Unexpected magnetic phase in the weakly ordered spin-$\frac{1}{2}$ chain cuprate ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$

The magnetic phase diagram of a spin-$\frac{1}{2}$ chain antiferromagnet ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ is studied by an ultrasound phase-sensitive detection technique. The system is in the extreme proximity of the Luttinger-liquid quantum-critical point and we observe an unusually strong effect of magnetic field, which is very weak compared to the in-chain interaction, on the Néel ordering temperature. Inside the ordered phase, we detect an unexpected, field-induced continuous phase transition. The transition is accompanied by softening of magnetic excitation observed by electron-spin resonance, which in previous work [E. G. Sergeicheva et al., Phys. Rev. B 95, 020411(R) (2017)] was associated with a longitudinal (amplitude) mode of the order parameter. These results suggest a transition from a transverse collinear antiferromagnet to an amplitude-modulated spin-density-wave phase in a very weak magnetic field, which is unexpected for a system of weakly coupled Heisenberg spin-$\frac{1}{2}$ chains.

Figure 1

The temperature dependence of the relative change of sound velocity and sound attenuation of ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ measured at several values of external magnetic field [(a), (b)], and their isothermal magnetic field dependence measured at various temperatures [(c), (d)]. Curves, from top to bottom, are vertically shifted for clarity. The magnetic field is applied along the $c$ axis, and magnetic ordering and field-induced transitions are marked by down ($\downarrow$) and up ($\uparrow$) arrows, respectively.

Figure 2

The relative change of sound velocity and sound attenuation measured vs temperature at several values of external magnetic field [(a), (b)], and vs magnetic field at various temperatures [(c), (d)]. Curves, from top to bottom, are vertically shifted for clarity. The magnetic field is applied along the $b$ axis, and magnetic ordering and field-induced transitions are marked by down ($\downarrow$) and up ($\uparrow$) arrows, respectively.

Figure 3

The magnetic phase diagram of ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ obtained from ultrasound measurements at $H\parallel b$ (left panel) and $H\parallel c$ (right panel). Open and solid symbols represent features observed in field and temperature scans, respectively, and error bars represent both the widths and systematic uncertainties in determining the positions of the corresponding features. Lines are shown as a guide for the eye; different magnetic phases are distinguished by colors. Arrows indicate the magnetic field and magnetic moment directions in the $a,b,c$ crystallographic coordinate system shown in the left panel.

Figure 4

High-field part of the frequency-field diagram of the magnetic resonance spectrum in the ordered phase of ${\mathrm{Sr}}_2{\mathrm{CuO}}_3$ measured at $T=1.5\mathrm{K}$ for $H\parallel c$; symbols are experimental points including data from Ref. [7]; the solid line is a fit to the equation $h\nu =\sqrt{{\left(h\delta \right)}^2+{\left(g_{\text{eff}}{\mu }_B\right)}^2{(H-H_c)}^2}$ with the critical field ${\mu }_0{H}_c=9.45\mathrm{T}$ (marked by arrow) and the residual gap $\delta =13\mathrm{GHz}$. The dashed line corresponds to a critical-type linear dependence with $\delta =0$. The lower panel shows the lowest-temperature curves for $\mathrm{\Delta }v/v$ and $\mathrm{\Delta }\alpha$ from Figs. 1 and 1(d); the anomalies at $H_c$ are pointed out by arrows and their width is shown by a horizontal bar.