Extremely well isolated two-dimensional spin-$\frac{1}{2}$ antiferromagnetic Heisenberg layers with a small exchange coupling in the molecular-based magnet CuPOF

We report on a comprehensive characterization of the newly synthesized ${\mathrm{Cu}}^{2+}$-based molecular magnet $\left[\mathrm{Cu}{\left(\mathrm{pz}\right)}_2{\left(2\text{−}\mathrm{HOpy}\right)}_2\right]{\left({\mathrm{PF}}_6\right)}_2$ (CuPOF), where $\mathrm{pz}={\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}_2$ and $2\text{−}\mathrm{HOpy}={\mathrm{C}}_5{\mathrm{H}}_4\mathrm{NHO}$. From a comparison of theoretical modeling to results of bulk magnetometry, specific heat, ${\mu }^{+}\mathrm{SR}$, ESR, and NMR spectroscopy, this material is determined as an excellent realization of the two dimensional square-lattice $S=\frac{1}{2}$ antiferromagnetic Heisenberg model with a moderate intraplane nearest-neighbor exchange coupling of $J/k_{\mathrm{B}}=6.80\left(5\right)$ K, and an extremely small interlayer interaction of about 1 mK. At zero field, the bulk magnetometry reveals a temperature-driven crossover of spin correlations from isotropic to $XY$ type, caused by the presence of a weak intrinsic easy-plane anisotropy. A transition to long-range order, driven by the low-temperature $XY$ anisotropy under the influence of the interlayer coupling, occurs at $T_{\mathrm{N}}=1.38\left(2\right)$ K, as revealed by ${\mu }^{+}\mathrm{SR}$. In applied magnetic fields, our ${}^1\mathrm{H}$-NMR data reveal a strong increase of the magnetic anisotropy, manifested by a pronounced enhancement of the transition temperature to commensurate long-range order at $T_{\mathrm{N}}=2.8$ K and 7 T.

Figure 1

(a) View of the Cu-pyrazine layers of CuPOF along the $c$ axis. The 2-pyridone molecules extend normal to the planes and are coordinated to the copper atoms through the oxygens. The uncoordinated ${\mathrm{PF}}_6^{-}$ anions occupy vacancies in the lattice. (b) View of CuPOF along the $a$ axis. The Cu-pyrazine layers extend horizontally and into the page. The interdigitation of the 2-pyridone molecules leads to the extreme isolation of the layers. The 2-pyridone molecules within one layer are all canted in the $+b$ direction while the molecules in the adjacent layers cant in the $-b$ direction.

Figure 2

Temperature dependence of the powder susceptibility (circles) in ${\mathrm{emuG}}^{-1}{\mathrm{mol}}^{-1}$ and the integrated ESR intensity at 9.4 GHz (diamonds) in arbitrary units. The red line shows the best fit of the 2D QHAF model calculations to the magnetic susceptibility of a polycrystalline sample. The black dash-dotted line represents the fit of the same model to the integrated ESR intensity of a polycrystalline CuPOF sample.

Figure 3

Temperature dependence of the out-of-plane molar susceptibility of a single-crystalline sample of CuPOF at different magnetic fields. The solid black triangles in the main panel indicate the crossover temperature $T_{\mathrm{co}}$, as discussed in the main text. The inset shows the low-temperature susceptibility of a single crystal of CuPOF. The data were collected in a field of 0.1 T. The susceptibilities normal to the plane and within the $ab$ plane are represented by the open triangles and circles, respectively. The vertical arrow indicates the crossover temperature $T_{\mathrm{co}}$ for $M/H\parallel c$ at 1.86(5) K. The broad anomaly of the in-plane static susceptibility at about 1.6(1) K is attributed to a background contribution.

Figure 4

Magnetization of single-crystalline CuPOF at 0.37 K in (a) out-of-plane and (b) in-plane direction and comparison with the respective QMC calculations (red line). The insets show the magnetization at 0.5 K in magnetic fields up to 1 T in an enlarged scale. The vertical arrow indicates the anisotropy field at ${\mu }_0{H}_{\mathrm{A}}=0.36\left(1\right)$ T. The bottom axis represents the relative magnetic field $H/H_{\mathrm{sat}}$. The corresponding absolute values of the magnetic fields are shown in the upper axis.

Figure 5

(a) Temperature dependence of the normalized specific heat of CuPOF denoted as open black circles, with the black line representing the best fit to these data by a sum of magnetic (solid red line) and phonon (black dashed line) contributions, $C_{\mathrm{pho}}$. (b) The black solid triangles represent $C_{\mathrm{mag}}$, which is the difference between $C$ and $C_{\mathrm{pho}}$.

Figure 6

(a) Representative ${\mu }^{+}\mathrm{SR}$ spectra of CuPOF at 0.30 and 1.60 K. Solid lines are fits to the data using Eq. (3). (b)–(d) Temperature dependence of the parameters $A_0$, ${\lambda }_1$, and $\nu$. The blue dashed line indicates $T_{\mathrm{N}}=1.38\left(2\right)$ K.

Figure 7

(a) ${}^1\mathrm{H}$-NMR spectra of CuPOF at selected temperatures in the regime of magnetic order, recorded at ${\mu }_{0}H\parallel c=7$ T. Temperature-dependent peak positions ${\nu }_{res}$ at out-of-plane fields of (b) 2 and (c) 7 T. Vertical arrows mark the onset temperature of LRO. The inset of panel (c) shows a typical ${}^1\mathrm{H}$-NMR spectrum at 7 T and 3.5 K. Two nonequivalent hydrogen sites can be assigned in the paramagnetic regime.

Figure 8

Normalized Néel temperature as a function of $J^{\prime }/J$ (black solid line), as well as the normalized crossover (blue dash-dotted line) and BKT transition temperatures (red dashed line) as functions of the anisotropy parameter $\mathrm{\Delta }$. The normalized Néel temperature, $k_{\mathrm{B}}{T}_{\mathrm{N}}/J$, as a function of intrinsic easy-plane anisotropy, $\mathrm{\Delta }$, for various Cu-pyrazine 2D QHAFs ($○$, $•$, $◐$, $★$) and ${\mathrm{Sr}}_2\mathrm{Cu}{\mathrm{O}}_2{\mathrm{Cl}}_2$ ($\oplus$) [71, 72]. The values indicated by $○$ are for CuPOF, $•$ are from Ref. [40], $◐$ is from Ref. [42], and $★$ are from Ref. [47]. The numbers denote 2D QHAF compounds according to the labeling in Table 1. The two distinct values for CuPOF and ${\mathrm{Sr}}_2\mathrm{Cu}{\mathrm{O}}_2{\mathrm{Cl}}_2$ denote slightly different values of $\mathrm{\Delta }$, determined from the DC susceptibility and low-field magnetization measurements, respectively.