磁性材料磁有序的分子场来源

齐伟华; 李壮志; 马丽; 唐贵德; 吴光恒; 胡凤霞

doi:10.7498/aps.66.067501

摘要

对于磁性材料磁有序能的来源，即外斯分子场来源，本文提出一个模型：在磁性金属和合金中的相邻离子实之间，以及磁性氧化物的相邻阴阳离子间，其外层轨道上高速运动的电子分别有一定概率形成三种不同的状态.1）具有一定寿命的自旋相反的电子对，称为外斯电子对（WEP）；2）距离很近且自旋方向相同的电子，容易发生互相交换，交换前后电子的自旋方向保持不变；3）当一个离子外层轨道有2个电子，其相邻的离子外层轨道只有1个电子时，前者多出的电子可以跃迁到后者的轨道上，并且保持自旋方向不变.我们认为，WEP两个电子间的静磁吸引能是分子场（即磁有序能）的主要来源.进而，推导出WEP的能量表达式、两电子的平衡间距和最大间距，探讨了在几种钙钛矿结构锰氧化物中形成外斯电子对的概率，用以解释居里温度附近晶格常数随温度变化的特点.结果表明这个模型是合理的.

关键词:

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:

作者及机构信息

1.
河北师范大学物理科学与信息工程学院, 河北省新型薄膜材料实验室, 石家庄 050024;

2.
中国科学院物理研究所磁学国家重点实验室, 北京 100190

通信作者: 唐贵德, tanggd@hebtu.edu.cn

基金项目: 国家自然科学基金（批准号：11174069）、河北省自然科学基金（批准号：A2015205111）、河北省应用基础研究计划重点基础研究项目（批准号：16961106D）和河北省教育厅青年基金（批准号：QN2016015）资助的课题.

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).

参考文献

[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]

施引文献

[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]

[1]	张梦, 姚若河, 刘玉荣. 纳米尺度金属-氧化物半导体场效应晶体管沟道热噪声模型. , 2020, 69(5): 057101. doi: 10.7498/aps.69.20191512
[2]	张梦, 姚若河, 刘玉荣, 耿魁伟. 短沟道金属-氧化物半导体场效应晶体管的散粒噪声模型. , 2020, 69(17): 177102. doi: 10.7498/aps.69.20200497
[3]	任县利, 张伟伟, 伍晓勇, 吴璐, 王月霞. 高熵合金短程有序现象的预测及其对结构的电子、磁性、力学性质的影响. , 2020, 69(4): 046102. doi: 10.7498/aps.69.20191671
[4]	唐贵德, 李壮志, 马丽, 吴光恒, 胡凤霞. 典型磁性材料价电子结构研究面临的机遇与挑战. , 2020, 69(2): 027501. doi: 10.7498/aps.69.20191655
[5]	李丹, 李国庆. 氧化物隔离对Si基片上生长L10相FePt薄膜磁性的影响. , 2018, 67(15): 157501. doi: 10.7498/aps.67.20180387
[6]	杨明宇, 杨倩, 张勃, 张旭, 蔡颂, 薛玉龙, 周铁戈. 5d过渡金属原子掺杂六方氮化铝单层的磁性及自旋轨道耦合效应:可能存在的二维长程磁有序. , 2017, 66(6): 063102. doi: 10.7498/aps.66.063102
[7]	宋建军, 包文涛, 张静, 唐昭焕, 谭开洲, 崔伟, 胡辉勇, 张鹤鸣. (100)Si基应变p型金属氧化物半导体[110]晶向电导率有效质量双椭球模型. , 2016, 65(1): 018501. doi: 10.7498/aps.65.018501
[8]	成泰民, 张龙燕, 孙腾, 张新欣, 朱林, 李林. 高压下有序晶态合金Fe3Pt的低能声子不稳定性及磁性反常. , 2015, 64(14): 146301. doi: 10.7498/aps.64.146301
[9]	周春宇, 张鹤鸣, 胡辉勇, 庄奕琪, 吕懿, 王斌, 王冠宇. 应变Si n型金属氧化物半导体场效应晶体管电荷模型. , 2014, 63(1): 017101. doi: 10.7498/aps.63.017101
[10]	胡妮, 刘雍, 汤五丰, 裴玲, 方鹏飞, 熊锐, 石兢. La0.4Ca0.6MnO3中Mn-位Fe和Cr掺杂对磁性质的影响. , 2014, 63(23): 237502. doi: 10.7498/aps.63.237502
[11]	郑小青, 杨洋, 孙得彦. 模型二元有序合金固液界面结构的分子动力学研究. , 2013, 62(1): 017101. doi: 10.7498/aps.62.017101
[12]	曹磊, 刘红侠, 王冠宇. 异质栅全耗尽应变硅金属氧化物半导体模型化研究. , 2012, 61(1): 017105. doi: 10.7498/aps.61.017105
[13]	孙鹏, 杜磊, 陈文豪, 何亮, 张晓芳. 金属-氧化物-半导体场效应管辐射效应模型研究. , 2012, 61(10): 107803. doi: 10.7498/aps.61.107803
[14]	何宝平, 姚志斌. 互补金属氧化物半导体器件空间低剂量率辐射效应预估模型研究. , 2010, 59(3): 1985-1990. doi: 10.7498/aps.59.1985
[15]	刘秀喜, 王公堂. 有机硅化合物-金属氧化物绝缘保护材料在制造高压晶闸管中的应用研究. , 2008, 57(1): 576-580. doi: 10.7498/aps.57.576
[16]	羊新胜, 赵勇. 铁磁性锰氧化物掺杂的ZnO压敏电阻性能研究. , 2008, 57(5): 3188-3192. doi: 10.7498/aps.57.3188
[17]	杨海涛, 申承民, 杜世萱, 苏轶坤, 王岩国, 汪裕萍, 高鸿钧. 钴纳米粒子自组装有序阵列与磁性. , 2003, 52(12): 3114-3119. doi: 10.7498/aps.52.3114
[18]	覃东欢, 彭勇, 王成伟, 力虎林. Co-Ni合金纳米线有序阵列的制备与磁性研究. , 2001, 50(1): 144-148. doi: 10.7498/aps.50.144
[19]	肖定全, 韦力凡, 李子森, 朱建国, 钱正洪, 彭文斌. 金属氧化物薄膜的多离子束反应共溅射模型(Ⅱ)——数值计算与结果讨论. , 1996, 45(2): 345-352. doi: 10.7498/aps.45.345
[20]	肖定全, 韦力凡, 李子森, 朱建国, 钱正洪, 彭文斌. 金属氧化物薄膜的多离子束反应共溅射模型(Ⅰ)——模型建立. , 1996, 45(2): 330-338. doi: 10.7498/aps.45.330

计量

文章访问数: 7104
PDF下载量: 397
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板