VI-1-2 Mn酸化物の磁気ダイナミクス—二重交換相互作用と軌道秩序
立方ペロブスカイトMn酸化物AMnO3はMnサイトへのホールの導入により巨大磁気抵抗効果が現れることで有名な物質であるが,スピン・軌道・電荷の自由度が絡み合うことで多彩な物性を示す代表的な系としてもよく知られている。この物質における各自由度の役割を明らかにする研究の中で中性子散乱は重要な役割を果たしてきた。AMnO3の基本物性やこの物質が示す代表的な磁気・軌道秩序について概説し,本物質に特徴的なスピン間相互作用である二重交換相互作用や軌道秩序によって生じるスピン相関の様子を,非弾性中性子散乱によるスピン波の解析から調べた研究例を紹介する。...
Saved in:
Published in | RADIOISOTOPES Vol. 65; no. 9; pp. 393 - 401 |
---|---|
Main Authors | , |
Format | Journal Article |
Language | Japanese |
Published |
公益社団法人 日本アイソトープ協会
2016
|
Subjects | |
Online Access | Get full text |
ISSN | 0033-8303 1884-4111 |
DOI | 10.3769/radioisotopes.65.393 |
Cover
Abstract | 立方ペロブスカイトMn酸化物AMnO3はMnサイトへのホールの導入により巨大磁気抵抗効果が現れることで有名な物質であるが,スピン・軌道・電荷の自由度が絡み合うことで多彩な物性を示す代表的な系としてもよく知られている。この物質における各自由度の役割を明らかにする研究の中で中性子散乱は重要な役割を果たしてきた。AMnO3の基本物性やこの物質が示す代表的な磁気・軌道秩序について概説し,本物質に特徴的なスピン間相互作用である二重交換相互作用や軌道秩序によって生じるスピン相関の様子を,非弾性中性子散乱によるスピン波の解析から調べた研究例を紹介する。 |
---|---|
AbstractList | 立方ペロブスカイトMn酸化物AMnO3はMnサイトへのホールの導入により巨大磁気抵抗効果が現れることで有名な物質であるが,スピン・軌道・電荷の自由度が絡み合うことで多彩な物性を示す代表的な系としてもよく知られている。この物質における各自由度の役割を明らかにする研究の中で中性子散乱は重要な役割を果たしてきた。AMnO3の基本物性やこの物質が示す代表的な磁気・軌道秩序について概説し,本物質に特徴的なスピン間相互作用である二重交換相互作用や軌道秩序によって生じるスピン相関の様子を,非弾性中性子散乱によるスピン波の解析から調べた研究例を紹介する。 |
Author | 吉沢, 英樹 梶本, 亮一 |
Author_xml | – sequence: 1 fullname: 吉沢, 英樹 organization: 東京大学物性研究所 – sequence: 1 fullname: 梶本, 亮一 organization: 国立研究開発法人日本原子力研究開発機構J-PARCセンター |
BookMark | eNpVkL9Kw0AAhw-pYK19A18h9S53ueRGKf6pVFxUcAqX5KIptSlJF7e0RUSpFLToUMHBgu2ijjXiy3hpY99CRBFcft_y8Q2_RZCp-TUBwDKCBaxTthJwx_O90G_4dREWqFbADM-BLDIMohCEUAZkIcRYMTDECyAfhp4FNYMwgijOgoP9koIUVUbRdm12Op50btLzkWw-pQ_N6cutbEeyNZDtC9m-l61n2Xr9iHpJ3JmdXSbxYNrtp_1xEl8l73dpbyibw8-3zqx5nT6OJnF3Ccy7vBqK_C9zYG99bbe4qZR3NkrF1bJSQQxyRWDDpUhXiYtVSDXCIbSphYmrC4sbjDKN6I6DLWyrUFhYEEJsilRH02zH1i0L58DWT7cSNvihMOuBd8yDE5MHDc-uCvPfPybVTPY9VIMMkj_JPuKBWeH4C-vgg2E |
ContentType | Journal Article |
Copyright | 2016 公益社団法人日本アイソトープ協会 |
Copyright_xml | – notice: 2016 公益社団法人日本アイソトープ協会 |
DOI | 10.3769/radioisotopes.65.393 |
DatabaseTitleList | |
DeliveryMethod | fulltext_linktorsrc |
Discipline | Medicine |
EISSN | 1884-4111 |
EndPage | 401 |
ExternalDocumentID | article_radioisotopes_65_9_65_650904_article_char_ja |
GroupedDBID | .55 123 ABWPA ALMA_UNASSIGNED_HOLDINGS CS3 DU5 E3Z F5P HH5 JSF JSH OK1 RJT RZJ X7M |
ID | FETCH-LOGICAL-j190a-e38f61724f320654a00c6b34f7eba8969547dd3b3c20eb3e444c612d55cdc7bb3 |
ISSN | 0033-8303 |
IngestDate | Wed Sep 03 06:29:14 EDT 2025 |
IsDoiOpenAccess | true |
IsOpenAccess | true |
IsPeerReviewed | false |
IsScholarly | true |
Issue | 9 |
Language | Japanese |
LinkModel | OpenURL |
MergedId | FETCHMERGED-LOGICAL-j190a-e38f61724f320654a00c6b34f7eba8969547dd3b3c20eb3e444c612d55cdc7bb3 |
