Magnetic ground state of the frustrated spin-$\frac{1}{2}$ chain compound $\beta \text{–}\mathrm{TeVO}{}_4$ at high magnetic fields

Frustrated spin-$\frac{1}{2}$ chains, despite the apparent simplicity, exhibit a remarkably rich phase diagram comprising vector-chiral (VC), spin-density-wave (SDW), and multipolar/spin-nematic phases as a function of the magnetic field. Here we report a study of $\beta \text{−}{\mathrm{TeVO}}_4$, an archetype of such compounds, based on magnetization and neutron diffraction measurements up to 25 T. We find the transition from the helical VC ground state to the SDW state at $\sim 3$ T for the magnetic field along the $a$ and $c$ crystal axes, and at $\sim 9$ T for the field along the $b$ axis. The high-field (HF) state, existing above $\sim 18$ T, i.e., above $\sim 1$/2 of the saturated magnetization, is an incommensurate magnetically ordered state and not the spin-nematic state, as theoretically predicted for the isotropic frustrated spin-1/2 chain. The HF state is likely driven by sizable interchain interactions and symmetric intrachain anisotropies uncovered in previous studies. Consequently, the potential existence of the spin-nematic phase in $\beta \text{−}{\mathrm{TeVO}}_4$ is limited to a narrow field range, i.e., a few tenths of a tesla bellow the saturation of the magnetization, as also found in other frustrated spin-$\frac{1}{2}$ chain compounds.

Figure 1

The crystal structure of $\beta \text{−}{\mathrm{TeVO}}_4$. Large blue spheres are vanadium atoms, small red spheres are oxygen atoms, and light brown spheres are tellurium atoms, whereas $J_1$ and $J_2$ denote the nearest- and next-nearest-neighbor exchange pathways.

Figure 2

Magnetic phase diagrams derived for the magnetic field applied (a) perpendicular and (b) parallel to the $b$ axis.

Figure 3

Magnetization measured for the magnetic field applied along the $a$, $b$, and $c$ crystallographic axes. Inset: Enlarged plot for easier visualization of the low-field transition for $B\left|\right|a$ and $B\left|\right|c$.

Figure 4

Neutron diffraction measurements of the ($-0.2$ 0 0.42) magnetic reflection and its satellite (existing only in the spin-stripe modulated phase) for magnetic field applied along the $b$ axis. The position of the magnetic reflection directly determines the magnetic wave vector. (a) The temperature dependencies of the intensity of the ($-0.2$ 0 0.42) reflection and its satellite in different magnetic fields. Solid lines are fits of the critical behavior $\propto {(T_{N1}-T)}^{2\beta }$, where $\beta$ is the critical exponent. (b)–(d) The temperature dependence of the measured $h$ and $l$ components ($k=0$) of the magnetic wave vector at 0, 4, and 12 T. Inset in (b) shows also the wave vector corresponding to the satellite reflection in the spin-stripe modulation. (e) The magnetic-field dependencies of the ($-0.2$ 0 0.42) reflection intensity at different temperatures. (f)–(h) The magnetic field dependence of the $h$ and $l$ components ($k=0$) of the magnetic wave vector measured at 1.7, 2.6, and 3.6 K. Inset in (g) shows also the wave vector corresponding to the satellite reflection in the spin-stripe modulation. Solid lines are guides to the eye, allowing for easier identification of the phase transitions indicated by the vertical arrows.

Figure 5

Neutron diffraction measurements of the (0.2 0 $-0.42$) magnetic reflection at 1.7 K for magnetic fields applied in the $ac$ plane, tilted by $\sim {30}^{\circ }$ from $a$ towards $c$. (a) The integrated intensity of the magnetic reflection, while (b) shows the measured $l$ and $h$ components ($k=0$) of the magnetic wave vector. The solid line indicates the theoretically predicted response for $l$ (see text for details).

Figure 6

Neutron diffraction maps of the reciprocal space at 1.7 K for several magnetic fields applied in the $ac$ plane, tilted for $\sim {30}^{\circ }$ from $a$ towards $c$. (a) Data collected in the VC phase at 3 T, (b) and (c) in the SDW phase at 12 and 17 T, respectively, and (d) in the HF phase at 21 T. The arrows show the magnetic reflections. Due to experimental limitation the maps are obtained by combining data sets measured at different field orientations within the $ac$ plane.