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As the first known metal-insulator transition, Verwey transition of Fe3O4 attracts much attention due to its fascinating physics. With the decreasing temperature across Verwey temperature, Fe3O4 undergoes the transition of lattice distortion, charge ordering, electricity, magnetic anisotropy, etc, but the magnetic ground state keeps the ferrimagnetism. The comprehension of the underlying physics in Verwey transition facilitates the understanding of metal–insulator transition in other strongly-correlated systems. Nevertheless, the mechanism of Verwey transition is still debated after the first glimpse of Verwey transition. In this paper, we summarize the research history and current status of Verwey transition in Fe3O4. The investigations of lattice structure, charge ordering, electronic transport, magnetic and ferroelectric properties of Fe3O4 across Verwey transition are reviewed. Finally, the summary and outlook are given.
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Keywords:
- Fe3O4 /
- Verwey transition /
- charge ordering /
- magnetic anisotropy
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图 5 (a)−(d) Fe3O4(001)薄膜的TEM研究结果; (e)−(h) Fe3O4(111)薄膜的TEM研究结果. 室温和95 K的衍射斑点分别由室温相和低温相Fe3O4密勒指数标注. 图(g)中黄字为Al2O3密勒指数. 图(b)和图(f)棕球和红球分别代表Fe和O原子[41,43]
Fig. 5. TEM results of ((a)−(d)) Fe3O4(001) and ((e)−(h)) Fe3O4(111) films. White Miller index above (below) TV are marked with cubic (monoclinic) Fe3O4. Yellow Miller index in Fig. (g) indicates Al2O3. Brown and red spheres in Fig. (b) and Fig. (f) represent Fe and O[41,43].
图 6 Fe3O4(110)面上APB的结构 (a)理想情况下Fe3O4的结构; (b)第一类APB(APB–I); (c)第二类APB(APB–II). APB的平移方向由绿色箭头表示, 红球为O原子, 蓝球为FeA离子, 灰球为FeB离子[48]
Fig. 6. {110} APB defects in Fe3O4: (a) The ideal cubic Fe3O4 structure; (b) APB-I; (c) APB-II. The APB crystal translations are indicated by green vectors. Red, blue and gray spheres represent the oxygen atoms, tetrahedral Fe and octahedral Fe atoms[48].
图 8 (a) Fe3O4薄膜的扫描隧道显微镜图像; (b)沿(a)中红线标记方向上的高度变化; (c)单斜结构Fe3O4; (d)由镜面对称单斜结构形成的Fe3O4[51]
Fig. 8. (a) STM image of Fe3O4(100) surface at 78 K; (b) profile along the line marked in red of (a); (c) the monoclinic unit cell of Fe3O4; (d) two mirrored monoclinic cells with opposite monoclinic c axis at a twin boundary[51].
图 9 Fe3O4孪晶界处的自旋极化态密度图(density of states, DOS) (a) I型; (b) II型; (c) III型. 费米能级由红色虚线表示. 图中给出了弛豫后的模型. 态密度表明I型孪晶界处为铁磁耦合, II型和III型为反铁磁耦合[52]
Fig. 9. Spin-polarized DOS of Fe3O4 twin boundaries (TBs): (a) Type I TB; (b) Type II TB; (c) Type III TB. EF is represented by the red dashed lines. The relaxed atomistic models are also given for reference. The DOS suggest that the magnetic coupling across the type I TB is ferromagnetic and those across the type II and III TBs are antiferromagnetic[52].
图 12 Fe3O4的FeB位的电子局域模型 (a) Verwey提出的简单四面体Fe2+/Fe3+电荷有序模型; (b)包含两个Fe2+和两个Fe3+的安德森四面体模型; (c) FeB4四面体内的键二聚化, 电子局域化在两个距离相近的FeB–FeB内, 由粗线表示[53]
Fig. 12. Models for electron localization on FeB sites of Fe3O4: (a) Verwey’s tetragonal model of Fe2+/Fe3+ charge order; (b) an Anderson tetrahedron of two Fe2+ and two Fe3+ ions; (c) bond-dimerization in the FeB4 tetrahedron, where the electrons are localized in two shortened FeB-FeB distances, shown as bold lines[53].
