First-principles study of superconductivity and magnetism

Abstract

Understanding superconductivity and magnetism has been one of the most important homework in condensed matter physics. Those phenomena are the representative material properties of the transition metal compounds in which the charge, lattice, spin, and orbital are strongly correlated. The complex interplay between the degree of freedoms significantly hampers a microscopic understanding of the phenomena. In this thesis, we adopt two independent and complementary approaches to achieve a better understanding of the challenging properties. One is to solve the approximate many-body Schr\"{o}dinger equation

density functional theory (DFT), DFT+U method, and GW approximation. The other is to directly estimate physically meaningful parameters such as Hubbard U and magnetic exchange coupling constant J

constrained random phase approximation (cRPA) and magnetic force theory (MFT). Armed with the methods above, we investigate transition metal compounds from which high-Tc superconductivity and magnetism emerge

cuprates, manganites, and magnetic van der Waals materials.

In the first part, we revisit the classical strongly-correlated systems

cuprates and manganites which are the representative materials of high-$T_c$ superconductivity and magnetism, respectively. We present the GW electronic structures of cuprates which show remarkable difference with those of LDA for the first time. The calculated GW results compare better than LDA with recent experimental results. The direct systematic estimation of Hubbard U by cRPA method in various cuprates shows that the electron-doped cuprates are less correlated than their hole-doped counterparts, which might support the Slater picture rather than the Mott picture. Further, the U values significantly vary even among the hole-doped families. Charge DFT+U study of $LaMnO_3$ shows that the use of spin-unpolarized charge-only density is crucial to correctly describe the phase diagram, electronic structure, and magnetic property. Using magnetic force linear response calculation, a long-standing issue is clarified regarding the second neighbor out-of-plane interaction strength. Our estimation of orbital-decomposed magnetic couplings shows that the inter-orbital $e_g-t_{2g}$ interaction is quite significant due to the Jahn-Teller distortion and orbital ordering.

In the second part, we investigate magnetic van der Waals materials which are promising systems for the realization of 2-dimensional magnetism

$CrI_3$ and $Fe_3GeTe_2$. We estimate magnetic force response J as well as total energy of bilayer $CrI_3$ to unveil its mysterious layered antiferromagnetism. Various van der Waals functionals unequivocally point to the ferromagnetic ground state for the low-temperature structured bilayer $CrI_3$ which is further confirmed independently by magnetic force response calculations. The calculated orbital-dependent magnetic interactions clearly show that $e_g-t_{2g}$ interaction is the key to stabilize this ferromagnetic order. By suppressing this ferromagnetic interaction, one can realize the desirable antiferromagnetic order. We show that high-temperature monoclinic stacking can be the case. Next, we performed the detailed first-principles study to understand the magnetic properties of $Fe_3GeTe_2$. Contrary to the conventional wisdom, it is unambiguously shown that $Fe_3GeTe_2$ is not ferromagnetic but antiferromagnetic carrying zero net moment in its stoichiometric phase. Fe defect and hole doping are the keys to make this material ferromagnetic, which are shown by the magnetic force response as well as the total energy calculation with the explicit Fe defects and the varied system charges. Further, we found that the electron doping also induces the antiferro- to ferromagnetic transition. It is a crucial factor to understand the notable recent experiment of gate-controlled ferromagnetism.