Use of Green Functions in the Theory of Ferromagnetism. I. General Discussion of the Spin-S Case
Use of Green Functions in the Theory of Ferromagnetism. I. General Discussion of the Spin-S Case
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DOI：
10.1103/physrev.127.88
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发表时间：
1962-07
期刊：
影响因子：
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通讯作者：
R. Tahir-Kheli;D. Haar
中科院分区：
文献类型：
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作者：
R. Tahir-Kheli;D. Haar
Tyablikov发展的自旋1/2粒子的铁磁性理论被推广到更高的自旋值。各种格林函数的方程链是通过解耦使之有限的，这种解耦完全类似于Tyablikov所用的解耦，当S=1 2时，我们的结果简化为他的结果。然而，这种解耦过程似乎对较大的S值更好。给出了S=1 2，1，3 2，2，5 2和3的磁化强度的显式表达式，并利用这些表达式得到了远低于居里温度、略低于居里温度和远高于居里温度时的级数展开式。将所得结果与Dyson的自旋波区结果、居里点附近球面模型的Lax结果以及高温下的分子场理论的结果进行了比较。有趣的是，我们得到了与球面模型相同的居里温度。这里得到的结果似乎是合理的。在附录中，我们考察了Izyumov和Yakovlev以及Kawasaki和Mori的批判性相似的工作。
The theory of ferromagnetism developed by Tyablikov for the case of spin-½ particles is extended to higher spin values. The chain of equations for the various Green functions is made finite by a decoupling which is completely analogous to the one used by Tyablikov and our results reduce to his for the case S= 1 2. This decoupling procedure seems, however, to be better for larger S values. Explicit expressions are given for the magnetization for S= 1 2, 1, 3 2, 2, 5 2, and 3 and those expressions are used to obtain series expansions at temperatures well below the Curie temperature, just below the Curie temperature, and well above the Curie temperature. The results obtained are compared with those of Dyson for the spin-wave region, with those of Lax obtained via the spherical model near the Curie point, and with those of the molecular-field theory at high temperatures. It is interesting to note that we obtain the same Curie temperatures as those following from the spherical model. The results obtained here seem to be reasonable. In the appendix we examine critically similar work by Izyumov and Yakovlev and by Kawasaki and Mori.