Gapped ground state in a spin-$\frac{1}{2}$ frustrated square lattice

We present a model compound with a spin-1/2 frustrated square lattice, in which three ferromagnetic (F) interactions and one antiferromagnetic (AF) compet. Considering the effective spin-1 formed by the dominant F dimer, this square lattice can be mapped to a spin-1 spatially anisotropic triangular lattice. The magnetization curve exhibits gapped behavior indicative of a dominant one-dimensional (1D) AF correlation. In the field-induced gapless phase, the specific heat and magnetic susceptibility show a phase transition to an ordered state with 2D characteristics. These results indicate that the spin-1 Haldane state is extended to the 2D system. We demonstrate that the gapped ground state observed in the present spin-1/2 frustrated square lattice originates from the one-dimensionalization caused by frustration.

Figure 1

(a) Spin-1/2 frustrated square lattice composed of F interactions, $J_{\mathrm{F}1}, J_{\mathrm{F}2}$, and $J_{\mathrm{F}3}$, and AF interaction $J_{\mathrm{AF}}$ in $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right]$(4-Br-$o$-Py-V). (b) Spin-1 spatially anisotropic triangular lattice in terms of the effective spin-1 formed through $J_{\mathrm{F}1}$. Thick colored lines along the $J_{\mathrm{AF}}$ chain represent the Haldane state with a spin gap. (c) Molecular structure of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right]$(4-Br-$o$-Py-V). (d) Crystal structure forming the square lattice in the $ac$ plane. Hydrogen atoms and $\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2$ are omitted for clarity.

Figure 2

(a) Temperature dependence of the magnetic susceptibility ($\chi =M/H$) and $\chi T$ of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right]$(4-Br-$o$-Py-V) at 0.5 T. (b) Magnetization curve and its field derivative of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right]$(4-Br-$o$-Py-V) at 85 mK. Thick arrows indicate the phase-transition fields.

Figure 3

Low-temperature region of (a) the magnetic susceptibility ($\chi =M/H$) and (b) its temperature derivative $d\chi /dT$ of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right]$(4-Br-$o$-Py-V) in various magnetic fields. Arrows indicate the broad extremum of $\chi$ and phase-transition peak of $d\chi /dT$.

Figure 4

(a) Temperature dependence of the specific heat $C/T$ of $\left[\mathrm{Zn}{\left(\mathrm{hfac}\right)}_2\right]$(4-Br-$o$-Py-V). For clarity, the values for 0.5, 1.0, 1.5, 2.0, 3.0, 4.0, 4.5, and 6.0 T have been shifted up by 0.54, 1.3, 2.0, 2.7, 3.5, 4.9, 6.3, and 8.5 J/ mol ${\mathrm{K}}^2$, respectively. (b) Magnetic field vs temperature phase diagram showing the domelike phase boundary of the 3D AF order. Open squares obtained from the extremum temperature of $\chi$ are related to the crossover to the TLL. (c) Low-temperature region of $C/T^2$ at 2.0 and 3.0 T. Solid lines are guides that show the asymptotic behavior to a constant value. For clarity, the values for 3.0 has been shifted up by 2.5 J/ mol ${\mathrm{K}}^3$. (d) Entropy obtained through integration of $C/T$ at 0 and 3.0 T.