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arXiv 1111.0267cond-mat.str-el
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双交换模型中$\rm La_{1-x}Ca_xMnO_3$的Phase diagrams

Phase diagrams of $\rm La_{1-x}Ca_xMnO_3$ in Double Exchange Model with added antiferromagnetic and Jahn-Teller interaction

Vasil Michev, Naoum Karchev

摘要:

多价锰氧化物$\rm La_{1-x}Ca_xMnO_3$在温度和掺杂$x$空间中的相图是对理论物理的挑战。这对研究这些化合物的模型和计算方法是一个重要的考验。为了从理论上得到$x<0.5$的这种图,我们考虑了锰氧化物的两带双交换模型,其中加入了Jahn-Teller耦合和反铁磁海森堡项。为了计算居里温度和内尔温度,我们推导出一个有效的海森堡模型的矢量描述的总磁化系统的局部取向。该模型的交换常数在不同的空间方向上是不同的,并依赖于$e_g$电子的密度,反铁磁常数和Jahn-Teller能量。为了再现低$x$时从A型反铁磁性到铁磁性以及大$x$时从C型反铁磁性到G型反铁磁性的相变,我们认为反铁磁性交换常数应该依赖于晶格方向.结果表明,铁磁到A型反铁磁的转变是由Jahn-Teller畸变引起的。充分考虑磁振子-磁振子相互作用,计算居里温度和内尔温度。计算结果与实验结果吻合得很好,并为模型参数提供了数值,这些参数最好地描述了$x<0.5$的临界温度行为。

英文摘要:

The phase diagram of the multivalent manganites $\rm La_{1-x}Ca_xMnO_3$, in space of temperature and doping $x$, is a challenge for the theoretical physics. It is an important test for the model used to study these compounds and the method of calculation. To obtain theoretically this diagram for $x<0.5$, we consider the two-band Double Exchange Model for manganites with added Jahn-Teller coupling and antiferromagnetic Heisenberg term. In order to calculate Curie and Néel temperatures we derive an effective Heisenberg model for a vector which describes the local orientation of the total magnetization of the system. The exchange constants of this model are different for different space directions and depend on the density of $e_g$ electrons, antiferromagnetic constants and the Jahn-Teller energy. To reproduce the well known phase transitions from A-type antiferromagnetism to ferromagnetism at low $x$ and C-type antiferromagnetism to G-type antiferromagnetism at large $x$, we argue that the antiferromagnetic exchange constants should depend on the lattice direction. We show that ferromagnetic to A-type antiferromagnetic transition results from the Jahn-Teller distortion. Accounting adequately for the magnon-magnon interaction, Curie and Néel temperatures are calculated. The results are in very good agreement with the experiment and provide values for the model parameters, which best describe the behavior of the critical temperature for $x<0.5$.

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