In three-dimensions, magnetism has revolutionized our everyday life, enabling familiar technologies which are of common use. A few examples include computers’ memories, RAM, hard-disks, key cards, credit cards, electric batteries, light, and distance sensors. This relentless pace of development has motivated the search for magnetism in systems with increasingly smaller sizes.

 With cooperation of experimental and theoretical physics, researchers discovered that spin-anisotropy can stabilize low-dimensional magnetism. In this, spin-orbit coupling plays an important role. Surface experimental probes, such as angle-resolved photoelectron spectroscopy provide researchers access to the electronic structure of solids. Despite the advances in the field, recently, new forms of surface local magnetism completely different from standard descriptions have appeared.

 Here, I aim to give an overview of a new powerful methodology to uncover hidden phases of electrons, including spins, and magnetism which was so fare elusive. I will do this by showing two of my research achievements.