Quantum critical phenomena in a spin-$\frac{1}{2}$ frustrated square lattice with spatial anisotropy

We present a model compound with a spin-$\frac{1}{2}$ spatially anisotropic frustrated square lattice, in which three antiferromagnetic interactions and one ferromagnetic interaction are competing. We observe an unconventional gradual increase in the low-temperature magnetization curve reminiscent of the quantum critical behavior between gapped and gapless phases. In addition, the specific heat and electron spin resonance signals indicate one-dimensional characteristics. These results demonstrate quantum critical behavior associated with one dimensionalization caused by frustrated interactions in the spin-$\frac{1}{2}$ spatially anisotropic square lattice.

Figure 1

(c) Molecular structure of $\left[m\text{−}\mathrm{Me}\mathrm{Py}\text{−}\mathrm{V}\text{−}{\left(p\text{−}\mathrm{F}\right)}_2\right]{\mathrm{SbF}}_6$. (d) Crystal structure forming the spin model in the $ab$ plane. Hydrogen atoms are omitted for clarity. (c) Spin-$\frac{1}{2}$ spatially anisotropic frustrated square lattice composed of three AF interactions $J_1$, $J_2$, and $J_4$, and one ferromagnetic interaction $J_3$ in $\left[m\text{−}\mathrm{Me}\mathrm{Py}\text{−}\mathrm{V}\text{−}{\left(p\text{−}\mathrm{F}\right)}_2\right]{\mathrm{SbF}}_6$. The mapped model corresponds to a spin-1 spatially anisotropic triangular lattice composed of the spins dimerized by $J_3$.

Figure 2

(a) Temperature dependence of the magnetic susceptibility ($\chi =M/H$) of $\left[m\text{−}\mathrm{Me}\mathrm{Py}\text{−}\mathrm{V}\text{−}{\left(p\text{−}\mathrm{F}\right)}_2\right]{\mathrm{SbF}}_6$ at 0.1 T. (b) Magnetization curves of $\left[m\text{−}\mathrm{Me}\mathrm{Py}\text{−}\mathrm{V}\text{−}{\left(p\text{−}\mathrm{F}\right)}_2\right]{\mathrm{SbF}}_6$ at 80 mK and 1.3 K. The arrow shows the contribution of the paramagnetic impurities.

Figure 3

(a) Temperature dependence of the specific heat $C_{\mathrm{p}}$ of $\left[m\text{−}\mathrm{Me}\mathrm{Py}\text{−}\mathrm{V}\text{−}{\left(p\text{−}\mathrm{F}\right)}_2\right]{\mathrm{SbF}}_6$ at 0 and 14 T. (c) Low-temperature region of $C_{\mathrm{p}}/T$. (b) Entropy $S_{\mathrm{p}}$ obtained via the integration of $C_{\mathrm{p}}/T$ at zero field. $S_{\mathrm{m}}$ is the magnetic entropy evaluated by subtracting the lattice contribution.

Figure 4

(a) Temperature dependence of the ESR absorption spectra of $\left[m\text{−}\mathrm{Me}\mathrm{Py}\text{−}\mathrm{V}\text{−}{\left(p\text{−}\mathrm{F}\right)}_2\right]{\mathrm{SbF}}_6$ at 34.13 GHz. Temperature dependence of the (b) resonance field shift and (c) linewidth (full-width at half-maximum) obtained from the ESR spectra. The solid line indicates the $T^{-p}$ fit.