双二次交换作用和各向异性对反铁磁体相变温度的影响

文林; 胡爱元

doi:10.7498/aps.69.20200077

摘要

本文基于双时格林函数方法, 通过对不同格点和同格点的高阶格林函数分别采用Tyablikov和Callen退耦近似, 系统研究了双二次型交换作用和各向异性对简单立方晶格反铁磁模型相变的影响. 得到了相变温度的解析表达式, 发现相变温度随着各向异性的增强而升高, 但随着双二次型相互作用的增强而下降.

关键词:

The existence of biquadratic exchange had been well established by Anderson, Huang and Allen. Early investigations indicated that the biquadratic exchange term in spin Hamiltonian was found to have significant effects on the magnetic properties of compounds containing iron-group ions or rare-earth metal ions. Recently, studying the anisotropic magnetic excitation of iron-based superconducting materials indicated that the experimental phenomenon cannot be explained well only by a simple collinear Heisenberg antiferromagnetic model. However, if the nearest neighbor biquadratic spin coupling is introduced, the experiment can be well explained. Similar results had also been obtained in the investigation of the superconducting material FeSe. As a result, exploring the effect of biquadratic exchange interactions on the magnetic properties of magnetic systems is significance. In this paper, we use the double-time Green's function method to study the properties of the spin-1 Heisenberg antiferromagnets with biquadratic exchange interactions and anisotropy on a three-dimensional lattice. We derive the equation of motion of the Green's function by a standard procedure. In the course of this, the higher order Green functions have to be decoupled. For the higher order Green functions of different lattice points, a Tyablikov or random phase approximation decoupling are used to decuple. For the higher order Green functions of the same lattice points, we adopt the Anderson-Callen decoupling to decouple. Based on the above procedures, the analytic expressions of the magnetization and critical temperature are obtained. The effects of biquadratic exchange interactions and anisotropy on the critical temperature are discussed in detailed. Our results show that the critical temperature increases with the increase of the anisotropy for a given biquadratic interaction. Regardless of the value of the anisotropy, the critical temperature always decreases with the increase of the biquadratic interaction. As the value of anisotropic parameter $\eta = 0$, there is an obvious linear relationship between the critical temperature and the biquadratic interaction. However, when the anisotropy of the system becomes weaker, there is no such linear relationship between them. By comparing similar ferromagnetic models, it is found that the results of this paper are significantly different from those of the ferromagnetic model. When the biquadratic interaction is equal to 0, our results agree with other theoretical results.

Keywords:

antiferromagnetic /
magnetic anisotropy /
general theory and models of magnetic ordering /
exchange and superexchange interactions

作者及机构信息

文林,
胡爱元

重庆师范大学物理与电子工程学院, 重庆　401331

通信作者: 胡爱元, huaiyuanhuyuanai@126.com

基金项目: 国家自然科学基金(批准号: 11875010)和重庆市自然科学基金(批准号: cstc2019jcyj-msxmX0217, cstc2019jcyj-msxmX0251)资助的课题

Authors and contacts

Wen Lin,
Hu Ai-Yuan

College of Physics and Electronic Engineering, Chongqing Normal University, Chongqing 401331, China

Corresponding author: Hu Ai-Yuan, huaiyuanhuyuanai@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11875010), and the Chongqing Natural Science Foundation (Grant Nos. cstc2019jcyj-msxmX0217, cstc2019jcyj-msxmX0251)

文章全文 : translate this paragraph

参考文献

[1]	Anderson P W 1959 Phys. Rev. 115 2 Google Scholar
[2]	Huang N L, Orbach R 1964 Phys. Rev. Lett. 12 275
[3]	Allan G A T, Betts D D 1967 Proc. Phys. Soc. London 91 341 Google Scholar
[4]	Joseph R I 1965 Phys. Rev. 138 1441 Google Scholar
[5]	Millet P, Mila F, Zhang F C, Mambrini M, Van Oosten A B, Pashchenko V A, Sulpice A, Stepanov A 1999 Phys. Rev. Lett. 83 4176 Google Scholar
[6]	Mila F, Zhang F C 2000 Eur. Phys. J. B 16 7 Google Scholar
[7]	Luo C, Datta T, Yao D X 2016 Phys. Rev. B 93 235148 Google Scholar
[8]	Wysocki A L, Belashchenko K D, Antropov V P 2011 Nat. Phys. 7 485 Google Scholar
[9]	Ergueta P B, Nevidomskyy A H 2015 Phys. Rev. B 92 165102 Google Scholar
[10]	Zhuo W Z, Qin M H, Dong S, Li X G, Liu J M 2016 Phys. Rev. B 93 094424 Google Scholar
[11]	Yu R, Si Q M 2015 Phys. Rev. Lett. 115 116401 Google Scholar
[12]	Köbler U, Mueller R M, Schnelle W, Fischer K 1998 J. Magn. Magn. Mater. 188 333 Google Scholar
[13]	Köbler U, Hoser A, Kawakami M, Chatterji T, Rebizant J 1999 J. Magn. Magn. Mater. 205 343 Google Scholar
[14]	Yu R, Nevidomskyy A H 2016 J. Phys. Condens. Matter 28 495702 Google Scholar
[15]	Chen H H, Levy P M 1973 Phys. Rev. B 7 4267 Google Scholar
[16]	Iwashita T, Uryu N 1976 Phys. Rev. B 14 3090 Google Scholar
[17]	Oitmaa J, Hamer C J 2013 Phys. Rev. B 87 224431 Google Scholar
[18]	Rabuffo I, De Cesare L, D’Auria A C, Mercaldo M T 2019 Eur. Phys. J. B 92 154 Google Scholar
[19]	Chaddha G S, Sharma A 1999 J. Magn. Magn. Mater. 191 373 Google Scholar
[20]	Stanek D, Sushkov O P, Uhrig G S 2011 Phys. Rev. B 84 064505 Google Scholar
[21]	Wang H Y 2012 Green’s Function in Condensed Matter Physics (Beijing: Alpha Science International Ltd and Science Press) p348
[22]	王怀玉, 夏青 2007 物理学报 56 5466 Google Scholar Wang H Y, Xia Q 2007 Acta Phys. Sin. 56 5466 Google Scholar
[23]	Callen H B 1963 Phys. Rev. 130 890 Google Scholar
[24]	Pan K K 2009 Phys. Rev. B 79 134414 Google Scholar
[25]	Gaunt D S, Guttman A J. 1974 Phase Transitions and Critical Phenomena (New York: Academic Press) p456
[26]	Pan K K 2005 Phys. Rev B 71 134524 Google Scholar

