Slow spin dynamics of cluster spin-glass spinel Zn(Fe 1−x Ru x )2O4: role of Jahn–Teller active spin-1/2 Cu2+ ions at B-sites

Abstract

Abstract We report the slow spin dynamics of cluster spin-glass (SG) spinel Zn(Fe 1 − x Ru x )2O4 by means of detailed d c -magnetization and a c -susceptibility studies combined with the heat capacity analysis. Two specific compositions (x = 0.5, 0.75) have been investigated in detail along with the substitution of Jahn–Teller (JT) active spin-1/2 Cu2+ ions at B-sites. Measurements based on the frequency and temperature dependence of a c -susceptibility ( χ a c ( f , T ) ) and the subsequent analysis using the empirical scaling laws such as: (a) Vogel–Fulcher law and (b) Power law reveal the presence of cluster SG state below the characteristic freezing temperature T S G (17.77 K (x = 0.5) and 14 K (x = 0.75)). Relaxation dynamics of both the compositions follow the non-mean field de Almeida–Thouless (AT)-line approach ( T S G ( H ) = T S G ( 0 ) ( 1 − A H 2 / ϕ ) ) , with an ideal value of φ = 3. Nevertheless, the analysis of temperature dependent high field d c -susceptibility, χ h f ( 2 kOe   ⩽   H DC   ⩽   20 kOe , T) provides evidence for Gabay–Toulouse type mixed-phase (coexistence of SG and ferrimagnetic (FiM)) behaviour. Further, in the case of Cu0.2Zn0.8FeRuO4 system, slowly fluctuating magnetic clusters persist even above the short-range FiM ordering temperature ( T F i M ) and their volume fraction vanishes completely across ∼6 T F i M . This particular feature of the dynamics has been very well supported by the time decay of the thermoremanent magnetization and heat-capacity studies. We employed the high temperature series expansion technique to determine the symmetric exchange coupling ( J S ) between the spins which yields J S = − 3.02 × 10 − 5  eV for Cu0.2Zn0.8FeRuO4 representing the dominant intra-sublattice ferromagnetic interactions due to the dilute incorporation of the JT active Cu2+ ions. However, the antiferromagnetic coupling is predominant in ZnFeRuO4 and Cu0.2Zn0.8Fe0.5Ru1.5O4 systems. Finally, we deduced the magnetic phase diagram in the H D C − T plane using the characteristic parameters obtained from the field variations of both a c - and d c -magnetization measurements.