OpenAccessLink | https://www.jstage.jst.go.jp/article/radioisotopes/65/9/65_650904/_article/-char/ja |
PageCount | 9 |
ParticipantIDs | jstage_primary_article_radioisotopes_65_9_65_650904_article_char_ja |
PublicationCentury | 2000 |
PublicationDate | 2016 |
PublicationDateYYYYMMDD | 2016-01-01 |
PublicationDate_xml | – year: 2016 text: 2016 |
PublicationDecade | 2010 |
PublicationTitle | RADIOISOTOPES |
PublicationYear | 2016 |
Publisher | 公益社団法人 日本アイソトープ協会 |
Publisher_xml | – name: 公益社団法人 日本アイソトープ協会 |
References | 22) Ewings, R. A., Perring, T. G., Sikora, O., Abernathy, D. L., Tomioka, Y. and Tokura, Y., Spin excitations used to uncover the nature of the magnetically ordered ground state of Pr0.5Ca0.5MnO3, Phys. Rev. B, 94, 014405 (2016 13) Martin, M. C., Shirane, G., Endoh, Y., Hirota, K., Moritomo, Y. and Tokura, Y., Magnetism and structural distortion in the La0.7Sr0.3MnO3 metallic ferromagnet, Phys. Rev. B, 53, 14285–14290 (1996 19) Senff, D., Krüger, F., Scheidl, S., Benomar, M., Sidis, Y., Demmel, F. and Braden, M., Spin-wave dispersion in orbitally ordered La1/2Sr3/2MnO4, Phys. Rev. Lett., 96, 257201 (2006 1) Wollan, E. O. and Koehler, W. C., Neutron diffraction study of the magnetic properties of the series of perovskite-type compounds [(1−x)La, xCa]MnO3, Phys. Rev., 100, 545–563 (1955 5) Rodríguez-Carvajal, J., Hennion, M., Moussa, F., Moudden, A. H., Pinsard, L. and Revcolevschi, A., Neutron-diffraction study of the Jahn-Teller transition in stoichiometric LaMnO3, Phys. Rev. B, 57, R3189–R3192 (1998 25) Khaliullin, G. and Kilian, R., Theory of anomalous magnon softening in ferromagnetic manganites, Phys. Rev. B, 61, 3494–3501 (2000 11) Kajimoto, R., Yoshizawa, H., Kawano, H., Kuwahara, H., Tokura, Y., Ohoyama, K. and Ohashi, M., Hole-concentration-induced transformation of the magnetic and orbital structures in Nd1−xSrxMnO3, Phys. Rev. B, 60, 9506–9517 (1999 16) Yoshizawa, H., Kawano, H., Fernandez-Baca, J. A., Kuwahara, H. and Tokura, Y., Anisotropic spin waves in a metallic antiferromagnet Nd0.45Sr0.55MnO3, Phys. Rev. B, 58, R571–R574 (1998 26) Kajimoto, R., Yoshizawa, H., Kawano-Furukawa, H., Kuwahara, H., Tomioka, Y. and Tokura, Y., Orbital-ordering-induced anomalous softening of the ferromagnetic spin waves in perovskite manganites, J. Magn. Magn. Mater., 226–230, 892–894 (2001 15) Hirota, K., Kaneko, N., Nishizawa, A. and Endoh, Y., Two-dimensional planar ferromagnetic coupling in LaMnO3, J. Phys. Soc. Jpn., 65, 3736–3739 (1996 27) Endoh, Y., Hiraka, H., Tomioka, Y., Tokura, Y., Nagaosa, N. and Fujiwara, T., Orbital nature of ferromagnetic magnons in manganites, Phys. Rev. Lett., 94, 017206 (2005 23) Zimmermann, M., Nelson, C. S., Hill, J. P., Gibbs, D., Blume, M., Casa, D., Keimer, B., Murakami, Y., Kao, C. C., Venkataraman, C., Gog, T., Tomioka, Y. and