Magnetization and specific heat ofTbFe3(BO3)4: Experiment and crystal-field calculations

We have studied the thermodynamic properties of single-crystalline $\mathrm{Tb}{\mathrm{Fe}}_{3}{(\mathrm{B}{\mathrm{O}}_{3})}_{4}$. Magnetization measurements have been carried out as a function of magnetic field (up to $50\phantom{\rule{0.3em}{0ex}}\mathrm{T}$) and temperature up to $350\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with the magnetic field both parallel and perpendicular to the trigonal $c$ axis of the crystal. The specific heat has been measured in the temperature range $2--300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with a magnetic field up to $9\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ applied parallel to the $c$ axis. The data indicate a structural phase transition at $192\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and antiferromagnetic spin ordering at ${T}_{N}\ensuremath{\approx}40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. A Schottky anomaly is present in the specific-heat data around $20\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, arising due to two low-lying energy levels of the ${\mathrm{Tb}}^{3+}$ ions being split by $f\text{\ensuremath{-}}d$ coupling. Below ${T}_{N}$, magnetic fields parallel to the $c$ axis drive a spin-flop phase transition, which is associated with a large magnetization jump. The highly anisotropic character of the magnetic susceptibility is ascribed mainly to the Ising-like behavior of the ${\mathrm{Tb}}^{3+}$ ions in the trigonal crystal field. We describe our results in the framework of a unified approach which is based on mean-field approximation and crystal-field calculations.