Magnetic properties of the geometrically frustrated $S=\frac{1}{2}$ antiferromagnets, ${\text{La}}_2{\text{LiMoO}}_6$ and ${\text{Ba}}_2{\text{YMoO}}_6$, with the B-site ordered double perovskite structure: Evidence for a collective spin-singlet ground state

Two B-site ordered double perovskites, ${\text{La}}_2{\text{LiMoO}}_6$ and ${\text{Ba}}_2{\text{YMoO}}_6$, based on the $S=\frac{1}{2}$ ion, ${\text{Mo}}^{5+}$, have been investigated in the context of geometric magnetic frustration. Powder neutron diffraction, heat capacity, susceptibility, muon-spin relaxation $\left(\mu \text{SR}\right)$, and ${}^{89}\text{Y}$ NMR-including magic-angle spinning (MAS) NMR data have been collected. ${\text{La}}_2{\text{LiMoO}}_6$ crystallizes in $P{2}_1/n$ with $a=5.59392\left(19\right)\text{Å}$, $b=5.69241\left(16\right)\text{Å}$, $c=7.88029\left(22\right)\text{Å}$, and $\beta =90.2601\left(30\right)°$ at 299.7 K, while ${\text{Ba}}_2{\text{YMoO}}_6$ is cubic, $Fm3m$, with $a=8.39199\left(65\right)\text{Å}$ at 297.8 K. ${\text{Ba}}_2{\text{YMoO}}_6$ shows no distortion from cubic symmetry even at 2.8 K in apparent violation of the Jahn-Teller theorem for a $t_{2\text{g}}^1$ ion. ${}^{89}\text{Y}$ NMR MAS data indicate about a 3% level of Y/Mo site mixing. ${\text{La}}_2{\text{LiMoO}}_6$ deviates strongly from simple Curie-Weiss (C-W) paramagnetic behavior below 150 K and zero-field-cooled/field-cooled (ZFC/FC) irreversibility occurs below 20 K with a weak, broad susceptibility maximum near 5 K in the ZFC data. A Curie-Weiss fit shows a reduced ${\mu }_{\text{eff}}=1.42{\mu }_{\text{B}}$, (spin $\text{only}=1.73{\mu }_{\text{B}}$) and a Weiss temperature, ${\theta }_{\text{C}}$, which depends strongly on the temperature range of the fit. Powder neutron diffraction and heat capacity show no evidence for long-range magnetic order to 2 K. On the other hand oscillations develop below 20 K in $\mu \text{SR}$ indicating at least short-range magnetic correlations. Susceptibility data for ${\text{Ba}}_2{\text{YMoO}}_6$ also deviate strongly from the C-W law below 150 K with a nearly spin only ${\mu }_{\text{eff}}=1.72{\mu }_{\text{B}}$ and ${\theta }_{\text{C}}=-219\left(1\right)\text{K}$. There is no discernible ZFC/FC irreversibility to 2 K. Heat capacity, neutron powder diffraction, and $\mu \text{SR}$ data show no evidence for long-range order to 2 K but a very broad, weak maximum appears in the heat capacity. The ${}^{89}\text{Y}$ NMR paramagnetic Knight shift shows a remarkable local spin susceptibility behavior below about 70 K with two components from roughly equal sample volumes, one indicating a singlet state and the other a strongly fluctuating paramagnetic state. Further evidence for a singlet state comes from the behavior of the relaxation rate, $1/T_1$. These results are discussed and compared with those from other isostructural $S=\frac{1}{2}$ materials and those based on $S=3/2$ and $S=1$.

Figure 1

(a) Crystal structure of ${\text{La}}_2{\text{LiMoO}}_6$, $P{2}_1/n$. Dark gray octahedra represent ${\text{MoO}}_6$ and light gray octahedral, ${\text{LiO}}_6$. Dashed circles represent the La ions. (b) Crystal structure of ${\text{Ba}}_2{\text{YMoO}}_6$, $Fm3m$. Dark gray octahedra represent ${\text{MoO}}_6$ and light gray octahedra, ${\text{YO}}_6$. The small crossed spheres represent the Ba ions.

Figure 2

(Color online) Rietveld refinement of neutron-diffraction data collected with two wavelengths, $2.37\text{Å}$ (a) and $1.33\text{Å}$ (b) at 297 K for ${\text{La}}_2{\text{LiMoO}}_6$. The vertical tick marks locate the Bragg peak positions and the lower horizontal line represents the difference between the data (crosses) and the model (solid line). A weak impurity peak near $70°$ was excluded for the $2.37\text{Å}$ pattern.

Figure 3

(Color online) The inverse magnetic susceptibility of ${\text{La}}_2{\text{LiMoO}}_6$ showing Curie-Weiss behavior below 150 K. (Inset) The susceptibility below 25 K at an applied field of 100 Oe. Note the ZFC/FC divergence below $\sim 20\text{K}$ and the broad maximum at 5 K in the ZFC data.

