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M. Satalkar et al.
to each other forming a collinear structure [13, 14] with certain resultant magnetization M = M B −M A , where M A and M B are, respectively, magnetic moment of A
and B site. But, according to Yafet-Kittel (Y-K) model, B sub-lattice can be divided
into two sub-lattices, B 1 and B 2 , having equal magnitude of magnetic moments,
each canted oppositely at identical angle, α Y-K . In this way, two sub-lattices B 1 and
B 2 have triangular spin arrangement which becomes more significant with changing
concentration and cationic redistribution.
Among other SF, most of the literature reports electromagnetic properties of
Ni-Zn-Mg-Cu ferrite [15–19], but the magnetic properties of Zn-Ni-Mg-Cu spinel
ferrite are less explored [16, 19–24]. Sujatha et al. [16] investigated Mg substituted
ann. (powder, 500 ◦ C/3 h.; pellets, 950 ◦ C/1 h.) Ni-Cu-Zn ferrite. The results depict
enhanced permeability, decrease in saturation magnetization (M s ), and dielectric
losses at higher frequencies with Mg substitution in Ni 0.5−x Mg x Cu 0.05 Zn 0.45 Fe 2 O 4
(x = 0.1, 0.2, 0.3, 0.4). Coercivity (H c ) and anisotropy constant (K 1 ) increase
up to x = 0.2 and then reduce with increasing Mg content. Maximum initial
permeability (μ i ) was obtained for x = 0.1. Abdullah Dar et al. [19] examined
Ni 0.5−x Cu 0.2 Zn 0.3 Mg x Fe 2 O 4 (x = 0.0–0.4) (900 ◦ C/5 h) ferrite system, synthesized
by sol-gel method. Results showed increased electrical resistivity, reduced H c ,
and dielectric losses with Mg substitution. Mg doping leads to increase in M s
up to x = 0.2, and thereafter it starts to decrease with increase in Mg content.
Sujatha et al. [20] explored Mg substituted ann. (powder, 500 ◦ C/3 h.; pellets,
950 ◦ C/1 h.) Ni 0.5 Cu 0.05 Mg x Zn 0.45−x Fe 2 O 4 (x = 0.09, 0.18, 0.27, 0.36, 0.45).
Results reveal decrease in M s , μ i and increase in H c , K 1 , Curie temperature (T c ) with
increasing Mg content. Sujatha et al. [21] studied co-substitution effect of Mg, Zn of
ann. (powder, 500 ◦ C/3 h.; pellets, 950 ◦ C/2 h.) Ni 0.5−2x Mg x Cu 0.05 Zn 0.45+x Fe 2 O 4
(x = 0.0, 0.04, 0.08, 0.12, 0.16) ferrite. Results demonstrate gradual decrease
of M s , H c , K 1 , dielectric constant, dielectric loss factor, improved permeability, and enhanced resistance of samples. Satalkar et al. [22] studied the synthesis, structural and soft magnetic properties, and cation distribution of asburnt Zn 0.8−x Ni x Mg 0.1 Cu 0.1 Fe 2 O 4 (x = 0.0–0.8) ferrites prepared by sol-gel autocombustion method. The paper reports increase in 50 Hz and quasi-static coercivity
and anisotropy constant values with nickel content. Best magnetization value of
25.04 emu/g was obtained for x = 0.60. Kane et al. [23] demonstrate the correlation between magnetic properties and cationic distribution of ann. (500 ◦ C/3 h)
Zn 0.85−x Ni x Mg 0.05 Cu 0.1 Fe 2 O 4 (x = 0.0–0.8). The paper depicts decrease in experimental, theoretical lattice constant (a exp. , a th. ), specific surface area (S), and the
distances between cations (Me-Me) (b, c, d, e, f) with increase in Ni doping.
H c and M s of Zn-Ni-Mg-Cu ferrite ranges between 0.97–167.5 Oe and 47.63–
136.93 Am 2 kg −1 , respectively, signifying the soft character of annealed samples.
The paper shows similar trend of M s , Néel/experimental magnetic moment (n B
N ,
n B
e ) with Ni content (x) which establishes the Néel’s two-sub-lattice model of
ferrimagnetism in ann. (500 ◦ C/3 h) Zn 0.7−x Ni x Mg 0.2 Cu 0.1 Fe 2 O 4 nano-ferrite.
