  In this paper, we study the initial-boundary value problem for the stochastic
Landau-Lifshitz-Baryakhtar (SLLBar) equation with Stratonovich-type noise in
bounded domains $\mathcal{O}\subset\mathbb{R}^d$, $d=1,2,3$. Our main results
can be briefly described as follows: (1) for $d=1,2,3$ and any
$\mathbf{u}_0\in\mathbb{H}^1$, the SLLBar equation admits a unique
local-in-time pathwise weak solution; (2) for $d=1$ and small-data
$\mathbf{u}_0\in\mathbb{H}^1$, the SLLBar equation has a unique global-in-time
pathwise weak solution and at least one invariant measure; (3) for $d=1,2$ and
small-data $\mathbf{u}_0\in\mathbb{L}^2$, the SLLBar equation possesses a
unique global-in-time pathwise very weak solution and at least one invariant
measure, while for $d=3$ only the existence of martingale solution is obtained
due to the loss of pathwise uniqueness.
