Two-dimensional artificial arrays of interacting nanomagnets are a powerful playground for probing the physics of the lattice spin models. Artificially designed spin systems were introduced to mimic the behaviour of the frustrated pyrochlore crystals. Recent improvement in nano-fabrication techniques allows us to fabricate any desired artificial system in the lab control environment. Therefore artificial simulators of the matter can be produced and used for more advanced study of the desired phenomenons.

The advantage of using nanomagnetic objects as building blocks of artificial lattices is that small magnetic structures can effectively be considered giant classical Ising spins. Therefore elevating the problem of frustrated spins in pyrochlore crystals into such dimensions so the system can be studied with real space imaging techniques.

With imaging techniques such as magnetic force microscopy, the ordering of each Ising macrospin can be visualised in real space, enabling us to look not only at the global property of the system as a whole but to see how local interactions are accommodated.

Being able to fabricate artificial systems capturing the desired physics and comparing it to the real nature counterpart measures our understanding of the problem. It can also offer a missing piece of information. Furthermore, there are properties of the systems which are emergent and not encoded in the theoretical Hamiltonians describing the systems. Such properties seem to come out of nowhere, and with artificial systems and the ability to visualise these systems, we can analyse such properties.

This thesis focus on studying two types of systems: kagome and square dipolar spin systems. Both these systems are the results of the projections of the three-dimensional pyrochlore crystals into a plane. Moreover, both systems exhibit rather unusual behaviour, which is still to be measured on a large scale in real space. The dipolar kagome spin system has a low energy phase called spin liquid 2, which hosts unusual spin behaviour. The spins in this phase are ordered and disordered simultaneously, a unique emergent property of the system with no equivalent.

On the other hand, the square spin system is a perfect playground for studying the exotic physics of spin liquids, the Columb phase, and the behaviour of magnetic monopole-like quasi-particles.

The usual approach when fabricating artificial spin systems is to build them up out of single-domain nanomagnets which interact via long-range dipolar interactions. Therefore the systems try to minimise the interactions between all pairs of the Ising macrospins. However, the central idea of this thesis is to connect all the nanomagnets into one macro lattice, therefore introducing the micromagnetic effects into the systems. Magnetisation tries to satisfy the micromagnetic energies at the vertex site. Hence, we effectively replace the spin degree of freedom with a micromagnetic knob which can be used to tune each vertex's energy by introducing specially designed topological defects.

Even though both systems have been the focus of researchers for almost twenty years, we believe that our modifications open a gateway to fully accessing the exotic physic yet to uncover.