Magnetic ground state of the two isostructual polymeric quantum magnets $\left[\mathrm{Cu}\right({\mathrm{HF}}_2\left)\right(\text{pyrazine}{)}_2]{\mathrm{SbF}}_6$ and $\left[\mathrm{Co}\right({\mathrm{HF}}_2\left)\right(\text{pyrazine}{)}_2]{\mathrm{SbF}}_6$ investigated with neutron powder diffraction

The magnetic ground state of two isostructural coordination polymers, (i) the quasi-two-dimensional $S=1/2$ square-lattice antiferromagnet $\left[\mathrm{Cu}\right({\mathrm{HF}}_2\left)\right({\mathrm{pyrazine})}_2]{\mathrm{SbF}}_6$ and (ii) a related compound $\left[\mathrm{Co}\right({\mathrm{HF}}_2\left)\right({\mathrm{pyrazine})}_2]{\mathrm{SbF}}_6$, was examined with neutron powder diffraction measurements. We find that the ordered moments of the Heisenberg $S=1/2$ Cu(II) ions in $\left[\mathrm{Cu}\right({\mathrm{HF}}_2\left)\right({\mathrm{pyrazine})}_2]{\mathrm{SbF}}_6$ are $0.6\left(1\right){\mu }_b$, while the ordered moments for the Co(II) ions in $\left[\mathrm{Co}\right({\mathrm{HF}}_2\left)\right({\mathrm{pyrazine})}_2]{\mathrm{SbF}}_6$ are $3.02\left(6\right){\mu }_b$. For Cu(II), this reduced moment indicates the presence of quantum fluctuations below the ordering temperature. We show from heat capacity and electron spin resonance measurements that due to the crystal electric field splitting of the $S=3/2$ Co(II) ions in $\left[\mathrm{Co}\right({\mathrm{HF}}_2\left)\right({\mathrm{pyrazine})}_2]{\mathrm{SbF}}_6$, this isostructual polymer also behaves as an effective spin-half magnet at low temperatures. The Co moments in $\left[\mathrm{Co}\right({\mathrm{HF}}_2\left)\right({\mathrm{pyrazine})}_2]{\mathrm{SbF}}_6$ show strong easy-axis anisotropy, neutron diffraction data, which do not support the presence of quantum fluctuations in the ground state, and heat capacity data, which are consistent with 2D or close to 3D spatial exchange anisotropy.

Figure 1

(Top) Structure $[\mathrm{Cu}$(${\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$ viewed along $c$. The ${\mathrm{SbF}}_6^{-}$ ions have been omitted for clarity. The Cu(II) ions in $[\mathrm{Cu}$(${\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$ occupy octahedral environments, consisting of two axial fluorine ions from ${\mathrm{HF}}_2^{-}$, and four equatorial nitrogen atoms from coordination-bonded pyrazine ligands. The pyrazine ligands form a sheet of co-planar Cu(II) ions, arranged on a square lattice in the $ab$ plane. (Bottom) Structure of $[\mathrm{Cu}$(${\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$ viewed within the $ab$ plane. Adjacent layers are linked by $\mathrm{Cu}\cdots \mathrm{F}$-H-$\mathrm{F}\cdots \mathrm{Cu}$ pillars along the $c$ axis, and the ${\mathrm{SbF}}_6^{-}$ counterions occupy the space in the center of the approximately cubic frameworks. Cu = pink, C = black, N = blue, F = yellow, Sb = green, and H = white (pyrazine hydrogen atoms omitted for clarity). The dashed red line shows the tetragonal structural unit cell boundary. $[\mathrm{Co}$(${\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$ is found to be isotructural, with the Co(II) ions taking the Cu(II) positions in the $P4/\mathit{nmm}$ unit cell.

