Magnetic phase diagram of helimagnetic Ba(Fe_1−xSc_x)₁₂O₁₉ (0 ≤ x ≤ 0.2) hexagonal ferrite

Highlights

• The magnetic phase diagram of Ba(Fe_1−xSc_x)₁₂O₁₉ was constructed in the T-x plane.

• From the phase diagram, it was determined that helimagnetism appeared at x ≳ 0.06.

• The antiferromagnetic phase appeared at x ≳ 0.19 through the coexistence region with helimagnetism.

• The turn angle of the helix as a function of x and T was clarified.

Abstract

Hexagonal ferrite Ba(Fe_1−xSc_x)₁₂O₁₉ is an important magnetic oxide material in both science and engineering because it exhibits helimagnetism around room temperature (300 K). In this study, the magnetic phase diagram of Ba(Fe_1−xSc_x)₁₂O₁₉ consisting of ferri-, heli-, antiferro-, and paramagnetic phases has been completed through magnetization and neutron diffraction measurements. The magnetic phase transition temperature to paramagnetism decreases with the increase in x, and the temperature at which the magnetization reaches a maximum, which corresponds to the magnetic phase transition from heli- to ferrimagnetism, is determined for low x crystals. The temperatures at which helimagnetism appears are precisely determined by observing the magnetic satellite reflection peaks in neutron diffraction at various temperatures, which characterize helimagnetism. Based on these results, the magnetic phase diagram of the Ba(Fe_1−xSc_x)₁₂O₁₉ system is constructed in the T-x plane. Helimagnetism appears at x ≳ 0.06, and magnetism with antiferromagnetic components appears as the extension phase of helimagnetism at x ≳ 0.19 through the coexistence region. The turn angle ϕ₀ of the helix for each x crystal is calculated from the relationship, ϕ₀ = 2πδ, where δ is the incommensurability. The turn angle ϕ₀ decreases with the increase in temperature for the same x crystal, and increases with the increase in x at the same temperature. Furthermore, it is found that there are clear thresholds at which ϕ₀ cannot take values between 0°<ϕ₀ ≲ 90° and 170° ≲ ϕ₀< 180°.

Introduction

Although hexagonal ferrites, a group of magnetic oxide materials, have been known for a relatively long time, they continue to be studied because of their scientific and industrial importance. Hexagonal ferrites are extensively applied in various industrial areas because of their high magnetic anisotropy, strong coercive force, high Curie temperature, and low cost. Among hexagonal ferrites, M-type BaFe₁₂O₁₉ is widely used in devices such as DC motors, speakers, and magnetic recording media, and has attracted attention as an electromagnetic wave-absorbing material for 5G mobile communication systems. Fig. 1(a) shows the crystal structure of BaFe₁₂O₁₉ in a unit cell, belonging to space group P6₃/mmc (No. 194) [1], [2]. Ba²⁺ and O²⁻ with a large ionic radius form a close-packed structure along the c-axis in the BaFe₁₂O₁₉ crystal, whereas Fe³⁺ with a small ionic radius occupies the interlayer octahedral (2a, 4f₂, and 12k), tetrahedral (4f₁), and bipyramid sites (2b). Fe³⁺ alone has a magnetic moment. The orientation of the Fe³⁺ magnetic moment is parallel to the c-axis in the 2a, 2b, and 12k sites, and is antiparallel in the 4f₁ and 4f₂ sites, resulting in ferrimagnetism collinear to the c-axis, as depicted in Fig. 1(a) [1], [3].

