Magnetic order in nuclear spin two-dimensional lattices due to electron–electron interactions

We focus on nuclear spins embedded in a two-dimensional (2D) electron gas. The nuclear spins interact with each other through the Ruderman–Kittel–Kasuya–Yosida (RKKY) interaction, which is carried by the electron gas. We show that a nuclear magnetic order at finite temperature relies on the anomalous behaviour of the 2D static electron spin susceptibility due to electron–electron interactions. This provides a connection between low-dimensional magnetism and non-analyticities in interacting 2D electron systems. We discuss the conditions for nuclear magnetism, and show that the associated Curie temperature increases with the electron–electron interactions and may reach up into the millikelvin regime. We also shortly discussed what happens when the dimensionality is further reduced to one dimension.