  Magnetic hopfions are string-like three-dimensional topological solitons,
characterised by the Hopf invariant. They serve as a fundamental prototype for
three-dimensional magnetic quasi-particles and are an inspiration for novel
device concepts in the field of spintronics. Based on a micromagnetic model and
without considering temperature, the existence of such hopfions has been
predicted in certain magnets with competing exchange interactions. However,
physical realisation of freely moving hopfions in bulk magnets have so far been
elusive. Here, we consider an effective Heisenberg model with competing
exchange interactions and study the stability of small toroidal hopfions with
Hopf number $Q_\text{H}=1$ by finding first-order saddle points on the energy
surface representing the transition state for the decay of hopfions via the
formation of two coupled Bloch points. We combine the geodesic nudged elastic
band method and an adapted implementation of the dimer method to resolve the
sharp energy profile of the reaction path near the saddle point. Our analysis
reveals that the energy barrier can reach substantial height and is largely
determined by the size of the hopfion relative to the lattice constant.
