Title: Multiple magnetic interactions and large inverse magnetocaloric effect in TbSi and TbSi$_{0.6}$Ge$_{0.4}$

Abstract: We present a comprehensive investigation of the electronic structure, magnetization, specific heat, and crystallography of TbSi (FeB structure type) and TbSi$_{0.6}$Ge$_{0.4}$ (CrB structure type) compounds. Both TbSi and TbSi$_{0.6}$Ge$_{0.4}$ exhibit two antiferromagnetic (AFM) transitions at T$_{\rm N1}\approx$ 58~K and 57~K, and T$_{\rm N2}\approx$ 36~K and 44~K, respectively, along with an onset of weak metamagnetic-like transition around 6~T between T$_{\rm N1}$ and T$_{\rm N2}$. High-resolution specific heat (C$_{\rm P}$) measurements show the second- and first-order nature of the magnetic transition at T$_{\rm N1}$ and T$_{\rm N2}$, respectively, for both samples. However, in the case of TbSi, the low-temperature (LT) AFM to high-temperature (HT) AFM transition takes place via an additional AFM phase at the intermediate temperature (IT), where both LT to IT AFM and IT to HT AFM phase transitions exhibit a first-order nature. Both TbSi and TbSi$_{0.6}$Ge$_{0.4}$ manifest significant magnetic entropy changes ($\Delta S_{\rm M}$) of 9.6 and 11.6~J/kg-K, respectively, for $\Delta \mu_0H$=7~T, at T$_{\rm N2}$. The HT AFM phase of TbSi$_{0.6}$Ge$_{0.4}$ is found to be more susceptible to the external magnetic field, causing a significant broadening in the peaks of $\Delta S_{\rm M}$ curves at higher magnetic fields. Temperature and field-dependent specific heat data have been utilized to construct the complex H-T phase diagram of these compounds. Furthermore, temperature-dependent x-ray diffraction measurements demonstrate substantial magnetostriction and anisotropic thermal expansion of the unit cell in both samples.