Freezing of molecular rotation in a paramagnetic crystal studied by ${}^{31}\mathrm{P}$ NMR

We present a detailed ${}^{31}\mathrm{P}$ nuclear magnetic resonance (NMR) study of the molecular rotation in the compound $[\mathrm{Cu}{\left(\mathrm{pz}\right)}_2{(2-\mathrm{HOpy})}_2]{\left({\mathrm{PF}}_6\right)}_2$, where $\mathrm{pz}={\mathrm{C}}_4{\mathrm{H}}_4{\mathrm{N}}_2$ and $2-\mathrm{HOpy}={\mathrm{C}}_5{\mathrm{H}}_4\mathrm{NHO}$. Here, a freezing of the ${\mathrm{PF}}_6$ rotation modes is revealed by several steplike increases of the temperature-dependent second spectral moment, with accompanying broad peaks of the longitudinal and transverse nuclear spin-relaxation rates. An analysis based on the Bloembergen-Purcell-Pound (BPP) theory quantifies the related activation energies as $E_a/k_B=250$ and 1400 K. Further, the anisotropy of the second spectral moment of the ${}^{31}\mathrm{P}$ absorption line was calculated for the rigid lattice, as well as in the presence of several sets of ${\mathrm{PF}}_6$ reorientation modes, and is in excellent agreement with the experimental data. Whereas the anisotropy of the frequency shift and enhancement of nuclear spin-relaxation rates is driven by the molecular rotation with respect to the dipole fields stemming from the Cu ions, the second spectral moment is determined by the intramolecular interaction of nuclear ${}^{19}\mathrm{F}$ and ${}^{31}\mathrm{P}$ moments in the presence of the distinct rotation modes.

Figure 1

(a) In CuPOF, quasi-2D planes of ${\mathrm{Cu}}^{2+}$ ions are linked by pyrazine molecules, forming the motif of a magnetic square lattice. Two structurally slightly inequivalent ${\mathrm{PF}}_6$ molecules are located in-between the layers. (b) View on two adjacent Cu-pyrazine layers, with hydrogen atoms omitted for clarity. (c) Temperature dependence of the static susceptibility (circles). The red line shows the best fit of 2D QHAF model calculations to the magnetic susceptibility of a polycrystalline sample [27]. The inset of (c) shows the temperature dependence of the inverse static susceptibility. The blue line denotes the best fit with a Currie-Weiss behavior.

Figure 2

(a) ${}^{31}\mathrm{P}$-NMR spectra of CuPOF at different temperatures and an external field of 7 T, applied parallel to the $c$ axis. The red, orange, and green shaded areas denote the modeling of the spectral lineshape by a Gaussian, Pseudo-Voigt, and Lorentzian function, respectively. The vertical line indicates the Larmor frequency for zero shift. (b) Comparison between conventional spin-echo ${}^{31}\mathrm{P}$-NMR and MAS spectra at about 200 K.

Figure 3

(a) Temperature dependence of the square root of the ${}^{31}\mathrm{P}$ second spectral moment at 7 T. The vertical arrows indicate the temperatures at which the angular-dependent ${}^{31}\mathrm{P}$ NMR spectra were recorded, see Figs. 4 and 5. (b) Temperature dependence of the ${}^{31}\mathrm{P}$ nuclear spin-spin relaxation rate at 7 T. (c) Temperature dependence of the ${}^{31}\mathrm{P}$ nuclear spin-lattice relaxation rate at 7 and 2 T. The black (red) lines represent fits with the BPP model to the 7 T (2 T) data.

Figure 4

Angular dependence of the ${}^{31}\mathrm{P}$-NMR frequency shift (full circles), recorded for a field rotation in the crystallographic $ac$ plane at 7 T and 10 K. For both the ${\mathrm{P}}_{11}$ and ${\mathrm{P}}_{21}$ sites, the experimental data are compared to the calculated anisotropy of the dipolar-field contribution, stemming from the ${\mathrm{Cu}}^{2+}$ ions. The sketch in the inset defines the polar and azimuthal angles $\theta$ and $\varphi$, respectively. The case $\varphi =0$ denotes the rotation in the $ac$ plane.

Figure 5

Angular dependence (with $H\parallel a$ or $\parallel c$ corresponding to $\theta =0$ or 90 degrees, respectively) of square root of the ${}^{31}\mathrm{P}$ second spectral moment at (a) 10, (b) 35, (c) 100, and (d) 200 K, compared to calculations for the nuclear ${\mathrm{P}}_{11}$ and ${\mathrm{P}}_{21}$ sites for (a) a rigid lattice and in the presence of ${\mathrm{PF}}_6$ molecular reorientations around the symmetry axes (b) $3C_4$, (c) $6C_2$, and (d) $4C_3$. The inset in (a) shows a sketch of the local ${\mathrm{P}}_{11}$ and ${\mathrm{P}}_{21}$ symmetry with respect to the in-plane ($H\parallel a$, horizontal) and out-of-plane ($H\parallel c$, vertical) field orientation. The insets in (b), (c), and (d) show sketches of the molecular symmetry axes, around which the ${\mathrm{PF}}_6$ molecular reorientations occur.