Electronic structure of the Ti 4 O 7 Magnéli phase
Electronic structure of the Ti 4 O 7 Magnéli phase
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Ti 4 O 7 Magnéli 相的电子结构
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
N. Harrison
中科院分区：
文献类型：
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作者：
L. Liborio;G. Mallia;N. Harrison
我们对${\Text{Ti}}_{4}{\Text{O}}_{7}$Magn\‘Eli相进行了密度泛函计算。我们的结果提供了对高温$(TensureMath298\Text{}\Text{K})$相、中温$(120\Text{}\text{K}\ensuremath{\le}T\ensuremath{\le}140\text{}\Text{K})$相和低温$(TensureMath298\Text{}\Text{K})$相的一致描述。所建立的低温相和中温相的电子结构模型表明，低温相中温相中存在有序双极化子，但在中温相中存在无序双极化子。在这项工作中，我们对${\Text{Ti}_{4}{\Text{O}}_{7}$中低温电子结构提出了不同的看法。我们认为，在低温阶段，强的现场库仑排斥和电子-声子耦合的共同作用导致未成对电子在形成电子对的离子中局域化。电子被安置在特定的类{文本{t}}_{2g}$轨道中有两个原因：最小化直接库仑斥力和最小化晶格扭曲引起的间接相互作用。局域电子是反铁磁耦合的，产生零自旋的双极化子。这种轨道有序性导致完全占据能级和未占据能级之间的差距变大。这是一个双极化态，但在形成对的${\Text{Ti}}^{3+}$之间没有键。在中间阶段，双极化子的子集解离，但电子保持强烈的局域化：这种状态由放置在具有长程有序的超结构中的极化子和双极化子的混合物组成。该模型对观察到的${\Text{Ti}_{4}{\Text{O}}_{7}$的电学和磁学性质提供了一致的解释。
We have performed density-functional calculations on the ${\text{Ti}}_{4}{\text{O}}_{7}$ Magn\'eli phase. Our results provided a consistent description of the high-temperature $(T\ensuremath{\ge}298\text{ }\text{K})$ phase, the intermediate-temperature $(120\text{ }\text{K}\ensuremath{\le}T\ensuremath{\le}140\text{ }\text{K})$ phase, and the low-temperature $(T\ensuremath{\le}120\text{ }\text{K})$ phase. The established model for the electronic structure of the low- and intermediate-temperature phases of ${\text{Ti}}_{4}{\text{O}}_{7}$ states that ${\text{Ti}}^{3+}{\text{-Ti}}^{3+}$ pairs, bonded through nonmagnetic metal-metal bonds, form ordered bipolarons in the low-temperature phase, and that these bipolarons exist but are disordered in the intermediate-temperature phase. In this work we propose a different picture for the ${\text{Ti}}_{4}{\text{O}}_{7}$ low- and intermediate-temperature electronic structure. We argue that, in the low-temperature phase, a combination of a strong on-site Coulomb repulsion and electron-phonon coupling results in the localization of unpaired electrons in the ${\text{Ti}}^{3+}$ ions forming the pairs. The electrons are accommodated in specific ${\text{t}}_{2g}$-like orbitals for two reasons: to minimize the direct Coulomb repulsion, and to minimize the indirect interaction that results from lattice distortion. The localized electrons are antiferromagnetically coupled, producing bipolarons with zero spin. This orbital ordering results in the widening of the gap between the fully occupied and unoccupied levels. This is a bipolaronic state, but there is no bond in between the ${\text{Ti}}^{3+}$ forming the pairs. In the intermediate phase, a subset of the bipolarons dissociate but the electrons remain strongly localized: this state consists of a mixture of polarons and bipolarons placed in a superstructure with long-range order. This model provides a consistent explanation of the observed electric and magnetic properties of ${\text{Ti}}_{4}{\text{O}}_{7}$.