Entropy-induced confinement in two-dimensional magnetic monopole gases

Abstract

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 proposed a two-dimensional magnetic monopole gas (2DMG), confined at the interface between spin-ice ($R_2$Ti$_2$O$_7$, $R$ = Dy, Ho) and antiferromagnetic iridate ($R_2$Ir$_2$O$_7$, $R$ = Dy, Ho), which hosts monopoles with a net charge. The mechanism behind the 2D confinement of the monopole gas remains unclear. In this work, we demonstrate that entropy is a key factor in the 2D confinement of this monopole gas. 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 model accurately reproduces the monopole distribution obtained from the 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. Our findings reveal the entropic mechanisms in 2DMG, enabling the manipulation of emergent quasiparticles at material interfaces.

Figures (4)

• Figure 1: Spin configurations of various monopole distributions in a $R_2$Ti$_2$O$_7$/$R_2$Ir$_2$O$_7$ heterostructure. Small black arrows represent the local moment of a rare earth ion, big white arrows represent the polarization direction of a tetrahedron. Tetrahedral sites are color-coded to show different magnetic charges: $Q$ = 0 for grey, $Q$ = $q_\text{M}$ for green, $Q$ = 2$q_\text{M}$ for blue, and $Q$ = -2$q_\text{M}$ for red. Spin and mononopole structures of two extreme cases are shown here: (a) all the monpoles live in the same layer, six layers off the interface, and (b) all the monopoles live in the same layer at the interface.
• Figure 2: Monopole distribution at $T \sim 0\,\text{K}$. (a) Illustration of monopole distribution in a $R_2$Ti$_2$O$_7$/$R_2$Ir$_2$O$_7$ heterostructure. More monopoles are concentrated near to interface. (b) Monopole concentration $\rho$ as a function of layer number $n$ of the 2DMG at $T \sim 0\,\text{K}$ from the spin Monte Carlo simulation and from the entropy maximization. (c) Schematics of Monte Carlo simulation on spin model, and entropy maximization on the monopole model, both are performed at the $T \sim 0\,\text{K}$. $\mathscr{H}$ is the energy of the system as defined in \ref{['Eq:twoadded']}.
• Figure 3: Monopole distribution at finite temperature with magnetic field. (a) and (b) Illustration of monopole distribution in a $R_2$Ti$_2$O$_7$/$R_2$Ir$_2$O$_7$ heterostructure with magnetic field point toward the iridate side and titanate side, respectively. (c) and (d) Monopole distribution function $\rho(n)$ calculated by spin Monte Carlo simulation and modified entropy maximization, at $T$ = 0.1 K ($k_{\text{B}}T / J_{\text{eff}} = 0.07$), with a field of 20 mT ($\mu B / J_{\text{eff}} = 0.05$) (point toward iridate side) and -4 mT ($\mu B / J_{\text{eff}} = -0.01$) (point toward titanate side), respectively. The calculation results without field at quasi-ground state for each model are overlayed with light green color for comparison.
• Figure 4: Temperature-magnetic field diagram of the 2DMG. (a) Interface monopole sheet density $n_\text{2D}$ defined as $n_\text{2D} = \sum_{n} \rho(n)$, as a function of out-of-plane relative magnetic field $\mu B / J_{\text{eff}}$ calculated by Monte Carlo simulation on spin model and entropy maximization method at $T$ = 0.1 K ($k_{\text{B}}T / J_{\text{eff}} = 0.07$). (b) $n_\text{2D}$ as a map of $T$ and $B$ calculated by both methods. (c) Interface monopole depth defined as $d = \sum_{n} n\rho(n)/\sum_{n} \rho(n)$ as a function of $\mu B / J_{\text{eff}}$ calculated by both method at $T$ = 0.1 K ($k_{\text{B}}T / J_{\text{eff}} = 0.07$). (d) $d$ as a map of $T$ and $B$ calculated by both methods. Three regions are labeled as I, II, and III. Dashed lines represent boundaries between different regions.