<p>In this paper, we study a two-phase model with a magnetic field in periodic domain <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {T}^{N} (N=2,3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mi>N</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi>N</mi> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, which was first derived by Wen and Zhu (J.Differ.Equ., 2018). By introducing a new quantity and utilizing the intrinsic structure of the system, we overcome the difficulty arising from the lack of dissipation for density of fluid and density of particles in the mixture, and establish the existence of global strong solutions in Sobolev spaces <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H^{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation>. Furthermore, we obtain the exponential decay of solutions. Our results considerably improve upon the recent works by Wen and Zhu (J.Differ.Equ., 2018) and Chen and Zhu(J.Differ.Equ., 2019).</p>