图 14 δ12和δ34置信因子的等值图. 最佳值为δ12 = 0.12 ± 0.025, δ34 = 0.10 ± 0.06. Fe1电子占据数为5.38和5.62, Fe4电子占据数为5.40和5.60[63]
Fig. 14. Isovalue of the confidence factor. The best agreement is obtained for δ12 = 0.12 ± 0.025 electrons and δ34 = 0.10 ± 0.06 electrons, where the charge occupancies of Fe1 and Fe4 are 5.38, 5.62 and 5.40, 5.60, respectively[63].
图 16 (a) 70 K和(b) 115 K下, 660 nm厚的Fe3O4薄膜的磁电阻随磁场变化关系; (c) 0.5, 1, 2和4 T磁场下磁电阻随温度的变化关系[71]
Fig. 16. Magnetoresistance of 660 nm thick Fe3O4 films at (a) 70 K and (b) 115 K; (c) Temperature dependent magnetoresistance of 660-nm thick Fe3O4 film at the magnetic fields of 0.5, 1, 2, 4 T. The dotted lines are simulations using Mott’s formula[71].
图 21 (a)测试示意图; (b) 80 K和50 kOe下, Fe3O4(100)薄膜的AMR与三极化子分布的关系; (c) 110 K和10 kOe下, Fe3O4(111)薄膜的AMR与三极化子分布的关系. 三极化子示意图如右上角所示[85]
Fig. 21. (a) Schematic of the measurements; (b) relation between AMR and distribution of in-plane trimeron of Fe3O4(100) film at 80 K and 50 kOe; (c) relation between AMR and distribution of in-plane trimeron of Fe3O4(111) film at 110 K and 10 kOe. The trimeron is shown in the upper right corner[85].
图 22 (a) Pd/Fe3O4/Nd:SrTiO3异质结构的电滞回线[92]; (b) P2/c (左图)和Cc空间群(右图)的FeB离子结构. 橙色和蓝色球表示Fe2+和Fe3+. 红色箭头表示电荷转移引起的电偶极矩[93]
Fig. 22. (a) Dielectric hysteresis loop of Pd/Fe3O4/Nd:SrTiO3 heterostructure[92]; (b) ionic structure of Fe octahedral sites with P2/c (left) and Cc (right) space groups. Orange and blue balls represent the Fe2+ and Fe3+ ions. Electric dipole moments caused by charge shifts are indicated by red arrows[93].
表 1 外延Fe3O4(001)薄膜中APB处的磁交换相互作用[46]
Table 1. Magnetic exchange interaction across APBs in the epitaxial Fe3O4(001) films[46].
交换相互作用 类型和角度 磁性和强度 出现位置 FeB-O-FeB 超交换, 180° 反铁磁, 强 APB处 FeA-O-FeA 超交换, 约140° 反铁磁, 强 APB处 FeB-O-FeA 超交换, 约120° 反铁磁, 强 块体和APB处 FeB-O-FeB 超交换, 90° 铁磁, 弱 块体和APB处 FeA-O-FeA 超交换, 约70° 反铁磁, 弱 APB处 FeB-FeB 直接 铁磁, 弱 块体和APB处 FeA-FeA 直接 反铁磁, 弱 APB处 FeB-FeA 直接 铁磁, 弱 APB处 表 2 在P2/c和
$Fd\overline 3 m$ 空间群下,${{{a_c}}/{\sqrt 2 }} \times {{{a_c}}/{\sqrt 2 }} \times 2{a_c}$ 晶胞Fe3O4的电荷差(CS)、轨道有序度(OO)及总能量Et[36]Table 2. Calculated charge separations (CS), orbital ordering (OO) and the total energy (Et) of Fe3O4 with
${{{a_c}}/{\sqrt 2 }} \times {{{a_c}}/{\sqrt 2 }} \times 2{a_c}$ unit cell in monoclinic P2/c and cubic phase[36].U/eV P2/c $Fd\overline 3 m$ ↓gap/eV CS/e OO(P) Et/eV·(f.u.)–1 ↓gap/eV CS/e OO(P) Et/eV·(f.u.)–1 0.0 No 0.00 No(0.55) –0.15 No 0.00 No(0.34) 0.00 4.0 No 0.11 Yes(0.98) –0.15 No 0.10 Yes(0.96) –0.22 4.5 0.2 0.15 Yes(0.98) –0.53 No 0.12 Yes(0.96) –0.27 5.0 0.42 0.17 Yes(0.97) –0.75 0.11 0.16 Yes(0.96) –0.35 5.5 0.63 0.19 Yes(0.96) –0.85 0.28 0.19 Yes(0.91) –0.47 -
[1] Verwey E J W 1939 Nature 144 327
[2] Renger K 1913 Ph. D. Dissertation (Zürich: Swiss Federal Institute of Technology Zürich)
[3] Parks G S, Kelly K K 1926 J. Phys. Chem. 30 47Google Scholar
[4] Millar R W 1929 J. Am. Chem. Soc. 51 215Google Scholar
