Hidden elastic softness of low-symmetry frustrated $A$Ti$_2$O$_5$ ($A$ = Co, Fe)

Orthorhombic pseudobrookites CoTi$_2$O$_5$ and FeTi$_2$O$_5$ have a low-symmetry crystal structure comprising magnetic Co$^{2+}$/Fe$^{2+}$ ions and nonmagnetic Ti$^{4+}$ ions, where the orbital-nondegenerate Co$^{2+}$/Fe$^{2+}$ ions form one-dimensional chains running along the orthorhombic $a$ axis. These compounds undergo an antiferromagnetic phase transition at $T_N \sim$ 26 K for CoTi$_2$O$_5$ and $T_N \sim$ 40 K for FeTi$_2$O$_5$. We perform ultrasound velocity measurements on single crystals of CoTi$_2$O$_5$ and FeTi$_2$O$_5$. The measurements of these compounds reveal that the symmetry-lowering elastic modes of shear elastic moduli exhibit unusual elastic softness in the paramagnetic phase above $T_N$. This elastic softness indicates the presence of spin-lattice-coupled fluctuations above $T_N$ that should be a precursor to the symmetry-lowering lattice distortion at $T_N$. Furthermore, it is revealed that the magnitude of the unusual elastic softness is larger in CoTi$_2$O$_5$ than in FeTi$_2$O$_5$, which indicates that the spin-lattice coupling is stronger in CoTi$_2$O$_5$ than in FeTi$_2$O$_5$. The present study suggests that CoTi$_2$O$_5$ and FeTi$_2$O$_5$ are unique spin Jahn--Teller systems with low crystal symmetry, where, although the nature of exchange interactions is quasi-one-dimensional, the three-dimensional spin-lattice coupling releases the frustration by further lowering the crystal symmetry.