Why Are Garnets Not Ferroelectric? A Theoretical Investigation of Y3Fe5O12

Results are presented on the electronic, electric, and magnetic properties of yttrium iron gat-net, Y3Fe5O12 using first-principles calculations. A cubic centrosymmetric structure and a tetragonally strained structure of Y3Fe5O12 are investigated. Frozen-phonon calculations are performed for both phases. We show, using symmetry arguments and by analyzing the crystal structure, that stoichiometric garnets are unlikely multiferroic materials despite their magnetization at room temperature and above.