Possible spin Jahn-Teller material: Ordered pseudobrookite ${\mathrm{FeTi}}_2{\mathrm{O}}_5$

We investigated spin-lattice coupling in orthorhombic pseudobrookite ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ single crystal with highly ordered $\mathrm{F}{\mathrm{e}}^{2+}$/$\mathrm{T}{\mathrm{i}}^{4+}$ occupation, which consists of quasi-one-dimensional (1D) $S=2$ chains running along the $a$ axis. Both the magnetization and specific heat measurements confirm that the antiferromagnetic phase transition of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ occurs at $T_N=42\mathrm{K}$. The structural distortions were also observed around $T_N$ in the thermal expansion $\mathrm{\Delta }L/L\left(T\right)$ data. Moreover, the magnetic field was found to strongly affect the thermal expansion both along chains and in the perpendicular direction clearly signaling a substantial magnetoelastic coupling, which was recently proposed to be the origin of a rare spin Jahn-Teller effect, when frustration is lifted via additional lattice distortions. Experimentally observed change in the thermal conductivity slope around $T_N$ is usually associated with the orbital ordering, but density functional theory (DFT)+$U$ calculations do not detect modification of the orbital structure across the transition. However, the first-principles calculation results confirm that ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ is a quasi-1D magnet with a ratio of frustrating interchain to intrachain exchanges $J^{\prime }/J=0.03$ and a substantial single-ion anisotropy $(A=4\mathrm{K})$ of easy-axis type making this material interesting for studying quantum criticality in transverse magnetic fields.

Figure 1

(a) The schematic diagram of the geometrical frustration in ${\mathrm{FeTi}}_2{\mathrm{O}}_5$, in which only $\mathrm{F}{\mathrm{e}}^{2+}$ (the green ball) and the corner-shared ${\mathrm{O}}^{2\text{–}}$ (the red ball) were shown. Fe chains run along the $a$ axis. The dashed line shows the triangular geometric frustration in ${\mathrm{FeTi}}_2{\mathrm{O}}_5$. (b) The Rietveld refinement results of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$.

Figure 2

The magnetic measurements of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ single crystal along different axes. (a) χ-$T$. The inset presents the broad peak along the $b$ axis in enlarged form. (b) Low-temperature susceptibilities at different fields along the $b$ axis. (c) $1/\chi \text{−}T$. (d) $M$($H$) curves.

Figure 3

(a), (b) The thermal expansion of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ single crystal along the $a$ axis and $b$ axis. The insets show the thermal expansion coefficient α of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$. (c) The magnetostriction of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ single crystal along the $a$ axis at different temperatures. (d) The magnetostriction of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ single crystal along the $b$ axis below $T_N$.

Figure 4

(a) The specific heat of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ under different magnetic fields. (b) The magnetic specific heat and change of magnetic entropy of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$.

Figure 5

The thermal conductivity of ${\mathrm{FeTi}}_2{\mathrm{O}}_5$ single crystal along the $a$ axis under different magnetic fields. (a) κ-$T$, (b) $1/\kappa \text{−}T$. The dashed line in the $1/\kappa \text{−}T$ at zero field is used to show the change in the slope.

Figure 6

(a) Crystal-field splitting of the Fe $3d$ shell as obtained by the Wannier function projection of nonmagnetic GGA calculations. (b) The lowest in energy $xz$ orbital (in the global coordinate system) in GGA nonmagnetic calculations; Fe ions are shown by red, while O is shown by violet balls.

Figure 7

Total and partial densities of states (DOS) as obtained in $\mathrm{GGA}+U$ calculations for the magnetic configuration, where spins in the same chain are AFM ordered. For O $2p$, Fe $3d$, and Ti $3d$ two spin projections are shown by positive DOS for spin majority and negative DOS for spin minority. The Fermi level is set to zero.