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.
Highlights
Magnetic-charge ordering and corresponding magnetic/monopole phase transitions in spin ices are the emergent topics of condensed matter physics
Such a spin alignment is reminiscent of proton positions in water ice following the so-called ‘ice rule’[5], while a huge difference of spin ice from water ice is the remarkable fluctuations and flips of these spins, which generate a set of highly interested physical issues
For the spin ice model with conserved monopoles, the ρ = 0 and ρ = 1 cases are especially important, because the ρ = 0 case corresponds to the long-range V1 ground state for an infinite lattice, and we need to mention that the case ρ = 0 is a reference model to study the monopole interactions
Summary
Magnetic-charge ordering and corresponding magnetic/monopole phase transitions in spin ices are the emergent topics of condensed matter physics. We employ the Monte Carlo simulation to investigate square spin ice lattices with different monopole densities. We employ the Monte Carlo method to track the magnetic states and associated phase transitions in such dipolar square spin ice model with different monopole density ρ.
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