Departament de Ciència de Materials i Química Física & Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, c/Martí i Franquès 1-11, 08028 Barcelona, Spain.
Phys Chem Chem Phys. 2023 Jul 5;25(26):17116-17127. doi: 10.1039/d3cp01617j.
The magnetic nature of TiC, TiC, and TiC MXenes is determined from periodic calculations within density functional theory and using the generalized gradient approximation based PBE functional, the PBE0 and HSE06 hybrids, and the on-site Hubbard corrected PBE+ one, in all cases using a very tight numerical setup. The results show that all functionals consistently predict a magnetic ground state for all MXenes, with spin densities mainly located at the Ti surface atoms. The analysis of solutions corresponding to different spin orderings consistently show that all functionals predict an antiferromagnetic conducting ground state with the two ferromagnetic outer (surface) Ti layers being antiferromagnetically coupled. A physically meaningful spin model is proposed, consistent with the analysis of the chemical bond, with closed shell, diamagnetic, Ti like ions in inner layers and surface paramagnetic Ti like centers with one unpaired electron per magnetic center. From a Heisenberg spin model, the relevant isotropic magnetic coupling constants are extracted from an appropriate mapping of total energy differences per formula unit to the expected energy values of the spin Hamiltonian. While the numerical values of the magnetic coupling constants largely depend on the used functional, the nearest neighbor intralayer coupling is found to be always ferromagnetic, and constitutes the dominant interaction, although two other non-negligible interlayer antiferromagnetic terms are involved, implying that the spin description cannot be reduced to NN interaction only. The influence of the MXene thickness is noticeable for the dominant ferromagnetic interaction, increasing its value with the MXene width. However, the interlayer interactions are essentially due to the covalency effects observed in all metallic solutions which, as expected, decay with distance. Within the PBE+ approach, a value of 5 eV is found to closely simulate the results from hybrid functionals for TiC and less accurately for TiC and TiC.
TiC、TiC 和 TiC MXenes 的磁性性质是通过密度泛函理论中的周期性计算确定的，并使用基于广义梯度近似的 PBE 泛函、PBE0 和 HSE06 杂化以及局域 Hubbard 修正的 PBE+，所有情况下都使用非常紧密的数值设置。结果表明，所有泛函都一致地预测所有 MXenes 的磁基态，自旋密度主要位于 Ti 表面原子上。对应于不同自旋排序的解的分析一致表明，所有泛函都预测具有反铁磁导电性的基态，两个铁磁外层（表面）Ti 层通过反铁磁耦合。提出了一个物理意义上的自旋模型，与化学键的分析一致，具有内层闭合壳层、抗磁性、类 Ti 离子和表面顺磁类 Ti 中心，每个磁性中心有一个未配对电子。从海森堡自旋模型中，通过将每个单位分子式的总能量差映射到自旋哈密顿量的预期能量值，提取出相关的各向同性磁耦合常数。虽然磁耦合常数的数值主要取决于所使用的泛函，但发现最近邻层内耦合总是铁磁的，并且构成主要相互作用，尽管涉及另外两个不可忽略的层间反铁磁项，这意味着自旋描述不能仅简化为近邻相互作用。对于主导的铁磁相互作用，MXene 的厚度的影响是明显的，随着 MXene 的宽度增加其值增加。然而，层间相互作用主要归因于所有金属溶液中观察到的共价键效应，这与预期的一样，随着距离的增加而衰减。在 PBE+方法中，发现 5 eV 的 值可以很好地模拟混合泛函对 TiC 的结果，对 TiC 和 TiC 的模拟精度较低。
