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Verwey相变处Fe3O4的结构、磁性和电输运特性

刘祥 米文博

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Verwey相变处Fe3O4的结构、磁性和电输运特性

刘祥, 米文博

Structure, magnetic and transport properties of Fe3O4 near verwey transition

Liu Xiang, Mi Wen-Bo
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  • 作为典型的金属–绝缘体转变, Fe3O4的Verwey相变蕴涵的丰富物理现象与微观机制, 因而受到了人们的广泛关注. 在Verwey相变处, Fe3O4的晶体结构、电子结构以及磁各向异性等均发生转变, 但其磁基态并未发生改变. 与其他强关联体系相比, Fe3O4的Verwey相变不需要考虑磁交换耦合作用的变化, 有利于揭示强关联体系中金属–绝缘体转变的物理本质. 本文从晶体结构、电荷有序、电输运特性、磁性和铁电特性等方面简要地介绍了Fe3O4的Verwey相变的研究历史和现状.
    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.
      通信作者: 米文博, miwenbo@tju.edu.cn
      Corresponding author: Mi Wen-Bo, miwenbo@tju.edu.cn
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  • 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]

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

    图 2  尖晶石晶胞 (a)次晶格的堆叠方式; (b)晶体结构[24]

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

    图 3  空间群为$Fd\overline 3 m$, P2/m, P2/cCc的Fe3O4单胞[35]

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

    图 4  (a)三极化子和(b)三极化子分布的示意图[23]

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

    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 7  立方相和单斜相Fe3O4晶格的相关性[49]

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

    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 10  Fe3O4中Fe离子的3d电子轨道排布和磁耦合示意图[53]

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

    图 11  Fe3O4的磁各向异性常数K1随温度的变化关系[27]

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

    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 13  Fe3O4中FeB离子的态密度图, 费米能级位于EF = 0 eV处[54]

    Fig. 13.  DOS of Fe3O4 with the monoclinic structure projected onto the FeB d orbitals. Fermi level EF is set at 0 eV[54].

    图 14  δ12δ34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 15  150和660 nm厚的Fe3O4外延薄膜的ρT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]

    Fig. 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].

    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 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]

    Fig. 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].

    图 18  在磁场作用下, Fe3O4薄膜反相边界处的磁矩分布[77]

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

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

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

    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]

    Fig. 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].

    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].

    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]

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

    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
    下载: 导出CSV

    表 2  P2/c$Fd\overline 3 m$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/eVP2/c$Fd\overline 3 m$
    ↓gap/eVCS/eOO(P)Et/eV·(f.u.)–1↓gap/eVCS/eOO(P)Et/eV·(f.u.)–1
    0.0No0.00No(0.55)–0.15No0.00No(0.34)0.00
    4.0No0.11Yes(0.98)–0.15No0.10Yes(0.96)–0.22
    4.50.20.15Yes(0.98)–0.53No0.12Yes(0.96)–0.27
    5.00.420.17Yes(0.97)–0.750.110.16Yes(0.96)–0.35
    5.50.630.19Yes(0.96)–0.850.280.19Yes(0.91)–0.47
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出版历程
  • 收稿日期:  2019-11-19
  • 修回日期:  2019-12-17
  • 刊出日期:  2020-02-20

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