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Opportunity and challenge for study of valence electron structure in typical magnetic materials

Tang Gui-De Li Zhuang-Zhi Ma Li Wu Guang-Heng Hu Feng-Xia

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Opportunity and challenge for study of valence electron structure in typical magnetic materials

Tang Gui-De, Li Zhuang-Zhi, Ma Li, Wu Guang-Heng, Hu Feng-Xia
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  • The conventional magnetic ordering models, exchange interaction, super-exchange (SE) interaction and double exchange (DE) interaction models relating to the valence electron structure in the materials, were proposed about in or before the 1950's, the time when there was little experimental evidence. Since the 1970's, more and more experimental results for the valence electron states have been reported. These experimental results suggested that the conventional magnetic ordering models need improving. i) Many experimental results, including the electron energy-loss spectra (EELS), X-ray absorption spectra (XAS), and X-ray photoelectron spectra (XPS), indicate that there are O anions in addition to O2– anions in oxides, and that the percentage of O anions may reach 30% or more. This suggests that the SE model and DE model both need to improving, in which all oxygen anions are assumed to be O2– anions. ii) Several experimental results, including gamma radiation diffraction, XAS and magnetic circular dichroism spectra (XMCD), suggest that part of 4s electrons enter into 3d orbits and transit into the 3d electrons in the process of forming metals from free atoms. The effect of the orbital magnetic moment on the magnetic moment of a bulk metal is far smaller than the spin magnetic moments. These provide the evidence of exploring the relation between magnetic moment and electrical resistivity of the magnetic metal. iii) Using density function theory (DFT) to fit physical properties yields plenty of results for many materials, but there exist serious difficulties for magnetic materials. This is due to magnetic ordering energy is included in the exchange correlation energy, which has been find no phenomenological expression so far, and has to be fitted using various models in DFT calculation. These investigations provide an opportunity to improve magnetic ordering models. Therefore, our group proposed three models of magnetic ordering in typical magnetic materials, they including an O 2p itinerant electron model for magnetic oxides (IEO model), a new itinerant electron model for magnetic metal (IEM model), and a Weiss electron pair (WEP) model for the origin of magnetic ordering energy. Replacing the SE model and DE model with the IEO model, the magnetic structures of Co, Ni, Cu doped spinel ferrites as well as Cr and Ti doped spinel ferrites can be explained. The dependence of the magnetic moment on the Sr content in perovskite manganites La1–xSrxMnO3 can also be explained, for which there have been many ongoing disputes about the cation distributions. With the IEM model, we can explain qualitatively the relation of the magnetic moment with the resitivity for each of Fe, Co, Ni, Cu metals, and fit the curves of the resistivity of NiCu alloy versus test temperature and the Cu doped level. With the WEP model, we can explain why Fe, Co, Ni metal, NiCu alloys, Fe3O4 and La0.7Sr0.3MnO3 oxides have different Curie temperature values. The new itinerant electron model is different from the classical model in the following three elementary characteristics. First, the s electrons in free 3d transition metal atoms are divided into two parts when they form a metal or alloy. One part of these s electrons enter into the d orbits and change into the d electrons. and the other part of those electrons are the free electrons which are no longer called the s electrons. Second, only the d electrons occupying the outer orbit of an ion core in a metal or alloy may form itinerant electrons with a certain probability, while the remaining d electrons are local electrons. Third, whether in a magnetic metal or in a magnetic oxide, the transition of the itinerant electrons is the spin-dependent transition below the Curie temperature, and the transition probability decreases with test temperature increasing. The transition of the itinerant electrons turns into the spin-independent transition when the temperature is above the Curie temperature. In this paper, first, we introduce several typical experimental results of the valence electron states. Then, we present the new magnetic ordering models proposed by our group and analyze the elementary differences between the new models and the conventional models. Finally, we point out the challenge to the future work.
      Corresponding author: Tang Gui-De, tanggd@hebtu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11174069) and the Natural Science Foundation of Hebei Province, China (Grant No. E2015205111)
    [1]

