Entropy-induced confinement in two-dimensional magnetic monopole gases

Magnetic monopole quasiparticles in spin ice materials hold the potential for exploring new frontiers of physics that extend beyond Maxwell's equations. We have previously presented a two-dimensional magnetic monopole gas (2DMG) with a net charge, confined at the interface between spin ice $({R}_{2}{\mathrm{Ti}}_{2}{\mathrm{O}}_{7},R=\mathrm{Dy},\phantom{\rule{0.16em}{0ex}}\mathrm{Ho})$ and antiferromagnetic iridate $({R}_{2}{\mathrm{Ir}}_{2}{\mathrm{O}}_{7},R=\mathrm{Dy},\phantom{\rule{0.16em}{0ex}}\mathrm{Ho})$, which is proposed to be driven by entropy. However, this mechanism needs to be verified and studied systematically. In this work, we quantitatively demonstrate that entropy is a key factor in the 2D confinement of the monopole gas. Starting from the nearest-neighbor interaction, we reveal that the competition between the entropy of spin ice, which favors the 2D confinement, and the entropy of the monopoles' random walks, which favors the deconfinement, dictates the distribution of the monopoles within a few layers close to the interface. Our entropy-based monopole model accurately reproduces the monopole distribution obtained from the energy-based spin model, affirming that 2D confinement is entropy driven. We further employ both models to show that the monopole distribution can be manipulated by an external magnetic field and temperature, holding promise for next-generation devices based on magnetic monopoles. In the presence of dipolar interactions, entropy continues to play a crucial role in controlling 2DMG behavior at finite temperatures. Our findings reveal the entropic mechanisms in 2DMG, enabling the manipulation of emergent quasiparticles at material interfaces.