Local imaging of the phase transition in single crystal Nd$_2$Fe$_{14}$B*

The magnetic microstructure of hard magnets is of interest for immediate industrial applications and for fundamental understanding of the relationship between microscopic and macroscopic magnetic properties in materials. Of particular interest is Nd$_2$Fe$_{14}$B, which shows strong anisotropy with an easy axis along the c-axis at room temperature, but undergoes a phase transition around T$\sim$135K to an easy cone magnetization where the magnetic moments are canted away from the c-axis. Here we present magneto-optical Kerr effect (MOKE) and magnetic force microscope (MFM) measurements to investigate the spin-reorientation phase transition in single crystal Nd$_2$Fe$_{14}$B. The MFM measurements resolve a continuous change in the domain structure from rounded flower-shaped domains of a lateral extent $\sim$200 nm-$\sim$7$\mu$m to larger rectangular features of typical width $\sim$1$\mu$m and length $\sim$10$\mu$m-$\sim$30$\mu$m. By imaging the same surface area in small temperature steps across the phase transition we track the evolution of single features.