Recent experiments have established a strong case for ${\mathrm{Ce}}_2$(Zr, Sn, ${\mathrm{Hf})}_2{\mathrm{O}}_7$ to host $\pi$-flux quantum spin ice (QSI). However, an irrefutable conclusion still requires strong, multifaceted evidence. In dipolar-octupolar (DO) compounds, external magnetic fields only strongly couple with the dipolar component ${\tau }_z$ along its local $z$-axis in contrast to octupolar components ${\tau }^{x,y}$. This gives rise to the unique ways magnetic fields interact with the system and, in turn, provides us with a variety of tuning knobs to generate comprehensive experimental results. In this work, we focus on magnetic fields along the (110), (111), and (001) directions and present a plethora of remarkable experimental signatures to probe the underlying physics of $\pi$-flux QSI using gauge mean field theory (GMFT) and Monte Carlo simulations. In particular, we present unique signatures in magnetic field-dependent phase diagrams, equal-time and dynamical structure factors, and magnetostriction signatures.

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• Frustrated magnetism
• Spin ice
• Pyrochlores
• Mean field theory
• Monte Carlo methods