Magnetic structure of hexagonal YMnO3and LuMnO3from a microscopic point of view

Abstract

The aim of this work is to unravel a basic microscopic picture behind complex magnetic properties of hexagonal manganites. For these purposes, we consider two characteristic compounds:YMnO 3 and LuMnO 3 , which form different magnetic structures in the ground state (P 6 3 cm and P 6 3 cm, respectively). First, we establish an electronic low-energy model, which describes the behavior of the Mn 3d bands of YMnO 3 and LuMnO 3 , and derive parameters of this model from the first-principles calculations. From the solution of this model, we conclude that, despite strong frustration effects in the hexagonal lattice, the relativistic spin-orbit interactions lift the degeneracy of the magnetic ground state so that the experimentally observed magnetic structures are successfully reproduced by the low-energy model. Then, we analyze this result in terms of interatomic magnetic interactions, which were computed using different approximations (starting from the model Hamiltonian as well as directly from the first-principles electronic structure calculations in the local-spin-density approximation). We argue that the main reason why YMnO 3 and LuMnO 3 tend to form different magnetic structures is related to the behavior of the single-ion anisotropy, which reflects the directional dependence of the lattice distortion: namely, the expansion and contraction of the Mn-trimers, which take place in YMnO 3 and LuMnO 3 , respectively. On the other hand, the magnetic coupling between the planes is controlled by the next-nearest-neighbor interactions, which are less sensitive to the direction of the trimerization. In the P 6 3 cm structure of YMnO 3 , the Dzyaloshinskii-Moriya interactions lead to the spin canting out of the hexagonal plane -in the same direction as the single-ion anisotropy. Finally, using the Berry-phase formalism, we evaluate the magnetic-state dependence of the ferroelectric polarization, and discuss potential applications of the latter in magnetoelectric switching phenomena.

Bulk magnetoelectricity in the hexagonal manganites and ferrites

“…Our approach to elucidate the bulk, cross-coupling between ferroelectricity and magnetism is to introduce a P6 3 /mmc PE reference structure that has the same AFM configuration as the P6 3 cm FE ground state. The minimal model required to describe the spin structure 28 is the following effective spin Hamiltonian…”

Study of magnetic behavior in hexagonal-YMn1−Fe O3 (x=0 and 0.2) nanoparticles using remanent magnetization curves

“…Contrary to the above, in h-YMn 0.8 Fe 0.2 O 3 system we see a small rise ( $ 8 K) in Néel temperature, which indicates a rise in the strength of the nearest neighbor Mn 3 þ -O-Mn 3 þ /Fe 3 þ super-exchange interactions. Thus, the origin of weak FM phase in h-YMn 0.8 Fe 0.2 O 3 can be attributed predominantly to Dzyaloshinskii-Moriya (DM) interaction between the Mn 3 þ and Mn 3 þ /Fe 3 þ spins [35]. In bulk YMnO 3 , it is shown theoretically that the D-M interactions along with single ion anisotropy are responsible for the canting of spins [35].…”

Spin-lattice coupling and frustrated magnetism in Fe-doped hexagonal LuMnO 3

“…The magnetic structure of LuFe 0.5 Mn 0.5 O 3 below T N was solved by assuming k = (0, 0, 0) propagation vector for the nuclear space group P 6 3 cm. Representation analysis for magnetic structure then allows six possible solutions: Γ 1 (P 6 3 cm), Γ 2 (P 6 3 c m ), Γ 3 (P 6 3 cm ), Γ 4 (P 6 3 c m), Γ 5 (P 6 3 ) and Γ 6 (P 6 3 ) [9,14]. The magnetic structure of hLuMnO 3 belongs to the representation Γ 4 (P 6 3 c m) [10,14].…”

“…Representation analysis for magnetic structure then allows six possible solutions: Γ 1 (P 6 3 cm), Γ 2 (P 6 3 c m ), Γ 3 (P 6 3 cm ), Γ 4 (P 6 3 c m), Γ 5 (P 6 3 ) and Γ 6 (P 6 3 ) [9,14]. The magnetic structure of hLuMnO 3 belongs to the representation Γ 4 (P 6 3 c m) [10,14]. However, non-zero intensity for the (100) reflection which is stronger compared to the (101) could suggest that the Γ 3 (P 6 3 cm ) or Γ 1 (P 6 3 cm) models are the correct one for the Fe-doped compound.…”