Tokura, Y., X-ray resonant scattering studies of orbital and charge ordering in Pr1−xCaxMnO3, Phys. Rev. B, 64, 195133 (2001 21) Johnstone, G. E., Perring, T. G., Sikora, O., Prabhakaran, D. and Boothroyd, A. T., Ground state in a half-doped manganite distinguished by neutron spectroscopy, Phys. Rev. Lett., 109, 237202 (2012 6) Ozawa, T. C. and Kang, S. J., Balls&Sticks: easy-to-use structure visualization and animation program, J. Appl. Cryst., 37, 679 (2004 10) Maezono, R., Ishihara, S. and Nagaosa, N., Orbital polarization in manganese oxides, Phys. Rev. B, 57, R13993–R13996 (1998 20) Ulbrich, H., Krüger, F., Nugroho, A. A., Lamago, D., Sidis, Y. and Braden, M., Spin-wave excitations in the ferromagnetic metallic and in the charge-, orbital-, and spin-ordered states in Nd1−xSrxMnO3 with x≈0.5, Phys. Rev. B, 84, 094453 (2011 14) Endoh, Y. and Hirota, K., Scaling of spin-wave stiffness constant to Curie temperature in the colossal magnetoresistance material La1−xSrxMnO3, J. Phys. Soc. Jpn., 66, 2264–2267 (1997 18) Doud-Aladine, A., Rodriguez-Carvajal, J., Pinsard-Gaudart, L., Fernandez-Diaz, M. and Revcolevschi, A., Zener polaron ordering in half-doped manganites, Phys. Rev. Lett., 89, 097205 (2002 8) Anderson, P. W. and Hasegawa, H., Considerations on double exchange, Phys. Rev., 100, 675–681 (1955 2) Goodenough, J. B., Theory of the role of covalence in the perovskite-type manganites [La, M(II)]MnO3, Phys. Rev., 100, 564–573 (1955 4) Glazer, A. M., Simple ways of determining perovskite structures, Acta Crystallogr. A, 31, 756–762 (1975 7) Zener, C., Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure, Phys. Rev., 82, 403–405 (1951 12) Kuwahara, H., Okuda, T., Tomioka, Y., Asamitsu, A. and Tokura, Y., Two-dimensional charge-transport and spin-valve effect in the layered antiferromagnet Nd0.45Sr0.55MnO3, Phys. Rev. Lett., 82, 4316–4319 (1999 24) Kajimoto, R., Mochizuki, H., Yoshizawa, H., Okamoto, S. and Ishihara, S., Ferromagnetic insulating phase in Pr1−xCaxMnO3, Phys. Rev. B, 69, 054433 (2004 3) Tokura, Y., Urushibara, A., Moritomo, Y., Arima, T., Asamitsu, A., Kido, G. and Furukawa, N., Giant magnetotransport phenomena in filling-controlled Kondo lattice system: La1−xSrxMnO3, J. Phys. Soc. Jpn., 63, 3931–3935 (1994 9) Millis, A. J., Littlewood, P. B. and Shraiman, B. I., Double exchange alone does not explain the resistivity of La1−xSrxMnO3, Phys. Rev. Lett., 74, 5144–5147 (1995 17) Kajimoto, R., Yoshizawa, H., Kawasaki, R., Noda, K. and Kuwahara, H., Spin wave and orbital ordering in the C-type antiferromagnetic phase of Nd1−xSrxMnO3, J. Phys. Soc. Jpn., 74, 502–503 (2005 |
