{'fraction_non_alphanumeric': 0.022539444027047332, 'fraction_numerical': 0.009015777610818933, 'mean_word_length': 5.0, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Half-Metallicity and Magnetism of the Quaternary Heusler Compound TiZrCoIn1−xGex from the First-Principles Calculations

The effects of doping on the electronic and magnetic properties of the quaternary Heusler alloy TiZrCoIn were investigated by first-principles calculations. Results showed that the appearance of half-metallicity and negative formation energies are associated in all of the TiZrCoIn1−xGex compounds, indicating that Ge doping at Z-site increases the stability without damaging the half-metallicity of the compounds. Formation energy gradually decreased with doping concentration, and the width of the spin-down gap increased with a change in Fermi level. TiZrCoIn0.25Ge0.75 was found to be the most stable half-metal. Its Fermi level was in the middle of the broadened gap, and a peak at the Fermi level was detected in the spin majority channel of the compound. The large gaps of the compounds were primarily dominated by the intense d-d hybridization between Ti, Zr, and Co. The substitution of In by Ge increased the number of sp valence electrons in the system and thereby enhanced RKKY exchange interaction and increased splitting. Moreover, the total spin magnetic moments of the doped compounds followed the Slater–Pauling rule of Mt = Zt − 18 and increased from 2 μB to 3 μB linearly with concentration.