Field-induced structures in a ferrofluid with well-defined magnetite nanoparticles with a permanent magnetic dipole moment are analyzed on a single-particle level by in situ cryogenic transmission electron microscopy (2D). The field-induced columnar phase locally exhibits hexagonal symmetry and confirms the structures observed in simulations for ferromagnetic dipolar fluids in 2D. The columns are distorted by lens-shaped voids, due to the weak interchain attraction relative to field-directed dipole-dipole attraction. Both dipolar coupling and the dipole concentration determine the dimensions and the spatial arrangement of the columns. Their regular spacing manifests long-range end-pole repulsions that eventually dominate the fluctuation-induced attractions between dipole chains that initiate the columnar transition. DOI: 10.1103/PhysRevLett.97.185702 PACS numbers: 64.70.Nd, 75.50.Mm, 82.70.Dd Nanoparticles dispersed in a solvent and with a sufficiently large permanent magnetic dipole moment selfassemble into a variety of magnetic equilibrium structures such as (flux-closure) rings and wormlike, branched dipole chains [1,2]. The morphology of these clusters, formed in absence of an external field, has been examined in detail, together with a determination of pair correlation functions and chain-length distributions [3]. In contrast, much less is known about the structural transitions induced by an external (homogeneous) magnetic field for fluids of permanent dipoles. Interestingly, magnetic colloids in an external field are nevertheless frequently encountered in practical applications [4] and biomedicine [5,6].The structure formation and phase behavior of colloidal systems in reduced dimensions is not necessarily equivalent to that of three-dimensional (3D) systems [7][8][9]. In particular, for permanent dipolar spheres confined to two dimensions (2D) a field-induced transition to a columnar phase with local hexagonal symmetry was predicted [10], although a conclusive experimental real-space analysis is still lacking. Elongated iron-particle clusters have been imaged [1] but the irregular particle shape and the bidisperse size distribution obstruct the wanted single-particle analysis. Parallel structures have also been observed for maghemite ferrofluids dried in the presence of a homogeneous field [11,12]. However, we have shown elsewhere that drying procedures may drastically change structure morphology [2]. Moreover, dipole interactions in conventional ferrofluids are in general too weak for a realistic comparison to the purely dipolar spheres from simulations.In this Letter, we report unequivocal real-space evidence for the predicted columnar phase transition [10] from in situ cryo-TEM images of monodisperse magnetic colloids with dominating dipolar interactions. The particle positions are confined by a 2D film whereas the dipole orientations can thermally fluctuate in 3D. Our imaging results, in addition, allow to quantify positional and angular interparticle correlations showing, among other things, a pr...