Viscoelastic moduli of suspensions of magnetic particles in solutions of alginate polymer, as a function of shear strain amplitude, for imposed oscillatory shear strain of fixed frequency (1 Hz), and under the application of magnetic fields of different strengths, H: unfilled star/filled star, H = 0 kA m−1; unfilled square/filled square, H = 73.5 kA m−1; unfilled diamond/filled diamond, H = 156 kA m−1; unfilled circle/filled circle, 229 kA m−1; unfilled triangle/filled triangle, 282 kA m−1. (a) Sample 5Fe-15LVSA and (b) 5Fe-8MVSA. Open symbols represent values of the storage modulus (G′) and full symbols represent values of the loss modulus (G′′). (Online version in colour.)