Abstract
Magnetostriction is the property of magnetic systems that describes strain produced by changing magnetisation.
In this thesis, we investigate the magnetostriction of concentrated rare earth antiferromagnetic systems.
Rare earth antiferromagnetic systems have promising applications in microwave to optical frequency upconversion.
We developed a novel optical interferometric technique to measure the magnetostriction of Neodymium Gallate.
Neodymium Gallate is a concentrated rare earth crystal that orders antiferromagnetically at T = 0.97 K.
At cryogenic temperatures of T = 49 mK this technique was used to measure magnetostriction of order $\lambda$ $\sim$ 10$^{-5}$ with a sensitivity of $\sim$ 10$^{-8}$.
A `kink' in the data at B = 1.65 T was observed within the magnetostriction measurement.
This `kink' was identified as a magnetic phase transition.
Further measurements at varying temperatures above and below the N$\acute{\text{e}}$el transition temperature explored the relationship between magnetostriction, external magnetic field strength, and temperature. An elementary 2D mean field model of the magnetic ordering of the system was developed to analyse these results. The model was used to compare the relationship between magnetisation and magnetostriction. The experiment and analysis opens up several avenues for further development; from increasing the sensitivity of magnetostriction experiments by several orders of magnitude to better understanding the magnetic ordering of Neodymium Gallate. The work of this thesis highlights the potential of quantum magno-mechanics.