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 [10–14].
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 [15–18]. 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 [19–21]. 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 [30–33]. In this regard, Akhter
et al. showed that Cu
1−x
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
1−x
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