  Quantum fluctuations are the key concepts of quantum mechanics. Quantum
fluctuations of quantum fields induce a zero-point energy shift under spatial
boundary conditions. This quantum phenomenon, called the Casimir effect, has
been attracting much attention beyond the hierarchy of energy scales, ranging
from elementary particle physics to condensed matter physics together with
photonics. However, the application of the Casimir effect to spintronics has
not yet been investigated enough, particularly to ferrimagnetic thin films,
although yttrium iron garnet (YIG) is one of the best platforms for
spintronics. Here we fill this gap. Using the lattice field theory, we
investigate the Casimir effect induced by quantum fields for magnons in
insulating magnets and find that the magnonic Casimir effect can arise not only
in antiferromagnets but also in ferrimagnets including YIG thin films. Our
result suggests that YIG, the key ingredient of magnon-based spintronics, can
serve also as a promising platform for manipulating and utilizing Casimir
effects, called Casimir engineering. Microfabrication technology can control
the thickness of thin films and realize the manipulation of the magnonic
Casimir effect. Thus, we pave the way for magnonic Casimir engineering.
