此研究以兩種釹基焦氯酸鹽體(Nd-pyrochlore):Nd2Ru2O7 和Nd2Sn2O7探討幾何阻挫系統(Geometrically Frustrated System) 的自旋動力學(其中Nd2Ru2O7 因構成之稀土元素和過渡金屬原素皆具磁性，系統較為複雜)，對Nd 4f 電子組態中的傳導電子和過渡金屬元素Ru 4d 半滿殼層的電子組態，或和貧金屬元素Sn 5p 電子組態的交互作用下數量級相同的自旋-軌道耦合和晶格場對系統基態能量的貢獻尤其感興趣。
我們利用中子散射磁性和比熱量測等方法探討Nd2Ru2O7 和Nd2Sn2O7的物理性質(溫度最低至300 mK)。在Nd2Ru2O7 觀察到三個不規則相變溫度:1.6 K(反鐵磁序)、22 K(弱鐵磁序) 及150 K(反鐵磁序)。此結果引起在同步輻射光源中心的合作者的興趣去詳細探討晶格常數、離子間鍵結角度及長度和溫度間的關係，並在後文與我們的實驗結果相互驗證。
於溫度等於1 K 時，在Nd2Sn2O7 觀察到由Nd3+ 子結構主導的反鐵磁磁序(magnetic order)。但加以高場後系統的順磁性排列會被極化，我們得以在較高溫度觀察此現象。透過Rietveld 方法分析中子磁性繞射結果，我們得知焦氯酸鹽體中單位四面體上的4 個磁矩形成單離子各項異性(single-ion anisotropy)。而取零場下的比熱量測結果積分熵得到的值不若加場下比熱所得到的對應兩個簡併基態的結果，故仍須比較不同場下的低溫比熱量測結果以得知此磁序形成的機制。

This project studies two frustrated materials, Nd2Ru2O7 and Nd2Sn2O7, with the previous one a double pyrochlore, i.e., magnetic moments from Nd3+ and Ru4+ all act in the system. The ground-state spin dynamics of the conduction electrons in the light lanthanide Nd 4f states with the 4d partially filled shell of transition-metal ions Ru, or with the 5p states in post-transition metal ions Sn, in which comparable magnitudes of the spin-orbit coupling and crystal electric field potential are available in the effective Hamiltonian are particularly of interest.
We present neutron scattering, bulk magnetization and heat capacity results which fully characterize the magnetic properties of the Nd2Ru2O7 and Nd2Sn2O7 at temperatures as low as 300 mK. Three anomalies, antiferromagnetic ordering at 1.6 K, weak ferromagnetic ordering at 22 K, antiferromagnetic ordering at 150 K, are observed in double pyrochlore Nd2Ru2O7 and each will be discussed in later sections. Behaviors of temperature associated features such as the discrepancies in lattice parameters, bonding angles and lengths are hence deeply investigated by synchrotron light source by collaborators, and anomalies are shown.
No spontaneously magnetic order reveals until 1 K in Nd2Sn2O7. It is then concluded to be a partial ordering of Nd3+ sublattice but the system can be polarized out of a paramagnetic state into an ordered state by a strong field. A refinement of the resultant neutron scattering pattern suggests some strong single-ion anisotropy in the system implying a possible exotic ground state. As the entropy integration of zero-field heat capacity doesn’t refer us to a doublet of the ground state as the results under applied fields, comparisons between heat capacity obtained in different fields at low temperature will give us more information about the mechanism of ordering.

[1] John B. Kogut. An introduction to lattice gauge theory and spin systems. Reviews of Modern Physics, 51(4):659–713, October 1979.
[2] M. F. Collins. Magnetic Critical Scattering. Oxford University Press, 1989.
[3] G. Wannier. Antiferromagnetism. The Triangular Ising Net. Physical Review, 79(2):357–364, July 1950.
[4] G. Wannier. Antiferromagnetism. The Triangular Ising Net. Physical Review B, 7(11):5017–5017, June 1973.
[5] M. A. Subramanian, G. Aravamudan, and G. V. Subba Rao. Oxide pyrochlores—A review. Progress in Solid State Chemistry, 15(2):55–143, January 1983.
