Γ-convergence techniques and relaxation results ofconstrained energy functionals are used to identify the limiting energy as thethickness ε approaches zero of a ferromagnetic thinstructure $\Omega_\varepsilon=\omega\times(-\varepsilon,\varepsilon)$ , $\omega\subset\mathbb R^2$ , whoseenergy is given by $${\cal E}_{\varepsilon}({\overline{m}})=\frac{1}{\varepsilon}\int_{\Omega_{\varepsilon}}\left(W({\overline{m}},\nabla{\overline{m}}) +{\frac{1}{2}}\nabla {\overline{u}}\cdot {\overline{m}}\right)\,{\rm d}x$$ subject to $$\hbox{div}(-\nabla {\overline{u}}+{\overline{m}}\chi_{\Omega_\varepsilon})=0\quad\hbox{ on }\mathbb R^3,$$ and to the constraint $$|\overline{m}|=1 \hbox{ on }\Omega_\varepsilon,$$ where W is any continuous function satisfying p-growth assumptionswith p> 1. Partial results are also obtained in the case p=1, underan additional assumption on W.