Journal: Nature Communications

Article Title: Thermally active nanoparticle clusters enslaved by engineered domain wall traps

doi: 10.1038/s41467-021-25931-7

Figure Lengend Snippet: a Schematic of the experimental setup used to visualize and control the Ferrite Garnet Film (FGF). b Detailed sketch of the FGF with magnetic bubble domains filled by different numbers of paramagnetic nanoparticles. The external magnetic field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{{{{\bf{B}}}}}}}}}_{{{{{{{{\rm{ext}}}}}}}}}={B}_{z}\hat{{{{{{{{\bf{z}}}}}}}}}$$\end{document} B ext = B z z ^ is applied perpendicular to the film ( z axis). c Polarization microscope image of trapped nanoparticles (of diameter d = 360 nm). The magnetic bubble domains are visible due to the polar Faraday effect. Scale bar is 10 μ m, see also VideoS in the Supporting Information. d Square of the bubble diameter D 2 versus applied field B z . Scattered points are experimental data while continuous line is a linear fit according to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${D}^{2}=4{a}^{2}[({B}_{z}/{B}_{{{{{{{{\rm{s}}}}}}}}}+1)\sin (\pi /3)/(2\pi )]$$\end{document} D 2 = 4 a 2 [ ( B z / B s + ) sin ( π / 3 ) / ( 2 π ) ] (see “Methods”), from which we extract the lattice constant a = 11.81 ± 0.02 μ m and the saturation magnetization B s = 21.3 ± 0.3 mT. Error bars in D 2 are obtained from the statistical average of different measurments. Insets show images of the magnetic domains. e Three-dimensional view of the magnetostatic potential U calculated at an elevation z = 1.3 μ m and for B z = 0 mT. The ( x , z ) positions are rescaled by a , while the potential U is rescaled by the parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${U}_{0}=\chi \pi {d}^{3}{B}_{{{{{{{{\rm{s}}}}}}}}}^{2}/(12{\mu }_{0})$$\end{document} U 0 = χ π d 3 B s 2 / ( 12 μ 0 ) , see text for the values of μ 0 , χ , and d .

Article Snippet: Above the magnetic lattice we deposit a water dispersion of paramagnetic nanoparticles with diameter d = 360 nm (Microparticles GmbH), and doped with ~40% by weight of iron oxide.

Techniques: Microscopy