[5] Okamura T 1932 Sci. Rep. Tohoku Imp. Univ. 21 231
[6] Ellefson B S, Taylor N W 1934 J. Chem. Phys. 2 58Google Scholar
[7] Weiss P, Forrer R 1929 Ann. Phys. 12 279
[8] Bragg W H 1915 Philos. Mag. 30 305Google Scholar
[9] Bragg W H and Brown G B 1926 Z. Kristallogr. 63 122
[10] Claassen A 1926 Proc. Phys. Soc. 38 482
[11] Néel L 1948 Ann. Phys. 3 137
[12] Verwey E J W, Heilmann E L 1948 J. Chem. Phys. 16 1091Google Scholar
[13] Verwey E J W, Haayman P W, Romeijn F C 1947 J. Chem. Phys. 15 181Google Scholar
[14] Westrum E F, Grønvold F 1969 J. Chem. Thermodyn. 1 543Google Scholar
[15] Cullen J R, Callen E R 1971 Solid State Commun. 9 1041Google Scholar
[16] Evans B J, Westrum E F 1972 Phys. Rev. B 5 3791Google Scholar
[17] Cullen J R, Callen E R 1973 Phys. Rev. B 7 397Google Scholar
[18] Chakraverty B K 1974 Solid State Commun. 15 1271Google Scholar
[19] Buckwald R A, Hirsch A A 1975 Solid State Commun. 17 621Google Scholar
[20] Bartel J J, Westrum E F, Haas J L 1976 J. Chem. Thermodyn. 8 575Google Scholar
[21] Matsui M, Todo S, Chikazumi S 1977 J. Phys. Soc. Jpn. 42 1517Google Scholar
[22] Rigo M O, Kleinclauss J 1980 Philos. Mag. B 42 393Google Scholar
[23] Senn M S, Wright J P, Attfield J P 2012 Nature 481 173Google Scholar
[24] Miles P A, Westphal W B, von Hippel A 1957 Rev. Mod. Phys. 29 279Google Scholar
[25] Wright J P, Attfield J P, Radaelli P G 2001 Phys. Rev. Lett. 87 266401Google Scholar
[26] Bohra M, Agarwal N, Singh V 2019 J. Nanomater. 2019 8457383
[27] Bickford Jr L R 1950 Phys. Rev. 78 449Google Scholar
[28] Kato K, Iida S 1981 J. Phys. Soc. Jpn. 50 2844Google Scholar
[29] Chikazumi S, Chiba K, Suzuki K and Chikazumi S 1970 Proceedings of the International Conference on Ferrites Kyoto, Japan, July 6−15, 1970 p595
[30] Iida S, Yamamoto M, Umemura S 1974 AIP Conf. Proc. 18 913
[31] Vieland L J 1975 Acta Crystallogr., Sect. A: Found. Crystallogr. 31 753
[32] Shirane G, Chikazumi S, Akimitsu J, Chiba K, Matsui M, Fujii Y 1975 J. Phys. Soc. Jpn. 39 949Google Scholar
[33] Iizumi M, Shirane G 1975 Solid State Commun. 17 433Google Scholar
[34] Iizumi M, Koetzle T F, Shirane G, Chikazumi S, Matsui M, Todo S 1982 Acta Crystallogr., Sect. B: Struct. Sci. 38 2121Google Scholar
[35] Wright J P, Attfield J P, Radaelli P G 2002 Phys. Rev. B 66 214422Google Scholar
[36] Jeng H T, Guo G Y, Huang D J 2006 Phys. Rev. B 74 195115Google Scholar
[37] Senn M S, Loa I, Wright J P, Attfield J P 2012 Phys. Rev. B 85 125119Google Scholar
[38] Anderson P W 1956 Phys. Rev. 102 1008Google Scholar
[39] Weng S C, Lee Y R, Chen C G, Chu C H, Soo Y L, Chang S L 2012 Phys. Rev. Lett. 108 146404Google Scholar
