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Resonant X-ray diffraction study of multipole ordering in CePd$$_3$$S$$_4$$

Michimura, Shinji; Inami, Toshiya; Matsuoka, Eiichi*; Watahiki, Masanori*; Onodera, Hideya*

Rare-earth palladium bronzes RPd$$_3$$S$$_4$$ (R = La-Yb) crystallize in a cubic structure with the space group $$P$$m-3n. Except for R = Tm, the degeneracy of the orbital degree of freedom is expected to remain in the crystalline electric field (CEF) ground states of R$$^{3+}$$ in RPd$$_3$$S$$_4$$. Accordingly, the physical properties will be different from the properties of simple magnetic ordering compounds, since mulitpole order becomes possible too. CePd$$_3$$S$$_4$$ orders ferromagnetically below T$$_{rm C}$$ = 6.3 K. It was found that the magnetic structure of CePd$$_3$$S$$_4$$ is canted with a canting angle of 51 $$^{circ}$$ by neutron powder diffraction experiments. Such structure occurs in HoB$$_2$$C$$_2$$ too, where is caused by the simultaneous occurrence of antiferroquadrupolar (AFQ) and ferromagnetic (FM) orders. This calls for investigating on the quadrupolar ordering in RPd$$_3$$S$$_4$$. We performed resonant X-ray diffraction at the Ce-$$L_3$$ absorption edge on CePd$$_3$$S$$_4$$ to study the states of quadrupolar ordering in the FM state. We observed two reflections forbidden for crystal structure, 300 and 410 reflections. Both reflections grow below T$$_{rm C}$$ and be unambiguously related to the order parameter. In the azimuthal angle dependence of 410 reflection for both $$pi$$-$$pi$$' and $$pi$$-$$sigma$$' scattering processes, the periodicals are about 180 $$^{circ}$$. The intensity of the $$pi$$-$$sigma$$' scattering process is about 20 $$%$$ of the intensity of the $$pi$$-$$pi$$' scattering process. This result suggests that an $$O_2^0$$ type - AFQ ordering coexists with FM ordering.



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