Strain fields and critical phenomena in manganites II: spin-lattice-energy Hamiltonians

The dynamic critical behavior at the paramagnetic-antiferromagnetic (PM-AFM) transition in manganites has recently been studied experimentally (Niermann et al 2015 Phys. Rev. Lett. 114 037204). 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 approach and calculate the dynamic critical exponents z , ν z and the line-width exponent Δ to leading order in the small expansion parameters ϵ = 4 − d + 2 σ and ϵ ′ = 4 − d . Here, d is the space dimension and σ is the long-range exponent. Using σ 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.