Single skyrmion creation and annihilation by spin waves in a crossbar geometry are theoretically analyzed. A critical spin-wave frequency is required both for the creation and the annihilation of a skyrmion. The minimum frequencies for creation and annihilation are similar, but the optimum frequency for creation is below the critical frequency for skyrmion annihilation. If a skyrmion already exists in the cross bar region, a spin wave below the critical frequency causes the skyrmion to circulate within the central region. A heat assisted creation process reduces the spin-wave frequency and amplitude required for creating a skyrmion. The effective field resulting from the Dzyaloshinskii-Moriya interaction and the emergent field of the skyrmion acting on the spin wave drive the creation and annihilation processes.
