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六角晶系磁铅石型(M型)锶铁氧体因其独特的磁性、介电性能和热稳定性, 在永磁材料领域备受关注. 但相比于稀土永磁Nd2Fe14B材料来说, M型锶铁氧体(SrFe12O19)永磁材料的综合磁性能较低, 这极大地限制了其使用范围. 本文基于密度泛函理论的第一性原理计算方法, 结合广义梯度近似(GGA+U), 系统研究了Ca-Co(Zn)共掺杂对M型锶铁氧体的电子结构、力学性能、导电性和磁性能的影响. 计算结果表明, Ca-Co(Zn)共掺杂SrFe12O19铁氧体均具有良好的结构稳定性和力学性能. Ca-Zn共掺杂可以使体系导电性增强, 这是因为二价Zn离子取代了4f1晶位的三价Fe离子. 同时, Ca-Co(Zn)共掺杂使体系的总磁矩增大, 磁晶各向异性能下降, 但相比于Co和Zn单掺杂体系, 磁晶各向异性能有所改善. 这表明, Ca-Co(Zn)共掺杂能够有效地提高M型锶铁氧体的磁性能, 并具备节约成本和环保的优点.M-type strontium ferrite has attracted widespread attention in the field of permanent magnet materials due to its unique magnetic properties, dielectric performance, and thermal stability. However, compared with rare-earth permanent magnets such as Nd2Fe14B, strontium ferrite (SrFe12O19) permanent magnets possess relatively low comprehensive magnetic properties, which limits their application range. The effects of Ca-Co (Zn) doping on the electronic structure, mechanical properties, and magnetic properties of M-type strontium ferrite are systematically investigated by first-principles plane-wave pseudopotential method based on density functional theory (DFT), combined with the generalized gradient approximation (GGA + U) in thiswork. The calculation results indicate that the Ca-Co (Zn) co-doped M-type strontium ferrite systems exhibit good structural stability and mechanical properties. In the Ca-Zn co-doped structures, the conductivity of the system is enhanced because of the substitution of divalent Zn ionsfortrivalent Fe ions at the 4f1 site. The Ca-Co (Zn) co-doping increases the total magnetic moment of the system, while the magnetocrystalline anisotropy energy decreases. However, compared with the single Codoped systemand singleZn doped system, theCo-Znco-doped systemhas themagnetocrystalline anisotropy energy improved, indicating that Ca-Co (Zn) co-doping can effectively enhance the magnetic properties of strontium ferrite. In thiswork, the mechanisms of the effects of Ca-Co and Ca-Zn co-doping on the magnetocrystalline anisotropy energy of strontium ferriteare also analyzed. The results indicate that the decrease ofmagnetocrystalline anisotropy energy in the Ca-Co co-doped system is mainly due to the effects of dxy and ${\mathrm{d}}_x^2 $-${_y} ^2 $ orbital electrons of Co3+ ion and dxy and ${\mathrm{d}}_x^2 $-${_y} ^2 $ orbital electrons of Fe ions at the 2b site. In the Ca-Zn co-doped system, the reduction is mainly influenced by Fe-3d orbitals at the 4f1 site, while the dxy and ${\mathrm{d}}_x^2 $-${_y} ^2 $ orbital electrons of the 2b site enhance the magnetocrystalline anisotropy energy of the system. These results provide theoretical guidance for modifyingM-type strontium ferritein future.
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图 1 (a) M型SrFe12O19的晶体结构模型; (b) M型SrFe12O19晶胞模型中Fe离子的自旋取向
Fig. 1. (a) 3D structural model of M-type strontium ferrite; (b) spin orientation of Fe ions depicted in M-type SrFe12O19.
