Magnetic phase transitions and exchange interactions in TbMnO₃: symmetry analysis

Alam-Samimi, Arash (2009) Magnetic phase transitions and exchange interactions in TbMnO₃: symmetry analysis. Masters thesis, Memorial University of Newfoundland.

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Abstract

This thesis is a theoretical approach to study the magnetic phase transitions and exchange interactions in the spiral magnet TbMnO₃ by using group theory. First, we study the magnetic and ferroelectric transitions by considering the symmetry breaking associated with each transition. Second, we write the exchange interactions for the Mn magnetic ions in terms of the magnetic order parameters which are associated with various irreducible representations of the magnetic space group. Third, considering the exchange interactions and single ion anisotropy we examine the interactions on the whole lattice. -- The most general form of the exchange interactions for Mn atoms in TbMnO₃ is formulated, including nearest neighbor and next-nearest neighbor interactions. Our phenomenological model also contains antisymmetric terms which lead to a mixing of spin-wave polarizations. It is found that for each exchange path there are six independent exchange terms, leading to a rather complicated Hamiltonian. -- Finally, equations of motions for spin waves are derived. Particular attention is given to the high-temperature phase (phase I) with the sinusoidal antiferromagnetic arrangement of spins and the incommensurate wave vector Q. The symmetric case and the degeneracy in the spin-wave spectrum in this phase are also discussed. More complex magnetic interactions lead to the spiral phase lying in the bc plane. This is the low-temperature phase (phase II) which needs further theoretical analyses.

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