[40] de Jong S, Kukreja R, Trabant C, Pontius N, Chang C F, Kachel T, Beye M, Sorgenfrei F, Back C H, Bräuer B, Schlotter W F, Turner J J, Krupin O, Doehler M, Zhu D, Hossain M A, Scherz A O, Fausti D, Novelli F, Esposito M, Lee W S, Chuang Y D, Lu D H, Moore R G, Yi M, Trigo M, Kirchmann P, Pathey L, Golden M S, Buchholz M, Metcalf P, Parmigiani F, Wurth W, Föhlisch A, Schüßler-Langeheine C, Dürr H A 2013 Nat. Mater. 12 882Google Scholar
[41] Mi W B, Guo Z B, Wang Q X, Yang Y, Bai H L 2013 Scr. Mater. 68 972Google Scholar
[42] Margulies D T, Parker F T, Spada F E, Goldman R S, Li J, Sinclair R, Berkowitz A E 1996 Phys. Rev. B 53 9175Google Scholar
[43] Liu X, Mi W B, Zhang Q, Zhang X X 2018 Appl. Phys. Lett. 113 012401Google Scholar
[44] Margulies D T, Parker F T, Rudee M L, Spada F E, Chapman J N, Aitchison P R, Berkowitz A E 1997 Physical Review Letters 79 5162
[45] Fitzgerald A G, May T G 1976 Thin Solid Films 35 201Google Scholar
[46] Celotto S, Eerenstein W, Hibma T 2003 Eur. Phys. J. B 36 271Google Scholar
[47] Liu X H, Liu W, Zhang Z D 2017 Phys. Rev. B 96 094405Google Scholar
[48] McKenna K P, Hofer F, Gilks D, Lazarov V K, Chen C, Wang Z C, Ikuhara Y 2014 Nat. Commun. 5 6740
[49] Kasama T, Church N S, Feinberg J M Dunin-Borkowski R E, Harrison R J 2010 Earth Planet. Sci. Lett. 297 10Google Scholar
[50] Kasama T, Harrison R J, Church N S, Nagao M, Feinberg J M, Dunin-Borkowski R E 2013 Phase Transitions 86 67Google Scholar
[51] de la Figuera J, Novotny Z, Setvin M, Liu T J, Mao Z Q, Chen G, N’Diaye T A, Schmid M, Diebold U, Schmid K A, S.Parkinson G 2013 Phys. Rev. B 88 161410Google Scholar
[52] Chen C L, Li H P, Seki T, Yin D Q, Sanchez-Santolino G, Inoue K, Shibata N, Ikuhara Y 2018 ACS Nano 12 2662Google Scholar
[53] Attfield J P 2014 J. Jpn. Soc. Powder Powder Metall. 61 S43Google Scholar
[54] Jeng H T, Guo G Y, Huang D J 2004 Phys. Rev. Lett. 93 156403Google Scholar
[55] Liu X, Yin L, Mi W B 2017 Sci. Rep. 7 43403Google Scholar
[56] Verwey E J W, Haayman P W 1941 Physica 8 979Google Scholar
[57] Cullen J R, Callen E 1970 J. Appl. Phys. 41 879Google Scholar
[58] Mott N F 1990 Metal-insulator transitions (2nd Ed.) (London: Taylor and Francis) p68
[59] Chakraverty B K 1980 Philos. Mag. B 42 473Google Scholar
[60] Seo H, Ogata M, Fukuyama H 2002 Phys. Rev. B 65 085107Google Scholar
[61] van den Brink J, Khomskii D I 2008 J. Phys. Condens. Matter 20 434217Google Scholar
[62] García J, Subías G, Proietti M G, Blasco J, Renevier H, Hodeau J L, Joly Y 2001 Phys. Rev. B 63 054110Google Scholar
[63] Nazarenko E, Lorenzo J E, Joly Y, Hodeau J L, Mannix D, Marin C 2006 Phys. Rev. Lett. 97 056403Google Scholar
[64] Leonov I, Yaresko A N, Antonov V N, Korotin M A, Anisimov V I 2004 Phys. Rev. Lett. 93 146404Google Scholar
[65] Liu X H, Chang C F, Rata A D, Komarek A C, Tjeng L H 2016 npj Quantum Mater. 1 16027Google Scholar
[66] Calhoun B A 1954 Phys. Rev. 94 1577Google Scholar
[67] Palmer W 1963 Phys. Rev. 131 1057Google Scholar
[68] Domenicali C A 1950 Phys. Rev. 78 458Google Scholar
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