    戴道生, 钱昆明 1987 铁磁学 (上册) (北京: 科学出版社) 第103−122, 198, 323页

    Dai D S, Qian K M 1987 Ferromagnetism (Vol. 1) (Beijing: Science Press) pp103−122, 198, 323 (in Chinese)

    [2]

    van Vleck J H 1937 Phys. Rev. 52 1178Google Scholar

    [3]

    Sato H, Arrott A 1959 Phys. Rev. 114 1427Google Scholar

    [4]

    Anderson P W 1950 Phys. Rev. 79 350Google Scholar

    [5]

    Zener C 1951 Phys. Rev. 82 403Google Scholar

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    Tang G D, Li Z Z, Ma L, Qi W H, Wu L Q, Ge X S, Wu G H, Hu F X 2018 Phys. Rep. 758 1Google Scholar

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    Li Z Z, Qi W H, Ma L, Tang G D, Wu G H, Hu F X 2019 J. Magn. Magn. Mater. 482 173Google Scholar

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    Qian J J, Qi W H, Li Z Z, Ma L, Tang G D, Du Y N, Chen M Y, Wu G H, Hu F X 2018 RSC Adv. 8 4417Google Scholar

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    Qian J J, Li Z Z, Qi W H, Ma L, Tang G D, Du Y N, Chen M Y 2018 J. Alloys Compd. 764 239Google Scholar

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    Nücker N, Fink J, Fuggle J C, Durham P J 1988 Phys. Rev. B 37 5158Google Scholar

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    Ju H L, Sohn H C, Krishnan K M 1997 Phys. Rev. Lett. 79 3230Google Scholar

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    Urushibara A, Moritomo Y, Arima T, Asamitsu A, Kido G, Tokura Y 1995 Phys. Rev. B 51 14103Google Scholar

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    Mizoroki T, Itou M, Taguchi Y, Iwazumi T, Sakurai Y 2011 Appl. Phys. Lett. 98 052107Google Scholar

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    Grenier S, Thomas K J, Hill J P, Staub U, Bodenthin Y, García-Fernández M, Scagnoli V, Kiryukhin V, Cheong S W, Kim B G, Tonnerre J M 2007 Phys. Rev. Lett. 99 206403Google Scholar

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    Ibrahim K, Qian H J, Wu X, Abbas M I, Wang J O, Hong C H, Su R, Zhong J, Dong Y H, Wu Z Y, Wei L, Xian D C, Li Y X, Lapeyre G J, Mannella N, Fadley C S, Baba Y 2004 Phys. Rev. B 70 224433Google Scholar

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    Papavassiliou G, Pissas M, Belesi M, Fardis M, Karayanni M, Ansermet J P, Carlier D, Dimitropoulos C, Dolinsek J 2004 Europhys. Lett. 68 453Google Scholar

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    Dupin J C, Gonbeau D, Vinatier P, Levasseur A 2000 Phys. Chem. Chem. Phys. 2 1319Google Scholar

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    Cohen R E 1992 Nature 358 136Google Scholar

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    Cohen R E, Krakauer H 1990 Phys. Rev. B 42 6416Google Scholar

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    Wu L Q, Li Y C, Li S Q, Li Z Z, Tang G D, Qi W H, Xue L C, Ge X S, Ding L L 2015 AIP Adv. 5 097210Google Scholar

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    Wu L Q, Li S Q, Li Y C, Li Z Z, Tang G D, Qi W H, Xue L C, Ding L L, Ge X S 2016 Appl. Phys. Lett. 108 021905Google Scholar

    [22]

    Chen C T, Idzerda Y U, Lin H J, Smith N V, Meigs G, Chaban E, Ho G H, Pellegrin E, Sette F 1995 Phys. Rev. Lett. 75 152Google Scholar

    [23]

    Wu R, Wang D, Freeman A J 1993 Phys. Rev. Lett. 71 3581Google Scholar

    [24]

    Wu R, Freeman A J 1994 Phys. Rev. Lett. 73 1994Google Scholar

    [25]