Furthermore the role of cationic distribution in determining magnetic properties
M. Satalkar et al.
to each other forming a collinear structure [13, 14] with certain resultant magnetization M = M B −M A , where M A and M B are, respectively, magnetic moment of A
and B site. But, according to Yafet-Kittel (Y-K) model, B sub-lattice can be divided
into two sub-lattices, B 1 and B 2 , having equal magnitude of magnetic moments,
each canted oppositely at identical angle, α Y-K . In this way, two sub-lattices B 1 and
B 2 have triangular spin arrangement which becomes more significant with changing
concentration and cationic redistribution.
Among other SF, most of the literature reports electromagnetic properties of
Ni-Zn-Mg-Cu ferrite [15–19], but the magnetic properties of Zn-Ni-Mg-Cu spinel
ferrite are less explored [16, 19–24]. Sujatha et al. [16] investigated Mg substituted
ann. (powder, 500 ◦ C/3 h.; pellets, 950 ◦ C/1 h.) Ni-Cu-Zn ferrite. The results depict
enhanced permeability, decrease in saturation magnetization (M s ), and dielectric
losses at higher frequencies with Mg substitution in Ni 0.5−x Mg x Cu 0.05 Zn 0.45 Fe 2 O 4
(x = 0.1, 0.2, 0.3, 0.4). Coercivity (H c ) and anisotropy constant (K 1 ) increase
up to x = 0.2 and then reduce with increasing Mg content. Maximum initial
permeability (μ i ) was obtained for x = 0.1. Abdullah Dar et al. [19] examined
Ni 0.5−x Cu 0.2 Zn 0.3 Mg x Fe 2 O 4 (x = 0.0–0.4) (900 ◦ C/5 h) ferrite system, synthesized
by sol-gel method. Results showed increased electrical resistivity, reduced H c ,
and dielectric losses with Mg substitution. Mg doping leads to increase in M s
up to x = 0.2, and thereafter it starts to decrease with increase in Mg content.
Sujatha et al. [20] explored Mg substituted ann. (powder, 500 ◦ C/3 h.; pellets,
950 ◦ C/1 h.) Ni 0.5 Cu 0.05 Mg x Zn 0.45−x Fe 2 O 4 (x = 0.09, 0.18, 0.27, 0.36, 0.45).
Results reveal decrease in M s , μ i and increase in H c , K 1 , Curie temperature (T c ) with
increasing Mg content. Sujatha et al. [21] studied co-substitution effect of Mg, Zn of
ann. (powder, 500 ◦ C/3 h.; pellets, 950 ◦ C/2 h.) Ni 0.5−2x Mg x Cu 0.05 Zn 0.45+x Fe 2 O 4
(x = 0.0, 0.04, 0.08, 0.12, 0.16) ferrite. Results demonstrate gradual decrease
of M s , H c , K 1 , dielectric constant, dielectric loss factor, improved permeability, and enhanced resistance of samples. Satalkar et al. [22] studied the synthesis, structural and soft magnetic properties, and cation distribution of asburnt Zn 0.8−x Ni x Mg 0.1 Cu 0.1 Fe 2 O 4 (x = 0.0–0.8) ferrites prepared by sol-gel autocombustion method. The paper reports increase in 50 Hz and quasi-static coercivity
and anisotropy constant values with nickel content. Best magnetization value of
25.04 emu/g was obtained for x = 0.60. Kane et al. [23] demonstrate the correlation between magnetic properties and cationic distribution of ann. (500 ◦ C/3 h)
Zn 0.85−x Ni x Mg 0.05 Cu 0.1 Fe 2 O 4 (x = 0.0–0.8). The paper depicts decrease in experimental, theoretical lattice constant (a exp. , a th. ), specific surface area (S), and the
distances between cations (Me-Me) (b, c, d, e, f) with increase in Ni doping.
H c and M s of Zn-Ni-Mg-Cu ferrite ranges between 0.97–167.5 Oe and 47.63–
136.93 Am 2 kg −1 , respectively, signifying the soft character of annealed samples.
The paper shows similar trend of M s , Néel/experimental magnetic moment (n B
N ,
n B
e ) with Ni content (x) which establishes the Néel’s two-sub-lattice model of
ferrimagnetism in ann. (500 ◦ C/3 h) Zn 0.7−x Ni x Mg 0.2 Cu 0.1 Fe 2 O 4 nano-ferrite.
Furthermore the role of cationic distribution in determining magnetic properties