[6] Y Yafet and C Kittel. Antiferromagnetic Arrangements in Ferrites. Physical Review, 87(2):290–294, July 1952.
[7] P. W. Anderson. Ordering and Antiferromagnetism in Ferrites. Physical Review, 102(4):1008–1013, May 1956.
[8] Roderich Moessner and Arthur P. Ramirez. Geometrical Frustration. Physics Today, 59(2):24, 2006.
[9] C. Castelnovo, R. Moessner, and S. L. Sondhi. Magnetic monopoles in spin ice. Nature, 451(7174):42–5, January 2008.
[10] Andrew Harrison. First catch your hare: the design and synthesis of frustrated magnets. Journal of Physics: Condensed Matter, 16(11):S553–S572, March 2004.
[11] Jason S. Gardner, Michel J. P. Gingras, and John E. Greedan. Magnetic pyrochlore oxides. Reviews of Modern Physics, 82(1):53–107, January 2010.
[12] M. Debauche, H. Diep, P. Azaria, and H. Giacomini. Exact phase diagram of a generalized Kagomé Ising lattice: Reentrance and disorder lines. Physical Review B, 44(5):2369–2372, August 1991.
[13] Jerry L. Atwood. Kagomé lattice: A molecular toolkit for magnetism. Nature materials, 1(2):91–2, October 2002.
[14] Jan Frunzke, Thomas Hansen, Andrew Harrison, James S. Lord, Gareth S. Oakley, Dirk Visser, and Andrew S. Wills. Magnetic ordering in diluted kagome antiferromagnets. Journal of Materials Chemistry, 11(1):179–185, 2001.
[15] K. Matsuhira, Z. Hiroi, T. Tayama, S. Takagi, and T. Sakakibara. A new macroscopically degenerate ground state in the spin ice compound Dy2Ti2O7 under a magnetic field. Journal of Physics: Condensed Matter, 14(29):L559–L565, July 2002.
[16] Jacques Villain. Insulating spin glasses. Zeitschrift für Physik B Condensed Matter and Quanta, 33(1):31–42, March 1979.
[17] R. Moessner and J. T. Chalker. Properties of a Classical Spin Liquid: The Heisenberg Pyrochlore Antiferromagnet. Physical Review Letters, 80(13):2929–2932, March 1998.
[18] B. Canals and C. Lacroix. Pyrochlore Antiferromagnet: A Three-Dimensional Quantum Spin Liquid. Physical Review Letters, 80(13):2933–2936, March 1998.
[19] J. Reimers, A. Berlinsky, and A.-C. Shi. Mean-field approach to magnetic ordering in highly frustrated pyrochlores. Physical Review B, 43(1):865–878, January 1991.
[20] R. Moessner and J. Chalker. Low-temperature properties of classical geometrically frustrated antiferromagnets. Physical Review B, 58(18):12049–12062, November 1998.
[21] G. Toulouse. Theory of the frustration effect in spin glasses I. Communications on Physics, 2:115–119, 1977.
[22] J. Villain. Spin glass with nonrandom interactions. Journal of Physics C-Solid State Physics, 10:1717–1734, 1977.
[23] L. Pauling. The structure and entropy of ice and of other crystals with some randomness of atomic arrangement. Journal of the American Chemical Society, 57:2680–2684, 1935.
[24] J. Reimers. Absence of long-range order in a three-dimensional geometrically frustrated antiferromagnet. Physical Review B, 45(13):7287–7294, April 1992.
[25] J. S. Gardner, S. R. Dunsiger, B. D. Gaulin, M. J. P. Gingras, J. E. Greedan, R. F. Kiefl, M. D. Lumsden, W. A. MacFarlane, N. P. Raju, J. E. Sonier, I. Swainson, and Z. Tun. Cooperative Paramagnetism in the Geometrically Frustrated Pyrochlore Antiferromagnet Tb2Ti2O7. Physical Review Letters, 82(5):1012–1015, February 1999.