References_xml | – reference: 7) Zener, C., Interaction between the d-shells in the transition metals. II. Ferromagnetic compounds of manganese with perovskite structure, Phys. Rev., 82, 403–405 (1951) – reference: 9) Millis, A. J., Littlewood, P. B. and Shraiman, B. I., Double exchange alone does not explain the resistivity of La1−xSrxMnO3, Phys. Rev. Lett., 74, 5144–5147 (1995) – reference: 1) Wollan, E. O. and Koehler, W. C., Neutron diffraction study of the magnetic properties of the series of perovskite-type compounds [(1−x)La, xCa]MnO3, Phys. Rev., 100, 545–563 (1955) – reference: 5) Rodríguez-Carvajal, J., Hennion, M., Moussa, F., Moudden, A. H., Pinsard, L. and Revcolevschi, A., Neutron-diffraction study of the Jahn-Teller transition in stoichiometric LaMnO3, Phys. Rev. B, 57, R3189–R3192 (1998) – reference: 6) Ozawa, T. C. and Kang, S. J., Balls&Sticks: easy-to-use structure visualization and animation program, J. Appl. Cryst., 37, 679 (2004) – reference: 16) Yoshizawa, H., Kawano, H., Fernandez-Baca, J. A., Kuwahara, H. and Tokura, Y., Anisotropic spin waves in a metallic antiferromagnet Nd0.45Sr0.55MnO3, Phys. Rev. B, 58, R571–R574 (1998) – reference: 15) Hirota, K., Kaneko, N., Nishizawa, A. and Endoh, Y., Two-dimensional planar ferromagnetic coupling in LaMnO3, J. Phys. Soc. Jpn., 65, 3736–3739 (1996) – reference: 20) Ulbrich, H., Krüger, F., Nugroho, A. A., Lamago, D., Sidis, Y. and Braden, M., Spin-wave excitations in the ferromagnetic metallic and in the charge-, orbital-, and spin-ordered states in Nd1−xSrxMnO3 with x≈0.5, Phys. Rev. B, 84, 094453 (2011) – reference: 21) Johnstone, G. E., Perring, T. G., Sikora, O., Prabhakaran, D. and Boothroyd, A. T., Ground state in a half-doped manganite distinguished by neutron spectroscopy, Phys. Rev. Lett., 109, 237202 (2012) – reference: 3) Tokura, Y., Urushibara, A., Moritomo, Y., Arima, T., Asamitsu, A., Kido, G. and Furukawa, N., Giant magnetotransport phenomena in filling-controlled Kondo lattice system: La1−xSrxMnO3, J. Phys. Soc. Jpn., 63, 3931–3935 (1994) – reference: 25) Khaliullin, G. and Kilian, R., Theory of anomalous magnon softening in ferromagnetic manganites, Phys. Rev. B, 61, 3494–3501 (2000) – reference: 27) Endoh, Y., Hiraka, H., Tomioka, Y., Tokura, Y., Nagaosa, N. and Fujiwara, T., Orbital nature of ferromagnetic magnons in manganites, Phys. Rev. Lett., 94, 017206 (2005) – reference: 10) Maezono, R., Ishihara, S. and Nagaosa, N., Orbital polarization in manganese oxides, Phys. Rev. B, 57, R13993–R13996 (1998) – reference: 12) Kuwahara, H., Okuda, T., Tomioka, Y., Asamitsu, A. and Tokura, Y., Two-dimensional charge-transport and spin-valve effect in the layered antiferromagnet Nd0.45Sr0.55MnO3, Phys. Rev. Lett., 82, 