Slow spin dynamics of cluster spin-glass spinel Zn(Fe1-xRu_x)₂O₄: role of Jahn-Teller active spin-1/2 Cu²⁺ions at B-sites

We report the slow spin dynamics of cluster spin-glass (SG) spinel Zn(Fe1-xRu_x)₂O₄by means of detaileddc-magnetization andac-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 ofac-susceptibility (χac(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 temperatureTSG(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(TSG(H)=TSG(0)(1-AH2/ϕ)), with an ideal value ofφ = 3. Nevertheless, the analysis of temperature dependent high fielddc-susceptibility,χhf(2kOe ⩽ HDC ⩽ 20kOe,T) provides evidence for Gabay-Toulouse type mixed-phase (coexistence of SG and ferrimagnetic (FiM)) behaviour. Further, in the case of Cu_0.2Zn_0.8FeRuO₄system, slowly fluctuating magnetic clusters persist even above the short-range FiM ordering temperature (TFiM) and their volume fraction vanishes completely across ∼6TFiM. 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 (JS) between the spins which yieldsJS=-3.02×10-5 eV for Cu_0.2Zn_0.8FeRuO₄representing the dominant intra-sublattice ferromagnetic interactions due to the dilute incorporation of the JT active Cu²⁺ions. However, the antiferromagnetic coupling is predominant in ZnFeRuO₄and Cu_0.2Zn_0.8Fe_0.5Ru_1.5O₄systems. Finally, we deduced the magnetic phase diagram in theHDC-Tplane using the characteristic parameters obtained from the field variations of bothac- anddc-magnetization measurements.