Resonant magnetic scattering of multiferroic HoMnO$_{3}$ in an applied electric field

The multiferroic material HoMnO$_{3}$ displays electrical polarization $P_{c}$~=~5.6~$\mu $C~cm$^{-2}$ along the hexagonal \textbf{c} axis below the Curie temperature $T_{C}$ = 875 K and antiferromagnetic Mn$^{3+}$ ordering at the N\'{e}el temperature, $T_{N}$~= 75 K. The recently reported ferromagnetic response of Ho$^{3+}$ by an applied electric field opens up the possibility of electric field controlled magnetic data storage. However, both the role of Ho$^{3+}$ in magnetism and details of the magnetic structure of Ho$^{3+}$ have been topics of significant debate. Using element specific x-ray resonant magnetic scattering and x-ray magnetic circular dichroism, we have focused on resolving this controversy. Both quadrupole and dipole Ho $L_{III}$ resonances were observed below 40 K. In zero field, Ho$^{3+}$ orders antiferromagnetically with moments along the c direction below 40 K and undergoes a transition to a different magnetic order below 4.5 K. The role of Ho$^{3+}$ upon the application of an external electric field in the temperature range 1.7-80~K will be discussed. -- The support by U.S. DOE (DE-AC02-07CH11358 and DE-AC02-06 CH11357) is acknowledged.