4316–4319 (1999) – reference: 17) Kajimoto, R., Yoshizawa, H., Kawasaki, R., Noda, K. and Kuwahara, H., Spin wave and orbital ordering in the C-type antiferromagnetic phase of Nd1−xSrxMnO3, J. Phys. Soc. Jpn., 74, 502–503 (2005) – reference: 24) Kajimoto, R., Mochizuki, H., Yoshizawa, H., Okamoto, S. and Ishihara, S., Ferromagnetic insulating phase in Pr1−xCaxMnO3, Phys. Rev. B, 69, 054433 (2004) – reference: 2) Goodenough, J. B., Theory of the role of covalence in the perovskite-type manganites [La, M(II)]MnO3, Phys. Rev., 100, 564–573 (1955) – reference: 26) Kajimoto, R., Yoshizawa, H., Kawano-Furukawa, H., Kuwahara, H., Tomioka, Y. and Tokura, Y., Orbital-ordering-induced anomalous softening of the ferromagnetic spin waves in perovskite manganites, J. Magn. Magn. Mater., 226–230, 892–894 (2001) – reference: 8) Anderson, P. W. and Hasegawa, H., Considerations on double exchange, Phys. Rev., 100, 675–681 (1955) – reference: 14) Endoh, Y. and Hirota, K., Scaling of spin-wave stiffness constant to Curie temperature in the colossal magnetoresistance material La1−xSrxMnO3, J. Phys. Soc. Jpn., 66, 2264–2267 (1997) – reference: 23) Zimmermann, M., Nelson, C. S., Hill, J. P., Gibbs, D., Blume, M., Casa, D., Keimer, B., Murakami, Y., Kao, C. C., Venkataraman, C., Gog, T., Tomioka, Y. and Tokura, Y., X-ray resonant scattering studies of orbital and charge ordering in Pr1−xCaxMnO3, Phys. Rev. B, 64, 195133 (2001) – reference: 13) Martin, M. C., Shirane, G., Endoh, Y., Hirota, K., Moritomo, Y. and Tokura, Y., Magnetism and structural distortion in the La0.7Sr0.3MnO3 metallic ferromagnet, Phys. Rev. B, 53, 14285–14290 (1996) – reference: 19) Senff, D., Krüger, F., Scheidl, S., Benomar, M., Sidis, Y., Demmel, F. and Braden, M., Spin-wave dispersion in orbitally ordered La1/2Sr3/2MnO4, Phys. Rev. Lett., 96, 257201 (2006) – reference: 18) Doud-Aladine, A., Rodriguez-Carvajal, J., Pinsard-Gaudart, L., Fernandez-Diaz, M. and Revcolevschi, A., Zener polaron ordering in half-doped manganites, Phys. Rev. Lett., 89, 097205 (2002) – reference: 22) Ewings, R. A., Perring, T. G., Sikora, O., Abernathy, D. L., Tomioka, Y. and Tokura, Y., Spin excitations used to uncover the nature of the magnetically ordered ground state of Pr0.5Ca0.5MnO3, Phys. Rev. B, 94, 014405 (2016) – reference: 11) Kajimoto, R., Yoshizawa, H., Kawano, H., Kuwahara, H., Tokura, Y., Ohoyama, K. and Ohashi, M., Hole-concentration-induced transformation of the magnetic and orbital structures in Nd1−xSrxMnO3, Phys. Rev. B, 60, 9506–9517 (1999) – reference: 4) Glazer, A. M., Simple ways of determining perovskite structures, Acta Crystallogr. A, 31, 756–762 (1975) |
SSID | ssib058494163 ssj0026507 ssib001535751 ssib008143087 |
