Title
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Spontaneous and induced magnetisation in two-dimensional and bulk Heisenberg ferromagnets : a quantum mechanical treatment
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Author
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Abstract
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Two-dimensional (2D) materials have dominated the fields of solid-state physics and technology in recent years. With the experimental discovery of several atomically thin ferromagnets in 2017, magnetism has also properly entered this exciting domain. From a technological perspective, understanding the exact thin-film magnetisation behaviour is essential in the ever-continuing down-scaling of integrated circuit components, striving for cheaper, faster and more energyefficient devices. While today predominantly present in memory devices, thin ferromagnets might also enter the realm of logic technologies, for example in the form of spin wave majority gates. From a scientific perspective, the origin of twodimensional ferromagnetism is not well understood, as it seemingly contradicts the (in)famous Mermin-Wagner theorem—excluding the possibility of two-dimensional ferromagnetic ordering. To address this dissatisfying situation, we studied a quantum Heisenberg model with beyond-nearest-neighbour, anisotropic exchange interactions at non-zero temperatures. This model is believed to accurately describe some of the experimentally discovered 2D ferromagnets, such as CrI3 , CrBr3 and MnSe2 . We obtained results using Zubarev’s double-time temperature-dependent Green functions with Tyablikov’s decoupling approximation, which are known to give meaningful results for the entire temperature range. We compared results for two- and three-dimensional materials, investigated the effect of an applied, homogeneous field in arbitrary direction and extended the methodology to properly account for magnetic dipolar interactions. This thesis reports on the calculated Curie temperatures, excitation spectra, and magnetisation magnitudes and angles. We managed to reproduce the predictions of the Mermin-Wagner theorem and find that spontaneous magnetisation in 2D materials is still possible when an easy-axis exchange anisotropy is present. Combining our results with ab initio calculations allowed us to reproduce Curie temperatures in agreement with experiments. The behaviour of magnetism in easy-axis two-dimensional materials turns out to be similar to that of their bulk counterparts, while being distinct from easy-plane 2D materials. Overall, the magnetisation aligns mostly with the internal anisotropy at low temperatures and fields, while getting reoriented towards the homogeneous external field direction otherwise. Dipolar interactions might lead to an additional easy-plane anisotropy for thin films, but its corresponding long-range character might stabilise the magnetisation. In conclusion, we found an effective way to describe some recently discovered 2D ferromagnets, explaining their non-zero Curie temperatures by the presence of easy-axis anisotropy. In such materials, our results allow predictions on the magnetisation at non-zero temperatures and applied fields at arbitrary angles. To stimulate further computational discoveries of monolayer ferromagnets, we made a computer program publicly available to calculate Curie temperatures based on our formalism. This application only requires ab initio calculated parameters as an input and can equally well be used to study effects of stress, strain or electrical fields on the transition temperature. Our methodology might further be extended to study multilayer materials, different magnetic interactions or even dynamical effects. |
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Language
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English
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Publication
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Antwerpen
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Universiteit Antwerpen, Faculteit Wetenschappen, Departement Fysica
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2020
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Volume/pages
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160 p.
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Note
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Magnus, Wim [Supervisor]
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Sorée, Bart [Supervisor]
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Full text (open access)
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