Figure 1: Synthesis, crystal structure and thermodynamic stability of ε-Rh_xFe_2−xO₃ nanomagnets.

(a) Upper row illustrates the synthesis of ε-Rh_xFe_2−xO₃. In the first step, a mesoporous silica template is synthesized in a conical flask to give a white powder. In the second step, an aqueous solution of Fe(NO₃)₃ and Rh(NO₃)₃ with methanol is impregnated into the silica to yield a yellow powder. In the third step, the resulting product is calcinated in air, and in the fourth step, the final product is obtained after etching the silica matrix with an aqueous NaOH solution. Lower left transmission electron microscope (TEM) image shows the obtained mesoporous silica where the small white dots are the mesopores. Illustration in the dotted frame depicts the formation process of ε-phase during calcination; as the temperature increases, Fe(NO₃)₃ and Rh(NO₃)₃ in the mesopores turn into γ-phase (~800 °C). Around the melting temperature of glass (1,000 °C), the particles begin to aggregate. As shown in the centre TEM image, ε-phase is the main phase at 1,200 °C. Lower right TEM image is the final product after etching the silica matrix. The scale bars below the three TEM images indicate 30 nm. (b) (left) Crystal structure of γ-phase. Green and light green indicate octahedral and tetrahedral Fe sites, respectively. (centre) Crystal structure of ε-phase. Dark red, red, orange and yellow indicate the four nonequivalent Fe sites for Fe_A, Fe_B, Fe_C and Fe_D, respectively. (right) Crystal structure of α-phase. Fe site is shown as blue octahedrons. Grey lines indicate the unit cell. (c) Calculated G_i/V_m,i versus d curves for i-phases (i=γ, ε and α). Green, red and blue curves correspond to γ-phase, ε-phase and α-phase, respectively. The curves are calculated under the condition of μ_γ >μ_ε >μ_α, σ_γ <σ_ε <σ_α and (σ_ε−σ_γ)/(σ_α−σ_ε) < (μ_ε−μ_γ)/(μ_α−μ_ε), where μ_i is the chemical potential of i-phase and σ_i is the surface energy of i-phase.