施引文献

图 1 当单粒子各向异性参数D取0和1时, 交换各向异性参数$\eta $为0, 0.5, 0.9, 1下相变温度${T_N}$与双二次型交换作用${J_2}$之间的关系曲线

Fig. 1. Nèel temperature as a function of biquadratic exchange for the exchange anisotropic parameter $\eta {\rm{ = 0, 0}}{\rm{.5, 0}}{\rm{.9, 1}}$ when the single-ion anisotropic parameter $D = {\rm{0}}$ and 1.

下载: 全尺寸图片幻灯片

图 2 当$D = 0, {\rm{ }}1$时, 系统在参数$\eta $和${J_2}$空间中的相图

Fig. 2. Phase diagram of the $D = 0, {\rm{ }}1$ in the $\eta $ and ${J_2}$ parameter space.

下载: 全尺寸图片幻灯片

[1]	Anderson P W 1959 Phys. Rev. 115 2 Google Scholar
[2]	Huang N L, Orbach R 1964 Phys. Rev. Lett. 12 275
[3]	Allan G A T, Betts D D 1967 Proc. Phys. Soc. London 91 341 Google Scholar
[4]	Joseph R I 1965 Phys. Rev. 138 1441 Google Scholar
[5]	Millet P, Mila F, Zhang F C, Mambrini M, Van Oosten A B, Pashchenko V A, Sulpice A, Stepanov A 1999 Phys. Rev. Lett. 83 4176 Google Scholar
[6]	Mila F, Zhang F C 2000 Eur. Phys. J. B 16 7 Google Scholar
[7]	Luo C, Datta T, Yao D X 2016 Phys. Rev. B 93 235148 Google Scholar
[8]	Wysocki A L, Belashchenko K D, Antropov V P 2011 Nat. Phys. 7 485 Google Scholar
[9]	Ergueta P B, Nevidomskyy A H 2015 Phys. Rev. B 92 165102 Google Scholar
[10]	Zhuo W Z, Qin M H, Dong S, Li X G, Liu J M 2016 Phys. Rev. B 93 094424 Google Scholar
[11]	Yu R, Si Q M 2015 Phys. Rev. Lett. 115 116401 Google Scholar
[12]	Köbler U, Mueller R M, Schnelle W, Fischer K 1998 J. Magn. Magn. Mater. 188 333 Google Scholar
[13]	Köbler U, Hoser A, Kawakami M, Chatterji T, Rebizant J 1999 J. Magn. Magn. Mater. 205 343 Google Scholar
[14]	Yu R, Nevidomskyy A H 2016 J. Phys. Condens. Matter 28 495702 Google Scholar
[15]	Chen H H, Levy P M 1973 Phys. Rev. B 7 4267 Google Scholar
[16]	Iwashita T, Uryu N 1976 Phys. Rev. B 14 3090 Google Scholar
[17]	Oitmaa J, Hamer C J 2013 Phys. Rev. B 87 224431 Google Scholar
[18]	Rabuffo I, De Cesare L, D’Auria A C, Mercaldo M T 2019 Eur. Phys. J. B 92 154 Google Scholar
[19]	Chaddha G S, Sharma A 1999 J. Magn. Magn. Mater. 191 373 Google Scholar
[20]	Stanek D, Sushkov O P, Uhrig G S 2011 Phys. Rev. B 84 064505 Google Scholar
[21]	Wang H Y 2012 Green’s Function in Condensed Matter Physics (Beijing: Alpha Science International Ltd and Science Press) p348
[22]	王怀玉, 夏青 2007 物理学报 56 5466 Google Scholar Wang H Y, Xia Q 2007 Acta Phys. Sin. 56 5466 Google Scholar
[23]	Callen H B 1963 Phys. Rev. 130 890 Google Scholar
[24]	Pan K K 2009 Phys. Rev. B 79 134414 Google Scholar
[25]	Gaunt D S, Guttman A J. 1974 Phase Transitions and Critical Phenomena (New York: Academic Press) p456
[26]	Pan K K 2005 Phys. Rev B 71 134524 Google Scholar

计量

文章访问数: 5966
PDF下载量: 85
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

双二次交换作用和各向异性对反铁磁体相变温度的影响