  A magnetic skyrmion is a spin whirl with topological protection and high
mobility to electric current. Intrinsic magnetoelastic coupling in chiral
magnets permits manipulation of magnetic skyrmions and their lattice using
mechanical loads, which is essential for developing future spintronics devices.
It is found in experiments that the stability and deformation of skyrmions are
sensitive to stresses, while the appearance of magnetic skyrmions in turn has a
significant effect on the mechanical properties of the underlying material.
However, a theory which explains these related phenomena within a unified
framework is not seen. Here we construct a thermodynamic model for B20
helimagnets incorporating a magnetoelastic functional with necessary higher
order interactions derived by group theory. Within the model, we establish the
methodology to calculate the phase diagram and equilibrium properties of
helimagnets under coupled temperature-magneto-elastic field. Applying the model
to bulk MnSi, we calculate the temperature-magnetic field phase diagram under
stress-free condition and its variation when uniaxial compression is applied.
We also calculate the variation of all the elastic constants with magnetic
field. The results obtained agree quantitatively with corresponding
experiments. Our model provides a reliable basis for further theoretical
studies concerning any magnetoelastic related phenomena in chiral magnets.