Figure 2

Refinement of neutron diffraction data from a powdered sample of $[\mathrm{Cu}$(${\mathrm{HF}}_2$)(pyz-$d_4$)${}_2]{\mathrm{SbF}}_6$ at 1.5 K. (Main panel) Bank 2 data ($I_{\text{obs}}$, red circles), fitted model ($I_{\text{calc}}$, black line), reflections of the $P4/\mathit{nmm}$ lattice (black ticks), and $I_{\text{obs}}-I_{\text{calc}}$ (blue line). Impurity peaks are marked by an asterisk, but do not affect the refinement. If the impurity is a copper based polymeric compound, the intensity of these impurity peaks imply it is $<1\%$ of the sample and was not detectable in the magnetometry measurements. (Inset) Magnetic peaks extracted from the data (see text). The $y$ axis of the inset is in the same units as that of the main panel.

Figure 3

(a) Susceptibility vs temperature measured in an applied field ${\mu }_{0}H=0.1$ T for an orientated single crystal of $\left[\mathrm{Cu}\right({\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$. Data have been fitted to a model of $S=1/2$ moments on a square lattice with nearest-neighbor interactions. The fit yields $g_{xy}=2.06\left(2\right), g_z=2.28\left(3\right)$, and $J_{\parallel }/k_b=13.3\left(1\right)$ K. For $H\perp c$, the fitted values of the parameters $J$ and $g$ did not change within the reported uncertainty when the tetragonal system was rotated by ${45}^{\circ }$ about $c$. (b) Magnetization at $T=2$ K (in units of Bohr magnetons per formula unit, $n_{\text{f.u.}}$) normalized by the relevant $g$ factor ($g_i$, where $i=z,xy$) vs applied field scaled by the same $g$ factor.

Figure 4

Refinement of powder neutron-diffraction data for $\left[\mathrm{Co}\right({\mathrm{HF}}_2$)(pyz-$d_4$)${}_2]{\mathrm{SbF}}_6$ at 4 K. Bank 2 data (red circles), fitted model (black line), reflections of the P4/nmm lattice (black ticks, top line), reflections of the magnetic moments with propagation vector $\mathbf{k}=(0,0,1/2)$ (black ticks, middle line) and $I_{\text{obs}}-I_{\text{calc}}$ (blue line). The third row of ticks indicate structural peaks of a 12.4(7)$\%$ nonmagnetic crystalline impurity of ${\mathrm{NaHF}}_2$ ($R\overline{3}m$) (black ticks, bottom line), likely formed in the synthesis of $\left[\mathrm{Co}\right({\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$ from a reaction of two precursor compounds ${\mathrm{NaSbF}}_6$ and ${\mathrm{NH}}_4{\mathrm{HF}}_2$. Inset (right) Magnetic peaks extracted from the data by subtracting a diffraction pattern collected at 10 K from the 4 K data set (the units of the $y$ axis are the same of those of the main panel). The lines represent the expected magnetic peaks when the moments are aligned parallel (solid line) and perpendicular (dashed line) to the $c$ axis. Inset (left) Schematic of the proposed magnetic supercell of the ground state. Pink = cobalt ion, blue arrow = ordered moment direction. All nonmagnetic ions have been omitted for clarity.

Figure 5

Atom labeling scheme for the refined atomic positions in the formula unit $\left[\mathrm{Co}\right({\mathrm{HF}}_2$)(pyz-$d_4$)${}_2]{\mathrm{SbF}}_6$. Note: site D1 is refined with the deuterium isotope (grey), whereas site H1 is refined with the hydrogen isotope (white). Duplicated labels are equivalent positions in the $P4/\mathit{nmm}$ space group.

Figure 6

Energy level diagram for high-spin Co(II) ions in an octahedral environment [20], applied to $[\mathrm{Co}\left({\mathrm{HF}}_2\right)$(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$. The axial compression of the ${\mathrm{CoN}}_4{\mathrm{F}}_2$ octahedra along the $\mathrm{Co}–\mathrm{F}$ bond lifts the degeneracy of the ${}^4{\mathrm{T}}_{1g}$ term resulting in an orbital singlet ground state. The effect of zero-field splitting is to produce two doublets, labeled by the $M_S$ component of spin, $S$. Neutron diffraction and ESR determined the $M_S=\pm 3/2$ state to be lowest in energy.

