Multiferroic properties in β-R2(MoO4)3 predicted fromsymmetry
Fumihito ShikanaiPrivate, 2-15-11-102 Tsukuho, Tsukuba, Ibaraki 300-3257, Japanβ-R2(MoO4)3 (R: rare earth) undergoes the first-order phase transition above 400 K
with the symmetrical change from P 421 m (phase I) to Pba2 (phase II). The materialshows ferroelectric below phase transition temperature (TC), and extremely small
spontaneous polarization appears along c axis. Dielectric permittivity varies from theCurrie-Weiss's law and no precursory phenomenon is observed above TC. Crystalstructure is constructed by two types of MoO4 layers and four R exist between thelayers. Small lattice strain about 3/100 Å in phase II is inverted by external stressshowing ferroelastic. Characteristic domain structure including anti-phase boundaries isobserved in phase II A thermodynamic free energy for zone-boundary system has been
proposed by group theoretical calculation, and the symmetrical change is explained bya two-dimensional real-representation, which unitary transformed from complexconjugate representations (CCRs). A soft optical mode has been observed at thezone-boundary, M-point, by inelastic neutron scattering; therefore, the phase transitionis classified both improper-ferroelectric and -ferroelastic type.
Recently, magnetic properties of β-Tb2(MoO4)3 have been reported. The saturation
magnetic moment depends on the direction of magnetic field showing magnetic
anisotropy. Furthermore, magneto-electric switching has been observed. The electric
polarization induced above threshold magnetic field, 100 kOe, along [100] direction
while no switching has been observed for [110] direction. These results indicate thatsome magnetic mechanism exist, which close relate to ferro-electricity and -elasticity;and remind us of that the symmetrical change is based on the CCRs. In this study, theauthor reexamined the symmetrical change, and applied the CCRs to crystal structure.
Furthermore, the author investigated the crystal filed splitting from change of point
group at R3+ site.
From the group theoretical analysis, it is proved that CCRs, M5 and M6, account forthe symmetrical change. Real part of both representations derives an alternativerotational displacement of MoO4 tetrahedra, which corresponds to the soft mode.
Freezing of the mode changes the arrangement of oxygen atoms around R3+, and tilts
the crystal filed from 8.5˚ in phase I to 27.1˚ and 20.3˚ in phase II from the c. Sitesymmetry at R3+changes from m to 1. By operating the CCRs, a magnetic structure inFig. 1 is obtained. Two R3+ atoms that have canting magnetic moments make a dimer
and two kinds of dimer exist. Both kinds of dimer induce negative dipole moment byDzyaloshinski-Moriya interaction, although each magnetic moment is inverted. From
the differences of initial magnetic moments, four kinds of the magnetic structure are
obtained and those correspond to magnetic andferroelectric domains. Two of them are composed of
the same dimers showing the same dipole while themagnetic moments are inversed. It demonstrates thatthe anti-phase boundary in phase II is that between
magnetic domains.
Grand state of Tb3+, 7F6 (13-ply), is reduced as
A1u+A2u+Eu+T1u+2T2u under the crystal filed in Oh.
Grand state is A1u in Tb3+ and shows non-magnetism.
The states are splitting with lowering the symmetry;all of states are described by one-dimensional
representations in C2v. The A1u state degenerates
again with |±4> in the site symmetry for phase I andII, m and 1, respectively; and shows magnetism.
Quantized axis in phase I is perpendicular to m andflips to the direction of crystal field in phase II.
FIG. 1 Magnetic structure and term of f 8