Thermal conductivity, electron transport, and magnetic properties of single-crystal ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$

A recent neutron-diffraction study on the magnetic insulator ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ shows that spins in the $c$-axis chains of alternating Co1 octahedral and Co2 trigonal-prismatic face-sharing ${\text{CoO}}_{6/2}$ sites are ordered below $T_N$ with a long-wavelength modulation instead of a simple ferromagnetic chain as thought previously. Frustrated antiferromagnetic interchain interactions compete with ferromagnetic intrachain coupling to invalidate an Ising model despite a strong spin-orbit coupling $\lambda \mathbf{L}\cdot \mathbf{S}$ on the Co2 ions. We have carried out thermal conductivity, electron transport, and magnetic measurements on single-crystal ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ in order to characterize this complicated magnetic system. An anisotropic thermal-conductivity component superimposed at high temperatures on an isotropic phonon component is consistent with an exchange-interaction-mediated heat transfer. This observation is incompatible with an Ising model. The ferromagnetic intrachain interactions are argued to reflect a one-dimensional itinerant-electron band that is split by the $c$-axis translational symmetry and the on-site intra-atomic Hund exchange interaction with a localized $S=3/2$ spin on the Co2 ions.

Figure 1

(Color online) The crystal structure of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$.

Figure 2

(Color online) The powder x-ray diffraction of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ at room temperature and parameters of the Rietveld refinement. The inset displays an SEM photograph of a ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ single crystal.

Figure 3

(Color online) Temperature dependences of (a) thermoelectric power and (b) resistivity of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$.

Figure 4

(Color online) Temperature dependence of thermal conductivity $\kappa$ with heat flow along the $c$ axis and within $ab$ plane in a ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ single crystal. Lines in the curves are the fitting results with the standard Debye formula for phonon thermal conductivity.

Figure 5

(Color online) Temperature dependence of the anisotropic inverse magnetic susceptibility of ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ single crystal. The magnetic field $H=5\text{T}$ was used in ${\chi }_{\perp }$ and $H=1\text{T}$ in ${\chi }_{\parallel }$.

Figure 6

(Color online) The magnetization at different temperatures of a ${\text{Ca}}_3{\text{Co}}_2{\text{O}}_6$ single crystal with the magnetic field (a) parallel to the $c$ axis and (b) perpendicular to the $c$ axis. Inset is the rocking angle dependence of the magnetization at $T=10\text{K}$ and $H=5\text{T}$ for the crystal used in $M\left(H_{\perp }\right)$.

Figure 7

(Color online) Cartoon of (a) the point-charge model of one-electron energies on Co2 and of (b) localized configuration $d^5$ on Co2 with itinerant states split by intra-atomic exchange $D_{\text{ex}}$, which concentrates the spin density on the Co2 atoms and by the translational symmetry.