Figure 7

(a) The ratio of heat capacity ($C_p$) to temperature ($T$) as a function of $T$ for $[\mathrm{Co}$(${\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$, collected in zero applied field. The solid line shows the result of fitting the data to a model of the lattice contribution (described in text). (Inset) Inverse susceptibility (${\chi }_{\text{mol}}^{-1}$) vs temperature for $[\mathrm{Co}$(${\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$, recorded with ${\mu }_{0}H=0.1$ T. (b) Entropy change vs temperature deduced by integrating the $C_{\text{mag}}$ using Eq. (2). The shaded region indicates the error on this calculation due to uncertainties in the subtraction of the lattice fit. (c) Magnetic contribution to the heat capacity vs temperature at representative fields in the range $0\le {\mu }_{0}H\le 12$ T.

Figure 8

(a) Transmission ESR spectra (in derivative mode) vs applied field at 416 GHz. At 30 K, two transitions are seen due to single Co(II) ion resonances with anisotropic $g$ tensor. Below $T_n=7.1$ K, a large AFM resonance is observed, and the frequency dependence of this mode is shown in Fig. 9. The asterisk marks paramagnetic impurities and $◯$ is attributed to a critical resonance mode at the spin-flop field. (b) The experimental (red) and simulated (black) 20 K ESR spectra at 416 GHz. The simulation was performed with an effective spin-1/2 paramagnetic model with an anisotropic $g$ factor: $g_x=g_y=3.6\left(4\right), g_z=5.5\left(7\right)$; and an isotropic line width (defined as the FWHM) of 800 mT.

Figure 9

(a) Transmission ESR spectra for $\left[\mathrm{Co}\right({\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$ as a function of applied field, for frequencies in the range $222.4\le \nu \le 609.6$ MHz. (b) Frequency dependence of ESR spectra recorded at 5 K, showing the experimentally measured antiferromagnetic resonances ($\square$) compared to those expected from simulations (lines). The solid and dashed lines (simulated with a powder average $g=4.21$ and ${\mu }_0{H}_{\text{sfI}}=4.9$ T) correspond to the ESR transitions for applied fields above and below $H_{\text{sfI}}$. Transitions corresponding to the dashed lines ($H\le H_{\text{sfI}}$) are weak, however, features indicated with diamonds in (a) follow a linear frequency-field dependence consistent with ${\mu }_0{H}_{\text{sfI}}=4.9$ T and $g_z\approx 6.3$. This larger $g$ factor is close to the full moment measured by neutron diffraction in zero field, which suggests these resonances correspond to the low-field state with the cobalt moments aligned to the $z$ axis.

Figure 10

(a) Magnetization vs applied field for a polycrystalline sample of $[\mathrm{Co}$(${\mathrm{HF}}_2$)(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$. As the temperature is lowered below $T_n=7.1$ K, a low-field kink in the magnetization develops, which tends to move to higher fields on cooling. Data at 0.8 K were recorded with pulsed fields, and the arrows indicate the direction of the field sweep. (b) $dM/dH$ vs applied field. Data collected at 0.8 K shows the derivative of the down-sweep measured from pulsed-field magnetization. On cooling, we see the development of two features in the magnetization, labeled at $H_{\text{sf}}$ and $H_c$.

Figure 11

Temperature-field phase diagram for $\left[\mathrm{Co}\right({\mathrm{HF}}_2$(${\mathrm{pyz})}_2]{\mathrm{SbF}}_6$ showing the transition to long-range order as measured by heat capacity (circles). The temperature dependencies of the spin-flop ($H_{\text{sf}}$) and critical field ($H_{\text{c}}$) are also shown, as measured from dc magnetization (triangles) and pulsed-field magnetization measured on decreasing field (diamonds). AFM(G) = G-type antiferromagnetic order (deduced from zero-field neutron diffraction at 4 K); PM(EA) = Paramagnetic phase with easy-axis anisotropy; and SF = spin-flop phase. The dotted lines are a guide to the eye only.