The authors study the Ishimori system \[ \begin{aligned} & \partial_tS = S\wedge (\partial^2_xS\pm\partial^2_y S)+b(\partial_x\phi\partial_y S+\partial_y\phi\partial_x S),\quad t\in\mathbb{R},\;x,y\in\mathbb{R},\\ & \partial^2_x\phi \mp \partial^2_y\phi = \mp 2S\cdot (\partial_x S\wedge \partial_y S),\end{aligned} \] where \(S(\cdot,t) : \mathbb{R}^2 \to \mathbb{R}^3\) with \(\|S\|= 1\), \(S\to (0,0,1)\) as \(\|(x,y)\|\to\infty\), and \(\wedge\) denotes the wedge product in \(\mathbb{R}^3\). This model was proposed by Y. Ishimori as a two-dimensional generalization of the Heisenberg equation in ferromagnetism, which corresponds to the case \(b = 0\) and signs \((-,+,+)\). Their main result shows that, subject to certain conditions, there exists a unique solution to an associated initial value problem, so showing the local well-posedness of this associated problem, with data of arbitrary size in a weighted Sobolev space.