The application of multi-scale magnetic matrix materials in high-gradient magnetic separation: From micro- and nano- to millimeter-scale

• This review comprehensively analyzes multi-scale magnetic matrix materials, spanning micro- and nano- to millimeter scales, for high-gradient magnetic separation applications. • Magnetic matrices composed of Fe, Co, Ti, and Ni alloys exhibit high magnetization rates, low elastic modulus, and high saturation magnetic field strengths, enhancing separation performance. • The separation mechanisms involve complex interactions among magnetic, gravitational, centrifugal, and van der Waals forces, which are critical for optimizing magnetic separator design. • Size and shape effects significantly influence the magnetic behavior of matrices, providing new insights for advanced applications in materials science and mineral processing.