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X-ray circular magnetic dichroism (XMCD), longitudinal ($\chi_{ac}$) andtransverse (TS) ac magnetic susceptibility have been measured in severalmembers of the $R$Co$_2$ series ($R$ = Dy, Ho, and Tm) as a function oftemperature and applied magnetic field. We show that parimagnetism is a generalbehavior along the $R$Co$_2$ ferrimagnetic series ($R$ being a heavy rare earthion). XMCD results evidence the presence of two compensation temperatures,defining two different parimagnetic configurations, which is a fully unexpectedresult. The inverse $\chi_{ac}$ curve exhibits a deviation from Curie-Weissbehavior which is recovered under applied magnetic field. The large excess ofpolarizability above the critical temperature proves the existence of anenhanced effective moment due to the presence of short range magneticcorrelations, which are also observed in TS measurements. The combination of TSand XMCD measurements allows to depict new magnetic phase diagrams for the$R$Co$_2$ series. A new scenario allowing to understand the observedphenomenology as a Griffiths phase-like behavior is proposed, where theamorphous $R$Co$_2$ represents the undiluted system case.

Parimagnetism in RCo$_2$ series (R=Dy, Ho, and Tm)