  In this paper, we introduce the cohomology theory of relative Rota-Baxter
operators on Leibniz algebras. We use the cohomological approach to study
linear and formal deformations of relative Rota-Baxter operators. In
particular, the notion of Nijenhuis elements is introduced to characterize
trivial linear deformations. Formal deformations and extendibility of order n
deformations of a relative Rota-Baxter operator are also characterized in terms
of the cohomology theory.
