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分子内部の有効電場と電子の電気双極子モーメントに
2P117 ࢠ෦ͷ༗ޮిͱిࢠͷిؾࢠۃϞʔϝϯτʹىҼ͢ΔεϐϯτϧΫ ʢژେӃɾʣ ીզ ߁ଠɺా কେɺ େɺཱՖ ໌ Effective electric field and spin torque induced by electron electric dipole moment in molecules (Kyoto Univ.) Kota Soga, Masahiro Fukuda, Masato Senami, Akitomo Tachibana ʲংʳిࢠͷӬؾిٱࢠۃϞʔϝϯτ (Electric Dipole Moment, EDM) ɺͦͷεϐϯʹਵ͢Δిՙ ͷภΓΛද͢ϕΫτϧྔͰ͋Δɻؒ࣌ʹܥస (T) มΛࢪͯ͠ిՙෆมʢ͢ͳΘͪɺEDM ෆมʣͰ͋ΔҰํɺεϐϯͦͷ͖Λม͑Δɻ͕ͨͬͯ͠ɺnon-zero ͷ EDM ͕ଘࡏ͢Ε T ରশੑ ഁΕΔɻT ରশੑͷഁΕΛࣔ͢ݱɺ࣌ؒͷෆՄٯੑӉʹ͓͚Δ࣭ɾ࣭ͷඇରশੑΛཧ ղ͢Δ্ͰॏཁͳͳͱݤΔͨΊɺEDM ͷ୳ࠪΛؚΊɺ͜Ε·Ͱʹ؍ଌͷࢼΈ͕ଟ͘ߦΘΕ͖ͯͨͷ ͷɺͷ؍ଌʹࢸ͍ͬͯͳ͍ɻ ૉཻࢠͷඪ४͕ܕ༧͢ݴΔిࢠ EDM ͷ (d e ) ඇৗʹখ͘͞ɺࡏݱͷ؍ଌݶքΛ͍͑ͯΔɻ͠ ͔͠ɺରশܕΛ͡Ίͱͨ͠ඪ४ʹܕର͢Δଟ͘ͷ֦ுཧͰɺࡏݱͷ࣮ݧਫ਼Ͱ؍ଌՄೳͳ ΄Ͳେ͖ͳ d e ͕༧͞ݴΕ͍ͯΔɻඇৗʹߴਫ਼ͷ࣮ ࢠి͍͓͑ͯ͞ʹݧEDM ͷଘࡏ͕؍ଌ͞Εͳ͍ ߹ɺ֦ுཧ࣍ʑʹഉআ͞Ε͍ͯ͘͜ͱʹͳΔ͕ɺ͠ EDM ͷଘࡏ͕ݕग़͞ΕΕඪ४ʹܕର͢Δ ৽ཧͷඞཁੑ͕࣮ݧతʹࣔ͞Εͨ͜ͱʹͳΔɻ͢ͳΘͪɺnon-zero ͷిࢠ EDM ͷଘࡏ T ରশੑͷഁ ΕͷతͳূͳͱڌΔ͚ͩͰͳ͘ɺඪ४ܕΛ͑ͨ৽͍͠ཧΛ୳ࡧ͢ΔࢦʹͳΔɻ ిࢠ EDM ͷ୳ࠪʹɺࢠ෦ͷ༗ޮిͱͦΕʹґଘ͢Δిࢠεϐϯͷࡀࠩӡಈ͕த৺తͳׂ ΛՌͨ͢ɻNon-zero ͷిࢠ EDM ͕ଘࡏ͢Δ͜ͱͰͲͷΑ͏ͳεϐϯτϧΫ͕ੜ͡Δ͔Λ໌Β͔ʹ͠ɺͦ Εʹ͏ిࢠεϐϯͷμΠφϛΫεΛਖ਼֬ʹ༧ଌ͢Δ͜ͱɺEDM ݕग़ͷͨΊʹෆՄܽͰ͋Δɻզʑͷ ڀݚάϧʔϓͰɺEDM ༗ޮిͷʹࢉܭՃ͑ɺͷཧʹͮ͘جεϐϯμΠφϛΫεͷ ڀݚ1 ߦͬ ͍ͯΔɻຊͰڀݚɺྔࢠిࢠεϐϯӔཧ 2−4 ʹΑͬͯಋ͔ΕΔͷཧʹॴہͮ͘جతͳిࢠεϐϯ ͷӡಈํఔࣜʹɺEDM ͷଘࡏʹىҼ͢ΔεϐϯτϧΫ͕ՃΘΔ͜ͱΛࣔ͠ɺ࣌ࠁ t = 0 Ͱఆৗঢ়ଶʹ͋ Δ֎ʹܥ෦੩ి࣓ΛҹՃͨ͠ࡍʹ༠͞ىΕΔॴہཧྔͷΛௐͨɻ ˆ ʲཧʳͷཧʹ͓͍ͯɺిࢠεϐϯ sˆe (x) ͷ࣌ؒൃలεϐϯτϧΫ tˆe (x) ͱπΣʔλྗ ζe (x) ʹΑͬ ͯࢧ͞ΕΔɻ ∂ ˆ ˆ s e (x) = tˆe (x) + ζe (x) ∂t (1) ͦΕͧΕͷཧྔిࢠ ψ̂(x) ͱޫࢠ  μ (x) Λ༻͍ͯ࣍ͷΑ͏ʹఆٛ͞ΕΔɻ † ic ŝ ei = ψ̂ † Σ i ψ̂, tˆei = − ε i j k ψ̂ † γ 0 γ k ∂ j ψ̂ − ∂ j ψ̂ γ 0 γ k ψ̂ − (Ze e) ε i j k ψ̂ † γ 0 γ k  j ψ̂ 2 2 μ i jˆ0, jˆ5 = Ze ecψ̄ˆ γ μ γ5 ψ̂, γ5 = iγ 0 γ 1 γ 2 γ 3, e = |e|, Ze = −1 ζˆe = −∂i φ̂5, φ̂5 = 2Ze e 5 (2) (3) , c, e ͦΕͧΕϓϥϯΫఆɺਅۭதͰͷޫɺૉిՙͰ͋Γɺγ μ , Σ i ͦΕͧΕΨϯϚߦྻɺ4 ࣍ Λ૬ରԽ͢Δ ݩύϦߦྻͰ͋ΔɻΤωϧΪʔͰͷ༗ޮ EDM ϋϛϧτχΞϯ HEDM = −de · E i ˆ μν ͜ͱͰಘΒΕΔ૬ରత༗ޮ EDM ϥάϥϯδΞϯ L̂ EDM (x) = −d e 2 ψ̄ (x)σ γ5 F̂μν (x) ψ̂(x) F̂μν (x) = ∂μ Âν (x) − ∂ν  μ (x), σ μν = 2i [γ μ , γν ] Λ༻͍Δ͜ͱͰɺిࢠεϐϯͷӡಈํఔࣜ (1) ͷӈลʹ࣍ࣜͰ༩͑ ˆEDM (x) ͕ิਖ਼߲ͱͯ͠ՃΘΔɻ ΒΕΔ EDM ͷଘࡏʹىҼ͢ΔεϐϯτϧΫ T ˆ ˆ ele ˆ mag TEDM (x) = TEDM (x) + TEDM (x) (4) ˆ ele mag ˆ ψ̂(x), TˆEDM ˆ ψ̂(x) × B(x) TEDM (x) = d e ψ̄ˆ (x)Σ × E(x) (x) = d e i ψ̄ˆ (x)γ 0 γ (5) ˆ ˆ ૬ରԽʹ͍ɺి E(x) ͚ͩͰͳ࣓͘ B(x) ͱ૬͢༻࡞ޓΔ͜ͱ͕Θ͔Δɻ ຊൃදͰɺYbF, ThO, BaF ࢠΛରʹɺզʑͷڀݚάϧʔϓ͕։ൃΛߦ͍ͬͯΔ QE Dynamics5 Λ ༻͍ͯߦͬͨ EDM ༗ޮిɺ͓Αͼॴہཧྔͷ݁ࢉܭՌΛࣔ͢ɻ M = (1, 0, 0) [a.u.] ΛҹՃͨ͠ͱ͖ͷ BaF ࢠ M = (1, 0, 0), B ʲ݁Ռͱߟʳ࣌ࠁ t = 0 ʹ֎෦੩ి࣓ E ele EDM ɺ࣓ʹىҼ͢Δ EDM τϧΫີ ෦ͷεϐϯ֯ӡಈྔີ s e ɺిʹىҼ͢Δ EDM τϧΫີ T mag ͷΛͦΕͧΕਤ 1-3 ࣔ͢ɻਤதͷ͕֤ʹ͓͚ΔϕΫτϧΛද͠ɺϊϧϜͷΛͦͷ৭ʹΑͬ TEDM ͯࢠݪ୯ҐͰද͍ͯ͠ݱΔɻ·ͨɺਤதͷ͍ ͕ٿBa ֩ࢠݪΛɺ੨͍ ͕ٿF ֩ࢠݪΛද͍ͯ͠Δɻ εϐϯ֯ӡಈྔີ͔֩ࢠݪΒΕͨҐஔʹภ͍ͬͯͯ͠Δ͜ͱ͕Θ͔ΔɻిىҼͷ EDM τϧΫີͷεϐϯ֯ӡಈྔີͷͱࣅ௨͍ͬͯΔ͕ɺ͜Εࣜ (5) ͔ΒཧղͰ͖Δɻ͢ͳΘͪɺ x ࣠ํʹҰ༷ͳిΛҹՃ͍ͯ͠ΔͨΊɺ1/c ͷ࣍·ͰΛऔΓѻ͏ඇ૬ରݶۃΛͱΕɺిىҼͷ EDM τϧΫີͷϊϧϜεϐϯ֯ӡಈྔີͷϊϧϜʹൺྫ͍ͯ͠ΔɻҰํɺ࣓ىҼͷ EDM τϧΫ ີ֩ࢠݪͷपғΛӔ͘רΑ͏ʹ͍ͯ͠Δ͜ͱ͕Θ͔Δɻࣜ (5) Λม͢ܗΔ͜ͱʹΑΓɺ࣓ىҼͷ EDM τϧΫີͷओཁ߲ిࢠີͷޯͱҹՃ࣓ͷ֎ੵͰॻ͚Δ͜ͱΛࣔͤΔɻిࢠີͷޯ ֩ࢠݪΛத৺ʹ์ࣹঢ়ͷΛ͍ͯ͠ΔͨΊɺҰ༷࣓ͱͷ֎ੵʹΑΓӔঢ়ͷʹͳͬͨͱཧղͰ͖Δɻ ύλʔϯ͔ΒΘ͔ΔΑ͏ʹɺશۭؒʹ͓͚Δظ ʹؔͯ͠ಉ͡ํΛ͍͍ͯΔిىҼͷτϧΫͷํ ͕࣓ىҼͷτϧΫΑΓͣͬͱେ͖͘ͳΔɻ͔͠͠ɺہ ॴతͳྖҬʹ͢Δͱɺ֓ͯ͑͠ݴ࣓ىҼͷτϧ Ϋͷํ͕ిىҼͷτϧΫΑΓେ͖͍ޮՌΛ༩͑Δɻ ͜ͷΑ͏ʹɺͷཧʹʹີݫͮ͘جఆٛ͞Εͨॴہత ͳཧྔΛऔΓѻ͏͜ͱʹΑΓɺશۭؒͰͷظͷΈ ΛऔΓѻ͏ྔࢠྗֶͰ༧ଌͰ͖ͳ͍ཧతੑ࣭Λཧղ ͢Δ͜ͱ͕Ͱ͖Δɻ εϐϯ֯ӡಈྔີ s e εϐϯτϧΫ t eɾπΣʔλྗ mag ele + TEDM ʹ ζe ɺͦͯ͜͜͠Ͱࣔͨ͠ EDM τϧΫີ TEDM ਤ 1 εϐϯ֯ӡಈྔີ s e Αͬͯۦಈ͞Εɺ࣌ؒͷܦաͱͱʹࡀࠩӡಈΛߦ͏͜ ͱʹͳΔɻ ele ਤ 2 ిʹىҼ͢Δ EDM τϧΫີ T EDM ਤ 3 ࣓ʹىҼ͢Δ EDM τϧΫີ T EDM mag ʲࠓޙͷలʳ্Ͱड़ͨεϐϯμΠφϛΫεͷΈͷཧʹཱͨ͠٭ͷͰ͋ΓɺͦΕΏ͑ॴہ తͳใ͕ࣦΘΕΔ͜ͱͳ͍ɻকདྷతͳ࣮ݧͷߴਫ਼ɾߴղೳԽʹͬͯɺશۭؒͰͷظͷΈΛ هड़͢Δैདྷͷྔࢠྗֶతͳࢉܭख๏Ͱ༧ଌͰ͖ͳ͍ɺॴہతͳޮՌ͕؍ଌ͞ΕΔ͜ͱ͕ظ͞ΕΔɻ 1. A. Tachibana, J. Mol. Model. 11, 301-311 (2005); J. Mol. Struct.: THEOCHEM 943, 138-151 (2010). 2. A. Tachibana, J. Math. Chem. 50, 669-688 (2012). 3. A. Tachibana, In Concepts and Methods in Modern Theoretical Chemistry, S. K. Ghosh and P. K. Chattaraj Eds., CRC Press, Florida (2013), pp 235-251. 4. A. Tachibana, J. Comput. Chem. Jpn. 13, 18-31 (2014). 5. QEDynamics, M. Senami, K. Ichikawa, A. Tachibana, http://www.tachibana.kues.kyoto-u.ac.jp/qed/index.html.