Vortex magnomechanics:

The last two decades have witnessed groundbreaking developments in the fields of nanomechanics and
optomechanics (including microwave cavity-electromechanics), ranging from sensing at the single-particle level to
the first demonstrations of quantum behaviour of macroscopic massive degrees of freedom. Though the latter
offer enormous promise for foundational studies of quantum mechanics, quantum sensing and quantum-
transducer devices, they have so far been restricted to the few-phonon level and/or Gaussian states. To
overcome these restrictions is arguably the next major challenge to be met in the field of "quantum" mechanical
resonators. Major stumbling blocks are the "smallness" of the corresponding quantum nonlinearities and the
difficulty of in-situ tuneability over a wide range. More recently, leading groups (Tang, Yale) have started
exploring a magnetic analogue of cavity optomechanics where the "photonic" optical (or microwave) cavity-mode
is replaced by a "magnonic" spin-wave mode of a suitable single-domain magnetic structure that couples via
magnetostriction to a nanomechanical mode. This conveniently allows tuneability of the frequency via an external
magnetic field. It also retains the parametric nature of the coupling (quadratic in the magnon and linear in the
phonon) that is the cornerstone of the various successes of cavity-optomechanics. This platform can be readily
combined with resonant coupling of the magnon mode to a cavity microwave.
All current experimental efforts in this emerging subfield of "magnomechanics" have so far been focusing on
magnetic excitations of a homogeneous magnetisation. In this joint theory and experimental project we will
explore the possibility of using instead the gyrotropic mode of a vortex core, i.e. realising vortex-
magnomechanics. This novel idea will bring together, and build upon, the applicants expertise in optomechanics,
nanomagnetism and nanolithography. The nontrivial magnetic texture afforded by a vortex is more versatile than
a homogeneous magnetisation allowing for the possibility of engineering the coupling between the magnon
modes of separate magnetic sites. Indeed, to couple the mechanical resonator to multiple (mutually coupled)
cavity modes is essential for many objectives in optomechanics, such as synchronisation, and is an important
current pursuit in the field. The counterpart of this multimode system could be realised in vortex-
magnomechanics in a way that circumvents the limitations imposed by the photon wavelength. The
nanostructure of choice for our experiments will be a commercial pre-stressed silicon nitride membrane that will
be modified by depositing a magnetostrictive ferromagnetic Nickel film in the form of microdisc arrays at
locations that maximise the magnetostrictive coupling to their gyrotropic modes. These thin membranes have
already been profusely used in optical and microwave optomechanical experiments, including demonstrations of
quantum behaviour. The membrane will be inserted in a driven 3D microwave cavity (broad bandwidth compared
to the magnon mode), similar to those used in microwave optomechanics, near-resonant with the magnon mode
in order to excite it. The student will measure and model room temperature classical phenomena such as
parametric amplification and dynamical backaction on the mechanical resonator as a function of the microdisc
array properties. Theoretical work will focus on both modelling these experiments and analysing proposals for
low-temperature extensions relevant to quantum phenomena. It will rely on FEM simulations, Langevin
equations, the secular perturbation theory of nonlinear dynamical systems, and quantum noise techniques. The
proposed research is at the centre of a range of EPSRC and government strategic priorities. Quantum
technologies are an EPSRC priority whilst magnonics is a key emerging area in which EPSRC is growing.