Ferrotoroidial properties of Non-Crystallographic Pointgroups

Primary ferroic crystals are the crystals with domain states that are distinguished by properties like spontaneous magnetization, strain, or polarisation. Secondary ferroic crystals are the crystals with domain states that are distinguished by piezoelectric tensor and they are named as Ferromagnetotoroidic (eV²), Ferromagnetoelastic (aeV [V²]) crystals respectively. Here "e" denotes zero rank tensor that changes under spatial inversion, "a" denotes zero rank tensor that changes under time inversion, and "V" denotes a polar vector. Recent observations (Van Aken et al., 2007) identified the fourth type of primary ferroic crystals, a ferrotoroidic crystal with domains distinguished by a toroidial moment. The number of independent constants of quasi crystals is theoretically derived by Wenge Yang et al., (1995). He also formulated the number of independent components of any physical property tensor of quasi crystals using group representation theory. This paper accounts the effect of symmetry on some ferrotoroidial properties of quasi Crystals with 5-fold, 8-fold, 10-fold and 12-fold symmetries using group theoretical methods. Also the number of independent constants is calculated and tabulated that helps in describing the ferrotoroidial properties. (paper)