Competing interactions in a long-range spin-lattice coupled model and tricriticality

Abstract

The interplay of spin and lattice degrees of freedom on the critical behavior of magnetic phase transitions in strongly correlated systems can be studied analytically by constructing an effective model Hamiltonian for the corresponding order parameters. Here we consider such a model C-type Hamiltonian involving the coupling between order parameter and the strain field. Taking the strain interaction to be long-range (LR) in nature, we carry out a renormalization-group analysis at one-loop order. This reveals a non-trivial critical behavior dictated by an LR fixed point. We show that the critical behavior differs in the presence of competing short-range interaction. For the case of purely nonlocal theory, we find a signature of first-order instability at the leading order of the perturbation expansion. We also discuss briefly the applicability of the model in capturing the experimental results.

Magnetoelastic coupling and critical behavior of some strongly correlated magnetic systems

“…is obtained by setting γ 0 = i 2λ 0 C −1 0 in equation (7). As derived explicitly in reference [57], one would arrive at the renormalization-group flow equations at lowest order as…”

“…It is generally expected that the different fixed points collide and exchange their stabilities in the presence of such a competing potential. A recent theoretical work [57] has revealed that the presence of short-range interaction affects the long-range critical behavior of such a model Hamiltonian.…”

“…Since the spin-lattice coupled Hamiltonian [equation ( 7)] generates the competing potential, one way to investigate the problem is to directly perform the renormalization-group analysis of equation ( 7) and to see how the stability of the nontrivial fixed point changes. Such an analysis has been performed in reference [57] within the framework of Wilson's momentumshell decimation renormalization-group scheme. In that work, the form of the long-range coupling function…”

“…However, since the stability of the long-range fixed point in three dimensions restricts ρ in the range 0 < ρ < 0.3, the tricritical exponents can not be recovered for this fixed point. To see what is happening here, further analysis was made in the same work [57] by setting u 0 = 0 and γ 0 = i 2λ 0 C −1 0 in equation ( 7) at the very beginning and then performed the renormalization-group calculations. From the resulting renormalization-group flow equations for r, c, C −1 and λ, the stability matrix for the same nontrivial fixed point was obtained as…”

“…Finally, the importance of spin-lattice coupling near a critical point of strongly correlated magnetic systems is discussed in section 4 with possible new directions of research. This review highlights the recent theoretical developments that have been made jointly by our group [51][52][53][54][55][56][57].…”