Summary: \(\Gamma \)-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness \(\varepsilon \) approaches zero of a ferromagnetic thin structure \(\Omega _\varepsilon =\omega \times (-\varepsilon ,\varepsilon)\), \(\omega \subset \mathbb{R} ^2\), whose energy is given by \[ {\mathcal E}_{\varepsilon }({\overline m})={1\over \varepsilon }\int _{\Omega _{\varepsilon }}\left (W({\overline m},\nabla {\overline m}) +{1\over 2}\nabla {\overline u}\cdot {\overline m}\right)dx \] 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 assumptions with \(p> 1\). Partial results are also obtained in the case \(p=1\), under an additional assumption on \(W\).