Find in Library

We combine theoretical and experimental X-ray absorption near-edge spectroscopy (XANES) to probe the local environment around cationic sites of bulk spinel cobalt tetraoxide (Co<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>O<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>). Specifically, we analyse the oxygen <i>K</i>-edge spectrum. We find an excellent agreement between our calculated spectra based on the density functional theory and the projector augmented wave method, previous calculations as well as with the experiment. The oxygen <i>K</i>-edge spectrum shows a strong pre-edge peak which can be ascribed to dipole transitions from O <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>s</mi></mrow></semantics></math></inline-formula> to O <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>p</mi></mrow></semantics></math></inline-formula> states hybridized with the unoccupied <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>d</mi></mrow></semantics></math></inline-formula> states of cobalt atoms. Also, since Co<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>O<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> contains two types of Co atoms, i.e., Co<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> and Co<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula>, we find that contribution of Co<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> ions to the pre-edge peak is solely due to single spin-polarized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>t</mi><mrow><mn>2</mn><mi mathvariant="normal">g</mi></mrow></msub></semantics></math></inline-formula> orbitals (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mrow><mi>x</mi><mi>z</mi></mrow></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mrow><mi>y</mi><mi>z</mi></mrow></msub></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mrow><mi>x</mi><mi>y</mi></mrow></msub></semantics></math></inline-formula>) while that of Co<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> ions is due to spin-up and spin-down polarized <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>e</mi><mi mathvariant="normal">g</mi></msub></semantics></math></inline-formula> orbitals (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><msup><mi>y</mi><mn>2</mn></msup></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><msup><mi>z</mi><mn>2</mn></msup></msub></semantics></math></inline-formula>). Furthermore, we deduce the magnetic moments on the Co<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> and Co<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> to be zero and 3.00 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>μ</mi><mi>B</mi></msub></semantics></math></inline-formula> respectively. This is consistent with an earlier experimental study which found that the magnetic structure of Co<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>O<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> consists of antiferromagnetically ordered Co<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> spins, each of which is surrounded by four nearest neighbours of oppositely directed spins.