The ability to use external magnetic fields to influence the microstructure in polycrystalline materials has potential applications in microstructural engineering. To explore this potential and to understand the complex interactions between electromagnetic fields and solid-state matter transport we consider a phase-field-crystal (PFC) model. Together with efficient and scalable numerical algorithms this allows the examination of the role that external magnetic fields play on the evolution of defect structures and grain boundaries, on diffusive time scales. Examples for planar and circular grain boundaries explain the essential atomistic processes and large scale simulations in 2D are used to obtain statistical data on grain growth under the influence of external fields.