Singlet ground state in the alternating spin-$\frac{1}{2}$ chain compound ${\mathrm{NaVOAsO}}_4$

We present the synthesis and a detailed investigation of structural and magnetic properties of polycrystalline ${\mathrm{NaVOAsO}}_4$ by means of x-ray diffraction, magnetization, electron spin resonance (ESR), and ${}^{75}\mathrm{As}$ nuclear magnetic resonance (NMR) measurements as well as density-functional band structure calculations. Temperature-dependent magnetic susceptibility, ESR intensity, and NMR line shift could be described well using an alternating spin-$1/2$ chain model with the exchange coupling $J/k_{\mathrm{B}}\simeq 52$ K and an alternation parameter $\alpha \simeq 0.65$. From the high-field magnetization measured at $T=1.5$ K, the critical field of the gap closing is found to be $H_{\mathrm{c}}\simeq 16$ T, which corresponds to the zero-field spin gap of ${\mathrm{\Delta }}_0/k_{\mathrm{B}}\simeq 21.4$ K. Both NMR shift and spin-lattice relaxation rate show an activated behavior at low temperatures, further confirming the singlet ground state. The spin chains do not coincide with the structural chains, whereas the couplings between the spin chains are frustrated. Because of a relatively small spin gap, ${\mathrm{NaVOAsO}}_4$ is a promising compound for further experimental studies under high magnetic fields.

Figure 1

(Left) Crystal structure of ${\mathrm{NaVOAsO}}_4$. The black dashed lines separate the spin chains. The ${\mathrm{VO}}_6$ and ${\mathrm{AsO}}_4$ polyhedra are shown in red and green colors, respectively. (Right) Spin model showing the alternating ($J,J^{\prime }$) crossing chains along the V-O-As-O-V path and the frustrated inter-chain couplings in a different orientation. $J_{\mathrm{c}}$ represents the interaction along the structural chains via V-O-V path.

Figure 2

Powder x-ray diffraction pattern (open circles) for ${\mathrm{NaVOAsO}}_4$ at two different temperatures ($T=15$ and 300 K). The solid line represents the full-profile refinement, with the vertical bars showing the expected Bragg peak positions, and the lower solid blue line representing the difference between the observed and calculated intensities.

Figure 3

The lattice constants ($a$, $b$, $c$), monoclinic angle ($\beta$), and unit cell volume ($V_{\mathrm{cell}}$) are plotted as a function of temperature. The solid line in the bottom panel represents the fit using Eq. (2).

Figure 4

$\chi \left(T\right)$ measured at $H=0.5$ T with the solid line representing the fit using Eq. (5). The dotted line shows the ${\chi }_{\mathrm{imp}}$, and the dashed line shows the fit on the ${\chi }_{\mathrm{spin}}$ data using Eq. (6). (Inset) $1/\chi \left(T\right)$ data along with the fit using Eq. (4) (solid line).

Figure 5

Magnetization ($M$) vs $H$ measured at $T=1.5$ K (after subtracting the paramagnetic background) using pulsed magnetic field. The critical field of gap closing $H_{\mathrm{c}}\simeq 16$ T is marked with an arrow. (Inset) $dM/dH$ vs $H$ highlights the position of $H_{\mathrm{c}}$.

Figure 6

(Top) Temperature-dependent ESR intensity, $I_{\mathrm{ESR}}\left(T\right)$, obtained by integrating the ESR spectra of the polycrystalline ${\mathrm{NaVOAsO}}_4$ sample. The solid line represents the fit as described in the text. (Inset) Typical spectra (symbols) at $T=300$ and 3.6 K together with the fits using the powder-averaged Lorentzian shape for the uniaxial $g$-factor anisotropy. (Bottom) $1/I_{\mathrm{ESR}}$ vs $T$ along with the fit (see the text). (Top inset) Temperature-dependent $g$-factor ($g_{\parallel }$ and $g_{\perp })$ obtained from the Lorentzian fit. (Bottom inset) $I_{\mathrm{ESR}}$ vs $\chi$ with temperature as an implicit parameter.

Figure 7

Temperature-dependent field-sweep ${}^{75}\mathrm{As}$ NMR spectra of ${\mathrm{NaVOAsO}}_4$ measured at $\nu =50.44$ MHz. The solid lines are the fits to the spectra at $T=70$ and 115 K. The vertical dashed line corresponds to the ${}^{75}\mathrm{As}$ resonance position of the reference GaAs sample.

Figure 8

(Top) ${}^{75}\mathrm{As}$ NMR shift as a function of temperature. The solid line is the fit of $K\left(T\right)$ by Eq. (11). (Inset) $K$ vs $\chi$ (measured at 7 T) with temperature as an implicit parameter. The solid line is the linear fit. (Bottom) $(K-K_0)T^{1/2}$ vs $1/T$ and $(K-K_0)T^{-1/2}$ vs $1/T$ along the left and right $y$ axes, respectively. The solid lines are the fits using activation laws $(K-K_0)T^{1/2}\propto e^{-{\mathrm{\Delta }}_{1\mathrm{D}}^K/k_{\mathrm{B}}T}$(1D model) with ${\mathrm{\Delta }}_{1\mathrm{D}}^K/k_{\mathrm{B}}\simeq 21.84$ K and $(K-K_0)T^{-1/2}\propto e^{-{\mathrm{\Delta }}_{3\mathrm{D}}^K/k_{\mathrm{B}}T}$(3D model) with ${\mathrm{\Delta }}_{3\mathrm{D}}^K/k_{\mathrm{B}}\simeq 13.2$ K, respectively.

Figure 9

(Top) $1/T_1$ is plotted as a function of temperature. (Inset) Recovery of the longitudinal magnetization as a function of waiting time $t$ at three different temperatures. Solid lines are the fits using Eq. (13). (Bottom) $1/T_1$ is plotted against $1/T$. The solid line is the fit in the low-temperature region using Eq. (16).

Figure 10

Comparison of magnetization curves for ${\mathrm{AgVOAsO}}_4$ and ${\mathrm{NaVOAsO}}_4$ measured at 1.5 K (paramagnetic background subtracted). Dashed lines are simulated curves for alternating spin chains uniformly coupled in 2D by an effective interchain coupling $J_{\perp }$. The fit parameters are $J=34\mathrm{K}$, $\alpha =0.60$, and $J_{\perp }/J=-0.15$ for ${\mathrm{AgVOAsO}}_4$ and $J=51\mathrm{K}$, $\alpha =0.63$, and $J_{\perp }/J=-0.05$ for ${\mathrm{NaVOAsO}}_4$.