PHYSICAL REVIEW B 106, 174402 (2022) Cationic redistribution induced spin-glass and cluster-glass states in spinel ferrite S. Nayak, 1 S. Ghorai , 2 A. M. Padhan, 3 S. Hajra, 3 P. Svedlindh, 2 and P. Murugavel 1 , * 1 Pervoskite Materials Laboratory, Functional Oxides Research Group (FORG), Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India 2 Solid State Physics, Department of Materials Science and Engineering, Uppsala University, Box 35, 75103 Uppsala, Sweden 3 Department of Robotics and Mechatronics Engineering, Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea (Received 17 July 2022; accepted 18 October 2022; published 2 November 2022) The effect of the cationic redistribution on the complex spinel structure and magnetic properties were investigated in Zn 0.7 Cu 0.3 Fe 2 O 4 ferrite. X-ray photoelectron spectroscopy and x-ray diffraction studies revealed that the system exhibits a mixed spinel structure with Fe 3+ , Zn 2+ , and Cu 2+ occupying both tetrahedral and octahedral sublattices. The DC magnetization results revealed the absence of long-range magnetic order in the system. Furthermore, the AC susceptibility data analysis using dynamic scaling laws suggests that the system exhibits magnetic relaxation below two different temperatures: (i) a spin-glass–like transition at low temperature (49.2 K) with critical exponent 10.3 and spin-flip time 10 11 s, and (ii) a cluster-glass–like transition at higher temperature (317 K) with critical exponent 4.6 and spin-flip time 10 10 s. The existence of glassy behavior and magnetic memory effects below the spin-glass transition temperature proves that the system is in nonequilibrium dynamical state. The coexistence of spin-glass and cluster-glass along with the thermal hysteresis between these two transitions could widen the technological applications of these systems. DOI: 10.1103/PhysRevB.106.174402 I. INTRODUCTION The effect of disorder on the properties of magnetic ma- terials has been one of the focused areas of research among the magnetism community because of the enthralling physics behind their properties [1]. In disorder-induced spin-glass system, spins are frozen in random directions below a crit- ical temperature [2,3]. Similarly, a cluster-glass is also a magnetically disordered system where blocks of spins are responsible for the slow magnetic relaxation behavior rather than the individual atomic spins [4]. Novel phenomena such as the magnetic memory effect have been discovered in spin- glass and cluster-glass systems below the glass transition temperature [5]. Moreover, the spin-glass theory has unique applications in various areas related to real-world problems. For example, spin-glass models are used to understand neu- ral networks and protein-folding dynamics [6], to design new algorithms for image restoration and machine learn- ing [7], to study the accuracy thresholds of algorithms in quantum computation [8], and to predict the collective price changes of stock portfolios [9]. All these spin-glass models are based on the magnetic disorder and competing magnetic interactions. The magnetic spinel with a chemical formula AB 2 O 4 is known for the interesting physics due to the competing mag- netic interactions that arise from their cationic distributions between tetrahedral (A) and octahedral (B) sites [1014]. Among them, ZnFe 2 O 4 is one of the important materials due to its exciting magnetic and catalytic properties which make * muruga@iitm.ac.in it useful in various technological applications [1518]. The crystal structure of the normal spinel [Zn 2+ ] A [Fe 3+ 2 ] B O 4 is a close-packed face-centered cubic with Zn 2+ and Fe 3+ situated at the A- and B sites, respectively [1921]. The two Fe 3+ ions are antiferromagnetically aligned (↓↑) at the octahedral sites and thereby make it into an antiferromagnetically ordered system with Néel temperature T N 10 K [22]. Moreover, the cationic redistribution between the A- and B sites plays a significant role in controlling the physical properties of the zinc ferrite [23]. Such cationic redistributions can be induced by ionic substitutions with different radii [24,25]. Singh et al. observed that incorporation of Mg 2+ in ZnFe 2 O 4 shifts Fe 3+ from B- to A sites, thereby strengthening the A-B interaction, which has led to large influence on the magnetic properties [26]. Also, Zaki et al. reported that Cu 2+ substitution in place of Zn 2+ in Mg 0.5 Zn 0.5 Fe 2 O 4 transforms the normal spinel structure into a partially inverted spinel and enhances the saturation magnetization along with the dielectric properties of the material [27]. Reports have shown that Cu 2+ exhibits high migration rate with low activation energy E A 0.1 eV (above 400 °C), which affects the chemical order and site occupancy of the cations in the A and B sublattices [28,29]. Consequently, several exciting magnetic phenomena such as spin-glass behavior, spin-liquid phase, bipolar exchange bias, etc. appeared in the system [3033]. In this regard, Akhter et al. showed that Cu 1x Zn x Fe 2 O 4 (x = 0.9) system exhibits spin-glass behavior when nonmagnetic Zn is substituted in place of Cu [34]. Very recently, the same research group showed that Curie temperature (T C ) shift towards the lower side upon increasing the Zn substitution in Cu 1x Zn x Fe 2 O 4 (0 x 1) system [35]. They have attributed the decrease in the transition temperature and variation in the magnetic 2469-9950/2022/106(17)/174402(8) 174402-1 ©2022 American Physical Society