Fig. 1. (a) Reverse electron transfer from F- to Ca2+; (b) Spin conversion of radical pairs under the magnetic excitation; (c) Detached dislocations from stoppers in a magnetic field.

Fig. 2. Relationship between cutting directions and slip systems relative to the (111) cutting plane.

Fig. 3. (a) Calculated M values versus six activated slip systems and their averages value along $\left[ 11\bar{2} \right]$ cutting direction at varying magnetic field directions; (b) Average values of M for all four cutting directions with respect to different magnetic field directions.

Fig. 4. (a) Experimental setup of micro-indentation tests under a weak magnetic field. (b) Magnetic field-assisted micro plunge-cutting setup on an ultra-precision machining centre. (c) Schematic of micro plunge-cutting tests. (d) Varying magnetic field direction during micro plunge-cutting tests. (NMF: no magnetic field; MF: magnetic field).

Fig. 5. Height images of residual impressions after micro-indentation tests: (a) 3D view; (b) 2D view.

Fig. 6. Surface pile-up height-distance curves of a pair of residual impressions under the magnetic field and a load of (a) 0.25 N and (b) 0.5 N.

Fig. 7. Pile-up heights for each path under the magnetic field and a load of (a) 0.25 N and (b) 0.5 N.

Fig. 8. Enlarged plastic zone with the application of the magnetic field and a load of (a) 0.25 N and (b) 0.5 N.

Fig. 9. Suppression of crack growth under the magnetic field and a load of (a) 0.25 N and (b) 0.5 N.

Fig. 10. Dislocation slip traces induced by the micro-indentation with a load of 0.5 N in the (a) absence and (b) presence of the magnetic field. Schematic of dislocation source, dislocation loops, surface slip traces during indentation: (c) front view; (d) top view.

Fig. 11. Machined surface morphology of micro-grooves along $\left[ 11\bar{2} \right]$ cutting direction with varying magnetic field directions.

Fig. 12. Plunge-cutting depth-distance curves of micro-grooves along $\left[ 11\bar{2} \right]$ cutting direction with varying magnetic field directions. (DBT: ductile–brittle transition).

Fig. 13. Critical undeformed chip thickness at ductile-brittle transition with varying magnetic field and cutting directions.

Fig. 14. Cutting force curves along $\left[ 11\bar{2} \right]$ cutting direction at varying magnetic field directions.

Fig. 15. Cutting force at ductile-brittle transition position with varying magnetic field and cutting directions.

Fig. 16. (a) Relative change in critical undeformed chip thickness; (b) Relative change in cutting force at ductile–brittle transition; (c) Value of M at 5° lattice rotation angle; (d) Value of M at 10° lattice rotation angle with different cutting directions under varying magnetic field directions. (${{d}_{\text{c}}}$: undeformed chip thickness).

Fig. 17. Schematic of crystal rotation induced by shear deformation or rotational deformation during the cutting process.

Fig. 18. Machined subsurface of CaF2 single crystal along $\left[ 11\bar{2} \right]$ cutting direction without magnetic field: (a) cross-sectional transmission electron microscopy TEM (XTEM) overview of subsurface damage; (b), (c), (d) high-resolution TEM (HRTEM) images and the corresponding selected area electron diffraction (SAED) patterns of Regions 1, 2, 3 in (a).

Fig. 19. Machined subsurface of CaF2 single crystal along $\left[ 11\bar{2} \right]$ cutting direction with a magnetic field (0°): (a) cross-sectional transmission electron microscopy TEM (XTEM) overview of subsurface damage; (b), (c), (d) high-resolution TEM (HRTEM) images and the corresponding selected area electron diffraction (SAED) patterns of Regions 1, 2, 3 in (a).

Fig. 20. Machined subsurface of CaF2 single crystal along $\left[ 11\bar{2} \right]$ cutting direction with a magnetic field (90°): (a) cross-sectional transmission electron microscopy TEM (XTEM) overview of subsurface damage; (b), (c), (d) high-resolution TEM (HRTEM) images and the corresponding selected area electron diffraction (SAED) patterns of Regions 1, 2, 3 in (a).