Molecular field origin for magnetic ordering of magnetic materials

Qi Wei-Hua; Li Zhuang-Zhi; Ma Li; Tang Gui-De; Wu Guang-Heng; Hu Feng-Xia

doi:10.7498/aps.66.067501

Abstract

In 1907, Weiss proposed that there is a molecular field to explain the magnetic ordering of magnetic materials. However, it has not been clarified where the molecular field comes from so far. In recent decades, the magnetic ordering of metals and alloys were explained by using the direct exchange interaction of between electrons on neighboring atoms, while magnetic ordering of oxides were explained by using the super exchange interaction and double exchange interaction models. The intrinsic relation between those exchange interactions has not been well explained. This resulted in the fact that there are many puzzles for magnetic ordering of the magnetic materials. For example, what role the Cr cations play in spinel ferrite CrFe2O4; why the calculated molecular magnetic moment (3.85B) for La0.85Sr0.15MnO3 by using double exchange interaction model is lower than its experimental value (4.20B); whether there is a relation between the average atom magnetic moment and their electrical resistivity for each of Fe, Co and Ni metals. These several puzzles have been explained recently by our group through using an O 2p itinerant electron model for magnetic oxides and a new itinerant electron model for magnetic metals. In this paper, a model for the molecular field origin is proposed. There are three states for the electrons rotating with high speed at the outer orbits of two adjacent ions of magnetic oxides or metals and alloys. 1) There is a probability with which form the electron pairs with opposite spin directions and a certain life time, named Weiss electron pairs (WEP); the static magnetic attraction energy between two electrons of WEP is the elementary origin of Weiss molecular field. 2) There is a probability with which two electrons with the same spin direction exchange mutually. 3) If there are two electrons at the outer orbit of an ion, then for its adjacent ion whose orbit has only one electron, the excess electron will itinerates between the ions. Furthermore, the energy equation of WEP, equilibrium distance, re0, and maximum distance, rem, between electrons of WEP are derived. The probability with which WEP forms in each of several perovskite manganites is investigated. For perovskite manganites La0.8Ca0.2MnO3, La0.75Ca0.25MnO3, La0.70Sr0.30MnO3, the crystal cell constants increase linearly with temperature when the temperature is much lower than the Curie temperature, TC, while they show a rapid increase nonlinearly near TC. We then calculate the difference in MnO bond length at TC between the linear and the nonlinear variation, △dobs. Obviously, when the distance between the two electrons of WEP, re, is larger than the rem, WEP and the magnetic ordering energy both disappear. Assuming △dobs=rem-re0, the probabilities with which WEP appears in La0.8Ca0.2MnO3, La0.75Ca.25MnO3, La0.70Sr0.30MnO3, are calculated to be 0.07%, 0.31% and 3.13%, respectively. These results indicate that the WEP model for the magnetic ordering energy is qualitatively reasonable.

Keywords:

Authors and contacts

1.
Hebei Advanced Thin Film Laboratory, College of Physics and Information Engineering, Hebei Normal University, Shijiazhuang 050024, China;
2.
State Key Laboratory of Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China

Corresponding author: Tang Gui-De, tanggd@hebtu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No.11174069), the Natural Science Foundation of Hebei Province, China (Grant No. A2015205111), the Key Item Science Foundation of Hebei Province, China (Grant No. 16961106D), and the Young scholar Science Foundation of the Education Department of Hebei Province, China (Grant No. QN2016015).

References

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[31]	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 105012
[32]	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 107503
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[34]	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 26
[35]	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 027501 (in Chinese) [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 65 027501]
[36]	Phillips J C 1970 Rev. Mod. Phys. 42 317
[37]	Ji D H, Tang G D, Li Z Z, Hou X, Han Q J, Qi W H, Bian R R, Liu S R 2013 J. Magn. Magn. Mater. 326 197
[38]	Cohen R E 1992 Nature 358 136
[39]	Cohen R E, Krakauer H 1990 Phys. Rev. B 42 6416
[40]	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 097210
[41]	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 021905
[42]	Dupin J C, Gonbeau D, Vinatier P, Levasseur A 2000 Phys. Chem. Chem. Phys. 2 1319
[43]	Chen C W 1977 Magnetism and Metallurgy of Soft Magnetic Materials (Amsterdam: North-Holland Publishing Company) p15
[44]	Qi W H, Ma L, Li Z Z, Tang G D, Wu G H 2016 Acta Phys. Sin. 66 027101 (in Chinese) [齐伟华, 马丽, 李壮志, 唐贵德, 吴光恒 2016 66 027101]
[45]	Shannon R D 1976 Acta Cryst. A 32 751
[46]	Gou Q Q 1978 Introduction to Solid State Physics (Beijing: People's Education Press) p21 (in Chinese) [苟清泉 1978 固体物理学简明教程 (北京: 人民教育出版社) 第21页]