    Jauch W, Reehuis M 2007 Phys. Rev. B 76 235121Google Scholar

    [26]

    Pacchioni G E, Gragnaniello L, Donati F, Pivetta M, Autès G, Yazyev O V, Rusponi S, Brune H 2015 Phys. Rev. B 91 235426Google Scholar

    [27]

    韩汝珊 1998 高温超导物理 (北京: 北京大学出版社) 第19−20 页

    Han R S 1998 Physics of High Temperature Super-conductor (Beijing: Peking University Press) pp19−20 (in Chinese)

    [28]

    Alexandrov A S, Bratkovsky A M, Kabanov V V 2006 Phys. Rev. Lett. 96 117003Google Scholar

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    Alexandrov A S, Bratkovsky A M 1999 Phys. Rev. Lett. 82 141Google Scholar

    [30]

    Xu J, Ma L, Li Z Z, Lang L L, Qi W H, Tang G D, Wu L Q, Xue L C, Wu G H 2015 Phys. Status Solidi B 252 2820Google Scholar

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    武力乾, 齐伟华, 李雨辰, 李世强, 李壮志, 唐贵德, 薛立超, 葛兴烁, 丁丽莉 2016 物理学报 65 027501Google Scholar

    Wu L Q, Qi W H, Li Y C, Li S Q, Li Z Z, Tang G D, Xue L C, Ge X S, Ding L L 2016 Acta Phys. Sin. 65 027501Google Scholar

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    齐伟华, 马丽, 李壮志, 唐贵德, 吴光恒 2017 物理学报 66 027101Google Scholar

    Qi W H, Ma L, Li Z Z, Tang G D, Wu G H 2017 Acta Phys. Sin. 66 027101Google Scholar

    [33]

    齐伟华, 李壮志, 马丽, 唐贵德, 吴光恒, 胡凤霞 2017 物理学报 66 067501Google Scholar

    Qi W H, Li Z Z, Ma L, Tang G D, Wu G H, Hu F X 2017 Acta Phys. Sin. 66 067501Google Scholar

    [34]

    Tang G D, Han Q J, Xu J, Ji D H, Qi W H, Li Z Z, Shang Z F, Zhang X Y 2014 Physica B 438 91Google Scholar

    [35]

    Shang Z F, Qi W H, Ji D H, Xu J, Tang G D, Zhang X Y, Li Z Z, Lang L L 2014 Chin. Phys. B 23 107503Google Scholar

    [36]

    Lang L L, Xu J, Qi W H, Li Z Z, Tang G D, Shang Z F, Zhang X Y, Wu L Q, Xue L C 2014 J. Appl. Phys. 116 123901Google Scholar

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    Lang L L, Xu J, Li Z Z, Qi W H, Tang G D, Shang Z F, Zhang X Y, Wu L Q, Xue L C 2015 Physica B 462 47Google Scholar

    [38]

    Xue L C, Lang L L, Xu J, Li Z Z, Qi W H, Tang G D, Wu L Q 2015 AIP Adv. 5 097167Google Scholar

    [39]

    Zhang X Y, Xu J, Li Z Z, Qi W H, Tang G D, Shang Z F, Ji D H, Lang L L 2014 Physica B 446 92Google Scholar

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    Tang G D, Shang Z F, Zhang X Y, Xu J, Li Z Z, Zhen C M, Qi W H, Lang L L 2015 Physica B 463 26Google Scholar

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    Xu J, Ji D H, Li Z Z, Qi W H, Tang G D, Zhang X Y, Shang Z F, Lang L L 2015 Phys. Status Solidi B 252 411Google Scholar

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    徐静, 齐伟华, 纪登辉, 李壮志, 唐贵德, 张晓云, 尚志丰, 郎莉莉 2015 物理学报 64 017501Google Scholar

    Xu J, Qi W H, Ji D H, Li Z Z, Tang G D, Zhang X Y, Shang Z F, Lang L L 2015 Acta Phys. Sin. 64 017501Google Scholar

    [43]