图 2 Sr铁氧体及Ca-Co(Zn)共掺杂结构的TDOS及Fe-3d和O-2p分波态密度 (a) Sr铁氧体; (b) Ca-Co-Sr铁氧体; (c) Ca-Zn-Sr铁氧体
Fig. 2. TDOS and PDOS of Fe-3d and O-2pfor Sr ferrite and Ca-Co (Zn) co-doped structures: (a) Sr ferrite; (b) Ca-Co-Srferrite; (c) Ca-Zn-Sr ferrite.
图 3 Ca-Co-Sr铁氧体的分波态密度 (a)不同晶位处Fe-3d; (b) Co-3d
Fig. 3. PDOS of Ca-Co-Sr ferrite: (a) Fe-3d at different sites; (b) Co-3d.
图 4 Ca-Zn-Sr铁氧体中不同晶位处Fe离子态密度以及Zn离子3d轨道分波态密度 (a) Fe离子; (b) Zn离子
Fig. 4. DOS of Fe ions at different sites and the PDOS of 3d electrons of Zn ion in Ca-Zn-Sr ferrites: (a) Fe ions; (b) Zn ion.
图 5 Ca-Co-Sr铁氧体Co离子分别沿[001]和[100]轴向磁化后的轨道态密度 (a) dxy; (b) $ {{\mathrm{d}}}_{z}^{2} $; (c) dyz; (d)dxz; (e) ${\mathrm{d}}_x^2 $-y2
Fig. 5. Orbital density of states of Co ion in Ca-Co-Sr ferrite magnetized along the [001] and[100] axes: (a) dxy; (b) $ {{\mathrm{d}}}_{z}^{2} $; (c) dyz; (d) dxz; (e) ${\mathrm{d}}_x^2 $-y2.
图 6 Ca-Co-Sr铁氧体2b晶位Fe离子分别沿[001]和[100]轴向磁化的轨道态密度 (a) dxy; (b) $ {{\mathrm{d}}}_{z}^{2} $; (c) dyz; (d) dxz; (e)${\mathrm{d}}_x^2 $-y2
Fig. 6. Orbital density of states for Fe ions at the 2b site in Ca-Co-Sr ferrite magnetized along the [001] and [100] axes, respectively: (a) dxy; (b) $ {{\mathrm{d}}}_{z}^{2} $; (c) dyz; (d) dxz; (e) ${\mathrm{d}}_x^2 $-y2.
图 7 Ca-Zn-Sr铁氧体2b和4f1晶位处Fe离子分别沿[001]和[100]轴向磁化的分波态密度 (a) 2b; (b) 4f1
Fig. 7. PDOS for Fe ions at the 2b site and 4f1site in Ca-Zn-Sr ferrite magnetized along the [001]and[100] axes: (a) 2b;(b) 4f1.
图 8 Ca-Zn-Sr铁氧体2b晶位处Fe离子分别沿[001]和[100]轴向磁化的轨道态密度 (a) dxy; (b) dxz; (c) dyz; (d) $ {{\mathrm{d}}}_{z}^{2} $; (e) ${\mathrm{d}}_x^2 $-y2
Fig. 8. Orbital density of states for Fe ions at the 2b site in Ca-Zn-Sr ferrite magnetized along the [001]and[100] axes: (a) dxy; (b) dxz; (c) dyz; (d) $ {{\mathrm{d}}}_{z}^{2} $; (e) ${\mathrm{d}}_x^2 $-y2.
表 1 Sr铁氧体、Co、Zn单掺杂以及Ca-Co(Zn)共掺杂体系的晶格参数、c/a值
Table 1. Lattice parameters and c/a values for Sr ferrite, single doping with Co or Zn, and co-doping withCa-Co (Zn).
体系 a/Å c/Å c/a Sr铁氧体 5.85 23.09 3.94 Co-Sr铁氧体 5.84 23.05 3.95 Zn-Sr铁氧体 5.80 22.94 3.96 Ca-Co-Sr铁氧体 5.85 23.10 3.95 Ca-Zn-Sr铁氧体 5.81 22.94 3.95 
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表 2 Sr铁氧体、Co、Zn单掺杂及Ca-Co(Zn)共掺杂体系的弹性常数和力学参数
Table 2. Elastic constants and mechanical parameters for Sr ferrite, single doping with Co or Zn, and co-doping with Ca-Co (Zn).
