Rotating Magnetocaloric Effect in Sintered La(Fe,Mn,Si)$_{13}$H$_z$ Plates
La-Fe-Si-based alloys are among the most application-ready magnetocaloric materials for room-temperature magnetic refrigeration. Powder metallurgy methods have been previously demonstrated to successfully produce structures with sub-mm features for magnetic refrigerators in a scalable method. In this work, we explore the rotating magnetocaloric effect (RMCE) present in a 0.27 mm thin plate of sintered and hydrogenated La(Fe,Mn,Si)$_{13}$. The high aspect ratio ($\sim$50) of the thin plate leads to an anisotropic magnetocaloric effect (MCE), dependent on the relative orientation of the external magnetic field, and an RMCE when the external field is rotated. We find a maximum rotating adiabatic temperature change ($\Delta T_{ad}^{rot}$) of 1.17 K with the rotation of a 1 T magnetic field and 1.12 K when rotating a 0.6 T magnetic field, a reduction of only 4% for a 40% reduction in applied field strength. Magnetostatic computations revealed a considerable rotating isothermal entropy change ($\Delta S_{iso}^{rot}$), comparable to the conventional MCE of Gd for similar fields, reaching 3.97 J K$^{-1}$ kg$^{-1}$ for 1 T and 3.68 J K$^{-1}$ kg$^{-1}$ for 0.6 T (7% reduction), highlighting La-Fe-Mn-Si alloys as high potential candidates for a magnetic refrigerator based on the RMCE utilizing relatively low external magnetic field amplitudes, such as 0.6 T.