    Ding L L, Xue L C, Li Z Z, Li S Q, Tang G D, Qi W H, Wu L Q, Ge X S 2016 AIP Adv. 6 105012Google Scholar

    [44]

    Du Y N, Xu J, Li Z.Z, Tang G D, Qian J J, Chen M Y, Qi W H 2018 RSC Adv. 8 302Google Scholar

    [45]

    Chen M Y, Xu J, Li Z Z, Zhang Y, Qi W H, Tang G D 2019 Results Phys. 14 102389Google Scholar

    [46]

    Wu L Q, Qi W H, Ge X S, Ji D H, Li Z Z, Tang G D, Zhong W 2017 Europhys. Lett. 120 27001Google Scholar

    [47]

    Ge X S, Wu L Q, Li S Q, Li Z Z, Tang G D, Qi W H, Zhou H J, Xue L C, Ding L L 2017 AIP Adv. 7 045302Google Scholar

    [48]

    Ge X S, Li Z Z, Qi W H, Ji D H, Tang G D, Ding L L, Qian J J, Du Y N 2017 AIP Adv. 7 125002Google Scholar

    [49]

    Li S Q, Wu L Q, Qi W H, Ge X S, Li Z Z, Tang G D, Zhong W 2018 J. Magn. Magn. Mater. 460 501Google Scholar

    [50]

    Qi W H, Li Z Z, Ma L, Tang G D, Wu G H 2018 AIP Adv. 8 065105Google Scholar

    [51]

    谢希德, 陆栋 1998 固体能带理论(上海: 复旦大学出版社) 第11页

    Xie X D, Lu D 1998 Energy Band Theory of Solids (Shanghai: Fudan University Press) p11 (in Chinese)

    [52]

    廖立兵 2000 晶体化学及晶体物理学 (北京: 地质出版社) 第161页

    Liao L B 2000 Crystal Chemistry and Crystal Physics (Beijing: Geological Publishing House) p161 (in Chinese)

    [53]

    Wagner C D, Davis W M, Moulder J F, Muilenberg G E 1979 Handbook of X-ray Photoelectron Spectroscopy (Eden Prairie, Minnesota, USA: Perkin-Elmer coporation) pp182–182

    [54]

    Ley L, Dabbousi O B, Kowalczyk S P, McFeely F R, Shiley D A 1977 Phys. Rew. B 16 5372Google Scholar

    [55]

    Ding L L, Wu L Q, Ge X S, Du Y N, Qian J J, Tang G D, Zhong W 2018 Results Phys. 9 866Google Scholar

    [56]

    Salamon M B, Jaime M 2001 Rev. Moder. Phys. 73 583Google Scholar

    [57]

    Dagotto E, Hotta T, Moreo A 2001 Phys. Rep. 344 1Google Scholar

    [58]

    Tokura Y, Tomioka Y 1999 J. Magn. Magn. Mater. 200 1Google Scholar

    [59]

    方俊鑫, 陆栋 1980 固体物理学(上册) (上海: 上海科学技术出版社) 第314页

    Fang J X, Lu D 1980 Solid State Physics (Shanghai: Shanghai Scientific & Technical Publishers) p314 (in Chinese)

  • 图 1  由Ju等[11]报道的La1–xSrxMnO3系列样品 (a)电阻率ρ随测试温度T的变化关系; (b)电子能量损失谱

    Figure 1.  La1–xSrxMnO3 reported by Ju et al.[11]: (a) Curves of the resistivity ρ versus the test temperature T; (b) electron energy loss spectra.

    图 2  Dupin等[17]提出的O 1s谱峰所对应的氧离子价态示意图

    Figure 2.  A binding energy scale for valence state of oxygen at the O 1s peaks, proposed by Dupin et al. [17]

    图 3  近邻离子外层电子轨道的(a)外斯电子对和(b), (c)巡游电子示意图[33]

    Figure 3.  Illustrations of (a) a Weiss electron pair and (b) and (c) itinerant electrons in the outer orbits of adjacent ions[33].

    图 4  晶体中离子对1s电子的束缚能Eb和自由原子中1s电子的电离能VN随原子序数N的变化[52,53]

    Figure 4.  Dependences on the atom number (N) of the binding energy (Eb) of 1 s electron in a crystal and the ionization energy (VN) of 1 s electron in an free atom[52,53]

    图 5  CaO, ZnO, MnFe2O4, ZnFe2O4的价带光电子谱[55]

    Figure 5.  Valence band photoelectron spectra of samples CaO, ZnO, MnFe2O4 and ZnFe2O4[55]

  • [1]

    戴道生, 钱昆明 1987 铁磁学 (上册) (北京: 科学出版社) 第103−122, 198, 323页

    Dai D S, Qian K M 1987 Ferromagnetism (Vol. 1) (Beijing: Science Press) pp103−122, 198, 323 (in Chinese)

    [2]

    van Vleck J H 1937 Phys. Rev. 52 1178Google Scholar

    [3]

    Sato H, Arrott A 1959 Phys. Rev. 114 1427Google Scholar

    [4]

    Anderson P W 1950 Phys. Rev. 79 350Google Scholar

    [5]

    Zener C 1951 Phys. Rev. 82 403Google Scholar

    [6]

    Tang G D, Li Z Z, Ma L, Qi W H, Wu L Q, Ge X S, Wu G H, Hu F X 2018 Phys. Rep. 758 1Google Scholar

    [7]

    Li Z Z, Qi W H, Ma L, Tang G D, Wu G H, Hu F X 2019 J. Magn. Magn. Mater. 482 173Google Scholar

    [8]

    Qian J J, Qi W H, Li Z Z, Ma L, Tang G D, Du Y N, Chen M Y, Wu G H, Hu F X 2018 RSC Adv. 8 4417Google Scholar

    [9]

    Qian J J, Li Z Z, Qi W H, Ma L, Tang G D, Du Y N, Chen M Y 2018 J. Alloys Compd. 764 239Google Scholar

    [10]

    Nücker N, Fink J, Fuggle J C, Durham P J 1988 Phys. Rev. B 37 5158Google Scholar

    [11]

    Ju H L, Sohn H C, Krishnan K M 1997 Phys. Rev. Lett. 79 3230Google Scholar

    [12]

    Urushibara A, Moritomo Y, Arima T, Asamitsu A, Kido G, Tokura Y 1995 Phys. Rev. B 51 14103Google Scholar

    [13]

    Mizoroki T, Itou M, Taguchi Y, Iwazumi T, Sakurai Y 2011 Appl. Phys. Lett. 98 052107Google Scholar

    [14]

    Grenier S, Thomas K J, Hill J P, Staub U, Bodenthin Y, García-Fernández M, Scagnoli V, Kiryukhin V, Cheong S W, Kim B G, Tonnerre J M 2007 Phys. Rev. Lett. 99 206403Google Scholar

    [15]

    Ibrahim K, Qian H J, Wu X, Abbas M I, Wang J O, Hong C H, Su R, Zhong J, Dong Y H, Wu Z Y, Wei L, Xian D C, Li Y X, Lapeyre G J, Mannella N, Fadley C S, Baba Y 2004 Phys. Rev. B 70 224433Google Scholar

    [16]

    Papavassiliou G, Pissas M, Belesi M, Fardis M, Karayanni M, Ansermet J P, Carlier D, Dimitropoulos C, Dolinsek J 2004 Europhys. Lett. 68 453Google Scholar

    [17]

    Dupin J C, Gonbeau D, Vinatier P, Levasseur A 2000 Phys. Chem. Chem. Phys. 2 1319Google Scholar

    [18]

    Cohen R E 1992 Nature 358 136Google Scholar

    [19]

    Cohen R E, Krakauer H 1990 Phys. Rev. B 42 6416Google Scholar

    [20]

    Wu L Q, Li Y C, Li S Q, Li Z Z, Tang G D, Qi W H, Xue L C, Ge X S, Ding L L 2015 AIP Adv. 5 097210Google Scholar

    [21]

