Tuning dipolar interactions in artificial spin ices - From Ising to Potts spins

Since the proposal in 2006 [1] to use nanomagnets patterned by top-down techniques to mimic "artificial spins", the studies of artificial spin systems has attracted wide interest [2]. As a matter of facts, the possibility to design "upon request" arbitrary network thanks to lithography and the possibility to determine completely the "spin" configuration with magnetic imaging offer a wide playground for statistical physics. Up to now only Ising spin systems have been studied. However, beyond Ising spins, statistical physics and condensed matter physics have shown the interest of other spin models like q-state Potts models (q different spin orientation) or even XY model (isotropic in plane orientation).
In this talk, we introduce the dipolar 4-state Potts model. It is shown that on a square lattice, depending on the angle between spins and lattice, the system present very different properties like antiferromagnetic order, spin ice state (2 in-2 out ice rule) and even dipolar ferromagnetism.

This model has been realized experimentally. At room temperature, the magnets present a uniform state with 4 equivalent directions. Upon heating at 350 °C the magnets switch from one direction to another. It is therefore possible to simply drive the system toward its ground state. The magnetic configurations determined by magnetic force microscopy reveals the importance of the dipolar coupling as the different expected ground states (antiferromagnetic, spin ice and ferromagnetic) are indeed observed [3]. It is noticeable that these very different properties are obtained with the same "spins" (magnetic elements) and same lattice. The exact process of magnetization evolution, differences with "Ising" systems and future prospects will be discussed.

[1] R. F. Wang et al., Nature 439, 04447 (2006)
[2] C. Nisoli et al., Rev. Mod. Phys. 85, 1473 (2013) and L.J. Heyderman and R.L. Stamps, J.of Physics: Cond. Matter 25, 363201 (2013)
[3] D. Louis et al., Nat. Mat. 17, 1076 (2018)