Spin dynamics and magnetic ordering in the quasi-one-dimensional $S=\frac{1}{2}$ antiferromagnet ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$

The $S=\frac{1}{2}$ quasi-one-dimensional antiferromagnet ${\mathrm{K}}_2{\mathrm{CuSO}}_4{X}_2(X=\mathrm{Cl}$, Br) exhibits peculiar Dzyaloshinskii-Moriya (DM) interactions that are uniform along its spin chains and antiparallel with respect to neighboring chains. This feature has received much attention recently because it leads to spin frustration, however, the spin dynamics around $T_{\mathrm{N}}$ and magnetic structure have not been reported. Here we report magnetic behaviors of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$. The orthorhombic crystal structure of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$, which is identical to $\mathrm{K}{}_2{\mathrm{CuSO}}_4{X}_2$, was verified. The results of the thermodynamic measurements suggest that this compound has moderately strong intra- and interchain interaction for investigation of the spin state around $T_{\mathrm{N}}$. The inelastic neutron scattering and muon spin relaxation and rotation measurements reveal the presence of a two-spinon continuum, and below $T_{\mathrm{N}}$, the long-range order develops. However, the obtained critical exponent is $\beta =0.18$, which is not indicative of a three-dimensional magnetic system; instead, one-dimensional (1D) spin correlation likely affects the formation of magnetic ordering in ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$. There is a possibility that ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ is a model compound for investigation of DM-induced frustration effects in a 1D quantum spin system.

Figure 1

(a) The crystal structure of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$. The ${\mathrm{Cu}}^{2+}$ ions (black) displayed with nearby oxygen (red) and chlorine ions (green). The linear spin chain of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$, which forms due to the intrachain exchange interaction through the Cu-Cl-Cl-Cu path (green solid line). The pink dashed lines indicate the interchain exchange interaction. (b) and (c) The ${\mathrm{Cu}}^{2+}$ ions are six coordinated in a distorted octahedral geometry. The ${\mathrm{Na}}^{+}$ ions (yellow balls) displayed with ${\mathrm{SO}}_4$ ions (yellow tetrahedra).

Figure 2

(a) Temperature dependence of the magnetic susceptibility $\chi$ (open red circles) of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ measured at 0.1 T. The blue solid line is a fit to the Bonner-Fisher curve for $S=\frac{1}{2}$ linear chain Heisenberg antiferromagnet. (b) The temperature dependence of the total specific heat (filled red circles) divided by temperature $\left(C/T\right)$ for zero magnetic field. The filled green squares are the theoretical data of the linear spin chain model, which was computed by the quantum Monte Carlo method. Inset shows a linear-linear plot of the theoretical data.

Figure 3

(a) Contour map at constant-$E$ cut and neutron scattering intensity at $T=1.5$ K with incident neutron energy of 3.68 meV. The energy window was from $E=1$ to 2 meV, and the scattering was integrated over $-1\le k\le 1$. INS spectra (b) along the $c^{*}$ axis and (c) along the $a^{*}$ axis of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ measured at 1.5 K with incident neutron energy of 3.68 meV. The intensities were integrated over $h$ from $-4$ to 4, $k$ from 2 to 2 and $k$ from $-2$ to 2, $l$ from 6 to 3. The superimposed gray solid lines indicate the lower and upper energy boundaries of the continuum given by $(\pi J_{\mathrm{Na}}/2)|sin\left(\pi h\right)|$ and $\pi J_{\mathrm{Na}}|sin(\pi h/2)|$ [25].

Figure 4

(a) Constant-$E$ cuts of the measured scattering intensity of Fig. 3. The superimposed orange and blue solid lines indicate the lower and upper energy boundaries of the continuum. The intensity in each panel is integrated within the energy range shown in the upper right corner. The gray thick lines are the fits using the approximate, semiempirical Müller ansatz expression (see Eq. (4) in Ref. [26]). (b) The intrachain interaction $J_{\mathrm{Na}}$ refined by fitting cuts at different $E$.

Figure 5

(a) INS spectrum along the $a^{*}$ axis of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ measured at 30 K with incident neutron energy of 3.68 meV. (b) Constant-$E$ cuts of the measured scattering intensity of (a). The superimposed blue solid lines indicate the upper energy boundaries of the continuum. The intensity in each panel is integrated within the energy range shown in the lower or upper right corner.

Figure 6

(a) ZF-$\mu \mathrm{SR}$ spectra measured on a powder sample of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ at representative temperatures. The thick lines behind the data points are curves fitted with a fixed constant background of $a_{\mathrm{BG}}=6.1$ (see text). (b) ZF-$\mu \mathrm{SR}$ spectra measured at 0.34 and 1.0 K, showing the fitted time window up to $20\mu \mathrm{s}$. (c) $\mu \mathrm{SR}$ spectra measured at 0.34 K under ZF and representative external fields. (d) Temperature dependence of the muon spin relaxation rates. (e) Temperature dependence of the internal magnetic fields, and the gray solid lines are power-law fit curves.

Figure 7

(a) Weak LF-$\mu \mathrm{SR}$ spectra measured on a single crystal of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ at 2.9 and 70 K in a longitudinal external magnetic field of 50 G. The thick lines behind the data points are curves fitted to the data by Eq. (5). (b) Temperature dependence of the muon spin relaxation rate $\lambda$. The gray solid line is guide to the eye.