Magnetic and structural properties of the intermetallic ${\mathrm{Ce}}_{(1-x)}{\mathrm{La}}_x{\mathrm{CrGe}}_3$ series of compounds

The ${\mathrm{Ce}}_{(1-x)}{\mathrm{La}}_x{\mathrm{CrGe}}_3$ $(x=0, 0.19, 0.43, 0.58, \mathrm{and} 1)$ intermetallic compound system has been investigated by magnetization measurements and neutron scattering techniques to determine the effect of La doping on the magnetic ordering and exchange interaction between Cr ions. The structural and magnetic characterization in this series was first verified by x-ray diffraction and bulk magnetization measurements. The samples exhibit the known hexagonal perovskite structure ($P{6}_3/\mathrm{mmc}$ space group) and have a single magnetic phase according to magnetization measurements. In this paper, the ferromagnetic ordering temperature for Cr evolves smoothly from a range of 68 K to 77 K for ${\mathrm{CeCrGe}}_3$ to a range of 91 K to 96 K for ${\mathrm{LaCrGe}}_3$ as La replaces Ce. Magnetization results indicate the formation of domain walls below the transition temperature for all ${\mathrm{Ce}}_{(1-x)}{\mathrm{La}}_x{\mathrm{CrGe}}_3$ systems investigated. Neutron results indicate ordered magnetic Cr moments aligned along the $c$ axis for the $x=1$ ${\mathrm{LaCrGe}}_3$ system, as well as for $x=0.19$, 0.43, and 0.58, which contrasts with the $x=0 {\mathrm{CeCrGe}}_3$ where the moments order in the ab plane.

Figure 1

(a) FC and ZFC ${\chi }_{\text{DC}}$ for ${\mathrm{CeCrGe}}_3$ and ${\mathrm{LaCrGe}}_3$. (b) Inverse of ${\chi }_{\text{DC}}$ as a function of temperature. Solid lines are the modified Curie-Weiss law fit. (c) Derivative of DC susceptibility as a function of temperature. All error bars are shown and represent 1 $\sigma$. However, the error bars may be smaller than the symbol.

Figure 2

(a) FC and ZFC ${\chi }_{\text{DC}}$ for ${\mathrm{Ce}}_{(1-x)}{\mathrm{La}}_x{\mathrm{CrGe}}_3$ ($x=0.19$, 0.43, 0.58). (b) Inverse of ${\chi }_{\text{DC}}$ as a function of temperature. Solid lines are the modified Curie-Weiss law fit. (c) Derivative of DC susceptibility as a function of temperature. All error bars are shown and represent 1 $\sigma$. However, the error bars may be smaller than the symbol.

Figure 3

${\chi }_{\text{AC}}$ for ${\mathrm{Ce}}_{(1-x)}{\mathrm{La}}_x{\mathrm{CrGe}}_3$ ($x=0$, 0.19, 0.43, 0.58) .(a) real component ($\chi$'). (b) Imaginary component ($\chi$”) and (c) derivative of ${\chi }_{\text{AC}}$ real component as a function of temperature. All error bars are shown and represent 1 $\sigma$. However, the error bars may be smaller than the symbol.

Figure 4

${\chi }_{\text{AC}}$ for ${\mathrm{LaCrGe}}_3$ (a) real component ($\chi$') (b) imaginary component ($\chi$”) and (c) Derivative of ${\chi }_{\text{AC}}$ real component as a function of temperature. All error bars are shown and represent 1 $\sigma$. However, the error bars may be smaller than the symbol.

Figure 5

Crystallographic structure of hexagonal perovskite-type ($P{6}_3$/mmc space group) ${R\text{CrGe}}_3$ (R = La, Ce) viewed (a) perpendicular to the $c$ direction in a polyhedral representation (b) in the $ab$ plane. d1 and d2 are the intralayer and interlayer distances, respectively.

Figure 6

NPD results with Rietveld refinement for ${\mathrm{Ce}}_{(1-x)}{\mathrm{La}}_x{\mathrm{CrGe}}_3$ ($x=0$, 0.19, 0.43, 0.58, 1) at room temperature. Blue continuous lines are the Rietveld refinement fit, red lines represent the difference between the observed and calculated intensities, and the small vertical black lines indicate the theoretical peaks position of the $P{6}_3$/mmc space group. The peaks distinguished by the symbol $*$ indicate the minor impurity phase (La($\mathrm{Ce}){\mathrm{Ge}}_2$). Insets ($x=0.19$ and $x=0.58$) display the impurity peak. All error bars are shown and represent 1 $\sigma$. However, the error bars may be smaller than the symbol.