[26] L. Corruccini and Steven White. Dipolar antiferromagnetism in the spin-wave approximation. Physical Review B, 47(2):773–777, January 1993.
[27] Steven White, M. Roser, Jingchun Xu, J. van der Noordaa, and L. Corruccini. Dipolar magnetic order with large quantum spin fluctuations in a diamond lattice. Physical Review Letters, 71(21):3553–3556, November 1993.
[28] Yasufumi Yamashita and Kazuo Ueda. Spin-Driven Jahn-Teller Distortion in a Pyrochlore System. Physical Review Letters, 85(23):4960–4963, December 2000.
[29] O. Tchernyshyov, R. Moessner, and S. L. Sondhi. Spin-Peierls phases in pyrochlore antiferromagnets. Physical Review B, 66, 2002.
[30] S. H. Lee, C. Broholm, T. H. Kim, W. Ratcliff, and S. W. Cheong. Local
spin resonance and spin-Peierls-like phase transition in a geometrically frustrated antiferromagnet. Physical Review Letters, 84:3718–3721, 2000.
[31] J. E. Greedan, M. Sato, Xu Yan, and F. S. Razavi. Spin-glass-like behavior in Y2Mo2O7, a concentrated, crystalline system with negligible apparent disorder. Solid State Communications, 59(12):895–897, September 1986.
[32] H. W. J. Blöte, R. F. Wielinga, and W. J. Huiskamp. Heat-capacity measurements on rare-earth double oxides R2M2O7. Physica, 43(4):549–568, September 1969.
[33] M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske, and K. Godfrey. Geometrical Frustration in the Ferromagnetic Pyrochlore Ho2Ti2O7. Physical Review Letters, 79(13):2554–2557, September 1997.
[34] J. Gardner, B. Gaulin, S.-H. Lee, C Broholm, N. Raju, and J. Greedan. Glassy Statics and Dynamics in the Chemically Ordered Pyrochlore Antiferromagnet Y2Mo2O7. Physical Review Letters, 83(1):211–214, July 1999.
[35] A. P. Ramirez. Strongly Geometrically Frustrated Magnets. Annual Review of Materials Science, 24(1):453–480, August 1994.
[36] S. F. Edwards and P. W. Anderson. Theory of spin glasses. Journal of Physics F: Metal Physics, 5(5):965–974, May 1975.
[37] David Sherrington and Scott Kirkpatrick. Solvable Model of a Spin-Glass. Physical Review Letters, 35(26):1792–1796, December 1975.
[38] P. Nordblad, L. Lundgren, and L. Sandlund. A link between the relaxation of the zero field cooled and the thermoremanent magnetizations in spin glasses. Journal of Magnetism and Magnetic Materials, 54-57:185–186, February 1986.
[39] John E. Greedan. Geometrically frustrated magnetic materials. Journal of Materials Chemistry, 11(1):37–53, 2001.
[40] K. Binder. Spin glasses: Experimental facts, theoretical concepts, and open questions. Reviews of Modern Physics, 58(4):801–976, October 1986.
[41] M. J. P. Gingras, C. V. Stager, N. P. Raju, B. D. Gaulin, and J. E. Greedan. Static critical behavior of the spin-freezing transition in the geometrically frustrated pyrochlore antiferromagnet Y2Mo2O7. Physical Review Letters, 78:947–950, 1997.
[42] S. T. Bramwell and M. J. Harris. Frustration in Ising-type spin models on the pyrochlore lattice. Journal of Physics: Condensed Matter, 10(14):L215–L220, April 1998.
[43] R. Siddharthan, B. Shastry, A. Ramirez, A Hayashi, R. Cava, and S Rosenkranz. Ising Pyrochlore Magnets: Low-Temperature Properties, “Ice Rules,”and Beyond. Physical Review Letters, 83(9):1854–1857, August 1999.
[44] Byron den Hertog and Michel Gingras. Dipolar Interactions and Origin of Spin Ice in Ising Pyrochlore Magnets. Physical Review Letters, 84(15):3430–3433, April 2000.
