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Nature of the field-induced charge ordered phase (phase II) ofSmRu$_4$P$_{12}$ has been investigated by resonant x-ray diffraction (RXD) andpolarized neutron diffraction (PND), focusing on the relationship between theatomic displacements and the antiferromagnetic (AFM) moments of Sm. From theanalysis of the interference between the non-resonant Thomson scattering andthe resonant magnetic scattering, combined with the spectral function obtainedfrom x-ray magnetic circular dichroism, it is shown that the AFM moment of Smprefers to be parallel to the field ($m_{\text{AF}} \parallel H$), giving riseto large and small moment sites around which the P$_{12}$ and Ru cage contractand expand, respectively. This is associated with the formation of thestaggered ordering of the $\Gamma_7$-like and $\Gamma_8$-like crystal-fieldstates, providing a strong piece of evidence for the charge order. PND was alsoperformed to obtain complementary and unambiguous conclusion. In addition,isotropic and continuous nature of the phase II is demonstrated by thefield-direction invariance of the interference spectrum in RXD. Crucial role ofthe $p$-$f$ hybridization is shown by resonant soft x-ray diffraction at the P$K$-edge ($1s\leftrightarrow 3p$), where we detected a resonance due to thespin polarized $3p$ orbitals reflecting the AFM order of Sm.

Isotropic parallel antiferromagnetism in the magnetic-field-induced charge-ordered state of SmRu$_4$P$_{12}$ caused by $p$-$f$ hybridization