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Register a new userGoldstone-like phonon modes in a (111)-strained perovskite
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Goldstone modes are massless particles resulting from spontaneous symmetry breaking. Although such modes are found in elementary particle physics as well as in condensed matter systems like superfluid helium, superconductors and magnons - structural Goldstone modes are rare. Epitaxial strain in thin films can induce structures and properties not accessible in bulk and has been intensively studied for (001)-oriented perovskite oxides. Here we predict Goldstone-like phonon modes in (111)-strained SrMnO3 by first-principles calculations. Under compressive strain the coupling between two in-plane rotational instabilities give rise to a Mexican hat shaped energy surface characteristic of a Goldstone mode. Conversely, large tensile strain induces in-plane polar instabilities with no directional preference, giving rise to a continuous polar ground state. Such phonon modes with U(1) symmetry could emulate structural condensed matter Higgs modes. The mass of this Higgs boson, given by the shape of the Mexican hat energy surface, can be tuned by strain through proper choice of substrate.
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Structural phase transitions described by Mexican hat potentials should in principle exhibit aspects of Higgs and Goldstone physics. Here, we investigate the relationship between the phonons that soften at such structural phase transitions and the Higgs- and Goldstone-boson analogues associated with the crystallographic Mexican hat potential. We show that, with the exception of systems containing only one atom type, the usual Higgs and Goldstone modes are represented by a combination of several phonon modes, with the lowest energy phonons of the relevant symmetry having substantial contribution. Taking the hexagonal manganites as a model system, we identify these modes using Landau theory, and predict the temperature dependence of their frequencies using parameters obtained from density functional theory. Separately, we calculate the additional temperature dependence of all phonon mode frequencies arising from thermal expansion within the quasi-harmonic approximation. We predict that Higgs-mode softening will dominate the low-frequency vibrational spectrum of InMnO$_3$ between zero kelvin and room-temperature, whereas the behavior of ErMnO$_3$ will be dominated by lattice expansion effects. We present temperature-dependent Raman scattering data that support our predictions, in particular confirming the existence of the Higgs mode in InMnO$_3$.
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