Anisotropic spin dynamics in the frustrated chain ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ detected by single-crystal ${}^{59}\text{C}\text{o}$ NMR

Static and dynamic magnetic properties are investigated by ${}^{59}\text{C}\text{o}$ NMR measurements on a single crystal of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$, a rare model of the ferromagnetic Ising chain coupled antiferromagnetically on a triangular lattice. Above a ferrimagnetic order transition temperature $T_{\text{N}}=25\text{K}$, the static spin susceptibility probed by the ${}^{59}\text{C}\text{o}$ Knight shift shows anisotropic behavior in the temperature dependence, consistent with ferromagnetic interactions along the $c$-axis chain and antiferromagnetic interactions in the $ab$ plane. Correspondingly, the dynamical spin susceptibility obtained from the ${}^{59}\text{C}\text{o}$ nuclear spin-lattice relaxation rate is also highly anisotropic. The intrachain ferromagnetic correlation steeply develops below 300 K while the interchain antiferromagnetic one does below 120 K with the critical exponent expected in the two-dimensional Ising antiferromagnet. Below $T_{\text{N}}$, the low-energy excitation arising from the predominant spin-wave magnons has an anisotropic full gap, reflecting the strongly Ising nature. Clear microscopic evidence of the ferrimagnetic order is demonstrated in the ${}^{59}\text{C}\text{o}$ NMR spectra at 5 K. Rotation of the external magnetic field from the $ab$ plane to the $c$ axis shows the first-order transition from the ferrimagnetic to the fully polarized state. The ferrimagnetic state with the uniform magnitude of magnetic moment is observed even in the transverse field adjusted parallel to the $ab$ plane.

Figure 1

(a) Angle dependence of ${}^{59}\text{C}\text{o}$ NMR spectra (Co1) of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ at 300 K. The magnetic field $H_0=9.4026\text{T}$ is rotated from the $c$ $\left(0°\right)$ to $a^{\ast }$ axis $\left(90°\right)$. (b) Angle dependence of the peak positions in the ${}^{59}\text{C}\text{o}$ NMR spectra in (a).

Figure 2

(Color online) Temperature dependence of (a) ${}^{59}\text{C}\text{o}$ NMR Knight shift $K$ and (b) magnetic susceptibility $\chi$ of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ in a magnetic field parallel and perpendicular to the $c$ axis. The applied magnetic field is 9.4 and 7 T for the $K$ and $\chi$ measurements, respectively. The solid curves and lines represent the fitting results to the Curie-Weiss law in the temperature range 200–300 K.

Figure 3

(Color online) ${}^{59}\text{C}\text{o}$ Knight shift $K$ vs magnetic susceptibility $\chi$ plots in ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ for the magnetic field parallel and perpendicular to the $c$ axis. The transferred hyperfine coupling constants with the nearest- and next-nearest-neighbor sites, $B_{\alpha }$ and $D_{\alpha }$, are schematically presented in the inset.

Figure 4

${}^{59}\text{C}\text{o}$ nuclear magnetization recovery measured for the magnetic field parallel to the $c$ axis at 160 K. The solid curve represents the theoretical curve of Eq. (4) with $T_1=2.63\text{ms}$.

Figure 5

(Color online) Temperature dependence of the ${}^{59}\text{C}\text{o}$ nuclear spin-lattice relaxation rate $1/T_1$ measured for the magnetic field parallel and perpendicular to the $c$ axis in ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$.

Figure 6

(Color online) Temperature dependence of ${\sum }_{\mathbf{q}}{\left|A_{\alpha }\left(\mathbf{q}\right)\right|}^2{\chi }_{\alpha }^{″}\left(\mathbf{q},\omega \right)$, measured for the magnetic field parallel $\left(\alpha =c\right)$ and perpendicular $\left(\alpha =ab\right)$ to the $c$ axis in ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$. The inset shows the log plots of ${\sum }_{\mathbf{q}}{\left|A_{\alpha }\left(\mathbf{q}\right)\right|}^2{\chi }_{\alpha }^{″}\left(\mathbf{q},\omega \right)$ vs $T/T_{\text{N}}-1$.

Figure 7

Angular dependence of the ${}^{59}\text{C}\text{o}$ NMR spectra measured at 5 K and $H_0=9.4026\text{T}$ rotated in the $c{a}^{\ast }$ plane for the single crystal of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$. The inset shows the spectra of the down branch in an angle range where the ferrimagnetic-ferromagnetic transition occurs.

Figure 8

The square of the central peak frequency of the ${}^{59}\text{C}\text{o}$ NMR spectra measured at 5 K and $H_0=9.4023\text{T}$ in Fig. 7, plotted as a function of $H_0\text{cos}\theta$.

Figure 9

(Color online) Temperature dependence of the ${}^{59}\text{C}\text{o}$ nuclear spin-lattice relaxation rate $1/T_1$ measured for $H_0\parallel c$ and $H_0\perp c$ in ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$. The inset shows the activation plot of $1/T_1$ below $T_{\text{N}}$.