    Wu L Q, Li S Q, Li Y C, Li Z Z, Tang G D, Qi W H, Xue L C, Ding L L, Ge X S 2016 Appl. Phys. Lett. 108 021905Google Scholar

    [22]

    Chen C T, Idzerda Y U, Lin H J, Smith N V, Meigs G, Chaban E, Ho G H, Pellegrin E, Sette F 1995 Phys. Rev. Lett. 75 152Google Scholar

    [23]

    Wu R, Wang D, Freeman A J 1993 Phys. Rev. Lett. 71 3581Google Scholar

    [24]

    Wu R, Freeman A J 1994 Phys. Rev. Lett. 73 1994Google Scholar

    [25]

    Jauch W, Reehuis M 2007 Phys. Rev. B 76 235121Google Scholar

    [26]

    Pacchioni G E, Gragnaniello L, Donati F, Pivetta M, Autès G, Yazyev O V, Rusponi S, Brune H 2015 Phys. Rev. B 91 235426Google Scholar

    [27]

    韩汝珊 1998 高温超导物理 (北京: 北京大学出版社) 第19−20 页

    Han R S 1998 Physics of High Temperature Super-conductor (Beijing: Peking University Press) pp19−20 (in Chinese)

    [28]

    Alexandrov A S, Bratkovsky A M, Kabanov V V 2006 Phys. Rev. Lett. 96 117003Google Scholar

    [29]

    Alexandrov A S, Bratkovsky A M 1999 Phys. Rev. Lett. 82 141Google Scholar

    [30]

    Xu J, Ma L, Li Z Z, Lang L L, Qi W H, Tang G D, Wu L Q, Xue L C, Wu G H 2015 Phys. Status Solidi B 252 2820Google Scholar

    [31]

    武力乾, 齐伟华, 李雨辰, 李世强, 李壮志, 唐贵德, 薛立超, 葛兴烁, 丁丽莉 2016 物理学报 65 027501Google Scholar

    Wu L Q, Qi W H, Li Y C, Li S Q, Li Z Z, Tang G D, Xue L C, Ge X S, Ding L L 2016 Acta Phys. Sin. 65 027501Google Scholar

    [32]

    齐伟华, 马丽, 李壮志, 唐贵德, 吴光恒 2017 物理学报 66 027101Google Scholar

    Qi W H, Ma L, Li Z Z, Tang G D, Wu G H 2017 Acta Phys. Sin. 66 027101Google Scholar

    [33]

    齐伟华, 李壮志, 马丽, 唐贵德, 吴光恒, 胡凤霞 2017 物理学报 66 067501Google Scholar

    Qi W H, Li Z Z, Ma L, Tang G D, Wu G H, Hu F X 2017 Acta Phys. Sin. 66 067501Google Scholar

    [34]

    Tang G D, Han Q J, Xu J, Ji D H, Qi W H, Li Z Z, Shang Z F, Zhang X Y 2014 Physica B 438 91Google Scholar

    [35]

    Shang Z F, Qi W H, Ji D H, Xu J, Tang G D, Zhang X Y, Li Z Z, Lang L L 2014 Chin. Phys. B 23 107503Google Scholar

    [36]

    Lang L L, Xu J, Qi W H, Li Z Z, Tang G D, Shang Z F, Zhang X Y, Wu L Q, Xue L C 2014 J. Appl. Phys. 116 123901Google Scholar

    [37]

    Lang L L, Xu J, Li Z Z, Qi W H, Tang G D, Shang Z F, Zhang X Y, Wu L Q, Xue L C 2015 Physica B 462 47Google Scholar

    [38]

    Xue L C, Lang L L, Xu J, Li Z Z, Qi W H, Tang G D, Wu L Q 2015 AIP Adv. 5 097167Google Scholar

    [39]

    Zhang X Y, Xu J, Li Z Z, Qi W H, Tang G D, Shang Z F, Ji D H, Lang L L 2014 Physica B 446 92Google Scholar

    [40]

    Tang G D, Shang Z F, Zhang X Y, Xu J, Li Z Z, Zhen C M, Qi W H, Lang L L 2015 Physica B 463 26Google Scholar

