This paper reports detailed maps of magnetic behavior in very small single crystals of α‑RuCl3. The crystals studied here are under 100 micrometers across and keep a monoclinic crystal structure when cooled. Using sensitive torque measurements, the authors trace how the material’s magnetic state changes with field direction and strength and find patterns that differ from larger, rhombohedral samples studied earlier.

The team used a piezo‑cantilever to measure magnetic torque. Magnetic torque is the twisting force a magnetic sample feels when a magnetic field is not aligned with its magnetization. They applied magnetic fields up to 16 tesla and rotated the field almost continuously in three orthogonal crystallographic planes. The experiment picked out phase transitions as sharp anomalies in the raw torque signal and in higher derivatives with respect to angle and field magnitude.

Why study this material? α‑RuCl3 is a leading candidate to show unusual magnetism driven by strong spin–orbit coupling and bond‑dependent interactions known from the Kitaev model. In many larger crystals α‑RuCl3 switches from a monoclinic to a rhombohedral structure on cooling and orders magnetically near 7 kelvin. The small crystals here remain monoclinic to low temperature and order more sharply at 14 kelvin. The new torque maps therefore show reduced rotational symmetry, require substantially higher fields to remove the spontaneous magnetic order, and reveal distinct field‑induced phases compared with rhombohedral samples.

The authors compare their torque measurements with mean‑field calculations of plausible magnetic Hamiltonians that respect the monoclinic symmetry. Mean‑field calculations are an approximate, widely used way to relate measurements to models of interacting magnetic moments. From this comparison they propose minimal magnetic structure models that explain the observed phase regions in their diagrams.