Investigations on Enhancing Thermomagnetic Properties in CoxZn1−xFe2O4

The effect of Co content on magnetocaloric effect (MCE) in Co_xZn_1−xFe₂O₄ (CZF) with x = 0, 0.1, 0.2, 0.3, and 0.4, prepared by auto-combustion technique, has been investigated by phenomenological model. The results show that MCE for CZF nanoparticles is enhanced strongly with Co content especially for high Co content samples. In addition, MCE in CZF nanoparticles is tunable with Co content over a large operating temperature range. MCE of CZF nanoparticles are significantly better than MCE of Ni₅₈Fe₂₆Ga₂₈, MnAs films, and Ge_0.95Mn_0.05. It is recommended that that MCE in CZF nanoparticles is favorable for magnetic refrigeration in a wide temperature range, including room temperature.

Keywords: Magnetocaloric effect; CoxZn1−xFe2O4; Phenomenological model

The ferrites have considerable scientific and technological attention due to their significant electrical and magnetic properties [[1]–[8]]. These properties of ferrites are widely used in numerous applications like information storage, gas sensors, communication, magnetic resonance imaging, magnetic switch, and magnetic refrigerator (MR) [[9]–[15]]. For these applications, the ferrites cannot be replaced by other magnetic materials for economic reasons. Among these ferrite materials, ZnFe2O4 is soft magnetic material which has a small coercivity, relatively high magnetization, and low dielectric loss [[16]–[18]]. Therefore, there is interest in improving the properties of ZnFe2O4 to increase the efficiency of these applications by doping [[19]–[22]]. There is a tendency to use MR in the cooling process, depending on the magnetocaloric effect (MCE) [[23]–[27]]. MCE is described as a change in temperature by removing or application of the magnetic field on a magnetic material [[28]–[30]]. This MR is distinguished from the traditional refrigerators as they have less pollution to the environment, more efficient cooling, and less electricity consumption [[31]–[35]]. Feng et al. reported Co doping effect on magnetic behavior for CoxZn1−xFe2O4 (CZF) nanoparticles with x = 0, 0.1, 0.2, 0.3, and 0.4 were prepared by auto-combustion method, showing the substitution of cobalt ions can remarkably enhance Curie temperature (TC) of the prepared CZF nanoparticles [[19]]. Furthermore, at room temperature, CZF nanoparticles show superparamagnetism for low cobalt content samples, while high cobalt content samples show ferrimagnetism [[19]]. This gives us a motivation to study Co doping effect on the thermomagnetic properties of the material using the phenomenological model (PM) which simulates the magnetization-temperature curves, concluding magnetic entropy change (∆SM), heat capacity change (ΔCP,H), and relative cooling power (RCP).

According to PM, described in [[36]–[39]], the dependence of magnetization on the temperature and TC is given by

1 $$M=\left(\frac{M_i-M_F}{2}\right)\left[\mathit{tanh}\left(A\left(T_c-T\right)\right)\right]+\mathit{BT}+C$$

Graph

where Mi is an initial value of magnetization at ferrimagnetic-paramagnetic transition and Mf is a final value of magnetization at ferrimagnetic-paramagnetic transition as shown in Fig. 1, where $=\frac{2\left(B-S_c\right)}{M_i-M_f}$ , B is the average magnetization sensitivity ( $\frac{\mathit{dM}}{\mathit{dT}}$ ) at ferrimagnetic state before transition, Sc is magnetization sensitivity $\frac{\mathit{dM}}{\mathit{dT}}$ at TC, and $C=\left(\frac{M_i+M_f}{2}\right)-{\mathit{BT}}_C$ .

Graph: Fig. 1 Temperature dependence of magnetization in constant applied field

ΔSM of a magnetic sample under adiabatic magnetic field shift (∆H) from 0 to final value Hmax is available by

2 $$\mathrm{\Delta }{S}_M=\left(-A\left(\frac{M_i-M_f}{2}\right){sech}^2\left(A\left(T_C-T\right)\right)+B\right)H_{\max }$$

Graph

A maximum of ΔSM (∆SMax) can be determined as follows:

3 $$\mathrm{\Delta }{S}_{\mathit{Max}}=H_{\max }\left(-A\left(\frac{M_i-M_f}{2}\right)+B\right)$$

Graph

The full-width at half-maximum (δTFWHM) can be obtained as follows:

4 $$\delta {\mathrm{T}}_{\text{FWHM}}=\frac{2}{A}{cosh}^{‐1}\left(\sqrt{\frac{2A\left(M_i-M_f\right)}{A\left(M_i-M_f\right)+2B}}\right)$$

Graph

RCP can be given as follows:

