Mean-field approximation model for multiferroicity and magnetoelectric coupling effects in polar magnet Co2Mo3O8

TANG Yongsen; WANG Hanyan; YU Bing; LI Xing’ao

doi:10.7498/aps.74.20250506

Abstract

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 (Co_t) and octahedron (Co_o). The Co²⁺ ions in these two sublattices, which are characterized by different molecular field coefficients, synergistically mediate a spin-induced spontaneous polarization of P_S ~ 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 7 × 10^–18 s/A near the T_N 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.

Keywords:

Authors and contacts

1.
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
2.
College of Mechanics and Engineering Science, Hohai University, Nanjing 211100, China
3.
Hubei Key Laboratory of Photoelectric Materials and Devices, School of Materials Science and Engineering, Hubei Normal University, Huangshi 435002, China

Corresponding author: TANG Yongsen, tangys@njupt.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 12304124).

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References

[1]	Kimura T, Goto T, Shintani H, Ishizaka K, Arima T, Tokura Y 2003 Nature 426 55 Google Scholar
[2]	Cheong S, Mostovoy M 2007 Nat. Mater. 6 13 Google Scholar
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Cited By

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) Crystal structure, (b) the out-of-plane and (c) in-plane magnetic structure of Co₂Mo₃O₈.

DownLoad: Full-Size Img PowerPoint

图 2 (a), (b) 基于分子场近似, Co_t和Co_o 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 (Co_t and Co_o); (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.

DownLoad: Full-Size Img PowerPoint

图 3 基于分子场近似, 得到的Co₂Mo₃O₈ (a) χ_im_j(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) χ_im_j(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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

