Origin of the magnetic anomaly and tunneling effect of europium on the ferromagnetic ordering inEu8−xSrxGa16Ge30(x=0,4)type-I clathrates

Abstract

Systematic dc magnetization studies using the Banerjee criterion, Kouvel-Fisher, and magnetocaloric effect methods provide physical insights into the origin of the magnetic anomaly and the tunneling effect of europium on the ferromagnetic ordering in Eu${}_{8}$Ga${}_{16}$Ge${}_{30}$ type-I clathrates. We show that Eu${}_{8}$Ga${}_{16}$Ge${}_{30}$ undergoes a second-order magnetic transition (SOMT) at ${T}_{C}$ \ensuremath{\sim} 35 K, resulting from the magnetic interaction between the Eu${}^{2+}$ ions at the Eu2 sites, followed by a secondary magnetic transition at ${T}_{L}$ \ensuremath{\sim} 10 K (indicated as a magnetic anomaly in previous studies), as a result of the magnetic interaction between the Eu${}^{2+}$ ions at the Eu1 and Eu2 sites. The critical exponent \ensuremath{\beta} = 0.388 is close to that predicted from the three-dimensional Heisenberg model (\ensuremath{\beta} = 0.365), while the critical exponent \ensuremath{\gamma} = 0.956 is close to that predicted from the mean-field model (\ensuremath{\gamma} = 1). The substitution of Sr${}^{2+}$ for Eu${}^{2+}$ retains the SOMT but largely reduces the transition temperatures (${T}_{C}$ \ensuremath{\sim} 15 K and ${T}_{L}$ \ensuremath{\sim} 5 K), with the critical exponents \ensuremath{\beta} = 0.521 and \ensuremath{\gamma} = 0.917 close to those predicted from the mean-field model (\ensuremath{\beta} = 0.5 and \ensuremath{\gamma} = 1). These results point to the important fact that the tunneling of Eu${}^{2+}$ between the four equivalent sites in the tetrakaidecahedral cage tends to prevent the occurrence of a long-range ferromagnetic ordering in the type-I clathrate materials.