Giant Pressure Dependence and Dimensionality Switching in a Metal-Organic Quantum Antiferromagnet

We report an extraordinary pressure dependence of the magnetic interactions in the metal-organic system $[{\mathrm{CuF}}_2({\mathrm{H}}_2\mathrm{O}{)}_2{]}_2\text{pyrazine}$. At zero pressure, this material realizes a quasi-two-dimensional spin-$1/2$ square-lattice Heisenberg antiferromagnet. By high-pressure, high-field susceptibility measurements we show that the dominant exchange parameter is reduced continuously by a factor of 2 on compression. Above 18 kbar, a phase transition occurs, inducing an orbital re-ordering that switches the dimensionality, transforming the quasi-two-dimensional lattice into weakly coupled chains. We explain the microscopic mechanisms for both phenomena by combining detailed x-ray and neutron diffraction studies with quantitative modeling using spin-polarized density functional theory.

Figure 1

(a) Measured TDO resonance frequencies $\omega$ at selected pressures $P$ (kbar) for $T=1.5\mathrm{K}$ (solid lines), shown with the magnetoresistive background of the resonator coil (dashed). (b) $\chi (B)$ for the same $T$ and $P$ values. (c) $M/M_c(B)$ at $P=37.1$, 31.9, and 25.8 kbar (dashed lines), measured at 0.4 K, and at the pressures shown in panels (a) and (b) (full lines), measured at 1.5 K. (d) $\chi (B)$ at 1.5 kbar and 1.5 K as obtained from experiment (full line) and from QMC simulations (dashed line).

Figure 2

(a) $T_N$ measured as a function of $P$ at field values corresponding to $B_{\mathrm{sf}}$. (b) $B_c$ obtained from self-consistent fitting procedure; black lines show linear fits. Blue circles show data obtained using the piston cell, red squares using the moissanite cell. (c) Ratio $T_N/B_c$ as a function of $P$, illustrating the evolution of dimensionality; the sharp drop marks the phase transition to the Q1D magnetic system. Two missing values of $T_N$ for calculating $T_N/B_c$ were obtained from linear interpolation based on panel (a). (d) Exchange parameters obtained from QMC fits to the experimental data, shown together with a linear fit (black lines).

Figure 3

Crystallographic structure of $[{\mathrm{CuF}}_2({\mathrm{H}}_2\mathrm{O}{)}_2{]}_2\text{pyz}$ in the $\alpha$ phase, showing (a) the $ac$ and (b) the $bc$ plane. The dominant exchange parameter $J_0$ is mediated by $\mathrm{Cu}\text{−}\mathrm{O}\text{−}\mathrm{H}\cdots \mathrm{F}\text{−}\mathrm{Cu}$ superexchange paths. (c) Calculated spin-density distribution of the ground state, with spins up and down represented, respectively, in cyan and green. Red lines mark the coordination octahedron of the ${\mathrm{Cu}}^{2+}$ ions and thick dashed lines the pseudo-Jahn-Teller axis. Structure in the $\beta$ phase, showing (d) the $ac$ and (e) the $ab$ plane. The dominant exchange parameter $J_3$ is mediated by $\mathrm{Cu}\text{−}\mathrm{O}\text{−}\mathrm{H}\cdots \mathrm{F}\text{−}\mathrm{Cu}$ paths. (f) Spin-density distribution; both the pseudo-Jahn-Teller axis and the magnetic orbitals are reoriented at the phase transition.

Figure 4

Exchange parameters calculated as function of pressure for the $\alpha$ and $\beta$ phases using spin-polarized DFT.