[45] S. T. Bramwell, M. J. Harris, B. C. den Hertog, M. J. P. Gingras, J. S. Gardner, D. F. McMorrow, a. R. Wildes, a. L. Cornelius, J. D. M. Champion, R. G. Melko, and T. Fennell. Spin Correlations in Ho2Ti2O7: A Dipolar Spin Ice System. Physical Review Letters, 87(4):047205, July 2001.
[46] Y. M. Jana, A. Sengupta, and D. Ghosh. Estimation of single ion anisotropy in pyrochlore Dy2Ti2O7, a geometrically frustrated system, using crystal field theory. Journal of Magnetism and Magnetic Materials, 248:7–18, 2002.
[47] S. Rosenkranz, A. P. Ramirez, A. Hayashi, R. J. Cava, R. Siddharthan, and B. S. Shastry. Crystal-field interaction in the pyrochlore magnet Ho2Ti2O7. Journal of Applied Physics, 87:5914–5916, 2000.
[48] Dennis J Flood. Magnetization and magnetic entropy of Dy2Ti2O7. Journal of Applied Physics, 45(9):4041, 1974.
[49] S. T. Bramwell, M. N. Field, M. J. Harris, and I. P. Parkin. Bulk magnetization of the heavy rare earth titanate pyrochlores - a series of model frustrated magnets. Journal of Physics: Condensed Matter, 12(4):483–495, January 2000.
[50] J. D. Bernal and R. H. Fowler. A Theory of Water and Ionic Solution, with Particular Reference to Hydrogen and Hydroxyl Ions. The Journal of Chemical Physics, 1(8):515, 1933.
[51] A. Cornelius and J. Gardner. Short-range magnetic interactions in the spin-ice compound Ho2Ti2O7. Physical Review B, 64(6):060406, July 2001.
[52] A. P. Ramirez, A. Hayashi, R. J. Cava, R. Siddharthan, and B. S. Shastry. Zeropoint entropy in ’spin ice’. Nature, 399:333–335, 1999.
[53] T. Fennell, P. P. Deen, A. R. Wildes, K. Schmalzl, D. Prabhakaran, A. T. Boothroyd, R. J. Aldus, D. F. McMorrow, and S. T. Bramwell. Magnetic
Coulomb phase in the spin ice Ho2Ti2O7. Science (New York, N.Y.), 326(5951): 415–7, October 2009.
[54] J. Snyder, B. G. Ueland, A. Mizel, J. S. Slusky, H. Karunadasa, R. J. Cava, and P. Schiffer. Quantum and thermal spin relaxation in the diluted spin ice Dy2-xMxTi2O7 (M=Lu,Y). Physical Review B, 70, 2004.
[55] Michel J. P. Gingras. Observing monopoles in a magnetic analog of ice. Science (New York, N.Y.), 326(5951):375–6, October 2009.
[56] R. Moessner. Magnets with strong geometric frustration. Canadian Journal of Physics, 79(11-12):1283–1294, 2001.
[57] Benjamin Canals and Claudine Lacroix. Quantum spin liquid: The Heisenberg antiferromagnet on the three-dimensional pyrochlore lattice. Physical Review B, 61(2):1149–1159, January 2000.
[58] Leon Balents. Spin liquids in frustrated magnets. Nature, 464(7286):199–208, March 2010.
[59] Lieh-Jeng Chang, Shigeki Onoda, Yixi Su, Ying-Jer Kao, Ku-Ding Tsuei, Yukio Yasui, Kazuhisa Kakurai, and Martin Richard Lees. Higgs transition from a magnetic Coulomb liquid to a ferromagnet in Yb2Ti2O7. Nature communications, 3:992, January 2012.
[60] Jens Jensen and Allan Mackintosh. Rare Earth Magnetism : Structure and Excitations. In The International Series of Momographs of Physics. Oxford University Press, 1991.
[61] K.A. McEwen and W.G. Stirling. Magnetic excitations in neodymium, a sinusoidally modulated antiferromagnet. Journal of Magnetism and Magnetic Materials, 30(1):99–105, November 1982.
[62] H. M. Rietveld. A profile refinement method for nuclear and magnetic structures. Journal of Applied Crystallography, 2(2):65–71, June 1969.
