# Nonlinear emergent elasticity and structural transitions of skyrmion crystal under uniaxial distortion

## TL;DR

This paper investigates the nonlinear elasticity and structural phase transitions of skyrmion crystals under uniaxial strain, revealing complex behaviors including multiple phase transitions, emergent polymorphism, and metastable states.

## Contribution

It provides a theoretical analysis of skyrmion crystal deformation under uniaxial stress using three methods, uncovering new phases and nonlinear elastic properties.

## Key findings

- Skyrmion crystals exhibit negative elastic stiffness under moderate tension.
- Up to six phase transitions occur under strong strain, forming four new metastable emergent crystals.
- Emergent crystals display global rotation and unlimited deformability, leading to exotic polymorphism.

## Abstract

Emergent crystals are periodic alignment of "emergent particles", i.e., localized collective behavior of atoms or their charges/spins/orbits. These novel states of matter, widely observed in various systems, may deform under mechanical forces with elasticity strikingly different from that of the underlying material. However, their nonlinear and critical behaviors under strong fields are hitherto unclear. Here we theoretically study the nonlinear elasticity and structural transitions of skyrmion crystals (SkX) suffering uniaxial distortion by using three different methods. Under moderate tension, SkX behaves like a ductile material, with a negative crossover elastic stiffness and a negative emergent Poisson's ratio at appropriate conditions of magnetic field. Under strong straining, we observe at most six phase transitions, leading to appearance of four novel emergent crystals that are thermodynamically metastable. When subject to external loads, emergent crystals rotate globally, and their composing "particles" have unlimited deformability, which render their exotic polymorphism.