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近年来, 极性磁体M2Mo3O8 (M: 3d过渡金属)因其独特的晶体结构、多重连续的磁电耦合态转变及潜在应用价值, 成为凝聚态物理和材料科学领域的研究热点. 特别是Co2Mo3O8基态下展现出显著的二阶非线性磁电耦合效应, 对应独特的磁电耦合微观机制和实际应用价值. 本文基于分子场唯象模型, 构建了Co2Mo3O8体系的两套不同的反铁磁子格子, 给出体系的自发磁矩、自旋诱导的铁电极化、一阶线性磁电耦合系数以及二阶非线性磁电耦合系数随温度的变化关系. 结果显示Co2Mo3O8的二阶磁电耦合系数要明显比同构的Fe2Mo3O8以及Mn2Mo3O8大, 这主要是因为Co2Mo3O8的两个不同子格子间的反铁磁交换作用能量更低, 体系所处的状态更加稳定. 这也表明, 在Co2Mo3O8体系拥有更加稳定的不可逆性, 展现了非常明显的磁电二极管(magnetoelectric diode)效应, 为磁电二极管(magnetoelectric diode)的发展提供了坚实的理论和实验基础.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
Fig. 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
Fig. 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
Fig. 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
Fig. 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
Fig. 5. Magnetic structures of (a) Co2Mo3O8, (b) Fe2Mo3O8, and (c) Fe2Mo3O8.
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