[63] Juan Rodríguez-Carvajal. Recent advances in magnetic structure determination by neutron powder diffraction. Physica B: Condensed Matter, 192(1-2):55–69, October 1993.
[64] SQUID VSM User’s Manual. Quantum Design, Inc.
[65] S. Foner. The vibrating sample magnetometer: Experiences of a volunteer (invited). Journal of Applied Physics, 79(8):4740, 1996.
[66] K. Gramm, L. Lundgren, and O. Beckman. SQUID Magnetometer for Mangetization Measurements. Physica Scripta, 13(2):93–95, February 1976.
[67] Heat Capacity Option User’s Manual. Quantum Design, Inc.
[68] Thomas Brückel, Gernot Heger, Dieter Richter, Georg Roth, and Reiner Zorn. Neutron Scattering-lectures. Forschungszentrum Jülich GmbH, 2012.
[69] Thomas Brückel, Gernot Heger, Dieter Richter, Georg Roth, and Reiner Zorn. Neutron Scattering-Experiment Manuals. Forschungszentrum Jülich GmbH, 2012.
[70] G. E. Bacon. Neutron Diffraction. Clarendon Press, Oxford, 1975.
[71] J. D. M. Champion. Theoretical and experimental investigations of frustrated pyrochlore magnets. PhD thesis, University College London, 2001.
[72] Erich H. Kisi and Christopher J. Howard. Applications of Neutron Powder Diffraction. Oxford University Press, 2008.
[73] G. Shirane. A note on the magnetic intensities of powder neutron diffraction. Acta Crystallographica, 12(4):282–285, April 1959.
[74] C. Shull and J. Smart. Detection of Antiferromagnetism by Neutron Diffraction. Physical Review, 76(8):1256–1257, October 1949.
[75] C. Shull, W. Strauser, and E. Wollan. Neutron Diffraction by Paramagnetic and Antiferromagnetic Substances. Physical Review, 83(2):333–345, July 1951.
[76] Juan Rodríquez-Carvajal. Magnetic Structure Determination from Powder Diffraction Symmetry Analysis and Simulated Annealing. Materials Science Forum, 378-381:268–273, 2001.
[77] A. Wills. Magnetic structures and their determination using group theory. Le Journal de Physique IV, 11(PR9):Pr9–133–Pr9–158, November 2001.
[78] Australian Nuclear Science and Technology Oranisation.
[79] M. Ito, Y. Yasui, M. Kanada, H. Harashina, S. Yoshii, K. Murata, M. Sato, H. Okumura, and K. Kakurai. Nature of spin freezing transition of geometrically frustrated pyrochlore system R2Ru2O7 (R=rare earth elements and Y). Journal of Physics and Chemistry of Solids, 62(1-2):337–341, January 2001.
[80] C. Bansal, H. Kawanaka, H. Bando, and Y. Nishihara. Structure and magnetic properties of the pyrochlore Ho2Ru2O7: A possible dipolar spin ice system. Physical Review B, 66(5):052406, August 2002.
[81] Nobuyuki Taira, Makoto Wakeshima, and Yukio Hinatsu. Magnetic susceptibility and specific heat studies on heavy rare earth ruthenate pyrochlores R2Ru2O7 (R= Gd–Yb). Journal of Materials Chemistry, 12(5):1475–1479, April 2002.
[82] Nobuyuki Taira, Makoto Wakeshima, and Yukio Hinatsu. Specific Heat and ac Susceptibility Studies on Ruthenium Pyrochlores R2Ru2O7 (R=Rare Earths). Journal of Solid State Chemistry, 152(2):441–446, July 2000.
[83] C. Wiebe, J. Gardner, S.-J. Kim, G. Luke, A. Wills, B. Gaulin, J. Greedan, I Swainson, Y Qiu, and C. Jones. Magnetic Ordering in the Spin-Ice Candidate Ho2Ru2O7. Physical Review Letters, 93(7):076403, August 2004.
