Exchange stiffness $A$ is a key micromagnetic parameter, yet in hard ferrites its value is still uncertain because earlier estimates came from thin-film spin-wave experiments that depend on many theoretical assumptions. We show that tilt-scan-averaged differential phase-contrast scanning transmission electron microscopy (tDPC-STEM) can measure $A$ more directly and locally in real space. Using this method we determined the ${180}^{\circ }$ domain-wall widths to be $17.8\pm 1.4\mathrm{nm}$ in $\mathrm{SrF}{\mathrm{e}}_{11.8}{\mathrm{O}}_{19}$ and $14.8\pm 1.4\mathrm{nm}$ in $\mathrm{C}{\mathrm{a}}_{0.5}\mathrm{L}{\mathrm{a}}_{0.5}\mathrm{F}{\mathrm{e}}_{10.1}\mathrm{C}{\mathrm{o}}_{0.3}{\mathrm{O}}_{19}$. Combining these widths with independently measured magnetocrystalline anisotropy constants gives the similar exchange stiffness, $\mathrm{A}=10.7\pm 1.8$ pJ/m and $\mathrm{A}=10.7\pm 2.7$ pJ/m, respectively. Because the technique probes individual domain walls, it also supplies truly local, nanometer-scale magnetic parameters inside the crystal.

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• Magnetic anisotropy
• Magnetic texture
• Magnetism
• Ferrites
• Scanning transmission electron microscopy