Structure, magnetic and transport properties of Fe<sub>3</sub>O<sub>4</sub> near verwey transition

Liu Xiang; Mi Wen-Bo

doi:10.7498/aps.69.20191763

Abstract

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.

Keywords:

Authors and contacts

Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparation Technology, School of Science, Tianjin University, Tianjin 300354, China

Corresponding author: Mi Wen-Bo, miwenbo@tju.edu.cn

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References

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Cited By

图 1 Fe₃O₄的电阻率随温度的变化关系. 样品I中FeO∶Fe₂O₃ = 1∶1.025, 样品II中FeO:Fe₂O₃ = 1∶1.08^[1]

Figure 1. Temperature-dependent resistivity of Fe₃O₄ sample I with FeO∶Fe₂O₃ = 1∶1.025 and sample II with FeO∶Fe₂O₃ = 1∶1.08^[1].

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图 2 尖晶石晶胞　(a)次晶格的堆叠方式; (b)晶体结构^[24]

Figure 2. Spinel unit cell: (a) Stacking pattern of sub-lattices; (b) crystal structure^[24].

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图 3 空间群为$Fd\overline 3 m$, P2/m, P2/c和Cc的Fe₃O₄单胞^[35]

Figure 3. Relationship between the unit cells referred to the structure with space group $Fd\overline 3 m$, P2/m, P2/c and Cc^[35].

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图 4 (a)三极化子和(b)三极化子分布的示意图^[23]

Figure 4. Schematic diagram of (a) trimeron and (b) distribution of trimeron^[23].

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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]

Figure 5. TEM results of ((a)−(d)) Fe₃O₄(001) and ((e)−(h)) Fe₃O₄(111) films. White Miller index above (below) T_V 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].

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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Fe_A离子, 灰球为Fe_B离子^[48]

Figure 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].

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图 7 立方相和单斜相Fe₃O₄晶格的相关性^[49]

Figure 7. Symmetrically distinct crystallographic relationships between cubic and monoclinic phases of magnetite^[49].

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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]

Figure 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].

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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]

Figure 9. Spin-polarized DOS of Fe₃O₄ twin boundaries (TBs): (a) Type I TB; (b) Type II TB; (c) Type III TB. E_F 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].

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图 10 Fe₃O₄中Fe离子的3d电子轨道排布和磁耦合示意图^[53]

Figure 10. Sketch map of the electronic ground state of Fe 3d electrons and magnetic couplings in Fe₃O₄^[53].

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图 11 Fe₃O₄的磁各向异性常数K₁随温度的变化关系^[27]

Figure 11. Temperature dependent Anisotropy constant K₁ of Fe₃O₄^[27].

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图 12 Fe₃O₄的Fe_B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) Fe_B₄四面体内的键二聚化, 电子局域化在两个距离相近的Fe_B–Fe_B内, 由粗线表示^[53]

Figure 12. Models for electron localization on Fe_B 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 Fe_B₄ tetrahedron, where the electrons are localized in two shortened Fe_B-Fe_B distances, shown as bold lines^[53].

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图 13 Fe₃O₄中Fe_B离子的态密度图, 费米能级位于E_F = 0 eV处^[54]

Figure 13. DOS of Fe₃O₄ with the monoclinic structure projected onto the Fe_B d orbitals. Fermi level E_F is set at 0 eV^[54].

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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]

Figure 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].

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图 15 150和660 nm厚的Fe₃O₄外延薄膜的ρ–T曲线及300 Oe磁场下660 nm厚的Fe₃O₄外延薄膜的磁化强度随温度的变化关系^[71]

Figure 15. Temperature dependent resistivity of 150 and 660-nm thick Fe₃O₄ films in the temperature range of 60–350 K. The temperature dependent magnetization of 660-nm thick film at a magnetic field of 300 Oe^[71].

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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]

Figure 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].

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图 17 块体Fe₃O₄和200, 50和15 nm厚的Fe₃O₄薄膜的(a)磁化强度和(b)零场电阻率随温度的变化关系^[73]

Figure 17. Temperature dependent (a) magnetization and (b) zero-field resistivity of Fe₃O₄ single crystal and films with the thickness of 200, 50 and 15 nm^[73].

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图 18 在磁场作用下, Fe₃O₄薄膜反相边界处的磁矩分布^[77]

Figure 18. Spin orientation of two ferromagnetic chains with antiferromagnetic coupling at an atomically sharp boundary at a magnetic field^[77].

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图 19 在5 T磁场下, (a) 67 nm厚的Fe₃O₄薄膜和(b) Fe₃O₄块体的AMR^[81]

Figure 19. AMR of the (a) 67 nm thick Fe₃O₄ film and (b) Fe₃O₄ single crystal at a magnetic field of 5 T^[81].

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图 20 外延Fe₃O₄(100)薄膜的AMR　(a) 50 kOe下AMR随温度的变化; (b) 110 K和(c)80 K下AMR随磁场的变化^[85]

Figure 20. AMR of the epitaxial Fe₃O₄(100) film: (a) Temperature-dependent AMR at a 50 kOe magnetic field; AMR at (b) 110 K and (c) 80 K^[85].

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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]

Figure 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].

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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Fe_B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]

Figure 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].

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图 23 (a)低温相Fe₃O₄铁电极化在x, z轴方向的分量; (b)体系总能随应力的变化^[94]

Figure 23. (a) Ferroelectric polarization along the x and z axes; (b) strain dependent total energy^[94].

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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
Fe_B-O-Fe_B	超交换, 180°	反铁磁, 强	APB处
Fe_A-O-Fe_A	超交换, 约140°	反铁磁, 强	APB处
Fe_B-O-Fe_A	超交换, 约120°	反铁磁, 强	块体和APB处
Fe_B-O-Fe_B	超交换, 90°	铁磁, 弱	块体和APB处
Fe_A-O-Fe_A	超交换, 约70°	反铁磁, 弱	APB处
Fe_B-Fe_B	直接	铁磁, 弱	块体和APB处
Fe_A-Fe_A	直接	反铁磁, 弱	APB处
Fe_B-Fe_A	直接	铁磁, 弱	APB处

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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E_t^[36]

Table 2. Calculated charge separations (CS), orbital ordering (OO) and the total energy (E_t) 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				$Fd\overline 3 m$
U/eV	↓gap/eV	CS/e	OO(P)	E_t/eV·(f.u.)^–1	↓gap/eV	CS/e	OO(P)	E_t/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

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[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 47 Google Scholar
[4]	Millar R W 1929 J. Am. Chem. Soc. 51 215 Google Scholar
[5]	Okamura T 1932 Sci. Rep. Tohoku Imp. Univ. 21 231
[6]	Ellefson B S, Taylor N W 1934 J. Chem. Phys. 2 58 Google Scholar
[7]	Weiss P, Forrer R 1929 Ann. Phys. 12 279
[8]	Bragg W H 1915 Philos. Mag. 30 305 Google Scholar
[9]	Bragg W H and Brown G B 1926 Z. Kristallogr. 63 122
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Structure, magnetic and transport properties of Fe₃O₄ near verwey transition

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Structure, magnetic and transport properties of Fe3O4 near verwey transition

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Structure, magnetic and transport properties of Fe₃O₄ near verwey transition