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In recent years, polar magnets M2Mo3O8 (M: 3d transition metal) have emerged as a research focus in condensed matter physics and materials science due to their unique crystal structures, multiple continuous magnetoelectric-coupled state transitions, and potential applications. Notably, Co2Mo3O8 exhibits a significant second-order nonlinear magnetoelectric coupling effect in its ground state, corresponding to a unique microscopic magnetoelectric coupling mechanism and practical value. In this work, based on a molecular field phenomenological model, two distinct antiferromagnetic sublattices for the Co2Mo3O8 system constructed and the temperature-dependent variations of its spontaneous magnetic moment, spin-induced ferroelectric polarization, first-order linear magnetoelectric coupling coefficient, and second-order nonlinear magnetoelectric coupling coefficient are presented. Particularly, the parameters t = –1 and o = –0.96 indicate distinct exchange energies between the magnetic sublattices associated with tetrahedron (Cot) and octahedron (Coo). The Co2+ ions in these two sublattices, which are characterized by different molecular field coefficients, synergistically mediate a spin-induced spontaneous polarization of PS~0.12 μC/cm2 through the exchange striction mechanism and p-d hybridization mechanism in Co2Mo3O8. In addition, the significant second-order magnetoelectric coupling effect with a coefficient peaking at 70 × 10–19 s/A near the TN in Co2Mo3O8, with this coefficient being significantly larger than those of isostructural Fe2Mo3O8 (1.81 × 10–28 s/A) and Mn2Mo3O8, implies that this enhancement primarily arises from the weaker inter-sublattice antiferromagnetic exchange between its two sublattices, leading to a stabilizes metastable spin configuration. This also indicates that the Co2Mo3O8 system possesses stronger irreversibility stability and exhibits a pronounced magnetoelectric diode effect, providing a solid theoretical and computational foundation for developing magnetoelectric diodes.
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Keywords:
- polar magnet /
- magnetoelectric coupling effect /
- mean-field approximation /
- exchange striction mechanism
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图 1 用Vesta软件做的Co2Mo3O8的(a)晶格结构图、(b)面外的磁结构图和(c)面内的磁结构
Figure 1. (a) The structure, (b) the out-of-plane and (c) in-plane magnetic structure of Co2Mo3O8.
图 2 (a), (b) 基于分子场近似, Cot和Coo 两个不同配位中Co2+自旋磁矩和总磁矩随温度的变化; (c), (d) 不同配位中Co2+的磁化率和总的磁化率随温度的关系; (e), (f) 磁矩对温度的微分和磁比热随温度的变化
Figure 2. (a), (b) Temperature-dependent variations of the Co2+ spin magnetic moment and total magnetic moment in two distinct coordination environments (Cot and Coo); (c), (d) temperature-dependent magnetic susceptibility and the total magnetic susceptibility; (e), (f) temperature derivative of the magnetic moment and temperature-dependent magnetic specific heat based on the molecular field approximation.
图 3 基于分子场近似, 得到的Co2Mo3O8 (a) χimj (i, j = t, o)、(b) 一阶线性磁电耦合系数、(c) 自旋诱导的铁电极化和(d) 二阶线性磁电耦合系数随温度的变化
Figure 3. Temperature-dependent variations of (a) χimj (i, j = t, o), (b) first-order linear magnetoelectric coupling coefficient, (c) spin-induced ferroelectric polarization, and (d) second-order linear magnetoelectric coupling coefficient for Co2Mo3O8 based on the molecular field approximation.
图 4 基于分子场近似, (a)—(c) Mn2Mo3O8和(d)—(f) Fe2Mo3O8 体系的基态下的磁电耦合效应数值计算结果
Figure 4. Numerical calculations on the magnetoelectric coupling effects in the ground state for (a)–(c) Mn2Mo3O8 and (d)–(f) Fe2Mo3O8 system based on the molecular field approximation.
图 5 (a) Co2Mo3O8、(b) Fe2Mo3O8和(c) Mn2Mo3O8的磁结构
Figure 5. Magnetic structures of (a) Co2Mo3O8, (b) Fe2Mo3O8, and (c) Fe2Mo3O8.
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