Coexistence of ferromagnetic ordering and spin glass-like behaviour in Er₂Cu₂In

Ternary RE₂T₂X (RE = rare earth, T = transition metal, X = p-block element) compounds crystallise in the Mo₂B₂Fe-type structure with space group P4/mbm. The geometrically frustrated lattice gives rise to unique magnetic interactions that lead to exotic ground states, including spin dimers and field-induced metamagnetic transitions. The system Er₂Cu₂In exhibits long-range ferromagnetic ordering below 39 K, accompanied by magnetic irreversibility features in the ordered state. We investigate the complex magnetic behaviour of Er₂Cu₂In using a combination of experimental techniques, including dc and ac magnetic susceptibility (χ_dc and χ_ac), magnetisation (M), magnetic relaxation (MTRM), and heat capacity (C_P) measurement. We employ the Vogel-Fulcher, Arrhenius activation, and critical-scaling methods to analyse the ac susceptibility (χ_ac(T, ω)) and estimate the dynamical parameters associated with the spin dynamics in Er₂Cu₂In. Our findings highlight the rich and complex magnetic properties of Er₂Cu₂In, where the coexistence of ferromagnetic ordering and a metastable spin-glass state, as well as the presence of stretched exponential decay and glassy behaviour, contribute to its unique magnetic behaviour.