[84] J. Lee, T. Noh, J. Bae, In-Sang Yang, T. Takeda, and R. Kanno. Strong spinphonon coupling in the geometrically frustrated pyrochlore Y2Ru2O7. Physical Review B, 69(21):214428, June 2004.
[85] K.-S. Lee, D.-K. Seo, and M.-H. Whangbo. Structural and Electronic Factors Governing the Metallic and Nonmetallic Properties of the Pyrochlores A2Ru2O7−y. Journal of Solid State Chemistry, 131(2):405–408, July 1997.
[86] Leqing Li and Brendan J. Kennedy. Structural and Electronic Properties of the Ru Pyrochlores Bi2- yYbyRu2O7- _. Chemistry of Materials, 15(21):4060–4067, October 2003.
[87] R. Kmieć, Ż. Świątkowska, J. Gurgul, M. Rams, A. Zarzycki, and K. Tomala. Investigation of the magnetic properties of Y2Ru2O7 by Ru99 Mössbauer spectroscopy. Physical Review B, 74(10):104425, September 2006.
[88] Masafumi Ito, Yukio Yasui, Masaki Kanada, Hiroshi Harashina, Shunsuke Yoshii, Kazuhiro Murata, Masatoshi Sato, Hajime Okumura, and Kazuhisa Kakurai. Neutron Diffraction Study of Pyrochlore Compound R 2 Ru 2 O 7 (R=Y, Nd) above and below the Spin Freezing Temperature. Journal of the Physics Society Japan, 69(3):888–894, March 2000.
[89] Nobuyuki Taira, Makoto Wakeshima, Yukio Hinatsu, Aya Tobo, and Kenji Ohoyama. Magnetic structure of pyrochlore-type Er2Ru2O7. Journal of Solid State Chemistry, 176(1):165–169, November 2003.
[90] J. Gurgul, M. Rams, Ż. Świątkowska, R. Kmieć, and K. Tomala. Bulk magnetic measurements and Ru99 and Gd155 Mössbauer spectroscopies of Gd2Ru2O7. Physical Review B, 75(6):064426, February 2007.
[91] Michael W. Gaultois, Phillip T. Barton, Christina S. Birkel, Lauren M. Misch, Efrain E. Rodriguez, Galen D. Stucky, and Ram. Seshadri. Structural disorder, magnetism, and electrical and thermoelectric properties of pyrochlore Nd2Ru2O7. Journal of physics. Condensed matter : an Institute of Physics journal, 25(18): 186004, April 2013.
[92] Shunsuke Yoshii and Masatoshi Sato. Studies on Metal-Insulator Transition of Pyrochlore Compound Y2 - xBixRu2O7. Journal of the Physics Society Japan, 68(9):3034–3040, September 1999.
[93] Shunsuke Yoshii, Satoshi Iikubo, Taketomo Kageyama, Keisuke Oda, Yasuyuki Kondo, Kazuhiro Murata, and Masatoshi Sato. Anomalous Hall Effect of Pyrochlore Molybdate Nd2Mo2O7. Journal of the Physics Society Japan, 69(12): 3777–3780, December 2000.
[94] B. J. Kennedy and T. Vogt. Structural and Bonding Trends in Ruthenium Pyrochlores. Journal of Solid State Chemistry, 126(2):261–270, November 1996.
[95] Stephen Blundell. Magnetism in condensed matter. In Oxford master series in condensed matter physics. Oxford University Press, 2001.
[96] R. M. White. Quantum Theory of Magnetism. McGraw-Hill, New York, 1970.
[97] Kazuyuki Matsuhira, Makoto Wakeshima, Ryo Nakanishi, Takaaki Yamada,
Akira Nakamura, Wataru Kawano, Seishi Takagi, and Yukio Hinatsu. Metal–
Insulator Transition in Pyrochlore Iridates Ln2Ir2O7 ( Ln = Nd, Sm, and Eu). Journal of the Physical Society of Japan, 76(4):043706, March 2007.
[98] V. Bondah-Jagalu and S. T. Bramwell. Magnetic Susceptibility Study of the Heavy Rare Earth Stannate Pyrochlores. Canadian Journal of Physics, 79(11-12):1381–1385, June 2001.
