Skyrmion crystals are regular arrangements of magnetic whirls that exist in a wide range of chiral magnets. Because of their topology, they cannot be created or destroyed by smooth rearrangements of the direction of the local magnetization. Using magnetic force microscopy, we tracked the destruction of the skyrmion lattice on the surface of a bulk crystal of Fe(1-x)Co(x)Si (x = 0.5). Our study revealed that skyrmions vanish by a coalescence, forming elongated structures. Numerical simulations showed that changes of topology are controlled by singular magnetic point defects. They can be viewed as quantized magnetic monopoles and antimonopoles, which provide sources and sinks of one flux quantum of emergent magnetic flux, respectively.

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We report on local measurements of the surface potential and quantum capacitance in single layer graphene as well as multilayers thereof as a function of the carrier density by using frequency-modulated Kelvin probe force microscopy. We find excellent agreement to tight-binding calculations reported for graphene monolayers and extract the minimum quantum capacitance from density sweeps at room temperature. The surface potential of graphene multilayers is found to depend linearly on the carrier density, which suggests treating them as two-dimensional electron gases. In addition, we demonstrate that the simultaneously detected second harmonic of the Kelvin modulation, proportional to |∂2C/∂z2|, is directly sensitive to local changes in the quantum capacitance of graphene.