Heusler alloys are peculiar type of materials, which exhibit a plenty of extraordinary properties [1,2], which leads to use in various fields such as thermoelectrics [3], spintronics [4], and data storage [5] and even as topological insulators [6]. Theoretical investigations have been extensively carried out on a wide range of Heusler alloys to understand their structural, electronic, and vibrational characteristics. For instance, XCrAl (X = Fe, Co, Ni, Cu) Heusler compounds have been analyzed to explore their electronic structures and magnetic ordering [7], while ternary systems of the type XVZ (X = Cr, Mn, Fe; Z = Sn, Sb) have been studied for their stability and half-metallic properties [8]. The structural, elastic, mechanical, electronic, magnetic, and thermoelectric properties of the half-Heusler CsVTe alloy were studied using density functional theory [9]. It was found that experimental thermal data and theoretical phonon properties of half-Heusler alloys based on zirconium (Zr) and titanium (Ti) were agreed with each other [10]. The theoretical calculations on structural, half-metallic and elastic properties of FeZrX (X = P, As, Sb and Bi) half-Heusler compounds were investigated using WIEN2k code. In all compounds, the ferromagnetic (FM) phase was more stable energetically than non-magnetic (NM) phase. Using the GGA and TB-mBJ approaches, the study primarily examined the electronic properties of these compounds, showing that the spin-up electrons exhibit semiconducting behavior with a finite band gap, while the spin-down electrons display metallic character [11]. The density functional theory (DFT) calculations were carried out to investigate the structural, electronic, magnetic, mechanical, and thermodynamic properties of CoYSb (Y = Cr, Mo and W) Heusler compounds [12]. The structural, elastic, electronic, magnetic, thermoelectric, and dynamic aspects of the CoCrS half-Heusler (HH) compound were examined [13]. The thermoelectric properties of the CoTiSi half-Heusler alloy were studied using density functional theory calculations [14]. The structural, elastic, electronic, magnetic and half metallic properties of Pt, Ni and Co based Heusler alloys [15], Mn-Ni-Sn based alloys [16] and magnetism of some 3d Heusler alloys [17] were analyzed. Comprehensive density functional theory (DFT) calculations were carried out in earlier studies for a variety of half-Heusler systems, such as, Mn-based [18], Li-based [19], Ni-based [20], RhFeZ (Z = P, As, Sb, Sn, Si, Ge, Ga, In, Al) [21], Co- and Ni-based Heusler alloys [22] and yttrium based half-Heusler compounds [23]. These studies provided insight into their ground-state structural, electronic, magnetic, and thermodynamical properties, laying the groundwork for exploring new compositions. The physical and chemical properties of some gas/solvent phases are analyzed based on density functional theory (DFT) [[24], [25], [26], [27], [28], [29], [30]].

In this work, zirconium-based half-Heusler compounds were chosen for investigation due to their favorable physical and chemical characteristics, including low toxicity, high thermal stability, and strong resistance to decomposition, which make them attractive for practical applications. Moreover, in the XYZ half-Heusler alloys, X element is chosen as Zr and Y element is Fe and Z elements are main group elements As, Sb and Bi. Though numerous works were carried out in Heusler compounds, all the physical properties of Zr based Heusler compounds ZrFeZ (Z = As,Sb,Bi) were not yet investigated. The present work broadens the scope of prior research by examining the optical, phonon, and thermal properties of these compounds, thereby providing a more comprehensive understanding of their multifunctional potential. This motivated us to predict new functional properties of ZrFeZ (Z = As, Sb, Bi) half-Heusler compounds by carrying out DFT calculations to find the applicability of these alloys for spintronic and optoelectronic applications.