  Viscoelastic liquids are characterized by a finite static viscosity and a
zero yield stress, whereas soft solids have an infinite viscosity and a
non-zero yield stress. The rheological nature of viscoelastic materials has
long been a challenge, and it is still a matter of debate. Here, we provide for
the first time the constitutive equations of linear viscoelasticity for
magnetic wires in yield stress materials, together with experimental
measurements using Magnetic Rotational Spectroscopy (MRS). With MRS, the wires
are submitted to a rotational magnetic field as a function of frequency and the
wire motion is monitored by time-lapse microscopy. The soft solids studied are
gel-forming polysaccharide aqueous dispersions (gellan gum) at concentrations
above the gelification point. It is found that soft solids exhibit a clear and
distinctive signature compared to viscous and viscoelastic liquids. In
particular, the wire average rotation velocity equals zero over a broad
frequency range. We also show the MRS technique is quantitative. From the wire
oscillation amplitudes, the equilibrium elastic modulus is retrieved and agrees
with polymer dynamics theory.
