Field-induced double dome and Bose-Einstein condensation in the crossing quantum spin chain system ${\mathrm{AgVOAsO}}_4$

We present inelastic neutron-scattering data on the quantum paramagnet ${\mathrm{AgVOAsO}}_4$ that establish this system as a $S=1/2$ alternating spin chain compound and provide a direct measurement of the spin gap $\mathrm{\Delta }=1.2\mathrm{meV}$. We also present experimental evidence for two different types of field-induced magnetic order between ${\mu }_0{H}_{c1}=8.4\mathrm{T}$ and ${\mu }_0{H}_{c2}=48.9\mathrm{T}$, which may be related to Bose-Einstein condensation (BEC) of triplons. Thermodynamic measurements in magnetic fields up to 60 T and temperatures down to 0.1 K reveal a $H-T$ phase diagram consisting of a dome encapsulating two ordered phases with maximum ordering temperatures of 3.8 and 5.3 K, respectively. This complex phase diagram is not expected for a single-$\vec{Q}$ BEC system and therefore establishes ${\mathrm{AgVOAsO}}_4$ as a promising multi-$\vec{Q}$ BEC candidate capable of hosting exotic vortex phases.

Figure 1

Crystal structure of ${\mathrm{AgVOAsO}}_4$. V atoms are large green spheres, O atoms are small yellow spheres, and As atoms are black spheres. The Ag atoms are not shown for clarity. (a) Crystal structure viewed obliquely along the $c$ axis. (b) Exchange paths viewed roughly along the $c$ axis. For clarity, the $J_a$ interaction is shown only for a single $ac$ plane and only the V sites are shown. (c) The crystal structure viewed along the (110) direction. (d) The crystal structure viewed along the ($1\overline{1}0$) direction. In (c) and (d), chains of type i and type ii are labeled accordingly. (e) Type-i structural chain with exchange interactions $J$ and $J^{\prime }$ labeled for vectors $d_i$ and $d_i^{\prime }$, respectively. (f) Type-ii structural chain with vectors $d_{ii}$ and $d_{ii}^{\prime }$ shown.

Figure 2

(a), (b) Color contour plots of the $E_i=7.5\text{−}\mathrm{meV}$ HYSPEC data for ${\mathrm{AgVOAsO}}_4$ at $T=50$ and $3.2\mathrm{K}$. A gapped magnetic excitation spectrum is clearly visible in the low-temperature data. The data to the left of the black dashed line in (b) were collected using a single orientation for the HYSPEC detector bank. (c) Color contour plot for the alternating chain model described in the text with best-fit parameters $J=3.43\left(7\right)\mathrm{meV}$ and $J^{\prime }=2.25\left(9\right)\mathrm{meV}$. The INS data were only fit over the $Q\text{−}\hslash \omega$ region presented in this figure.

Figure 3

The powder-averaged first frequency moment as a function of wave-vector transfer for both incident energies used in the HYSPEC measurement. An overall normalization factor has been applied so the two datasets can be plotted with the same $y$ axis. The solid curves represent a simultaneous fit of the data to the first frequency moment expression described in the text with a single exchange interaction.

Figure 4

Temperature dependence of a constant-$Q$ cut with an integration range $Q=[0.35,2]{\AA }^{-1}$ from the $E_i=7.5\mathrm{meV}$ HYSPEC dataset. The solid curve superimposed on the 3.2 K data represents a constant-$Q$ cut taken from the best-fit simulation shown in Fig. 2.

Figure 5

Specific heat divided by temperature $C\left(T\right)/T$ vs $T$ for magnetic fields between 9 and 14 T with nuclear Schottky contributions subtracted. The measurement at 11 T is the first curve that develops a broad maximum at $\sim 2.2\mathrm{K}$ that becomes more pronounced and shifts to higher $T$ in stronger fields (marked with black arrows). Additionally, a second anomaly appears at $\sim 1\mathrm{K}$ in the 14-T measurement, as indicated by the red arrow. The upper inset shows $C\left(T\right)/T$ in zero magnetic field, with a broad hump around 13 K arising from the thermal population of the triplet state. The lower inset displays the energy-level scheme for a spin dimer system with both intradimer and interdimer exchange coupling under the application of an external magnetic field.

Figure 6

Specific heat divided by temperature $C\left(T\right)/T$ vs $T$ for magnetic fields between 15 and 27.6 T. Two distinct maxima are observed that move to higher temperatures with increasing field and represent clear evidence for multiple field-induced phase transitions below the onset of the saturated paramagnetic phase at $H_{c2}$. The left inset displays $C\left(T\right)/T$ for the 10 T and maximum field 27.6 T measurements. The right inset shows the calculated entropy $S=\int C\left(T\right)/TdT$ in units $\mathrm{R}ln2$ for the 27.6 T measurement with (i.e., $\mathrm{\Delta }S$) and without (i.e., $S$) subtraction of the 10 T $C\left(T\right)/T$ data.

Figure 7

Magnetization $M\left(H\right)$ vs magnetic field $H$ measured in high fields to 60 T shown for initial temperatures $T_0$ between 0.56 and 10 K (data are offset vertically for better visibility). The inset shows $dM/dH$ close to $H_{c2}$ for the measurements at 0.56 and 4 K with a clear maximum followed by a step down indicating a double phase transition. In contrast, a more smooth behavior in $dM/dH$ is observed at 10 K.

Figure 8

Magnetization $M\left(H\right)$ vs magnetic field $H$ in the field range 7.4 to 12 T for $T$ between 0.1 and 0.5 K. The measurements are offset from one another to ensure better visibility. We observe two changes of slope in $M\left(H\right)$ at ${\mu }_0{H}_{c1}=8.4\mathrm{T}$ and ${\mu }_0{H}_{c{1}^{\prime }}=10.5\mathrm{T}$, which identify two field-induced phase transitions. The inset shows $M\left(T\right)/H$ vs $T$ collected in fields of 8.5, 8.8, and 9 T. A broad maximum is observed in these data that is used to define the $H_{c1}$ phase boundary.

Figure 9

$H-T$ phase diagram of ${\mathrm{AgVOAsO}}_4$ obtained from specific heat, MCE, and magnetization experiments. We observe clear signatures of two different field-induced ordered states. Lines of constant entropy obtained under adiabatic conditions in pulsed fields illustrate the MCE and confirm the double dome structure of the phase diagram. A power-law fit $T\propto |H-H_{c1}{|}^{\nu }$ of the phase boundary at $H_{c1}$ reveals 0.51 as the critical exponent. The inset shows the derivative $\partial T/\partial H$ for MCE measurements with zero-field temperatures $T_0=3$ and 7 K. Arrows mark the critical fields $H_{c1}$, $H_{c{1}^{\prime }}$, $H_{c{2}^{\prime }}$, and $H_{c2}$.