Field-Dependent Magnetic Domain Behavior in van der Waals Fe$_3$GeTe$_2$

Abstract: Two-dimensional magnetic van der Waals (vdW) materials can show a variety of topological nontrivial spin textures, such as Bloch- or N\'eel-type stripe, skyrmion or bubble domains under certain external stimuli. It is critical to understand the magnetic domain behavior in vdW materials in order to control their size, and density in response to external stimuli such as electric and magnetic fields. Here we examine the magnetic field dependence of topologically non-trivial magnetization spin textures in vdW Fe$_3$GeTe$_2$. N\'eel-type stripe domains and skyrmions are formed depending on the magnetic field-cooling protocol used during in-situ Lorentz transmission electron microscopy (LTEM) experiments. Use of quantitative reconstruction of magnetic induction maps, and micromagnetic simulations, allow for understanding the LTEM results of N\'eel-type stripe domains as well as skyrmions. In addition, the deformation of skyrmion contrast is observed as a result of the introduction of an in-plane magnetic field. We demonstrate the stability of the stripe domains and skyrmions in response to externally applied magnetic field due to energy barrier for domain wall annihilation. Our results establish an understanding of the energy landscape that governs the behavior of the topologically non-trivial spin textures in vdW materials which can be harnessed for spintronic applications.