Magnetic-charge ordering and phase transitions in monopole-conserved square spin ice

Abstract

Magnetic-charge ordering and corresponding magnetic/monopole phase transitions in spin ices are the emergent topics of condensed matter physics. In this work, we investigate a series of magnetic-charge (monopole) phase transitions in artificial square spin ice model using the conserved monopole density algorithm. It is revealed that the dynamics of low monopole density lattices is controlled by the effective Coulomb interaction and the Dirac string tension, leading to the monopole dimerization which is quite different from the dynamics of three-dimensional pyrochlore spin ice. The condensation of the monopole dimers into monopole crystals with staggered magnetic-charge order can be predicted clearly. For the high monopole density cases, the lattice undergoes two consecutive phase transitions from high-temperature paramagnetic/charge-disordered phase into staggered charge-ordered phase before eventually toward the long-range magnetically-ordered phase as the ground state which is of staggered charge order too. A phase diagram over the whole temperature-monopole density space, which exhibits a series of emergent spin and monopole ordered states, is presented.

Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice

“…The lack of monopole crystallization in our quasi–three-dimensional artificial square ice stands in contrast to charge crystallites observed in two-dimensional artificial kagome spin ice ( 12 ). This can be attributed to the chemical potential in this type of system being well above the critical chemical potential ( 33 ) of μ c = 0.80777 under which charge crystallization can be expected.…”

“…The Bjerrum association approach assumes charges to be either correlated or uncorrelated. However, images of charge distributions reveal that charges also exist in more complicated states ( 33 ). For example, charges may slightly correlate by aligning with next-next nearest neighbors, lie adjacent to two or more charges, or any other combinatoric possibilities.…”

Effects of magnetic monopoles charge on the cracking reversal processes in artificial square ices

“…11 , where more details about the model can be found. We have to lay emphasis on the fact that the emergent model introduced here is somewhat related to several works, which deal with models of emergent monopoles and Coulomb phase, usually applied to study the monopole density during magnetization or thermal processes in square or pyrochlore lattices 17,[19][20][21][22][23][24][25] .…”

Magnetization dynamics of weakly interacting sub-100 nm square artificial spin ices

“…1 were also theoretically investigated using a standard Metropolis Monte Carlo algorithm, assuming that the nanoelements forming the system are identical. Here, the spin Hamiltonian has the form 53 :denoting terms for the dipolar interaction and externally applied field, respectively.…”