Supplementary Information

Transcription

1 Supplementary Information Supplementary Figure S1 Aspect ratio distributions of ε-rh.1 Fe 1.6 O 3 nanoparticles. Aspect ratio distributions of ε-rh.1 Fe 1.6 O 3 nanoparticles sintered at 1 C, where the aspect ratio is the ratio of the long axis and short axis of the ellipsoid. Red and blue indicate the ε- and α-phases, respectively. The present sample is basically composed of pseudo-spherical particles. (9% of the nanoparticles are below the aspect ratio of 1.3.) 1

2 (a) x= ε-fe 2 O 3 (1 %) a= 5.933(5) Å b=.7912(9) Å c= 9.(9) Å (b) x=. ε-rh. Fe 1.96 O 3 (9 %) a= 5.9(3) Å b=.792(6) Å c= 9.766(5) Å α-rh.2 Fe 1.9 O 3 (2 %) a= 5.3(15) Å c= (5) Å (c) x=.7 ε-rh.7 Fe 1.93 O 3 (96 %) a= 5.96() Å b=.7927() Å c= 9.751() Å α-rh.12 Fe 1. O 3 ( %) a= 5.3(2) Å c= (7) Å (d) x=.11 ε-rh.11 Fe 1.9 O 3 (91 %) a= 5.1(5) Å b=.793(9) Å c= 9.751(9) Å α-rh.16 Fe 1. O 3 (9 %) a= 5.51(5) Å c= (13) Å (e) x=.1 ε-rh.1 Fe 1.6 O 3 (71 %) a= 5.13(5) Å b=.7957(9) Å c= 9.7(1) Å α-rh.2 Fe 1.76 O 3 (29 %) a= 5.(6) Å c= (13) Å Supplementary Figure S2 XRD patterns and Rietveld analyses of ε-rh x Fe 2 xo 3. XRD patterns and Rietveld analyses of the samples for x = (a), (b)., (c).7, (d).11, and (e).1. Red dots, black lines, and blue lines are the observed patterns, calculated patterns, and their differences, respectively. Green and gray bars represent the calculated positions of the Bragg reflections of the ε-phase (orthorhombic, Pna2 1 ) and the α-phase (rhombohedral, R3 c ). Composition ratios of the ε- and α-phases are derived from the composition of the products obtained by ICP-MS and the cell parameters of α-fe 2 O 3 and Rh 2 O 3. 2

3 Supplementary Figure S3 Particle size distributions of ε-rh.1 Fe 1.6 O 3 nanoparticles. Particle size distributions of ε-rh.1 Fe 1.6 O 3 nanoparticles sintered at C, 15 C, and 1 C. Green, red, and blue indicate the γ-, ε-, and α-phases, respectively. Size range of each phase is estimated from the existence ratio of each phase based on the XRD measurements and Rietveld analyses. 3

4 (a) 12 x= (b) 1-1 x= - 12 x= x=. x= x= x=.11 1 x= x=.1 - x=.1 1 Temperature / K H / koe Supplementary Figure S Magnetic properties. Magnetic properties of the powder samples (without silica matrices, non-oriented). (a) Field-cooled magnetization curves (external field H ex = 1 Oe). (b) Magnetization versus external magnetic field measured at K.

5 2 Total Unoccupied Fe3d, Rhd Energy / ev Energy / ev -2 Rh ( 1) O Occupied O2p Rhd - -6 Fe Occupied Fe3d - Density of states Density of states Supplementary Figure S5 DOS of ε-rh.125 Fe 1.75 O 3 from first-principles calculation. Total DOS (gray lines), iron DOS (red lines), rhodium DOS (green lines), and oxygen DOS (blue lines) are shown. 5

6 β spin α spin Fe A Fe B unoccupied occupied β spin Fe3d α spin Fe3d Fe C Fe D Rhd Supplementary Figure S6 DOS of each Fe site. Right and left side of each DOS indicate α spin and β spin, respectively. Colored regions denote occupied regions. Red and pink indicate α and β spins of iron, and green and light green indicate α and β spins of rhodium, respectively. 6

7 c a O O6 O6 Fe A Fe3dz 2 O1 O2 O1 O2p covalency O2 Rh hybridization Rhdzx O5 O5 O Supplementary Figure S7 Charge density map of ε-rh.125 Fe 1.75 O 3. A representative charge density map of ε-rh.125 Fe 1.75 O 3 projected from a axis (upper left) and b axis (upper right). The lower figure is a close up of the Rh O Fe hybridization (left) and its schematic illustration (right). 7

8 (P3) (P2) (P1) Supplementary Figure S Millimeter wave absorption and rotation measurements. Schematic diagram of the THz-TDS measurement system.

9 Supplementary Table S1 Atomic positions refined by Rietveld analyses. Atomic positions of ε-rh x Fe 2 x O 3 and α-rh x Fe 2 x O 3 for each sample obtained by Rietveld refinement of the XRD patterns. ε-fe 2 O 3 ε-rh. Fe 1.96 O 3 ε-rh.7 Fe 1.93 O 3 ε-rh.11 Fe 1.9 O 3 ε-rh.1 Fe 1.6 O 3 Fe A x.316 (2).6 (3).313 (2). (5). (2) y.33 (9).37 (2).351 (11).35 (13).376 (1) z.15 (2).153 ().151 (2).15 (3).156 (2) Fe B x.32 (1).31 (2).3196 (1).3 (2).36 (1) y.3 ().31 (7).3 ().319 (5).32 () z.371 (2).365 ().366 (2).372 ().36 (2) Fe C x. (9).9 (13).3113 (7).3119 (9).311 (6) y.65 (5).6591 (7).65 ().6596 (6).6597 () z.37 (2).377 ().372 (2).379 (3).32 (2) Fe D x.197 (2).16 (3).191 (2).17 (3).15 (2) y.517 (7).9 (2).96 (1).51 (1).9 (9) z.77 (2).71 ().6 (2).75 (3).72 (2) O1 x.15 ().27 (7).19 ().1 (7).32 () y.32 (2).323 (3).32 (2).325 (2).329 (2) z O2 x.993 ().92 (6).992 ().976 (5).92 () y.2 (2).5 (3).6 (2). (2).7 (2) z.9 (5).995 ().997 (5) 1. (6) 1.2 () O3 x.17 (5).29 (7).2 ().22 (6).21 () y.667 (2).671 (3).666 (2).6 (3).669 (2) z.12 (2). ().6 (3).7 (3).15 (2) O x.16 ().157 (7).15 ().1 (6).15 () y.9 (2).97 (3).96 (2).9 (2).9 (2) z.266 (2).266 (3).26 (2).272 (3).276 (2) O5 x.15 (5).159 (7).15 (5).167 (6).1 () y.7 (3).2 ().2 (3).39 ().1 (2) z.26 (2).267 ().265 (2).273 (3).267 (2) O6 x.152 (5).156 ().153 (5).152 (7).156 () y.163 (3).166 ().16 (3).1 (3).169 (2) z.2 (2).2 ().21 (2).22 (3).23 (2) α-rh.2 Fe 1.9 O 3 α-rh.12 Fe 1. O 3 α-rh.16 Fe 1. O 3 α-rh.2 Fe 1.76 O 3 Fe x y z.352 (6).351 (5).3529 () (1) O x.9 (6).311 ().323 (). (9) y z