Investigation of the monopole magneto-chemical potential in spin ices using capacitive torque magnetometry.

The single-ion anisotropy and magnetic interactions in spin-ice systems give rise to unusual non-collinear spin textures, such as Pauling states and magnetic monopoles. The effective spin correlation strength ($J_{eff}$) determines the relative energies of the different spin-ice states. With this work, we display the unique capability of capacitive torque magnetometry (CTM) in characterizing the magneto-chemical potential (MCP) associated with monopole formation. We build a magnetic phase diagram of Ho$_2$Ti$_2$O$_7$, showing that the field-induced magnetic phase transitions cannot be described by a single value of $J_{eff}$. Rather, the MCP depends on the spin sublattice ($\alpha$ or $\beta$), i.e., the Pauling state, involved in the transition. Monte-Carlo simulations using the dipolar-spin-ice (DSI) Hamiltonian support our findings of a field-dependent MCP, but the model underestimates $J_{eff}$ for the $\beta$-sublattice. The inclusion of long-range exchange terms in the Hamiltonian is needed for a full description of spin ices.