We study the phase behavior of two-dimensional paramagnetic colloidal systems on square pinning arrays, the latter being created by a holographic optical tweezer technique. When the particle interaction strength is decreased, a transition from an incommensurate to a commensurate solid is observed. At even smaller pair potentials, the interstitial particles start to melt, whereas the particles at the substrate pinning sites are still localized. Our results are in good agreement with recent numerical studies on vortex melting in periodic pinning arrays. DOI: 10.1103/PhysRevLett.90.158302 PACS numbers: 82.70.Dd, 64.70.Dv, 64.70.Rh Properties of two-dimensional (2D) systems are well known to be crucially affected by the presence of periodic substrate pinning sites. One intriguing example is a type II superconductor in the mixed state where vortices are arranged in a flux-line lattice. In the case of regularly ordered substrate pinning sites, strong anomalies in the temperature and magnetic-field dependencies of the magnetization, electrical resistance, and critical current are observed [1,2]. Those anomalies are particularly pronounced at matching fields where the number of flux lines coincides with the number of the pinning sites and essentially all of the magnetic field inside the film resides in quantized fluxoids centered on the artificial pinning sites. Several groups investigated recently the melting behavior of such vortex lattices in square, triangular, and kagome pinning lattices by means of molecular dynamics and Langevin dynamics simulations [3,4]. For weak pinning and matching field conditions, on square lattices, an order-order transition from a commensurate square vortex array to a triangular floating solid phase was observed. In contrast, for strong pinning, only a single transition from the square pinned lattice to the liquid state was found. Under nonmatching field conditions and strong substrates a multistage melting process was observed in which vortex motion takes place by an exchange process of interstitial and pinned vortices [3].Another example where pinning effects play an important role is the phase behavior of adsorbates interacting with periodic substrates. This is important for a wide variety of condensed matter systems including, e.g., physisorbed atomic or molecular monolayers on crystalline surfaces [5][6][7][8] or colloidal particles interacting with patterned surfaces [9][10][11][12]. In all cases, the detailed understanding of how periodic substrate pinning sites modify the properties of a 2D system remains a sophisticated task because it is the delicate interplay between the adsorbate-adsorbate interaction and the adsorbate-substrate interaction which leads to a complex phenomenology.In this Letter we investigate the phase behavior of a colloidal monolayer of superparamagnetic particles on a square patterned substrate potential, the latter being produced by a holographic optical tweezer technique [13]. Because the colloidal pair potential can be precisely adjusted by an externa...

We study the melting behavior of a binary system (R ¼ 4.5 mm, r ¼ 2.8 mm) of paramagnetic colloidal spheres in two-dimensional (2D) circular cavities. A repulsive interaction between the particles is caused by an external magnetic field B that induces magnetic dipole moments perpendicular to the sample plane. By means of video microscopy, we investigate the positions of the particles and their trajectories. For small interaction strengths, we observe a completely liquid phase where large and small particles diffuse across the entire system. With increasing B the larger particles become-due to their larger magnetic moment-localized and form a stable structure while the smaller particles behave still as a liquid. For even higher magnetic fields, the small particles also become increasingly localized and preferentially arrange as interstitial sites between the structures formed by the large particles. We present a systematic study of this rather complex multi-stage melting process which strongly depends on the particle numbers of large and small particles.

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