Electronic structure of rare-earth nitrides using the LSDA plus U approach:: Importance of allowing 4f orbitals to break the cubic crystal symmetry
Electronic structure of rare-earth nitrides using the LSDA plus U approach:: Importance of allowing 4f orbitals to break the cubic crystal symmetry
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DOI：
10.1103/physrevb.75.045114
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发表时间：
2007-01-01
影响因子：
3.7
通讯作者：
van Schilfgaarde, Mark
中科院分区：
文献类型：
--
作者：
Larson, P.;Lambrecht, Walter R. L.;van Schilfgaarde, Mark
采用密度泛函LSDA+U方法(Hubbard-U修正的局域自旋密度近似)对岩盐结构中稀土氮化物的电子结构进行了计算。LSDA+U方法是在全势线性化的松饼-锡轨道方法中实现的，并应用于4f和5d态。参数U和J是由原子计算结合实验光电子能谱和反光电子能谱数据和光吸收数据确定的。F电子密度矩阵的解不是唯一的，因此需要研究几种构型来确定最低能态。除了被发现是四价的CEN外，三价溶液的能量在所有情况下都是最低的。洪德第二定律要求最大化轨道动量分量L-z，这打破了立方对称性，降低了总能量。我们发现，除了Eun和YBN外，所有情况下都遵守洪德第二定律，在这两种情况下，立方对称解的能量较低。在这些情况下，二价溶液也与三价溶液竞争。对称破缺在大多数情况下会降低总能量，在某些情况下，那些离封闭或半充满壳层有两个电子或空穴的能级，对于从费米能级中移除f态是必不可少的。自旋磁矩几乎是整数，由填充的4f态的数量定义。轨道磁矩的大小与自旋矩相当。根据洪德的第三定律，轨道和自旋矩在序列的前半部分是相反的，但在序列的后半部分是平行的，也被发现是符合的。有趣的是，这导致SmN的净磁矩为零，除了少数情况下f态保持在费米能级附近外，大多数情况下能带结构是半导体到半金属的交界处，在X处有一个RE5d导带最小，在Gamma处有一个N2p价带最大。GdN之前的早期成员(NdN除外)在大多数自旋通道中只是轻微的半金属，因此是半金属的，而Gd之后的后来的成员有一个很小的间接间隙。在EUN中，在E-F处钉扎的f能级和N_2p态之间发生了复杂的杂化，导致金属带结构。在这些铁磁体的居里温度以上，在顺磁状态下，人们预计大多数和少数自旋能隙的平均值，从而使能隙增加。
Electronic structure calculations were performed for the rare-earth (RE) nitrides in the rocksalt structure using density functional theory calculations within the LSDA+U approach (local spin density approximation with Hubbard-U corrections). The LSDA+U method is implemented in the full-potential linearized muffin-tin orbital method and applied to the 4f as well as 5d states. Parameters U and J were determined from atomic calculations complemented with experimental photoemission and inverse photoemission data and optical absorption data for Gd pnictides. The solution for the density matrix of f electrons is not unique and thus several configurations need to be investigated to determine the lowest energy state. A trivalent solution is found to have the lowest energy in all cases except CeN, which was found to be tetravalent. Hund's second rule requires maximizing the orbital momentum component L-z, which breaks the cubic symmetry and lowers the total energy. We find Hund's second rule to be obeyed in all cases except EuN and YbN, where a cubic symmetry solution has lower energy. In these cases, the divalent solution is also in competition with the trivalent solution. The symmetry breaking in most cases lowers the total energy and in some cases, those with two electrons or holes away from a closed or half-filled shell, is essential to remove f states from the Fermi level. The spin magnetic moments are nearly integer, defined by the number of filled 4f states. The orbital magnetic moment is of comparable magnitude to the spin moment. Hund's third rule, according to which the orbital and spin moment are opposite to each other in the first half of the series but parallel to each other in the second half, is also found to be obeyed. Interestingly, this leads to zero net magnetic moment for SmN.Apart from the few cases where f states remain close to the Fermi level, the band structure is borderline semiconductor to semimetallic in most cases, a RE 5d conduction band minimum at X, and a N 2p valence band maximum at Gamma. The early members of the series before GdN (with the exception of NdN) are slightly semimetallic in the majority spin channel only and are thus half-metals, while the later members after Gd have a small indirect gap. In EuN a complicated hybridization occurs between an f level pinned at E-F and the N 2p states, leading to a metallic band structure. Above the Curie temperature of these ferromagnets, in the paramagnetic state, one expects an average of majority and minority spin gaps and thus an increase in the gap.