Score | 2.0226777 |
Snippet | ... |
SourceID | jstage |
SourceType | Publisher |
StartPage | 393 |
SubjectTerms | cubic perovskite manganese oxides double-exchange interaction inelastic neutron scattering orbital ordering spin wave |
Title | VI-1-2 Mn酸化物の磁気ダイナミクス—二重交換相互作用と軌道秩序 |
URI | https://www.jstage.jst.go.jp/article/radioisotopes/65/9/65_650904/_article/-char/ja |
Volume | 65 |
hasFullText | 1 |
inHoldings | 1 |
isFullTextHit | |
isPrint | |
ispartofPNX | RADIOISOTOPES, 2016/09/15, Vol.65(9), pp.393-401 |
link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrR3LbtNA0CpFQlwQT_FWD-wJpTjetb17tBNXLVIpghaVk-VXpOaQVG164ZS0QghUVAkqOBSJA5VoL8CxBMHH4LShf8HMrp0H6gEqLqvJ7nhmdsb2zGx2x5p2KzKoCFkUQ24iIEGhdgTvQYDA0xtGESLmSiirfd6zJufY3XlzfuTEj4FdSyuNcDx6cuS5kuNYFfrArnhK9h8s2yMKHQCDfaEFC0P7VzZ-NAWpmUE8ivsVuD5dI54g3CQuJ55JeIkIi3g24YI4QmIVieNhjyNhzyKuToQthyQNBAzisLzHyQAxkQ_lgCvybRKAzIjrIDvkDuzKWQ_SsQifIMJFptCiYHJIGBIoE1GSQ4w4PJcQAE5cNydYJIJKmW05C1PyGtqN-MApT81MPZyZnbnfj20RU-g4d5wmSG7g3YSkOcghJw-cXNHHtxDHtRAAqZySwlcz8SQA1-qDyyTq_Ka8paXCTbxKzRRVZ6MGXE9K4qLOURJQpplRdZ3bkhngmX2umaKNYWMYqKzMKjwD3FJuHluyL-fGAMM7g-6I0gKnunrDJ8oDcc4KLPdAmYtSn9PIHkUx4G-ooAOhC1PrQn96RfAhWFR2KYgX6gvL9UZ9MVket8zx3sVD9cazu9kfQvct0xfYYMFFnfk5Eh4N9KuQn5w0bLsoqyxPDpb_o_i3Xu83h-Bc76cDEPsKzAd6CyRAXNW4zdSijrqi-HeOEh6CxiqkUPn2SxkRzp7VzmSp3JijhDynjVSD89qp6WyzygXtsXo802Zzunb4dG9__U33-W7a-tT90Dr48jZda6ar2-nai3Ttfbr6OV39-rO52WmvHz572WlvH2xsdbf2Ou1Xne_vups7aWvn17f1w9br7sfd_fbGRW1uwpstTRayL5kUqhBwB4WE8gqmCqxCDTzNHeh6ZIWUVewkDLiwhMnsOKYhjQw9CWnCGIsg9YhNM4ojOwzpJW20Vq8ll7UxQYuxnkR2ElViPIYehCKhgc3BMycRj9kVraSU4i-qcjX-cQx69b9QuaadxkdRrVhe10YbSyvJDYjhG-FNeaP8BmuMz20 |
linkProvider | ABC ChemistRy |
openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=VI-1-2%E3%80%80Mn%E9%85%B8%E5%8C%96%E7%89%A9%E3%81%AE%E7%A3%81%E6%B0%97%E3%83%80%E3%82%A4%E3%83%8A%E3%83%9F%E3%82%AF%E3%82%B9%E2%80%94%E4%BA%8C%E9%87%8D%E4%BA%A4%E6%8F%9B%E7%9B%B8%E4%BA%92%E4%BD%9C%E7%94%A8%E3%81%A8%E8%BB%8C%E9%81%93%E7%A7%A9%E5%BA%8F&rft.jtitle=RADIOISOTOPES&rft.au=%E5%90%89%E6%B2%A2%2C+%E8%8B%B1%E6%A8%B9&rft.au=%E6%A2%B6%E6%9C%AC%2C+%E4%BA%AE%E4%B8%80&rft.date=2016&rft.pub=%E5%85%AC%E7%9B%8A%E7%A4%BE%E5%9B%A3%E6%B3%95%E4%BA%BA+%E6%97%A5%E6%9C%AC%E3%82%A2%E3%82%A4%E3%82%BD%E3%83%88%E3%83%BC%E3%83%97%E5%8D%94%E4%BC%9A&rft.issn=0033-8303&rft.eissn=1884-4111&rft.volume=65&rft.issue=9&rft.spage=393&rft.epage=401&rft_id=info:doi/10.3769%2Fradioisotopes.65.393&rft.externalDocID=article_radioisotopes_65_9_65_650904_article_char_ja |
thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0033-8303&client=summon |
thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0033-8303&client=summon |
thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0033-8303&client=summon |