  Manipulating the spontaneous emission rate of optical emitters with
all-dielectric nanoparticles benefits from their low-loss nature and thus
provides relatively large extrinsic quantum yield. However, such Purcell effect
greatly depends on the orientation of the dipole emitter. Here, we introduce
the concept of isotropic magnetic Purcell effect with Purcell factors about 300
and large extrinsic quantum yield (more than 80%) for a magnetic dipole emitter
of arbitrary orientation in an asymmetric silicon nanocavity. The extrinsic
quantum yield can be even boosted up to nearly 100% by utilizing a GaP
nanocavity. Isotropy of the Purcell factor is manifested via the
orientation-independent emission of the magnetic dipole source. This isotropic
Purcell effect is robust against small displacement of emitter on the order of
10 nm, releasing the requirement of precise alignment in experiments.
