${\text{Tb}}^{3+}$ in ${\text{TbCo}}_3{\text{B}}_2$: A singlet ground state system studied by inelastic neutron scattering

The results of inelastic neutron scattering on the hexagonal compounds ${\text{TbCo}}_3{\text{B}}_2$ and ${\text{Tb}}_{0.75}{\text{Y}}_{0.25}{\text{Co}}_3{\text{B}}_2$, at several temperatures, are reported. The crystal-field level scheme of ${\text{Tb}}^{3+}$ ions in the paramagnetic phase is determined. This scheme contains a nonmagnetic singlet $\left({\Gamma }_1\right)$ as the ground state. Inelastic neutron scattering at low temperature (10 K) leads to a different energy-level scheme, where the singlet ground state is ferromagnetic with $⟨J_x⟩\ne 0$. This is a “self-induced” ferromagnetism on the Tb sublattice, resulting from the admixture of higher crystal-field levels into the singlet ground state by the exchange field. The resulting magnitudes of these ground state magnetic moments are $5.6\left(3\right){\mu }_B$ and $3\left(1\right){\mu }_B$ for ${\text{TbCo}}_3{\text{B}}_2$ and ${\text{Tb}}_{0.75}{\text{Y}}_{0.25}{\text{Co}}_3{\text{B}}_2$, respectively. These values are much smaller than the free ion value of $9{\mu }_B$ and are in agreement with previously observed values. Such large reductions are characteristic of the “self-induced” ferromagnetism. The temperature dependences of the magnetic moment, magnetic anisotropy, Tb sublattice dilution, and magnetic susceptibility are discussed.

Figure 1

(Color online) Response function, $S\left(Q,\omega \right)$, vs neutron energy loss, $\hslash \omega$, for ${\text{TbCo}}_3{\text{B}}_2$, with incident energy of $E_0=35\text{meV}$, at four temperatures (the lines are guides for the eyes). All nonelastic INS lines are of magnetic origin, as was verified using measurement of the nonmagnetic analog ${\text{YCo}}_3{\text{B}}_2$ at 200 K. These signals are noted by A, B, and C above magnetic ordering and ${\text{A}}^{\prime }$, ${\text{B}}^{\prime }$, and ${\text{C}}^{\prime }$ below magnetic ordering. The measured momenta and angle ranges are $Q∊\left(2.01,3.88\right){\text{Å}}^{-1}$ and $2\theta ∊\left(12°,68.4°\right)$, respectively. Errors are smaller than the symbol size.

Figure 2

(Color online) Response function, $\text{S}\left(Q,\omega \right)$, vs neutron energy loss, $\hslash \omega$, for ${\text{Tb}}_{0.75}{\text{Y}}_{0.25}{\text{Co}}_3{\text{B}}_2$, with incident energy of $E_0=35\text{meV}$, at four temperatures (the lines are guides for the eyes). All nonelastic INS lines are of magnetic origin, as was verified using measurement of the nonmagnetic analog ${\text{YCo}}_3{\text{B}}_2$ at 200 K. These signals are noted by A, B, and C above magnetic ordering and ${\text{A}}^{\prime }$, ${\text{B}}^{\prime }$, and ${\text{C}}^{\prime }$ below magnetic ordering. The measured momenta and angle ranges are $Q∊\left(2.01,3.88\right){\text{Å}}^{-1}$ and $2\theta ∊\left(12°,68.4°\right)$, respectively. Errors are smaller than the symbol size.

Figure 3

(Color online) INS of ${\text{TbCo}}_3{\text{B}}_2$ at $T=200\text{K}$. Observed data are represented by open circles. Calculated data were obtained using the least-squares fit algorithm (solid line; see text). The line shape was calculated (semiempirically) using a convolution of Gaussian and Lorentzian. Experimental errors are smaller than symbol size.

Figure 4

(Color online) Energy level scheme of the eigenvalues of CEF Hamiltonian [Eq. (3)], $T>T_{\text{Tb}}$, for the ${\text{Tb}}^{3+}$ ion in both samples. The levels are labeled by their eigenstate symmetries (Ref. 13). The solid lines, noted by A, B, and C, represent experimentally observed transitions using INS. The zero of the energy scale corresponds to the ground state at $T>T_{\text{Tb}}$.

Figure 5

(Color online) Energy level scheme of the eigenvalues of the magnetic Hamiltonian [Eq. (4)], $T<T_{\text{Tb}}$, for the ${\text{Tb}}^{3+}$ ion in ${\text{TbCo}}_3{\text{B}}_2$. The levels are labeled by their eigenstate symmetries (Ref. 13). The solid lines (vertical short), noted by ${\text{A}}^{\prime }$, ${\text{B}}^{\prime }$, and ${\text{C}}^{\prime }$, represent experimentally observed transitions (Fig. 1). The zero of the energy scale corresponds to the ground state at $T>T_{\text{Tb}}$.

Figure 6

Calculated magnetic anisotropy energy of the ground state of the magnetic Hamiltonian for ${\text{TbCo}}_3{\text{B}}_2$. The zero of the energy scale corresponds to the ground state at $T>T_{\text{Tb}}$.