Cited By

[1]	Han B S, Nie X F, Tang G D, Xi W 1985 Acta Phys. Sin. 34 1396 (in Chinese) [韩宝善, 聂向富, 唐贵德, 奚卫 1985 34 1396]
[2]	Tang G D, Ma C S, Yang L X, Ma L M 2003 Modern Physics Experiments (Shijiazhuang: Hebei Science and Technology Press) p148 (in Chinese) [唐贵德, 马长山, 杨连祥, 马丽梅 2003 近代物理实验 (石家庄: 河北科学技术出版社) 第148页]
[3]	Dai D S, Qian K M 1987 Ferromagnetism (Beijing: Science Press) p103 (in Chinese) [戴道生, 钱昆明 1987 铁磁学(上册) (北京: 科学出版社) 第103页]
[4]	Hibble S J, Cooper S P, Hannon A C, Fawcett I D, Greenblatt M 1999 J. Phys.: Condens. Matter 11 9221
[5]	Radaelli P G, Cox D E, Marezio M, Cheong S W, Shiffer P E, Ramirez A P 1995 Phys. Rev. Lett. 75 4488
[6]	Schiffer P, Ramirez A P, Bao W, Cheong S W 1995 Phys. Rev. Lett. 75 3336
[7]	Mahendiran R, Tiwary S K, Raychaudhuri A K, Ramakrishnan T V 1996 Phys. Rev. B 53 3348
[8]	Urushibara A, Moritomo Y, Arima T, Asamitsu A, Kido G, Tokura Y 1995 Phys. Rev. B 51 14103
[9]	Chikazumi S 1997 Physics of Ferromagnetism 2e (London: Oxford University Press) p150
[10]	Sthr J, Siegmann H C (translated by Ji Y) 2012 Magnetism: From Fundamentals to Nanoscale Dynamics (Beijing: Higher Education Press) p450 (in Chinese) [Sthr J, Siegmann H C 著 (姬扬译) 2012 磁学: 从基础知识到纳米尺度超快动力学 (北京: 高等教育出版社) 第450页]
[11]	Gabal M A, Ata-Allah S S 2004 J. Phys. Chem. Solids 65 995
[12]	Li Y H, Kouh T, Shim I B, Kim C S 2012 J. Appl. Phys. 111 07B544
[13]	Fayek M K, Sayed Ahmed F M, Ata-Allah S S, Elnimer M K, Mostafa M F 1992 J. Mater. Sci. 27 4813
[14]	Lee D H, Kim H S, Yo C H, Ahn K, Kim K H 1998 Mater. Chem. Phys. 57 169
[15]	Sakurai S, Sasaki S, Okube M, Ohara H, Toyoda T 2008 Physica B 403 3589
[16]	Harrison F W, Osmond W P, Teale R W 1957 Phys. Rev. 106 865
[17]	Roumaih K 2011 J. Mol. Struct. 1004 1
[18]	Pervaiz E, Gul I H 2012 J. Magn. Magn. Mater. 324 3695
[19]	Singhal S, Chandra K 2007 J. Solid State Chem. 180 296
[20]	Kadam R H, Birajdar A P, Alone S T, Shirsath S E 2013 J. Magn. Magn. Mater. 327 167
[21]	Srivastava M, Layek S, Singh J, Das A K, Verma H C, Ojha A K, Kim N H Lee J H 2014 J. Alloys Compd. 591 174
[22]	Wahba A M, Mohamed M B 2014 Ceram. Int. 40 6127
[23]	Iqbal M J, Ahmad Z, Meydan T, Melikhov Y 2012 J. Appl. Phys. 111 033906
[24]	More S S, Kadam R H, Kadam A B, Shite A R, Mane D R, Jadhav K M 2010 J. Alloys Compd. 502 477
[25]	Ghatage A K, Patil S A, Paranjpe S K 1996 Solid State Commun. 98 885
[26]	Ida S, Ono K, Kozaki H (translated by Zhang Z X) 1979 Data on Physics in Common Use (Beijing: Science Press) p133 (in Chinese) [饭田修一, 大野和郎, 神前熙合编 (张质贤译) 1979 物理学常用数表 (北京: 科学出版社) 第133页]
[27]	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 91
[28]	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 252 411
[29]	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 2820
[30]	Xue L C, Lang L L, Xu J, Li Z Z, Qi W H, Tang G D, Wu L Q 2015 AIP Adv. 5 097167
[31]	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 105012
[32]	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 107503
[33]	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 017501 (in Chinese) [徐静, 齐伟华, 纪登辉, 李壮志, 唐贵德, 张晓云, 尚志丰, 郎莉莉 2015 64 017501]
[34]	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 26
[35]	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 027501 (in Chinese) [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 65 027501]
[36]	Phillips J C 1970 Rev. Mod. Phys. 42 317
[37]	Ji D H, Tang G D, Li Z Z, Hou X, Han Q J, Qi W H, Bian R R, Liu S R 2013 J. Magn. Magn. Mater. 326 197
[38]	Cohen R E 1992 Nature 358 136
[39]	Cohen R E, Krakauer H 1990 Phys. Rev. B 42 6416
[40]	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 097210
[41]	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 021905
[42]	Dupin J C, Gonbeau D, Vinatier P, Levasseur A 2000 Phys. Chem. Chem. Phys. 2 1319
[43]	Chen C W 1977 Magnetism and Metallurgy of Soft Magnetic Materials (Amsterdam: North-Holland Publishing Company) p15
[44]	Qi W H, Ma L, Li Z Z, Tang G D, Wu G H 2016 Acta Phys. Sin. 66 027101 (in Chinese) [齐伟华, 马丽, 李壮志, 唐贵德, 吴光恒 2016 66 027101]
[45]	Shannon R D 1976 Acta Cryst. A 32 751
[46]	Gou Q Q 1978 Introduction to Solid State Physics (Beijing: People's Education Press) p21 (in Chinese) [苟清泉 1978 固体物理学简明教程 (北京: 人民教育出版社) 第21页]

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