Physics at the level of an atom is dominated by laws of quantum mechanics. Often, this is entangled with a high complexity in behavior of the systems at that length scale. Unravelling the properties of a material at the atomic level is, therefore, a challenging task that easily supersedes current computational capabilities. A route to circumvent this problem is found in physical realization of simpler quantum systems that are representative of the complex quantum systems one is interested in. These simpler physical systems, unlike their more complex counterparts, can actually be measured and information about the complex system, otherwise inaccessible, gained. This thesis describes experimental work focusing mainly on the property of magnetism in spin chains. To mimic these complex systems, we employ a scanning tunneling microscope (STM) to build atomic chains on solid state surfaces and probe their magnetic properties. The intrinsic strength of STM in building and testing structures with single atom precision makes STM a great candidate for simulation of complex quantum systems. In addition to STM having a role of a quantum simulator, I present work supporting STM as a control device determining the very existence of the magnetic excitations of the atom it measures. Finally, I present experimental findings that suggest we are able to probe the magnetic excitations of the atom with subatomic resolution. In summary, this thesis work presents STM as a powerful probing and control tool for studies on quantum magnetism at the level of a single atom.@en

The advent of devices based on single dopants, such as the single-atom transistor, the single-spin magnetometer and the single-atom memory, has motivated the quest for strategies that permit the control of matter with atomic precision. Manipulation of individual atoms by low-temperature scanning tunnelling microscopy provides ways to store data in atoms, encoded either into their charge state, magnetization state or lattice position. A clear challenge now is the controlled integration of these individual functional atoms into extended, scalable atomic circuits. Here, we present a robust digital atomic-scale memory of up to 1 kilobyte (8,000 bits) using an array of individual surface vacancies in a chlorine-terminated Cu(100) surface. The memory can be read and rewritten automatically by means of atomic-scale markers and offers an areal density of 502 terabits per square inch, outperforming state-of-the-art hard disk drives by three orders of magnitude. Furthermore, the chlorine vacancies are found to be stable at temperatures up to 77 K, offering the potential for expanding large-scale atomic assembly towards ambient conditions.

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The ability to manipulate single atoms has opened up the door to constructing interesting and useful quantum structures from the ground up. On the one hand, nanoscale arrangements of magnetic atoms are at the heart of future quantum computing and spintronic devices; on the other hand, they can be used as fundamental building blocks for the realization of textbook many-body quantum models, illustrating key concepts such as quantum phase transitions, topological order or frustration as a function of system size. Here, we use low-temperature scanning tunnelling microscopy to construct arrays of magnetic atoms on a surface, designed to behave like spin-1/2 XXZ Heisenberg chains in a transverse field, for which a quantum phase transition from an antiferromagnetic to a paramagnetic phase is predicted in the thermodynamic limit. Site-resolved measurements on these finite-size realizations reveal a number of sudden ground state changes when the field approaches the critical value, each corresponding to a new domain wall entering the chains. We observe that these state crossings become closer for longer chains, suggesting the onset of critical behaviour. Our results present opportunities for further studies on quantum behaviour of many-body systems, as a function of their size and structural complexity.

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