DownLoad: Full-Size Img PowerPoint

[1]	Kimura T, Goto T, Shintani H, Ishizaka K, Arima T, Tokura Y 2003 Nature 426 55 Google Scholar
[2]	Cheong S, Mostovoy M 2007 Nat. Mater. 6 13 Google Scholar
[3]	Spaldin N A 2017 MRS Bulletin 42 385 Google Scholar
[4]	Lu C L, Wu M H, Lin L, Liu J M 2019 Nat. Sci. Rev. 6 653 Google Scholar
[5]	Dong S, Liu J M, Cheong S W, Ren Z 2015 Adv. Phys. 64 519 Google Scholar
[6]	南策文 2015 中国科学: 技术科学 45 339 Google Scholar Nan C W 2015 Sci. Sin.: Tech. 45 339 Google Scholar
[7]	刘俊明, 南策文 2014 物理 43 88 Google Scholar Liu J M, Nan C W 2014 Physics 43 88 Google Scholar
[8]	Li Z W, Zhang S Y, Li Q S, Liu H 2023 J. Adv. Dielect. 13 2345002 Google Scholar
[9]	Liang M C, Yang J, Yang H Y, Liang C, Nie Z Y, Ai H, Zhang T, Ma J, Huang H B, Wang J 2024 J. Adv. Dielect. 14 2440002 Google Scholar
[10]	Khade V, Wuppulluri M 2024 J. Adv. Dielect. 14 2340001 Google Scholar
[11]	Wu F, Bao S, Zhou J, Wang Y, Sun J, Wen J, Wan Y, Zhang Q 2023 Nat. Phys. 19 1868 Google Scholar
[12]	Wang J, Neaton J B, Zheng H, Nagarajan V, Ogale S B, Liu B, Viehland D, Vaithyanathan V, Schlom D G, Waghmare U V, Spldin N A, Rabe K M, Wuttig M, Ramesh R 2003 Science 299 1719 Google Scholar
[13]	Wang Y Z, Pascut G L, Gao B, Tyson T A, Haule K, Kiryukhin V, Cheong S W 2015 Sci. Rep. 5 12268 Google Scholar
[14]	Spaldin N A, Ramesh R 2019 Nat. Mater. 18 203 Google Scholar
[15]	Kurumaji T, Ishiwata S, Tokura Y 2015 Phys. Rev. X 5 031034 Google Scholar
[16]	Chang Y, Weng Y, Xie Y, You B, Wang J, Li L, Liu J M, Dong S, Lu C 2023 Phys. Rev. Lett. 131 136701 Google Scholar
[17]	Tang Y, Wang S, Lin L, Li C, Zheng S, Li C, Zhang J, Yan Z, Jiang X, Liu J M 2019 Phys. Rev. B 100 134112 Google Scholar
[18]	Kim J, Artyukhin S, Mun E, Jaime M, Harrison N, Hansen A, Yang J, Oh Y, Vanderbilt D, Zapf V, Cheong S 2015 Phys. Rev. Lett. 115 137201 Google Scholar
[19]	Rivera J P 1994 Ferroelectrics 161 165 Google Scholar
[20]	Kurumaji T, Ishiwata S, Tokura Y 2017 Phys. Rev. B 95 045142 Google Scholar
[21]	Kurumaji T, Takahashi Y, Fujioka J, Masuda R, Shishikura H, Ishiwata S, Tokura Y 2017 Phys. Rev. B 95 020405(R Google Scholar
[22]	俞斌, 胡忠强, 程宇心, 彭斌, 周子尧, 刘明 2018 物理学报 67 157507 Google Scholar Yu B, Hu Z Q, Cheng Y X, Peng B, Zhou Z Y, Liu M 2018 Acta Phys. Sin. 67 157507 Google Scholar
[23]	申见昕, 尚大山, 孙阳 2018 物理学报 67 127501 Google Scholar Shen J, Shang D, Sun Y 2018 Acta Phys. Sin. 67 127501 Google Scholar
[24]	Yu S, Gao B, Kim J, Cheong S W, Man M, Madéo J, Dani K, Talbayev D 2018 Phys. Rev. Lett. 120 037601 Google Scholar
[25]	Tang Y, Zhou G, Lin L, Chen R, Wang J, Lu C, Huang L, Zhang J, Yan Z, Lu X, Huang X, Jiang X P, Liu J M 2022 Phys. Rev. B 105 064108 Google Scholar
[26]	Reschke S, Farkas D, Strinić A, Ghara S, Guratinder K, Zaharko O, Prodan L, Tsurkan V, Szaller D, Bordács S, Deisenhofer J, Kézsmárki I 2022 npj Quantum Mater. 7 1 Google Scholar
[27]	McAlister S, Strobel P 1983 J. Magn. Magn. 30 340 Google Scholar
[28]	Tang Y, Zhang J, Lin L, Chen R, Wang J, Zheng S, Li C, Zhang Y, Zhou G, Huang L, Yan Z, Lu X, Wu D, Huang X, Jiang X, Liu J M 2021 Phys. Rev. B 103 014112 Google Scholar
[29]	Schmid H 1973 Int. J. Magn. 4 337
[30]	Johnston D, McQueeney R, Lake B, Honecker A, Zhitomirsky M, Nath R, Furukawa Y, Antropov V, Yogesh Singh 2011 Phys. Rev. B 84 094445 Google Scholar
[31]	Solovyev I V, Streltsov S V 2019 Phys. Rev. Matter. 3 114402 Google Scholar
[32]	Taniguchi K, Abe N, Takenobu T, Iwasa Y, Arima T 2006 Phys. Rev. Lett. 97 097203 Google Scholar
[33]	Balents L 2010 Nature 464 199 Google Scholar
[34]	Joshua S J 1984 Aust. J. Phys. 37 305 Google Scholar
[35]	豆树清, 杨晓阔, 夏永顺, 袁佳卉, 崔焕卿, 危波, 白馨, 冯朝文 2023 物理学报 72 157501 Google Scholar Dou S, Yang X, Xia Y, Yuan J, Cui H, Wei B, Bai X, Feng C 2023 Acta Phys. Sin. 72 157501 Google Scholar
[36]	宋骁, 高兴森, 刘俊明 2018 物理学报 67 157512 Google Scholar Song X, Gao X, Liu J M 2018 Acta Phys. Sin. 67 157512 Google Scholar
[37]	Tang Y, Zhou S, Weng Y, Zhang A, Zhang Y, Zheng S, Li X 2025 Phys. Rev. B 111 134423 Google Scholar
[38]	Wei X, Zhang X, Yu H, Gao L, Tang W, Hong M, Chen Z, Kang Z, Zhang Z, Zhang Y 2024 Nat. Electron. 7 138 Google Scholar

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Mean-field approximation model for multiferroicity and magnetoelectric coupling effects in polar magnet Co₂Mo₃O₈