  The Landau--Lifshitz--Baryakhtar (LLBar) equation perturbed by a
space-dependent noise is a system of fourth order stochastic PDEs which models
the evolution of magnetic spin fields in ferromagnetic materials at elevated
temperatures, taking into account longitudinal damping, long-range
interactions, and noise-induced phenomena at high temperatures. In this paper,
we show the existence of a martingale solution (which is analytically strong)
to the stochastic LLBar equation posed in a bounded domain $\mathscr{D}\subset
\mathbb{R}^d$, where $d=1,2,3$. We also prove pathwise uniqueness of the
solution, which implies the existence of a unique probabilistically strong
solution. Finally, we show the Feller property of the Markov semigroup
associated with the strong solution, which implies the existence of invariant
measures.
