Absence of structural correlations of magnetic defects in the heavy-fermion compound ${\text{LiV}}_2{\text{O}}_4$

Magnetic defects arising from structural imperfections have pronounced effects on the magnetic properties of the face-centered cubic normal-spinel structure compound ${\text{LiV}}_2{\text{O}}_4$. High-energy x-ray diffraction studies were performed on ${\text{LiV}}_2{\text{O}}_4$ single crystals to search for superstructure peaks or other evidence of spatial correlations in the arrangement of the crystal defects present in the lattice. Entire reciprocal lattice planes were mapped out with the help of synchrotron radiation. No noticeable differences in the x-ray diffraction data between a crystal with high magnetic defect concentration and a crystal with low magnetic defect concentration were found. This indicates the absence of any long-range periodicity or short-range correlations in the arrangements of the crystal/magnetic defects.

Figure 1

(Color online) Magnetic susceptibilities $\chi$ versus temperature $T$ of ${\text{LiV}}_2{\text{O}}_4$ crystals containing different concentrations of magnetic defects (see Table ). The susceptibilities are measured in 1 T magnetic field.

Figure 2

(Color online) Molar magnetization $M$ versus applied magnetic field $H$ isotherms at low temperatures $\left(T\le 5\text{K}\right)$ for crystals (a) 2, (b) 9, and (c) 10, respectively. The four data sets shown in each of Figs. 2a, 2b, 2c are the $M\left(H\right)$ isotherms at four different temperatures 5, 3, 2.5, and 1.8 K. Figure 2d shows the magnetic defect contribution to the magnetization for each crystal $M_{\text{defect}}=M-\chi H$ plotted versus $H/\left(T-{\theta }_{\text{defect}}\right)$. The solid lines are plots of the second term in Eq. (1) for each crystal with the parameters listed in Table .

Figure 3

High-energy x-ray diffraction patterns of ${\text{LiV}}_2{\text{O}}_4$ single crystals 2 and 9. Figures 3a, 3b, 3c show the patterns for reciprocal planes of crystal 2 perpendicular to the [001], $\left[\overline{1}01\right]$, and $\left[\overline{1}11\right]$ directions, respectively. Figures 3d, 3e, 3f show the patterns for reciprocal planes of crystal 9 perpendicular to the [001], $\left[\overline{1}01\right]$, and $\left[\overline{1}11\right]$ directions, respectively. In (f), the extended features indicated by white circles are reflections that are not allowed by the symmetry. The reflection spots enclosed by the white lines in (c) and (f) are from the reciprocal $\left(hkl\right)$ layer through the origin which is perpendicular to the $\left[\overline{1}11\right]$ direction with $\left(hkl\right)\cdot \left[\overline{1}11\right]=0$. The outer spots are from the next layers with $\left(hkl\right)\cdot \left[\overline{1}11\right]=\pm 1$. The patterns shown have the same aspect ratio as that of the patterns recorded in the detector.

Figure 4

High-energy x-ray diffraction pattern of the reciprocal lattice plane perpendicular to the $\left[\overline{1}11\right]$ direction of ${\text{LiV}}_2{\text{O}}_4$ crystal 10.