Strain Fields and Critical Phenomena in Manganites II: Spin-Lattice-Energy Hamiltonians

TL;DR

This paper extends a Hamiltonian model for manganites to include an energy field, uses dynamic RG to compute critical exponents, and matches theoretical predictions with experimental data at the PM-AFM transition.

Contribution

It introduces an energy field into the Hamiltonian and applies dynamic RG to Model C, providing a better understanding of critical dynamics in manganites.

Findings

Calculated dynamic critical exponents $z$, $ u z$, and $ riangle$ to leading order.

Good agreement between theory and experimental critical exponents.

Adjusted the long-range exponent $\sigma$ for optimal fit.

Abstract

The dynamic critical behavior at the paramagnetic-antiferromagnetic (PM-AFM) transition in manganites has recently been studied experimentally [Niermann et al., Phys. Rev. Lett. {\bf 114}, 037204 (2015)]. We extend the Hamiltonian of Paper I by incorporating an energy field, and study the corresponding Model C of critical dynamics. We use the dynamic renormalization group (RG) approach and calculate the dynamic critical exponents $z$, $\nu z$ and the line-width exponent $\Delta$ to leading order in the small expansion parameters $\epsilon=4-d+2\sigma$ and $\epsilon'=4-d$. Here, $d$ is the space dimension and $\sigma$ is the long-range exponent. Using $\sigma$ as an adjustable parameter, the theory gives us a good match to the experimentally available static and dynamic critical exponents at the PM-AFM transition.