Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides
Cerium oxides (ceria) are materials that exhibit weak, room-temperature ferromagnetism without <i>d</i>-electrons. The latter are usually responsible for magnetism in a variety of other oxide compounds, but the underlying mechanism for such a magnetic response in ceria without the <i&...
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MDPI AG
2021-12-01
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| Series: | Condensed Matter |
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| Online Access: | https://www.mdpi.com/2410-3896/6/4/53 |
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| author | Cengiz Şen |
| author_facet | Cengiz Şen |
| author_sort | Cengiz Şen |
| collection | DOAJ |
| description | Cerium oxides (ceria) are materials that exhibit weak, room-temperature ferromagnetism without <i>d</i>-electrons. The latter are usually responsible for magnetism in a variety of other oxide compounds, but the underlying mechanism for such a magnetic response in ceria without the <i>d</i>-electrons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mn>0</mn></msup></semantics></math></inline-formula>-magnetism) is still under debate. A possible explanation is Zener double-exchange, where itinerant electrons polarize the localized spins via Hund-coupling as they hop from site to site. Here, we report magnetization and spin-spin correlation results using various values of the Hund-coupling in a one-orbital double-exchange model with Ising spins. In the real material with formula CeO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>2</mn><mo>−</mo><mi>x</mi></mrow></msub></semantics></math></inline-formula>, the oxygen-deficient sites are denoted by <i>x</i>. These sites are related to the density of tetravalent cerium spins (the Ising spin background in our model), which we denoted as and set at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>0.50</mn></mrow></semantics></math></inline-formula> in our simulations. Our results at this value of localized spin concentration show ferromagnetic tendencies at low carrier densities (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.25</mn></mrow></semantics></math></inline-formula>). However, ferromagnetism is lost at intermediate carrier concentrations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.50</mn><mo>)</mo></mrow></semantics></math></inline-formula> due to charge localization at high temperatures, as evident from density of states calculations and Monte Carlo snapshots. To our knowledge, our study based on a realistic Zener-type double exchange mechanism is a first in the study of magnetism in cerium oxides. Our results are also consistent with previous studies using similar Hamiltonians in the context of diluted magnetic semiconductors, where Heisenberg spins were used. |
| first_indexed | 2024-03-10T04:22:00Z |
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| language | English |
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| spelling | doaj.art-80dbeb12d9974f53a66ff2b4052bad502023-11-23T07:47:02ZengMDPI AGCondensed Matter2410-38962021-12-01645310.3390/condmat6040053Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium OxidesCengiz Şen0Department of Physics, Lamar University, P.O. Box 10046, Beaumont, TX 77710, USACerium oxides (ceria) are materials that exhibit weak, room-temperature ferromagnetism without <i>d</i>-electrons. The latter are usually responsible for magnetism in a variety of other oxide compounds, but the underlying mechanism for such a magnetic response in ceria without the <i>d</i>-electrons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>d</mi><mn>0</mn></msup></semantics></math></inline-formula>-magnetism) is still under debate. A possible explanation is Zener double-exchange, where itinerant electrons polarize the localized spins via Hund-coupling as they hop from site to site. Here, we report magnetization and spin-spin correlation results using various values of the Hund-coupling in a one-orbital double-exchange model with Ising spins. In the real material with formula CeO<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>2</mn><mo>−</mo><mi>x</mi></mrow></msub></semantics></math></inline-formula>, the oxygen-deficient sites are denoted by <i>x</i>. These sites are related to the density of tetravalent cerium spins (the Ising spin background in our model), which we denoted as and set at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>=</mo><mn>0.50</mn></mrow></semantics></math></inline-formula> in our simulations. Our results at this value of localized spin concentration show ferromagnetic tendencies at low carrier densities (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.25</mn></mrow></semantics></math></inline-formula>). However, ferromagnetism is lost at intermediate carrier concentrations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>0.50</mn><mo>)</mo></mrow></semantics></math></inline-formula> due to charge localization at high temperatures, as evident from density of states calculations and Monte Carlo snapshots. To our knowledge, our study based on a realistic Zener-type double exchange mechanism is a first in the study of magnetism in cerium oxides. Our results are also consistent with previous studies using similar Hamiltonians in the context of diluted magnetic semiconductors, where Heisenberg spins were used.https://www.mdpi.com/2410-3896/6/4/53magnetismceriadouble exchangemonte carlodiluted systems<i>d</i><sup>0</sup>-magnetism |
| spellingShingle | Cengiz Şen Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides Condensed Matter magnetism ceria double exchange monte carlo diluted systems <i>d</i><sup>0</sup>-magnetism |
| title | Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides |
| title_full | Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides |
| title_fullStr | Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides |
| title_full_unstemmed | Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides |
| title_short | Weak Ferromagnetism in a One-Orbital Double-Exchange Model with Ising Spins for Cerium Oxides |
| title_sort | weak ferromagnetism in a one orbital double exchange model with ising spins for cerium oxides |
| topic | magnetism ceria double exchange monte carlo diluted systems <i>d</i><sup>0</sup>-magnetism |
| url | https://www.mdpi.com/2410-3896/6/4/53 |
| work_keys_str_mv | AT cengizsen weakferromagnetisminaoneorbitaldoubleexchangemodelwithisingspinsforceriumoxides |