5 $$\mathrm{RCP}=‐\mathrm{\Delta }{S}_{\mathit{Max}}\left(T,H_{\max }\right)\times \delta {\mathrm{T}}_{\text{FWHM}}=\left(M_i-M_f-2\frac{B}{A}\right)H_{\max }\times {cosh}^{‐1}\left(\sqrt{\frac{2A\left(M_i-M_f\right)}{A\left(M_i-M_f\right)+2B}}\right)$$

Graph

According to the PM model [[35]], Δ CP, H is given by

6 $$\mathrm{\Delta }{C}_{P,H}=-{\mathit{TA}}^2\left(M_i-M_f\right){sech}^2\left(A\left(T_C-T\right)\right)tanh\left(A\left(T_C-T\right)\right)H_{\max }$$

Graph

To simulate MCE, the phenomenological parameters for CZF nanoparticles were determined directly from experimental data (temperature dependence of magnetization) as in Ref. [[19]]. Figure 2 shows the temperature dependence of magnetization for CZF. The symbols represent experimental data from Ref. [[19]], while the solid lines represent simulated data by PM. We can see from Fig. 2 that there is a good agreement between the experimental and the theoretical results of M(T), confirming a good fitting of this model. This work demonstrates the good coincidence between the experimental data and the continuous curves given by PM, indicating that this model allows us to predict MCE for CZF nanoparticles under moderate magnetic field. The M(T) curves reveal that all the samples are showing a magnetic transition from the ferrimagnetic to paramagnetic state. Furthermore, the high cobalt content enhances remarkably the magnetization and consequently a rise in TC. This behavior indicates that the cobalt content has a strong effect on MCE of CZF nanoparticles. This a rise in TC with cobalt content due to the replacement of non-magnetic Zn2+ ions with magnetic Co2+ ions, leading to strengthening the exchange interaction between A site and B site [[40]]. Figures 3 and 4 show simulated temperature dependence of ∆SM and ∆CP,H for CZF nanoparticles, respectively. The behavior of ∆SM and ∆CP,H curves proposes how to expand the range of temperatures for exploiting CZF nanoparticles in the MR. It is clear that ∆SM and ∆CP,H peaks of CZF nanoparticles extend over a large temperature range. Figures 5, 6, 7, and 8 show the values of |∆SMax| (maximum value of |∆SM|), δTFWHM, RCP, and ∆CP,H(Max) (maximum value of ∆CP,H) for CZF nanoparticles, respectively. It is clear that |∆SMax|, RCP, and ∆CP,H(max) show a systematic increase with increase in Co content up to x = 0.30.

Graph: Fig. 2 Magnetization vs. temperature for CZF nanoparticles. The dashed curves are modeled results and symbols represent experimental data from Ref. [19]

Graph: Fig. 3 ∆SM vs. temperature for CZF nanoparticles

Graph: Fig. 4 ∆CP,H vs. temperature for CZF nanoparticles

Graph: Fig. 5 |∆SMax| vs. temperature for CZF nanoparticles

Graph: Fig. 6 δTFWHM vs. Co content for CZF nanoparticles

Graph: Fig. 7 RCP vs. Co content for CZF nanoparticles

Graph: Fig. 8 ∆CP,H(max) vs. Co content for CZF nanoparticles

This is due to when the non-magnetic Zn2+ ions are replaced with magnetic Co2+ ions, the super-exchange interaction among A–B intra-sublattice is enhanced. Since Co2+ prefers to occupy B sites while Zn2+ prefers to occupy A sites. When the Zn2+ ions (magnetic moment of 0 μB) are substituted with Co2+ ions (magnetic moment of 3 μB), the magnetic Fe3+ ions (magnetic moment of 5 μB) are moved from B sites to A sites, leading to increase remarkably the total magnetic moments at the A sites and causing an increase in super-exchange interaction among A–B [[40]]. These results show that MCE in CZF nanoparticles is tunable, which is leading to recommend that MCE in CZF nanoparticles is beneficial for MR in wide temperature range, including room temperature. Furthermore, the eddy current loss and hysteresis energy loss are not considered for CZF nanoparticles due to high resistivity and very small hysteresis of CZF nanoparticles [[40]].

Table 1 shows comparisons between CZF nanoparticles and other compositions in previous works. The MCE parameters of CZF nanoparticles are significantly larger and comparable with some MCE parameters of Ni58Fe26Ga28, MnAs films, and Ge0.95Mn0.05, Gd3Ni2, Gd3CoNi, and La0.67Sr0.33MnO3 nanofibers as shown in Table 1 [[41]–[45]]. Finally, MCE and electrocaloric effect give the perspectives of practical applications of modern refrigeration technology in our society [[46]–[75]].

The predicted values of applied magnetocaloric properties for CZF nanoparticles and other compositions in low applied magnetic field changes

In conclusion, MCE for CZF nanoparticles with different Co contents is investigated theoretically by PM. MCE for CZF nanoparticles is enhanced with Co content. Furthermore, MCE in CZF nanoparticles is tunable with Co content and continues in high temperature range.

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.