GLYPH<s45>GLYPH<s52> GLYPH<s45>GLYPH<s50> GLYPH<s48> GLYPH<s50> GLYPH<s52> GLYPH<s45>GLYPH<s49> GLYPH<s48> GLYPH<s49> GLYPH<s32>GLYPH<s48> GLYPH<s32>GLYPH<s48> GLYPH<s46>GLYPH<s48>GLYPH<s48>GLYPH<s53>GLYPH<s116> GLYPH<s32>GLYPH<s48> GLYPH<s46>GLYPH<s48>GLYPH<s49>GLYPH<s116> GLYPH<s32>GLYPH<s48> GLYPH<s46>GLYPH<s48>GLYPH<s50>GLYPH<s116> GLYPH<s79> GLYPH<s114>GLYPH<s98>GLYPH<s105>GLYPH<s116>GLYPH<s97>GLYPH<s108>GLYPH<s32>GLYPH<s109>GLYPH<s97>GLYPH<s103>GLYPH<s110>GLYPH<s101>GLYPH<s116>GLYPH<s105>GLYPH<s122>GLYPH<s97>GLYPH<s116>GLYPH<s105>GLYPH<s111>GLYPH<s110> GLYPH<s67>GLYPH<s104>GLYPH<s101>GLYPH<s109>GLYPH<s105>GLYPH<s99> GLYPH<s97>GLYPH<s108>GLYPH<s32>GLYPH<s112>GLYPH<s111>GLYPH<s116>GLYPH<s101>GLYPH<s110>GLYPH<s116>GLYPH<s105>GLYPH<s97>GLYPH<s108> FIG. 8: (Color online). The magnetization M as a function of the electron chemical potential at the field f =12 / 49 with different temperatures. In the above discussions on the orbital magnetization of the 2D kagom´ e lattice, we have concentrated on the zero-temperature limit and omitted finite-temperature effect. Now let us briefly consider the more realistic cases in which the finite-temperature effect is included. Figure 8 plots the orbital magnetization at the field f =12 / 49 with different temperatures k$_{B}$T =0, 0 . 005, 0 . 01, and 0 . 02, respectively. From Fig. 8, one can find that the magnetic oscillations are suppressed by thermal broadening. In summary, we have theoretically investigated the orbital magnetization of a 2D kagom´ e lattice in a perpendicular magnetic field. Here, the orbital magnetization includes a con- ventional term and a Berry-phase term, which play different roles in metallic and insulating regions. As examples, we have carefully discussed the orbital magnetization and its two components at the fields f =1 / 4, 1 / 3, and 1 / 6, respectively. By varying the Fermi energy µ$_{0}$ , we have obtained the following results: (i) The conventional term and the Berry-phase term give the opposite contributions, with their magnitudes increasing (decreasing) with in- creasing (decreasing) the Fermi energy in metallic regions; (ii) The conventional term keeps unchanged in insulating regions; (iii) The slope of the Berry-phase term in insulating regions is proportional to the system’s Hall conductance. When the flux is applied near a commen- surate one (for example, 1 / 4), the magnetic dHvA oscillations develop a fractal structure, i.e., the orbital magnetization rapidly oscillates when the Fermi energy varies through the split subbands. The finite-temperature effect has also been shown to suppress the oscillating 12 IV. SUMMARY