Theoretical prediction of a charge-transfer phase transition

Phase transition materials are attractive from the viewpoints of basic science as well as practical applications. For example, optical phase transition materials are used for optical recording media. If a phase transition in condensed matter could be predicted or designed prior to synthesizing, the development of phase transition materials will be accelerated. Herein we show a logical strategy for designing a phase transition accompanying a thermal hysteresis loop. Combining first-principles phonon mode calculations and statistical thermodynamic calculations considering cooperative interaction predicts a charge-transfer phase transition between the A–B and A+–B− phases. As an example, we demonstrate the charge-transfer phase transition on rubidium manganese hexacyanoferrate. The predicted phase transition temperature and the thermal hysteresis loop agree well with the experimental results. This approach will contribute to the rapid development of yet undiscovered phase transition materials.


Theoretical prediction of charge-transfer phase transition
Hiroko Tokoro, 1,2,* Asuka Namai, 1 Marie Yoshikiyo, 1 Rei Fujiwara, 2 Kouji Chiba, 3 and Shin-ichi Ohkoshi, 1,4,* Table S1. Crystal structure (upper) and calculated phonon frequencies obtained by first-principles calculations (lower) of the Fe II -Mn III phase. The list contains the optical phonon frequencies at the Brillouin zone center, Γ points, multiplicities, irreducible representations, and IR and Raman activities. §2. Crystal structure and calculated phonon frequencies of the Fe II -Mn III phase.

Crystal system
Space group  The reason why U -J = 4eV in GGA+U is used for the phonon mode calculation is as follows. We have to use the same U -J value for Fe II -Mn III and Fe III -Mn II phases. The value of (U -J)/eV should be the number of d-electrons on the metal ions or a smaller number. For example, in Fe III (3d 5 )-CN -Mn II (3d 5 ) phase, the numbers of the d-electrons are 5, and thus, U -J value should be below 5 eV. In Fe II (3d 6 )-CN-Mn III (3d 4 ) phase, the numbers of d-electrons are 6 and 4 for Fe II and Mn III , respectively, and hence, U -J should be below 4 eV, i.e., U -J ≤ 4eV. Thus, we used U -J = 4 eV as the common parameter for the Fe II -Mn III and Fe III -Mn II phases. It is noted that we also investigated a calculation with U -J = 0 eV. The result with U -J = 0 eV shows a disappearance of the band gap, i.e., conducting property, despite the isolating property of the present system. A small U − J value is not appropriate for the present system, and we used U -J = 4 eV as the maximum value in the condition of U -J ≤ 4eV. §4. First-principles phonon mode calculations.. §5. Contribution from orbital degeneracy and spin multiplicity on the entropy.
Contributions from the orbital degeneracy and the spin multiplicity, i.e., S os values, are Rln5 for the Fe II -Mn III phase and Rln36 for the Fe III -Mn II phase. This is because the Fe II -Mn III phase consists of Fe II ( 1 A 1g ) and Mn III ( 5 B 1g ), in which 1 A 1g has a one (= 1 (orbital degeneracy) ×1 (spin multiplicity))-fold degeneracy and 5 B 1g has a five (= 1×5)-fold degeneracy. Therefore, the degeneracy of the Fe II -Mn III phase is five (= 1×5)-fold. In contrast, the degeneracy of the Fe III -Mn II phase is 36 (= 6×6)-fold since the Fe III -Mn II phase consists of Fe III ( 2 T 2g ) and Mn II ( 6 A 1g ), where 2 T 2g has a six (= 3×2)-fold degeneracy and 6 A 1g has a six (= 1×6)-fold degeneracy.
S5 §6. Schematic crystal structure of the virtual transient structure.  Figure S1. a, Schematic crystal structure of the virtual transient structure as an alternating mixed phase of (A-B layer)-by-(A + -B − layer) (i.e., (Fe II -Mn III layer)-by-(Fe III -Mn II layer)) along the c-axis of the tetragonal structure (a = b ≠ c). Green, blue, light blue, red, and orange spheres represent Rb I , Mn II , Fe II , Mn II , and Fe III , respectively. b, Schematic illustration of Fe II -Mn III structure (lower left), layer-by-layer structure (tr-phase) (upper middle), and Fe III -Mn II structure (lower right). Diagram in the center shows the calculated excess enthalpies at the transition temperature (ΔH E (325)) for the Fe II -Mn III phase (blue square), tr-phase (black square), and Fe III -Mn II phase (red square).

S8
We performed Raman spectroscopy measurements. The Raman spectrum of the Fe III -Mn II phase shows a strong peak at 2162 cm −1 with a shoulder peak at 2155 cm −1 . These peaks almost correspond to the calculated Raman active modes at 2220 cm −1 and 2212 cm −1 . On the other hand, in the Raman spectrum of the Fe II -Mn III phase, peaks are observed at 2091 cm −1 , 2109 cm −1 , 2162 cm −1 , and 2202 cm −1 . The peaks at 2091 cm −1 , 2109 cm −1 , and 2202 cm −1 correspond to the calculated peaks due to the C≡N stretching modes at 2127 cm −1 , 2148 cm −1 , and 2207 cm −1 . The peak at 2162 cm −1 is due to the remaining Fe III -Mn II phase. The Fe III -Mn II phase was remained because the measurement was conducted at room temperature after cooling the sample by indirect contact with liquid N 2 .  Figure S3. Raman spectra of Rb 0.94 Mn[Fe(CN) 6 ] 0.98 ·0.3H 2 O. a, Observed spectrum of the Fe II -Mn III phase measured at room temperature after cooling the sample by indirect contact with liquid N 2 . Pink shadow indicates the peak assigned to the remaining Fe III -Mn II phase. b, Observed spectrum of the Fe III -Mn II phase measured at room temperature. c, Calculated Raman spectrum using the probability of each phonon mode of the Fe II -Mn III phase. d, Calculated Raman spectrum using the probability of each phonon mode of the Fe III -Mn II phase.