Collinear Magnetism

For the Group II compounds of RMnO3, the magnetic orders have been identified to turn into the E-type AFM magnetic structure which exhibits collinear spins [2, 3, 5, 8, 39, 58]. Within the context of the abovementioned magnetism-induced FE, the collinear AFM shouldn’t be able to result in the complex magnetoelectric polarization described above. In 2004, Lorenz et al. reported the anomaly dielectric behavior in YMnO3 and HoMnO3 materials [16]. The results have led to the scientists to reconsider the role of collinear AFM in magnetoelectric effect. Sergienko et al. [22] by considering mechanisms other than spin-orbit interaction have estimated the polarization of the E-type RMnO3 can have up to “2” orders of magnitude enhancement over that of the spiral phase RMnO3. The polarization in this case is induced along the a-axis in Pbnm space group setting. In their calculation, the polarization was estimated about 0.5~12 μC/cm² which is compatible with the hexagonal RMnO3 (see in Table 1.2). As depicted in

Fig. 1.7, in this scenario the ferroelectricity is originated from the oxygen displacement perpendicular to the Mn-Mn bond resulted from the competition between electron hoping and elastic energy within the framework of the double exchange model [22]. For HoMnO3 with E-type AFM, the Mn-O-Mn bond angle is close to 144^o(ψ^o). Since deviation of the bond angleψ^o from 180˚ will cost hoping energy while it may reduce the elastic energy by having a smallerψ^o. This calculation, though was put forth for the E-type AFM system, is also useable for noncollinear TbMnO3 compounds. Picozzi et al.

[59, 60] redo the calculation with first principle calculation and find that the magnetoelectric polarization is induced along mainly c-axis (consistent with the previous report [22]) and partially a-axis. The crystalline axis was set in Pnma space group which

Fig. 1.7 (a) The starting configuration of a Mn-O-Mn bond. Numbers 1–4 enumerate the O atoms surrounding one Mn. (b) An MC snapshot of the IMF E-phase at T = 0.01. The ferromagnetic zigzag chain links are shown as solid lines. The displacements of the oxygen atoms are exaggerated. (c) Left: The local arrangement of the Mn-O bonds with disordered Mn spins (full circles). Right: Oxygen displacements (arrows) within the chains of opposite Mn spins (open and crossed circles) in the E-phase. [22]

could be also transferred to Pbnm space group setting. The polarization was induced by the quantum mechanism in spin-orbital interaction, and the crystal and electronic structure both needed to be considered in magnetoelectric behaviors. The first principle calculation also gave more exact estimation on the strength of the polarization caused by collinear AFM and other mechanisms.

1.5 Motivation

As has been mentioned in length, multiferroic materials have rich physical properties arising from the complicated and yet subtle interactions among the charge, spin, and orbital degree of freedoms of the carriers and the lattice. Especially, the ultimate routes of obtaining effective magnetoelectric coupling between spin and polarization are still needed to be clarified. The rare-earth manganites (RMnO3) in particular are the interesting playgrounds featuring simultaneously the magnetism and ferroelectricity with the Jahn-Teller distortion playing an important role in mingling all these ingredients to result in various emergent physical properties like the magnetoelectric behaviors. As shown in Fig. 1.3, YMnO3 and HoMnO3 are of particular interest because they locate right at the verge of the crystal transition point. In addition, they were also identified to have the collinear magnetic AFM structure for Mn³⁺ at low temperature [2, 3], that makes them ideal for testing the mechanism beyond the DM spin-orbital interaction. It is also interesting to note that YMnO3 does not have the 4f spin electrons, making it unique in clarifying the prominent role played by the Mn³⁺ spin orders. Unfortunately, up to now suitable samples of orthorhombic RMnO3 from the Group II manganites are still lacking for measuring the directly the actual orientations of the spin ordering and the polarization associated with its transition, which couldn’t be decided exactly with polycrystalline ones.

Due to the inherent difficulties of obtaining the single crystalline orthorhombic Group II manganites, thin films seem to be the only choice for resolving these hindrances.

Therefore, in this work, we will first concentrate on fabricating suitable thin film samples of the orthorhombic Group II manganites. Then we will show how these films help us in characterizing the magnetism, ferroelecticity, and electronic structure that would eventually demonstrate the effects of anisotropic bonding predicted by Picozzi et al. [59].

1.6 Outline

This dissertation consists of seven chapters. We simply guide the multiferroics and its magnetoelectric coupling and mechanism in chapter 1. In Chapter 2, we will describe the basic physical properties of RMnO3 manganites and origin of the magnetic behaviors.

The relative magnetic and crystal structure in RMnO3 compound will be also described here. In chapter 3, we will discuss the feasible routes of obtaining the orthorhombic crystal structure from the thermodynamically stable hexagonal RMnO3 phases by substrate stabilization. We will also describe the relation between ionic size, crystal, and electronic structure in structural stabilization. Ca and Sr were used to dope YMnO3 to investigate the effect of ionic size on the electronic structures and associated magnetic properties. In chapter 4 and 5, we clarify the role of substrate in stabilizing thin film with both hexagonal and orthorhombic structures. The strain dominates the stabilization of metastable orthorhombic structure in Group II RMnO3 compounds. In the temperature dependence of magnetization behavior, the YMnO3 thin films revealed significant anisotropic behavior both in hexagonal and orthorhombic structures. The spin reordering behavior was only seen along a- and c-axis which was different from the E-type HoMnO3. In chapter 6, x-ray absorption spectra are used to unveil the anisotropic bonding behavior

along the primary crystalline axes. Because of the MnO6 octahedron in orthorhombic structure and MnO5 bipyramid in hexagonal structure, the spectra show entirely different bonding behavior. Finally, we give a conclusion and future work in chapter 7.

Table 1.2 Crystallographic, polarization, and magnetic properties of RMnO3 compounds for R = Y and Eu to Lu. [1-11].

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Chapter 2