    [41]

    Xu J, Ji D H, Li Z Z, Qi W H, Tang G D, Zhang X Y, Shang Z F, Lang L L 2015 Phys. Status Solidi B 252 411Google Scholar

    [42]

    徐静, 齐伟华, 纪登辉, 李壮志, 唐贵德, 张晓云, 尚志丰, 郎莉莉 2015 物理学报 64 017501Google Scholar

    Xu J, Qi W H, Ji D H, Li Z Z, Tang G D, Zhang X Y, Shang Z F, Lang L L 2015 Acta Phys. Sin. 64 017501Google Scholar

    [43]

    Ding L L, Xue L C, Li Z Z, Li S Q, Tang G D, Qi W H, Wu L Q, Ge X S 2016 AIP Adv. 6 105012Google Scholar

    [44]

    Du Y N, Xu J, Li Z.Z, Tang G D, Qian J J, Chen M Y, Qi W H 2018 RSC Adv. 8 302Google Scholar

    [45]

    Chen M Y, Xu J, Li Z Z, Zhang Y, Qi W H, Tang G D 2019 Results Phys. 14 102389Google Scholar

    [46]

    Wu L Q, Qi W H, Ge X S, Ji D H, Li Z Z, Tang G D, Zhong W 2017 Europhys. Lett. 120 27001Google Scholar

    [47]

    Ge X S, Wu L Q, Li S Q, Li Z Z, Tang G D, Qi W H, Zhou H J, Xue L C, Ding L L 2017 AIP Adv. 7 045302Google Scholar

    [48]

    Ge X S, Li Z Z, Qi W H, Ji D H, Tang G D, Ding L L, Qian J J, Du Y N 2017 AIP Adv. 7 125002Google Scholar

    [49]

    Li S Q, Wu L Q, Qi W H, Ge X S, Li Z Z, Tang G D, Zhong W 2018 J. Magn. Magn. Mater. 460 501Google Scholar

    [50]

    Qi W H, Li Z Z, Ma L, Tang G D, Wu G H 2018 AIP Adv. 8 065105Google Scholar

    [51]

    谢希德, 陆栋 1998 固体能带理论(上海: 复旦大学出版社) 第11页

    Xie X D, Lu D 1998 Energy Band Theory of Solids (Shanghai: Fudan University Press) p11 (in Chinese)

    [52]

    廖立兵 2000 晶体化学及晶体物理学 (北京: 地质出版社) 第161页

    Liao L B 2000 Crystal Chemistry and Crystal Physics (Beijing: Geological Publishing House) p161 (in Chinese)

    [53]

    Wagner C D, Davis W M, Moulder J F, Muilenberg G E 1979 Handbook of X-ray Photoelectron Spectroscopy (Eden Prairie, Minnesota, USA: Perkin-Elmer coporation) pp182–182

    [54]

    Ley L, Dabbousi O B, Kowalczyk S P, McFeely F R, Shiley D A 1977 Phys. Rew. B 16 5372Google Scholar

    [55]

    Ding L L, Wu L Q, Ge X S, Du Y N, Qian J J, Tang G D, Zhong W 2018 Results Phys. 9 866Google Scholar

    [56]

    Salamon M B, Jaime M 2001 Rev. Moder. Phys. 73 583Google Scholar

    [57]

    Dagotto E, Hotta T, Moreo A 2001 Phys. Rep. 344 1Google Scholar

    [58]

    Tokura Y, Tomioka Y 1999 J. Magn. Magn. Mater. 200 1Google Scholar

    [59]

    方俊鑫, 陆栋 1980 固体物理学(上册) (上海: 上海科学技术出版社) 第314页

    Fang J X, Lu D 1980 Solid State Physics (Shanghai: Shanghai Scientific & Technical Publishers) p314 (in Chinese)

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Metrics
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Publishing process
  • Received Date:  29 October 2019
  • Accepted Date:  25 November 2019
  • Published Online:  20 January 2020

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