Structural correlation with the Griffiths phase in disordered magnetic systems

In this work we report detailed experimental results and band structure calculations to establish a subtle link between the crystal structure and Griffiths phase (GP) behavior for the geometrically frustrated intermetallic $\mathrm{Gd}{\mathit{M}}_x{\mathrm{Sn}}_{2-\delta }$ (M = Co, Ni, Cu; $0<\mathit{x}<1,0\le \delta \le 0.22$) compounds. The crystal structure analysis through powder x-ray diffraction patterns reveals that the atomic positions of the M atoms in the GP analogs are slightly displaced in comparison to those of non-GP members of this series. Further, the band structure calculation shows that this slightly differing atomic position of M atoms results in narrowing in M d bands and the ferromagnetic clusters centered on the T atoms are responsible for GP behavior. This effect is insignificant in non-GP members.

Figure 1

XRD patterns measured at 12 K (top) and at room temperature (bottom) for (a) ${\mathrm{GdCo}}_{0.17}{\mathrm{Sn}}_{2-\delta }$, (b) ${\mathrm{GdCo}}_{0.27}{\mathrm{Sn}}_{2-\delta }$, (c) ${\mathrm{GdNi}}_{0.32}{\mathrm{Sn}}_{2-\delta }$, and (d) ${\mathrm{GdCu}}_{0.17}{\mathrm{Sn}}_{2-\delta }$.

Figure 2

SEM image in the BSE mode for (a) ${\mathrm{GdCo}}_{0.17}{\mathrm{Sn}}_{2-\delta }$ and (b) ${\mathrm{GdCo}}_{0.27}{\mathrm{Sn}}_{2-\delta }$.

Figure 3

Temperature dependence of the magnetic susceptibilities of $\mathrm{Gd}{\mathit{M}}_x{\mathrm{Sn}}_{2-\delta }$ (M = Co, Ni, and Cu) measured at 100 Oe magnetic field in the ZFC configuration. Inset: Temperature dependence of heat capacity of $\mathrm{Gd}{\mathit{M}}_x{\mathrm{Sn}}_{2-\delta }$ (M = Co, Ni, and Cu) in the absence of any externally applied magnetic field, plotted in units of the universal gas constant R.

Figure 4

Temperature dependence of the inverse magnetic susceptibilities of ${\mathrm{GdCo}}_{0.27}{\mathrm{Sn}}_{2-\delta }$ measured at different externally applied magnetic fields under FC (top) and ZFC (bottom) configurations during a warming cycle. Inset (a): Temperature dependence of the inverse magnetic susceptibilities of ${\mathrm{GdCo}}_{0.17}{\mathrm{Sn}}_{2-\delta }$ measured at $H=100$ Oe in the ZFC configuration. Inset (b): Temperature dependence of the inverse magnetic susceptibilities of ${\mathrm{GdNi}}_{0.32}{\mathrm{Sn}}_{2-\delta }$ measured at $H=100$ Oe in the ZFC configuration. Inset (c): Temperature dependence of the inverse magnetic susceptibilities of ${\mathrm{GdCu}}_{0.27}{\mathrm{Sn}}_{2-\delta }$ measured at $H=100$ Oe in the ZFC configuration.

Figure 5

(a) ${\mathrm{CeNiSi}}_2$-type crystal structure of $\mathrm{Gd}{\mathit{M}}_x{\mathrm{Sn}}_{2-\delta }$ (M = Co, Ni, and Cu) compounds, showing intergrowth sequences of ${\mathrm{BaAl}}_4$ and ${\mathrm{AlB}}_2$-like slabs. (b) Part of the atomic arrangement in the crystal structure emphasizing different interatomic distances and angles. (c) ${\mathrm{BaAl}}_4$ slab viewed approximately down the $b$ axis, i.e., the planar square nets of 4(Sn2) capped alternatively above and below with M atoms.

Figure 6

Distances and angles between various atoms of (a) ${\mathrm{GdCo}}_{0.17}{\mathrm{Sn}}_{2-\delta }$, a representative of non-GP, and (b) ${\mathrm{GdCo}}_{0.27}{\mathrm{Sn}}_{2-\delta }$, a representative of GP, in $\mathrm{Gd}{\mathit{M}}_x{\mathrm{Sn}}_{2-\delta }$ (M = Fe, Co, Ni, and Cu; $0<x<1$).

Figure 7

Partial density of states (PDOS) for ${\mathrm{GdCoSn}}_2$ using the structural parameters of (a) ${\mathrm{GdCo}}_{0.17}{\mathrm{Sn}}_{2-\delta }$ and (b) ${\mathrm{GdCo}}_{0.27}{\mathrm{Sn}}_{2-\delta }$. (c) PDOS for ${\mathrm{GdFeSn}}_2$ using the structural parameters of ${\mathrm{GdFe}}_{0.17}{\mathrm{Sn}}_{2-\delta }$. $E_F$ represents Fermi energy at 0 K.