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Impurity-induced frustration: Low-energy model of diluted oxides

机译：杂质引起的挫败：稀释氧化物的低能模型

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We provide a detailed derivation of the low-energy model for Zn-diluted La_2CuO_4 in the limit of low doping together with a study of the ground-state properties of that model. We consider Zn-doped La_2CuO_4 within a framework of the three-band Hubbard model, which closely describes high-T_c cuprates on the energy scale of the most relevant atomic orbitals. To obtain the low-energy effective model, we first determine hybridized electronic states of CuO_4 and ZnO_4 plaquettes within the CuO_2 planes. Qualitatively, we find that the hybridization of zinc and oxygen orbitals can result in an impurity state with the energy ε, which is lower than the effective Hubbard gap U. In the limit of the effective hopping integral t ＜＜ε, U, the low-energy, spin-only Hamiltonian includes terms of the order t~2/ U and t~4/ε~3. That is, besides the usual nearest-neighbor superexchange J terms of order t~2/U, the low-energy model contains impurity-mediated, further-neighbor frustrating interactions among the Cu spins surrounding Zn sites in an otherwise unfrustrated antiferromagnetic background. These terms, denoted as J_(Zn)~'and J_(Zn)~", are of order t~4/ε~3 and can be substantial when ε ～ U/2, the latter value corresponding to the realistic CuO_2 parameters. In order to verify this spin-only model, we subsequently apply the 7"-matrix approach to study the effect of impurities on the antiferromagnetic order parameter. Previous theoretical studies, which include only the dilution effect of impurities, show a large discrepancy with experimental data in the doping dependence of the staggered magnetization at low doping. We demonstrate that this discrepancy is eliminated by including impurity-induced frustrations into the effective spin model with realistic CuO_2 parameters. Recent experimental study shows a significantly stronger suppression of spin stiffness in the case of Zn-doped La_2CuO_4 compared to the Mg-doped case and thus gives strong support to our theory. We argue that the proposed impurity-induced frustrations should be important in other strongly correlated oxides and charge-transfer insulators.
机译：我们提供了在低掺杂范围内锌稀释的La_2CuO_4的低能模型的详细推导，以及对该模型基态性质的研究。我们在三波段Hubbard模型的框架内考虑了Zn掺杂的La_2CuO_4，该模型在最相关的原子轨道的能级上密切描述了高T_c铜酸盐。为了获得低能量有效模型，我们首先确定CuO_2平面内CuO_4和ZnO_4球团的混合电子态。定性地，我们发现锌和氧轨道的杂化可以产生具有能量ε的杂质态，其能量低于有效的Hubbard间隙U。在有效跳跃积分t ＜＜ε的极限范围内，U为低-能量，仅自旋的哈密顿量包括t〜2 / U和t〜4 /ε〜3的项。也就是说，除了通常的最邻近的超级交换J项t〜2 / U阶外，低能模型还包含杂质介导的，围绕Zn位置的Cu自旋，在其他情况下未受阻的反铁磁背景之间的进一步受阻的相互作用。这些项分别表示为t_4 /ε〜3，表示为J_（Zn）〜'和J_（Zn）〜“，当ε〜U / 2时可以是实质性的，后者对应于实际的CuO_2参数。为了验证此仅自旋模型，我们随后采用7“-矩阵方法研究杂质对反铁磁有序参数的影响。先前的理论研究（仅包括杂质的稀释作用）显示出与实验数据在低掺杂下的交错磁化强度的掺杂依赖性存在很大差异。我们证明，通过将杂质引起的挫败感纳入具有实际CuO_2参数的有效自旋模型中，可以消除这种差异。最近的实验研究表明，与掺杂Mg的情况相比，掺杂Zn的La_2CuO_4的自旋刚度抑制作用明显更强，因此为我们的理论提供了有力的支持。我们认为，提出的杂质引起的挫折在其他高度相关的氧化物和电荷转移绝缘子中应该很重要。

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