Substituted M-type hexagonal ferrites have also been studied for a long time, and a lot of papers have been published recently. From a scientific point, they attract a great deal of attention because chemical compositions such as the type and concentration of substituents (Ga, Ti, Nd-Zn) strongly correlate with the crystal structure, the magnetic structure, and microwave characteristics [4], [5], [6]. From an application point, they have been studied as permanent magnets for Nd-NbZn co-substitution [7], as multiferroics for In-substitution [8], and as an electromagnetic wave absorber for Al- and In-substitution [9]. In the Sc-substitution system we discuss in this paper, the magnetic structure and microwave characteristics of powder samples were also studied, and the rapid frustration of the magnetic structure and weakening of the intrasublattice exchange interaction were discussed [10]. Among those substituted M-type hexagonal ferrites, we focused on the Sc-substituted Ba(Fe_1−xSc_x)₁₂O₁₉ system exhibiting helimagnetism [11], [12]. It is not clear why helimagnetism appears in this system. We hypothesize that helimagnetism is caused by the competition of superexchange interactions. Because the superexchange interaction energy is strongly influenced by the cation distribution (Fe³⁺ and Sc³⁺) and the steric configuration of ions, a small amount of Sc-substitution has a strong impact on the magnetic structure. It is necessary to discuss these two factors to clarify the appearance mechanism of helimagnetism. Since Ba(Fe_1−xSc_x)₁₂O₁₉ is a relatively simple system without electrical charge deviation, in which only Fe³⁺ is magnetic, these issues should be solved. The helimagnetism of the Ba(Fe_1−xSc_x)₁₂O₁₉ system has been extensively explored from both scientific and industrial points of view. This helimagnetism was discovered by Russian research groups in the 1960s; Perekalina et al. investigated the magnetization and magnetic anisotropy of single crystals of Ba(Fe_1−xSc_x)₁₂O₁₉ and concluded that some of the Fe³⁺ magnetic moments were parallel to the ab plane direction [11]. Subsequently, Aleshko-Ozhevskiĭ et al. performed neutron diffraction experiments on single crystals to observe the magnetic satellite reflection peaks, which characterize the helimagnetism [12]. Since then, the crystal structure containing Fe³⁺ and Sc³⁺ distributions, and the magnetic structures have been actively analyzed through magnetization measurement, neutron diffraction, and Mössbauer spectroscopy. Shchurova et al. observed that a large difference occurred in the magnetic anisotropy depending on the external magnetic field and proposed a model in which two magnetic sublattices were connected by weak exchange interactions [13]. Further detailed neutron diffraction studies by Aleshko-Ozhevskiĭ et al. proposed a block helix model and revealed that Sc³⁺ first occupied the octahedral 4f₂ sites and the bipyramid 2b sites subsequently [12], [14]. Significant efforts have been made to clarify the Sc³⁺ site preferences for polycrystalline samples [15], [16] and single crystals [17] through Mössbauer spectroscopy, which revealed that Sc³⁺ first occupied the 2b sites in the low Sc concentration region and the 4f₂ sites subsequently. This is consistent with the neutron diffraction results reported by Aleshko-Ozhevskiĭ et al. [12]. Very recently, Jiang et al. studied the cation distribution and magnetic properties of textured Ba(Fe_1−xSc_x)₁₂O₁₉ through Raman experiments and theoretical evaluations [18]. Meanwhile, a breakthrough related to multiferroic material research was made in a hexagonal ferrite system exhibiting helimagnetism [19], [20], [21], [22], [23], [24], [25]. It became clear that a conical spin structure is crucial for generating macroscopic electric polarization. Tokunaga et al. demonstrated that Ba(Fe_1−xSc_x)₁₂Mg_0.5O₁₉ was in a longitudinal conical spin state up to room temperature through magnetization and neutron diffraction measurements, and that a transverse magnetic field could induce electric polarization [25]. They concluded that Ba(Fe_1−xSc_x)₁₂Mg_0.5O₁₉ is a promising magnetically and electrically controllable multiferroic material. Other studies on the magnetic and magnetoelectric properties of Ba(Fe_1−xSc_x)₁₂O₁₉ include a study by Gupta et al. on polycrystalline samples, which have a longitudinal cone-shaped magnetic structure coexisting with a spin-glass-like phase and exhibit ferroelectricity even at zero field [26], [27].

Although active research is being conducted as described above, there is still room for research on Ba(Fe_1−xSc_x)₁₂O₁₉, including the detailed helimagnetic structure and the appearance mechanism of helimagnetism that have not been elucidated. Further research on this material is desired in anticipation of future applications. In our previous paper, we had reported the single-crystal growth of Ba(Fe_1−xSc_x)₁₂O₁₉ using the flux method [28]. X-ray diffraction and elemental analysis revealed that the single crystals obtained were of good quality and included a single phase of Ba(Fe_1−xSc_x)₁₂O₁₉ with various Sc concentrations x. Based on the results of neutron diffraction and magnetization measurements of the x = 0.128 crystal, it was clarified that the magnetic phase transition temperature from ferrimagnetism, depicted in Fig. 1(b), to the helimagnetism, depicted in Fig. 1(c), was 211 K. Similarly, the magnetic phase diagram in the T-x plane can be completed by clarifying the magnetic phase transition temperature from heli- to ferrimagnetism, and the paramagnetic phase transition temperature for all the x crystals. Furthermore, information on the incommensurability of the turn angle of the helix depending on T and x can be obtained through neutron diffraction. The magnetic phase diagram and information on the incommensurability of the helix are of considerable scientific value and are also significant for applications such as multiferroics. In this study, the temperature dependence of magnetization and time-of-flight (TOF)-Laue single-crystal neutron diffraction were measured at various temperatures for Ba(Fe_1−xSc_x)₁₂O₁₉ with various values of x. The magnetic phase diagram of Ba(Fe_1−xSc_x)₁₂O₁₉ constructed by determining the magnetic phase transition temperature is presented. Furthermore, the change in the turn angle of the helix is reported as a function of x and T determined from the incommensurability of the magnetic satellite reflection of neutron diffraction. The single crystal samples used and the magnetization and neutron diffraction measurement methods are described in Section 2. The determination of the magnetic phase transition point through magnetization and neutron diffraction measurements and the construction of the magnetic phase diagram are detailed in Section 3, and the turn angle of the helix is discussed. Finally, the paper is concluded in Section 4 and the scope for further research is indicated.