Inverse dependence of exchange bias and coercivity on cooling field caused by interfacial randomization in nanosystems with Co sparsely distributed in CoFe2O4 matrix

doi:10.1016/j.jmst.2021.04.067

Abstract

Abstract:

We conceive a model of nanosystems where Co is uniformly, randomly distributed into a CoFe₂O₄ (CFO) matrix, and study the influences of composition and CFO antiferromagnetic exchange coupling (J_CFO) on zero-field-cooled/field-cooled magnetization behavior and the dependencies of exchange bias field (H_E) and coercivity (H_C) on Co/CFO interfacial coupling (J_Co/CFO), composition and cooling field (H_FC), based on a modified Monte Carlo method. With decreasing temperature, the zero-field-cooled and field-cooled magnetization curves are overlapped and increasing initially, and then splitting at a critical temperature (T_P), below which the field-cooled magnetization continues increasing while the zero-field-cooled magnetization exhibits a peak and drops, indicating a magnetically frozen state. A larger J_CFO induces an elevated T_P and a reduced magnetization, while the opposite results are obtained by a higher Co occupation fraction (P_Co). On the other hand, H_E is nonmonotonic with J_Co/CFO and the peak decreases and shifts to a lower J_Co/CFO value for a larger P_Co. H_C increases monotonically with increasing J_Co/CFO. Moreover, H_E is inversely proportional to P_Co when P_Co varies from 0.11 to 0.30, indicating the exchange bias is still an interfacial effect. Finally, for a nonzero J_CFO, H_E may be suppressed and accompanied by the recovery of H_C with increasing H_FC. Otherwise, H_C for zero J_CFO becomes high and insensitive to H_FC. It is ascribed to the uniform contact between Co and CFO, leading to the Co magnetization reversal and the CFO magnetization precisely controlled by H_FC. This work opens a new avenue to control the exchange bias in nanosystems through interfacial randomization.

Key words: Exchange bias, Ferromagnetic occupation fraction, Cooling field, Monte Carlo simulation

Song Yang, Yong Hu. Inverse dependence of exchange bias and coercivity on cooling field caused by interfacial randomization in nanosystems with Co sparsely distributed in CoFe₂O₄ matrix[J]. J. Mater. Sci. Technol., 2022, 98: 258-267.

Figures/Tables 8

Fig. 1. Energy density as a function of azimuthal angle under selected effective fields for ϑ = 57.3° (1 rad), where the energy barrier is labelled. Inset shows the normalized critical field as a function of ϑ.

Fig. 2. Zero-field-cooled and field-cooled magnetization as a function of temperature under H=100 Oe for selected PCo and JCFO.

Fig. 3. Hysteresis loop at T=50 K after cooling under HFC=4 T at selected JCo/CFO for (a) PCo=0.11 and (b) PCo=0.30. (c) Exchange bias field (HE) and (d) coercivity (HC) as a function of JCo/CFO for PCo=0.11 and PCo=0.30.

Fig. 4. Number of magnetic moment bonds between Co and Co, between CFO and CFO, and between Co and CFO as a function of PCo, where L is the cell length, Z is the coordination number, and error bars are determined by 30 sets of independent initial, random configurations. Insets show the two-dimensional views of configurations with PCo = 0.10 and 0.20, where red and blue spheres denote the magnetic moments of Co and CFO and colored dashed lines are bonds between them.

Fig. 5. Hysteresis loop at T=50 K after cooling under HFC=4 T at selected PCo for (a) JCFO=0 and (b) JCFO=4 meV. (c) Exchange bias field (HE) and (d) coercivity (HC) as a function of PCo. Inset shows the exchange bias field linearly inversely proportional to PCo.

Fig. 6. Hysteresis loop at T=50 K after cooling under HFC=-0.5 T, 0 T, and 0.5 T for selected PCo and JCFO.

Fig. 7. Exchange bias field and coercivity as a function of cooling field at T=50 K for selected PCo and JCFO.

Fig. 8. (a, b) Magnetization of CFO at Co/CFO interface during Co magnetization reversal, indicated by purple rings in (c, d), as a function of cooling field at PCo=0.11 for (a) JCFO=0 and (b) JCFO=4 meV at T=50 K. (c, d) Representative hysteresis loops of the whole CFO component and the CFO component at Co/CFO interface under HFC=0.5 T, where blue curves indicate the overlap of two hysteresis loops of CFO and the hysteresis loops of Co are also given (gray). Error bars are determined by 30 sets of independent initial, random configurations.

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Inverse dependence of exchange bias and coercivity on cooling field caused by interfacial randomization in nanosystems with Co sparsely distributed in CoFe₂O₄ matrix

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