The strongly correlated magnetic systems are attracting continuous attention in current condensed matter research due to their very compelling physics and promising technological applications. Being a host to charge, spin, and lattice degrees of freedom, such materials exhibit a variety of phases, and investigation of their physical behavior near such a phase transition bears an immense possibility. This review summarizes the recent progress in elucidating the role of magnetoelastic coupling on the critical behavior of some technologically important class of strongly correlated magnetic systems such as perovskite magnetites, uranium ferromagnetic superconductors, and multiferroic hexagonal manganites. It begins with encapsulation of various experimental findings and then proceeds toward describing how such experiments motivate theories within the Ginzburg-Landau phenomenological picture in order to capture the physics near a magnetic phase transition of such systems. The theoretical results that are obtained by implementing Wilson's renormalization-group to nonlocal Ginzburg-Landau model Hamiltonians are also highlighted. A list of possible experimental realizations of the coupled model Hamiltonians elucidates the importance of spin-lattice coupling near a critical point of strongly correlated magnetic systems.
Keywords: competing interaction; magnetic phase transition; magnetoelastic coupling; strongly correlated magnetic systems.
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