Elastic coupling and quantum critical fluctuations in complex magnetic structures

Magnetism plays an undeniable role in modern life, from storing data in computers, to anti-lock braking systems in cars, many pieces of technology being commonly used most likely rely on something magnetic. Recently emerging fields include spintronics [1, 2], in which spin polarised currents are used to send information more efficiently than charge currents, magnonics [3] in which magnons are used to send information, as well as materials with a large magnetoelectric effect, in which only a small current is needed to switch the magnetisation in a system, implying use in highly efficient memory devices [4]. Fields such as these require an understanding of the materials which host the complex magnetic structures whose attributes can be leveraged to create such devices and this is the contribution this thesis hopes to make.
When one first learns of magnetic systems, two types immediately come to mind, ferro-magnets and antiferromagnets. In a ferromagnet, the individual magnetic moments align, leading to an overall magnetisation in the system which is easily detectable in an experiment, even without the presence of a magnetic field. In antiferromagnets, the magnetic moments anti-align, producing a magnetic state with no-net magnetisation. ... mehrSuch a state can still be detected, for example, through neutron scattering, where the magnetic moment of the neutron interacts with the magnetic ions in the lattice, giving magnetic diffraction peaks [5].
These considerations naturally lead to the question as to what else could there be? In both cases mentioned above, the formation of a magnetically ordered state is associated with the breaking of a symmetry, in a ferromagnet, order sets in below the Curie temperature and time-reversal symmetry is broken, while the translation symmetry of the system is maintained. In antiferromagnets below the Néel temperature, time-reversal symmetry is broken and translation of one lattice spacing is also broken, while the combined operation of the two remains a symmetry. This then suggests that it could be worth investigating what would happen if the operation in question were not translation but some other operation which leaves the lattice invariant. If the operation in question is, for example, a rotation, one is left
with something of a relation to an antiferromagnet but with a new set of properties which are of use in the production of highly efficient electronics. We see a simple depiction of this in Fig. 1. Such a system would combine the zero net-magnetisation of an antiferromagnet with the spin-splitting exhibited by ferromagnets. This would allow for the formation of spin currents used in spintronic devices, without the danger of such devices coupling to one another through a magnetic field generated by the material [2]. This type of magnetism has been dubbed an altermagnet, it is related to the Pomeranchuk instability [6] in the spin channel for higher angular momentum, in which the Fermi surface becomes unstable with respect to de-
formations and can exhibit the symmetries described above. The properties of an altermagnet make their detection highly non-trivial. One would need a way to test whether a particular material, which may look like an antiferromagnet, is actually an altermagnet. The fact that the altermagnet breaks a symmetry of the overall crystal system suggests that it could couple to strain and can therefore be manipulated by applied strain. There already exists a wealth of literature dedicated to measurements of strain and strain fluctuations (phonons) [7–9] which implies that if such couplings exist, they would offer a route to indirectly detect altermagnetism. We consider the regime where quantum fluctuations of the order parameter are at their strongest and using group theory, we construct symmetry-allowed coupling terms between magnetism and strain and see how this is manifested physically through observable
properties of the system.
This thesis is not just restricted to altermagnetism, we also discuss orbital magnetism in twisted bilayer graphene [10–13] with large magnetoelectric effect, of interest due to applications in memory devices [4]. Twisted bilayer graphene is an incommensurate system which allows for an extended elasticity theory and additional couplings not possible in commensurate crystals. We also briefly discuss the implications of our analysis for nematic order, relevant to iron-based superconductors [14–16], which, much like altermagnets, break rotational symmetry but not time-reversal.