Determining the structural phase transition point from the temperature of ⁴⁰Ca⁺ Coulomb crystal

We observed the linear-to-zigzag structural phase transition of a ⁴⁰Ca⁺ crystal in a homemade linear Paul trap. The values of the total temperature of the ion crystals during the phase transition are derived using the molecular-dynamics (MD) simulation method. A series of simulations revealed that the ratio of the radial to axial secular frequencies has a dependence on the total temperature that obeys different functional forms for linear and zigzag structures, and the transition point occurs where these functions intersect; thus, the critical value of the ratio of secular frequencies that drives the structure phase transition can be derived.