  Magnetic monopole, a hypothetical elementary particle with isolated magnetic
pole, is crucial for the quantization of electric charge. In recent years,
analogues of magnetic monopoles, represented by topological defects in
parameter spaces, have been studied in a wide range of physical systems. These
works mainly focused on Abelian Dirac monopoles in spin-1/2 or non-Abelian Yang
monopoles in spin-3/2 systems. Here we propose to realize three types of spin-1
topological monopoles and study their geometric properties using the parameter
space formed by three hyperfine states of ultracold atoms coupled by
radio-frequency fields. These spin-1 monopoles, characterized by different
monopole charges, possess distinct Berry curvature fields and spin textures,
which are directly measurable in experiments. The topological phase transitions
between different monopoles are accompanied by the emergence of spin "vortex",
and can be intuitively visualized using Majorana's stellar representation. We
show how to determine the Berry curvature, hence the geometric phase and
monopole charge from dynamical effects. Our scheme provides a simple and highly
tunable platform for observing and manipulating spin-1 topological monopoles,
paving the way for exploring new topological quantum matter.
