Magnetization plateaus

Magnetization plateaus in SrCu₂(BO₃)₂

With T. Jolicoeur and S. M. Girvin we studied the magnetization plateaus which have been observed experimentally in the strontium-copper borate compound SrCu₂(BO₃)₂ (picture above) by Kageyama et al.. At low temperatures this quasi two-dimensional spin-1/2 system shows plateaus at 1/8, 1/4 and 1/3 of its fully saturated magnetic moment as a function of applied magnetic field. We proposed an approach based on a two-dimensional Jordan-Wigner transformation which establishes a connection between these plateaus and the well-known integer quantum Hall effect.
We performed a mean-field approximation for the statitistical gauge field. Within this approximation, the problem maps onto fermions hoping onto the lattice in the presence of a static and uniform magnetic field, that is the Hofstadter problem. An Hofstadter spectrum corresponding to the Shastry-Sutherland lattice is displayed below, it is caracterized by a fractal structure.

References:

• Article for non-specialists (.pdf, in French) published in Phases Magazine, Lettre du DRECAM et du SPhT.
• G. Misguich, T. Jolicoeur, S. M. Girvin, Phys. Rev. Lett. 87, 097203 (2001).
• Th. Jolicoeur, G. Misguich and S. M. Girvin, cond-mat/0204161