We report here a tight-binding model study of frequency-dependent ferromagnetic spin susceptibility of the graphene system. The tight-binding Hamiltonian consists of electron hoppings up to third-nearest-neighbors, substrate and impurity effects in the presence of Coulomb interaction of electrons separately at two in-equivalent A and B sub-lattices of graphene. To calculate magnetic susceptibility, we calculate the two-particle electron Green’s functions by using Zubarev’s double time Green’s function technique. The electron occupations at A and B sub-lattices for both up and down spins are computed numerically and self-consistently. The frequency-dependent real part of ferromagnetic susceptibility of the system is computed numerically by taking [Formula: see text] grid points of the electron momentum. The susceptibility displays a sharp peak at the neutron momentum transfer energy at low energies and another higher energy resonance peak appearing at substrate-induced gap. The [Formula: see text]-peak shifts to a higher energy with the increase of momentum [Formula: see text]. The susceptibility shows that the high energy peak shifts to higher energies due to the corresponding increase of substrate-induced gap observed experimentally. It is observed that the Coulomb interaction suppresses the substrate-induced gap, but the impurity doping at A site enhances the substrate-induced gap, while doping at B site suppresses it.

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铁磁状态下石墨烯的磁自旋磁化率：紧密结合模型研究

我们在这里报告了石墨烯系统的频率相关铁磁自旋磁化率的紧束缚模型研究。紧束缚哈密顿量包括在石墨烯的两个不等价的 A 和 B 亚晶格上分别存在电子的库仑相互作用的情况下，电子跃迁到第三近邻、底物和杂质效应。为了计算磁化率，我们利用祖巴列夫的双倍格林函数技术计算了两粒子电子格林函数。向上和向下自旋在 A 和 B 子晶格处的电子占据是通过数值和自洽方式计算的。系统铁磁化率的频率相关实部通过采用电子动量的[公式：见文本]网格点进行数值计算。磁化率在低能量下的中子动量转移能量处显示一个尖峰，而在衬底诱导间隙处出现另一个更高能量的共振峰。[公式：见正文]-峰值随着动量的增加[公式：见正文]向更高的能量移动。敏感性表明，由于实验观察到的底物诱导间隙的相应增加，高能峰向更高的能量转移。观察到库仑相互作用抑制了衬底引起的间隙，但在 A 位的杂质掺杂增强了衬底引起的间隙，而在 B 位的掺杂抑制了它。见正文]。敏感性表明，由于实验观察到的底物诱导间隙的相应增加，高能峰向更高的能量转移。观察到库仑相互作用抑制了衬底引起的间隙，但在 A 位的杂质掺杂增强了衬底引起的间隙，而在 B 位的掺杂抑制了它。见正文]。敏感性表明，由于实验观察到的底物诱导间隙的相应增加，高能峰向更高的能量转移。观察到库仑相互作用抑制了衬底引起的间隙，但在 A 位的杂质掺杂增强了衬底引起的间隙，而在 B 位的掺杂抑制了它。