${}^{51}\mathrm{V}$ NMR study of the quasi-one-dimensional alternating chain compound ${\mathrm{BaCu}}_2{\mathrm{V}}_2{\mathrm{O}}_8$

${}^{51}\mathrm{V}$ nuclear magnetic resonance (NMR) studies in polycrystalline sample of ${\mathrm{BaCu}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ reveal the existence of nonzero spin densities, with unequal magnitudes, at the two vanadium sites, viz., ${\mathrm{V}}_1$ and ${\mathrm{V}}_2$ and hence the participation of ${\mathrm{VO}}_4$ tetrahedra to the intrachain and interchain exchange interaction. The behavior of $K_{\mathrm{iso}}$ below 200 K provide a clear signature of the reduction of ${\mathrm{Cu}}^{2+}$ spin susceptibility within the chain. Furthermore, there exist unique hyperfine coupling constants for ${\mathrm{V}}_1$ and ${\mathrm{V}}_2$ sites. This data also confirms the existence of only one spin component and the ground state corresponds to a nonmagnetic spin singlet. The $T$ dependence of $K_{\mathrm{iso}}$ above 120 K follows the nature of ${\chi }_{\text{spin}}\left(T\right)$ proposed by Hatfield for alternating chain model. While below 80 K, it follows the expression for ${\chi }_{\mathrm{spin}}$ of a one-dimensional chain with a spin gap $\Delta$. From the $K_{\mathrm{iso}}$ data we have obtained $\Delta =215\pm 5\mathrm{K}$, which is smaller than that determined from the magnetic susceptibility $(\Delta =230\mathrm{K})$ data. The hyperfine field for ${\mathrm{V}}_1$ and ${\mathrm{V}}_2$ sites are 24.6 and $14.4\pm 1.0\mathrm{kOe}∕{\mu }_B$, respectively, with a ratio of 1.7 between them. Thus the exchange path $\mathrm{Cu}-\mathrm{O}-{\mathrm{V}}_2-\mathrm{O}-\mathrm{Cu}$ in ${\mathrm{BaCu}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ is not negligible. The spin-lattice relaxation time, $T_1$, for both the sites are identical in the range 300–40 K and vary from 3 ms to 10 s. $1∕T_1$ follows an activated behavior and provides a gap parameter $\Delta =380\mathrm{K}$, which is much higher than that obtained from shift data. Moreover, the magnitude of $1∕T_{1}T$ decreases more rapidly than that of $K_{\mathrm{iso}}$ below 75 K.

Figure 1

(Color online) Temperature dependence of magnetic susceptibility of ${\mathrm{BaCu}}_2{\mathrm{V}}_2{\mathrm{O}}_8$. ▵: the raw data; 엯: the data after subtraction the ${\chi }_0$ and the Curie term. The thick solid line below 120 K represents the result of fitting to the equation $\chi \left(T\right)={\chi }_0+{\chi }_{\mathrm{cw}}\left(T\right)+{\chi }_{\text{spin}}\left(T\right)$. The thin dotted line above 120 K represents the results of the fitting to the chain model given by Eq. (1).

Figure 2

(Color online) Typical ${}^{51}\mathrm{V}$ NMR spectra of polycrystalline ${\mathrm{BaCu}}_2{\mathrm{V}}_2{\mathrm{O}}_8$ at different temperatures recorded at 7 tesla. The dotted vertical line represents the ${}^{51}\mathrm{V}$ reference position. Inset shows the ${}^{51}\mathrm{V}$ NMR spectrum at 295 K along with a theoretically fitted line obtained as mentioned in the text.

Figure 3

(Color online) Temperature dependence of $K_{\mathrm{iso}}$ for ${}^{51}\mathrm{V}$ NMR in ${\mathrm{BaCu}}_2{\mathrm{V}}_2{\mathrm{O}}_8$. 엯: ${\mathrm{V}}_1$; ●: ${\mathrm{V}}_2$. The dotted lines above 100 K represent the functional form given by Hatfield [Eq. (1)]. Inset shows the functional form given by the spin term ${\chi }_{\text{spin}}\left(T\right)=a{T}^{-0.5}\exp (-\Delta ∕T)$.

Figure 4

(Color online) Variation of ${}^{51}\mathrm{V}$ NMR shift against ${\chi }_{\text{spin}}$, determined as mentioned in Sec. 3A, with temperature as implicit parameter. Inset shows the variation of shift for ${\mathrm{V}}_1$ site against ${\mathrm{V}}_2$ site.

Figure 5

(Color online) Temperature dependence of ${}^{51}\mathrm{V}$ spin-lattice relaxation time $\left(T_1\right)$; ●: at 7 tesla; 엯: at 2.14 tesla. Inset shows variation of $1∕T_1$ with $T^{-1}$.

Figure 6

(Color online) Temperature dependence of $1∕\left(T_{1}T{K}_{\mathrm{iso}}\right)$ corresponding to ${\mathrm{V}}_1$ and ${\mathrm{V}}_2$ sites of ${}^{51}\mathrm{V}$ NMR.