If you throw a stone into a still pond then the wave set up on the surface of the water
dies away, both at a distance far from the initial disturbance and after a relatively short
interval of time. However, some waves in Nature are not like this. They are, instead,
localised in space and trapped in existence for long periods, their removal costing a great
deal of energy. There are many examples of these long-lived, wave-like topological objects
in physics such as magnetic domain walls, vortices, and skyrmions [1,2]. Recently, many
more have been discovered, including more exotic textures known as hopfions, torons and
blochions. Topology, the study of the shapes of objects, provides an organising principle
to understand the existence and extraordinary properties of these objects. Topology also
allows us to understand and classify large families of unusual quantum-mechanical states
of materials.
In this lecture, we will discuss the existence of topological excitations based on ideas
from symmetry breaking in phase transitions. We will see how topological objects occur
in magnetic materials, where they can be readily measured and visualized. Finally, we will
see how these ideas can be applied to a pressing problem: the possible fate of the
Universe!
[1] Lancaster, T. (2019). Skyrmions in magnetic materials. Contemporary Physics, 60(3),
246–261. https://doi.org/10.1080/00107514.2019.1699352
[2] Lancaster, T. and Blundell, S.J. (2015) Quantum Field Theory for
the Gifted Amateur (OUP, Oxford).

Tailored light excitation and nonlinear control of lattice vibrations have emerged as powerful strategies to manipulate the properties of quantum materials out of equilibrium. Generalizing the use of coherent phonon-phonon interactions to nonlinear couplings among other types of collective modes would open unprecedented opportunities in the design of novel dynamic functionalities in solids. For example, the collective excitations of magnetic order –magnons– can carry quantum information with little energy dissipation, and their coherent and nonlinear control would provide an attractive route to achieve collective-mode-based information processing and storage in forthcoming spintronics and quantum information science.

In this talk, I will show that intense terahertz (THz) fields can initiate processes of magnon up-conversion and magnon mixing mediated by an intermediate magnetic resonance. By using a suite of advanced spectroscopic tools, including a newly demonstrated two-dimensional THz polarimetry technique, we unveil these anharmonic magnon coupling phenomena in a canted antiferromagnet. These results demonstrate a route to inducing desirable energy transfer pathways between coherent magnons in solids and pave the way for a new era in the development of ultrafast control of magnetism.