Figure 4

(Color online) Hysteresis loops for ${\text{La}}_2{\text{LiMoO}}_6$ at 5 and 20 K.

Figure 5

The difference neutron-diffraction pattern for ${\text{La}}_2{\text{LiMoO}}_6$, 3.3–25.0 K. The arrows show the positions expected for magnetic reflections assuming a type 1 fcc magnetic structure as found for ${\text{La}}_2{\text{LiRuO}}_6$ (Ref. 17).

Figure 6

(a) The heat capacity $C_{\text{p}}$ as a function of temperature for ${\text{La}}_2{\text{LiMoO}}_6$. (b) The region below 25 K showing two broad peaks at $\sim 18$ and 5 K.

Figure 7

(Color online) (a) $\mu \text{SR}$ results for ${\text{La}}_2{\text{LiMoO}}_6$. Corrected asymmetry at selected temperatures. (b) Temperature dependence of the amplitudes of the three frequencies (1–3) obtained from a fast Fourier transform (see text) of the data. The inset shows the result at 1.7 K where a fourth, low amplitude frequency at $\sim 2\text{MHz}$ is seen. This feature disappears above 5 K.

Figure 8

The refinement result of neutron-diffraction pattern for two wavelengths, $2.37\text{Å}$ (a) and $1.33\text{Å}$ (b), collected at 2.7 K for ${\text{Ba}}_2{\text{YMoO}}_6$. (c) Higher resolution $\left(\Delta d/d\sim 2\times {10}^{-3}\right)$, high angle data showing that cubic symmetry is retained. The vertical tick marks locate the Bragg peaks and the lower horizontal line is the difference between the data (circles) and the fit (solid line).

Figure 9

${}^{89}\text{Y}$ magic-angle spinning (MAS) NMR of ${\text{Ba}}_2{\text{YMoO}}_6$ at 288 K. The top is a simulation and the bottom are the data. The relative intensities of the two peaks are 19%/81% with an error of $+/-3\mathrm{\%}$.

Figure 10

(Color online) The susceptibility and inverse susceptibility of ${\text{Ba}}_2{\text{YMoO}}_6$ at an applied field of 200 Oe.

Figure 11

(Color online) Neutron-diffraction difference pattern, 2.7–297.5 K for ${\text{Ba}}_2{\text{YMoO}}_6$. The arrows show the expected positions of magnetic reflections assuming a type 1 fcc magnetic structure as found for ${\text{Ba}}_2{\text{YRuO}}_6$ (Ref. 6).

Figure 12

(Color online) (a) The heat capacity of ${\text{Ba}}_2{\text{YMoO}}_6$ and ${\text{Ba}}_2{\text{YNbO}}_6$. (b) Magnetic heat capacity of ${\text{Ba}}_2{\text{YMoO}}_6$.

Figure 13

(Color online) ZF $\mu \text{SR}$ data for ${\text{Ba}}_2{\text{YMoO}}_6$ for two temperatures. The lines are fits to a single exponential relaxation function, see text.

Figure 14

(Color online) ${}^{89}\text{Y}$ NMR line shape at various temperatures. (a) Representative line shapes at selected temperatures for ${\text{Ba}}_2{\text{YMoO}}_6$. (b) Evolution of the line shape below 75 K.

Figure 15

(Color online) Temperature dependence of the paramagnetic Knight shift, $-{}^{89}K$ (a) and the relaxation rate, $1/T_1$ (b) for the “main” (lower frequency) peak and the singletlike (higher frequency) peak of Fig. 14b. The dotted line is an empirical fit $1/T_1\sim C/T\text{exp}\left(-\Delta /k_{\text{B}}T\right)$ with $\Delta /k_{\text{B}}\sim 140\text{K}$. Integrated intensities of the two are roughly equal.

Figure 16

(Color online) Scaling of the paramagnetic Knight shift $\left(-{}^{89}K\right)$ with the bulk susceptibility for ${\text{Ba}}_2{\text{YMoO}}_6$. The derived hyperfine coupling constant, $A=-23.4\text{kOe}/{\mu }_{\text{B}}$. The intercept gives the sum of the Van Vleck and diamagnetic susceptibility components.

Figure 17

The Curie-tail subtracted bulk susceptibility of ${\text{Ba}}_2{\text{YMoO}}_6$.

Figure 18

${\text{Mo}}^{5+}\left({\text{Re}}^{6+}\right)$ sites in ${\text{La}}_2{\text{LiMoO}}_6$ $\left({\text{Sr}}_2{\text{CaReO}}_6\right)$ showing two edge-sharing tetrahedra within the monoclinic unit cell. The four exchange pathways calculated in Table are indicated.