Elastic Coupling at Quantum Phase Transitions and in Chiral Magnets

We investigate two topics in which elastic coupling to microscopic degrees of freedom shapes the physics on
large scales: Continuous phase transitions and chiral magnetism.

In the first part, we explore how elasticity influences the universal, critical behavior of classical and quantum phase transitions.
While the classical theory is well-established,
with lattice coupling leading to, depending on the thermodynamic ensemble, Fisher-renormalized critical exponents at constant volume or a first-order transition in the case of constant pressure,
quantum criticality coupled with elasticity presents different features.
Elastic coupling is non-perturbative if the critical exponent of specific heat is positive
and, in the quantum theory, induces microscopic instabilities.
We also investigate criticality in elastic ferroelectrics,
where coupling to shear strain leads to much richer physics for both classical and quantum phase transitions.

The second part focuses on chiral magnets, where inversion symmetry breaking gives rise to modulated spin textures such as helices and skyrmions,
which, when coupled to lattice degrees of freedom, induce modulated strain textures.
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We investigate the effect of elastic coupling on chiral surface twists.
While magnetoelastic effects lead to surface strains and can modify twist profiles,
they fail to explain the large-scale surface reconstructions observed experimentally in the skyrmion phase.