Advanced First-Principle Modeling of Relativistic Ruddlesden—Popper Strontium Iridates

• Main Authors: Peitao Liu, Cesare Franchini
• Format: Article
• Language: English
• Published: MDPI AG 2021-03-01
• Series: Applied Sciences
• Subjects: iridates; first-principle methods; computational modeling; spin-orbit coupling; correlated materials; metal-insulator transition
• Online Access: https://www.mdpi.com/2076-3417/11/6/2527

In this review, we provide a survey of the application of advanced first-principle methods on the theoretical modeling and understanding of novel electronic, optical, and magnetic properties of the spin-orbit coupled Ruddlesden–Popper series of iridates Sr<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula>Ir<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>n</mi></msub></semantics></math></inline-formula>O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>3</mn><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub></semantics></math></inline-formula> (<i>n</i> = 1, 2, and <i>∞</i>). After a brief description of the basic aspects of the adopted methods (noncollinear local spin density approximation plus an on-site Coulomb interaction (LSDA+<i>U</i>), constrained random phase approximation (cRPA), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>W</mi></mrow></semantics></math></inline-formula>, and Bethe–Salpeter equation (BSE)), we present and discuss select results. We show that a detailed phase diagrams of the metal–insulator transition and magnetic phase transition can be constructed by inspecting the evolution of electronic and magnetic properties as a function of Hubbard <i>U</i>, spin–orbit coupling (SOC) strength, and dimensionality <i>n</i>, which provide clear evidence for the crucial role played by SOC and <i>U</i> in establishing a relativistic (Dirac) Mott–Hubbard insulating state in Sr<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>IrO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>4</mn></msub></semantics></math></inline-formula> and Sr<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>Ir<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>7</mn></msub></semantics></math></inline-formula>. To characterize the ground-state phases, we quantify the most relevant energy scales fully ab initio—crystal field energy, Hubbard <i>U</i>, and SOC constant of three compounds—and discuss the quasiparticle band structures in detail by comparing <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>W</mi></mrow></semantics></math></inline-formula> and LSDA+<i>U</i> data. We examine the different magnetic ground states of structurally similar <i>n</i> = 1 and <i>n</i> = 2 compounds and clarify that the origin of the in-plane canted antiferromagnetic (AFM) state of Sr<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>IrO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>4</mn></msub></semantics></math></inline-formula> arises from competition between isotropic exchange and Dzyaloshinskii–Moriya (DM) interactions whereas the collinear AFM state of Sr<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>3</mn></msub></semantics></math></inline-formula>Ir<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>2</mn></msub></semantics></math></inline-formula>O<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>7</mn></msub></semantics></math></inline-formula> is due to strong interlayer magnetic coupling. Finally, we report the dimensionality controlled metal–insulator transition across the series by computing their optical transitions and conductivity spectra at the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>G</mi><mi>W</mi></mrow></semantics></math></inline-formula>+BSE level from the the quasi two-dimensional insulating <i>n</i> = 1 and 2 phases to the three-dimensional metallic <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mspace width="3.33333pt"></mspace><mo>=</mo><mspace width="3.33333pt"></mspace><mi>∞</mi></mrow></semantics></math></inline-formula> phase.