Figure 7

NPD patterns of ${\mathrm{Ce}}_1-x{\mathrm{La}}_x{\mathrm{CrGe}}_3$ ($x=0$, 0.19, 0.43, 0.58, 1) at 5 K collected on BT1. Vertical red lines indicate the theoretical magnetic peak positions with hexagonal $P{6}_3$/mm'c' symmetry (Cr spin align to the c axis). Arrow for the ${\mathrm{LaCrGe}}_3$ pattern points to the FM peak at $2\theta$ = $22.5^{\circ }$. The peaks distinguished by the symbol $*$ indicate the minor impurity phase $\left[\mathrm{La}\right(\mathrm{Ce}){\mathrm{Ge}}_2]$. All error bars represent 1 $\sigma$ and are shown, but they may be smaller than the symbol.

Figure 8

Normalized magnetic intensity peaks from the difference in intensity between 5 K and high temperature in the paramagnetic phase for ${\mathrm{CeCrGe}}_3$, ${\mathrm{Ce}}_{0.81}{\mathrm{La}}_{0.19}{\mathrm{CrGe}}_3$, ${\mathrm{Ce}}_{0.58}{\mathrm{La}}_{0.43}{\mathrm{CrGe}}_3$, ${\mathrm{Ce}}_{0.42}{\mathrm{La}}_{0.58}{\mathrm{CrGe}}_3$, and ${\mathrm{LaCrGe}}_3$. All error bars represent 1 $\sigma$ and are shown, but they may be smaller than the symbol.

Figure 9

NPD for ${\mathrm{CeCrGe}}_3$ measured at 5 K with Rietveld refinement fit. Top: Direction of Cr magnetic moment (${\mu }_{\text{Cr}}$) along the $c$ axis. Bottom: Direction of Cr magnetic moment parallel to the ab plane. Blue lines are the Rietveld refinement fit and brown lines are the residual. On the top, vertical black lines indicate the theoretical magnetic peak positions with hexagonal $P{6}_3$/mm'c' symmetry. On the bottom, vertical black lines indicate the position of theoretical peaks for the structural phase and vertical red lines indicate the theoretical magnetic peak positions with one-bar triclinic symmetry. All error bars represent 1 $\sigma$ and are shown, but they may be smaller than the symbol.

Figure 10

${\mathrm{CeCrGe}}_3$ results. (a) Magnetic intensity peaks from the difference between 5 K and 90 K and (b) the difference between 0 T and 7 T at 5 K. All error bars represent 1 $\sigma$ and are shown but they may be smaller than the symbol.

Figure 11

Temperature dependence of the (1 0 0) integrated magnetic Bragg peak intensities. Because the (1 0 0) intensity is strong for LaCrGe3 and weak for the Ce doped compositions, it was necessary to count longer to obtain sufficient signal to measure the order parameter. The blue solid curves show the mean-field function fit. The vertical red dashed arrows indicate the $T_C$ obtained from the fit. All error bars are shown and represent 1 $\sigma$. However, the error bars may be smaller than the symbol.

Figure 12

Lattice parameters $a$, $c$, and unit cell volume at room temperature as a function of La doping at room temperature. The error bars represent 1 $\sigma$.

Figure 13

(a) Effective magnetic moment (${\mu }_{\text{eff}}$), (b) transition temperature ($T_C^{\left(\text{DC}\right)}$, $T_C^{\left(\text{AC}\right)}$, and $T_C^{(\text{BT}-7)}$), and (c) magnetic moment of the Cr atoms (${\mu }_{\text{Cr}}$) from NPD as a function of La doping ($x$) at room temperature. The value ${\mu }_{\text{Cr}}$ in this paper is calculated in units of ${\mu }_B$/Cr. [The value ${\mu }_{\text{Cr}}$(Ref.) for ${\mathrm{CeCrGe}}_3$ is parallel to the ab plane and for ${\mathrm{LaCrGe}}_3$ is parallel to the $c$ axis]. Error bars where indicated represent one standard deviation.