体系 C11 C12 C13 C33 C44 B/GPa G/GPa B/G ν E/GPa Sr铁氧体 311 158 116 280 70 186 77 2.43 0.32 202 Co-Sr铁氧体 287 163 110 259 36 167 66 2.51 0.32 176 Zn-Sr铁氧体 363 168 133 280 73 205 82 2.50 0.32 217 Ca-Co-Sr铁氧体 456 103 179 159 107 188 80 2.37 0.32 208 Ca-Zn-Sr铁氧体 347 163 128 258 76 199 83 2.40 0.32 218
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表 3 Sr铁氧体及掺杂体系各离子及总磁晶各向异性能 (单位: meV)
Table 3. Magnetocrystalline anisotropy energies (unit: meV) of ionsand the total for Sr ferrite and doped systems.
晶位 Co(4f2) Zn(4f1) Fe(2a) Fe(2b) Fe(4f1) Fe(4f2) Fe(12k) Total $ {\text{E}}_{\text{Sr}}^{\text{MAC}} $ — — 0.007 0.872 –0.086 –0.042 0.466 0.830 $ {\text{E}}_{\text{Co-Sr}}^{\text{MAC}} $ –2.377 — 0.010 0.406 –0.069 –0.084 0.067 0.257 $ {\text{E}}_{\text{Zn-Sr}}^{\text{MAC}} $ — 0.000 0.189 0.381 –1.031 –0.035 0.058 0.308 $ {\text{E}}_{\text{Ca-Co-Sr}}^{\text{MAC}} $ –2.329 — 0.001 0.397 –0.046 –0.081 0.058 0.370 $ {\text{E}}_{\text{Ca-Zn-Sr}}^{\text{MAC}} $ — –0.015 0.040 0.225 –0.280 –0.017 0.037 0.490
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表 4 Sr铁氧体中各晶位Fe离子沿c轴方向轨道磁矩值(单位: μB)
Table 4. Orbital magnetic moment (unit: μB) of Fe ions at different sites in Sr ferrite along the c-axis.
晶位 Fe(2a) Fe(2b) Fe(4f1) Fe(4f2) Fe(12k) Total p轨道 0.000 0.001 –0.002 –0.001 0.000 0.021 d轨道 0.001 0.015 –0.012 –0.010 0.011 0.113 总磁矩 0.001 0.016 –0.014 –0.011 0.011 0.135
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表 5 Ca-Co-Sr铁氧体中各离子沿c轴方向的平均轨道磁矩值(单位: μB)
Table 5. Average orbital magnetic moment (unit: μB) of each ion in Ca-Co-Sr ferrite along the c-axis.
晶位 Co(4f2) Fe(2a) Fe(2b) Fe(4f1) Fe(4f2) Fe(12k) Total p轨道 –0.001 0.000 0.001 –0.002 –0.001 0.000 0.015 d轨道 –0.033 0.012 0.015 –0.012 –0.010 0.011 0.096 总磁矩 –0.033 0.012 0.016 –0.014 –0.011 0.011 0.111
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表 6 Ca-Zn-Sr铁氧体各离子沿c轴方向的平均轨道磁矩(单位: μB)
Table 6. Average orbital magnetic moment (unit: μB) of each ion in Ca-Zn-Sr ferrite along the c-axis.
晶位 Zn(4f1) Fe(2a) Fe(2b) Fe(4f1) Fe(4f2) Fe(12k) Total p轨道 0.000 0.000 0.000 0.000 0.000 0.000 0.020 d轨道 0.000 0.011 0.015 –0.017 –0.012 0.011 0.099 总磁矩 –0.001 0.011 0.015 –0.017 –0.012 0.011 0.119
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