotic lattices and 3D states)

Reporting period: 2023-01-01 to 2024-06-30

Summary of the context and overall objectives of the project

The main goal of the Consolidator grant "Enforce" is to power a series of experimental research lines based on the combined use of magnetic and optical forces to explore geometric frustration phenomena in soft colloidal systems. Geometric frustration refers to the inability of a system to satisfy competing interactions between its elements in presence of spatial constraints and it is widespread in condensed matter physics. Understanding the fundamental mechanisms of geometric frustration and how it emerges will contribute significantly to advancing fundamental science and will also unveil emerging phenomena in interacting many-body systems. Moreover, from the technological side, frustrated systems display topological defects and controlling their dynamics could provide guidelines for engineering similar states in nanoscale magnetic spin ice. Such systems could potentially enable a new class of dissipation free memories and devices, with vast technological applications.

While geometric frustration phenomena have been traditionally investigated with artificial spin ice systems, namely lattice of lithographically designed nano scale islands, in this project we propose to investigate an alternative, microscopic version of it named the colloidal ice. Such system is based on interacting colloidal particles placed within a lattice of topographic double wells, allowing to directly visualize the particle dynamics and to tune in real time their pair interactions. The features of the colloidal ice allow to address several fundamental questions in frustrated systems from a completely different perspective and thus with a radically innovative approach.

The project is divided in three Workpackages (WPs) each with specific Objectives (OBJs). In WP1, OBJ1 aims at restoring the residual entropy in the two-dimensional square ice, a current challenge in nanoscale spin ice systems. The goal of OBJ2 is to miniaturize the colloidal ice to the nanoscale in order to explore the effect of strong thermal fluctuations on the particle dynamics. In WP2, OBJ1 focused on complex lattices characterized by mixed coordination and their low energy states, while in OBJ2 the group will investigate annealing effects of these lattice via precessing magnetic field. Finally, WP3 aims at realizing a three-dimensional version of a coloidal ice.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

In these 2.5 years of the project, the group have advanced in fulfilling all the OBJs of WP1 and part of that of WP2. First, we investigated the low energy state in a bi-disperse ice system by using two types of particles with different susceptibilities and size. We find a re-entrant transition when the applied field is cyclically ramped and discover novel hysteretic and memory effects that results from the presence of disorder in the form of different in the particle interactions. Further, we demonstrated experimentally a way to partially recover the degeneracy in a square colloidal ice via application of a shear to a lattice of double wells (WP1, OBJ1). This research was done in collaboration with Erdal C. Oğuz and Yair Shokef at Tel Aviv university. In OBJ2 of WP1 the group succeed in finding a way to miniaturize the colloidal ice and in trapping magnetic nanoparticles by using a ferrite garnet film (FGF) that self-assembled into a lattice of ferromagnetic bubbles. In OBJ1 of WP2, the group demonstrated a way to control the bulk phase of a colloidal ice by suitable engineering of the boundary of the system with an antiferromagnetic order. Moreover, it was discovered that strategically placing defects at the corners could be used to generate novel bistable states, or topological strings which result from competing ground state regions in the bulk. The group also realized exotic lattices and observe that during transition from different geometries that preserve the lattice connectivity, there is an inversion in the topological charge transfer between sublattices. In OBJ2 of WP2 the group experimentally demonstrated a novel annealing protocol for a square colloidal ice by using a precessing magnetic field and it is now working on applying machine learning approach and feedback protocol to the system. Parallel to these works, the group demonstrated several other results in the field of driven colloidal systems under strong confinement, such as the role of hydrodynamic interactions between particles either driven across periodic potentials or by rotating magnetic fields. Also, the group demonstrated the organization of active chiral rotors, their phase separation and develop a technique to induce current in magnetic colloids by using uniform time dependent magnetic field rather than gradient.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

With the sheared square system, the group progressed beyond the state of the art by demonstrating a way to partially recover the degeneracy in a colloidal ice system. This research was conducted in collaboration with Dr. Erdal C. Oğuz and Prof. Yair Shokef at Tel-Aviv university. Further, by engineering proper boundary conditions in a square ice, the group also reach a breakthrough in the field of artificially frustrated systems, demonstrating a way to force a square ice to reach rapidly the ground state. These results can be applied to other nanoscale systems on a smaller length scale, and thus could be of particular appeal for realizing novel memory and devices based on the motion of magnetic charges. The group also discovered that driven colloids across periodic potential could display collective directional locking effect, which could be used to realize novel sorting device at the microscale. By confining paramagnetic particles, we were able to generate currents of magnetic particles using uniform time dependent magnetic fields. The letter result goes beyond the state of the art in magnetophoresis, which usually require a gradient and thus dis-homogeneous field to move magnetic particles.

In the near future, the group is working to develop a three-dimensional version of the colloidal ice system, in agreement with WP3 in the DOW. Although challenging, this will revolutionize the field of geometric frustration since it will allow direct observation of topological charge and defect in a three dimensional solid via confocal microscopy.

A lithographic structure of a Cairo lattice used for a colloidal ice.