[99] Hiroaki Kadowaki, Yoshinobu Ishii, Kazuyuki Matsuhira, and Yukio Hinatsu. Neutron scattering study of dipolar spin ice Ho2Sn2O7: Frustrated pyrochlore magnet. Physical Review B, 65(14):144421, March 2002.
[100] K. Matsuhira, Y. Hinatsu, K. Tenya, and T. Sakakibara. Low temperature magnetic properties of frustrated pyrochlore ferromagnets Ho2Sn 2O7 and Ho2Ti2O7. Journal of Physics: Condensed Matter, 12(40):L649–L656, October 2000.
[101] J. Stewart, J. Gardner, Y. Qiu, and G. Ehlers. Collective dynamics in the Heisenberg pyrochlore antiferromagnet Gd2Sn2O7. Physical Review B, 78(13):132410, October 2008.
[102] J. R. Stewart, G. Ehlers, A. S. Wills, S. T. Bramwell, and J. S. Gardner. Comment on“Magnetic structure of Gd2Ti2O7”. Physical Review B, 85(10):106401, March 2012.
[103] Y. Chapuis, A. Yaouanc, P. Dalmas de Réotier, S. Pouget, P. Fouquet, A. Cervellino, and A Forget. Ground state of the geometrically frustrated compound Tb 2 Sn 2 O 7. Journal of Physics: Condensed Matter, 19(44):446206, November 2007.
[104] S. Giblin, J. Champion, H. Zhou, C. Wiebe, J. Gardner, I. Terry, S. Calder, T. Fennell, and S. Bramwell. Static Magnetic Order in Tb2Sn2O7 Revealed by Muon Spin Relaxation with Exterior Muon Implantation. Physical Review Letters, 101(23):237201, December 2008.
[105] K. C. Rule, G. Ehlers, J. S. Gardner, Y. Qiu, E. Moskvin, K. Kiefer, and S. Gerischer. Neutron scattering investigations of the partially ordered pyrochlore Tb2Sn2O7. Journal of physics. Condensed matter : an Institute of Physics journal, 21(48):486005, December 2009.
[106] J. S. Gardner, A. Keren, G. Ehlers, C. Stock, Eva Segal, J. M. Roper, B. Få k, M. B. Stone, P. R. Hammar, D. H. Reich, and B. D. Gaulin. Dynamic frustrated magnetism in Tb2Ti2O7 at 50 mK. Physical Review B, 68(18):180401, November 2003.
[107] O. V. Kovalev. Representation of Crystallographic Space Groups. Gordon and Breach Science Publishers, 1993.
[108] J. Champion, M. Harris, P. Holdsworth, A. Wills, G. Balakrishnan, S. Bramwell, E. Čižmár, T. Fennell, J. Gardner, J. Lago, D. McMorrow, M. Orendáč, A. Orendáčová, D. Paul, R. Smith, M. Telling, and A. Wildes. Er2Ti2O7: Evidence of quantum order by disorder in a frustrated antiferromagnet. Physical Review B, 68(2):020401, July 2003.
[109] A Poole, A S Wills, and E Lelièvre-Berna. Magnetic ordering in the XY pyrochlore antiferromagnet Er 2 Ti 2 O 7 : a spherical neutron polarimetry study. Journal of Physics: Condensed Matter, 19(45):452201, November 2007.
[110] Hamid R. Molavian, Michel J. P. Gingras, and Benjamin Canals. Dynamically Induced Frustration as a Route to a Quantum Spin Ice State in Tb2Ti2O7 via Virtual Crystal Field Excitations and Quantum Many-Body Effects. Physical Review Letters, 98(15):157204, April 2007.
[111] I. Mirebeau, P. Bonville, and M. Hennion. Magnetic excitations in Tb2Sn2O7 and Tb2Ti2O7 as measured by inelastic neutron scattering. Physical Review B, 76, 2007.
[112] H. Zhou, C. Wiebe, J. Janik, L. Balicas, Y. Yo, Y. Qiu, J. Copley, and J. Gardner. Dynamic Spin Ice: Pr2Sn2O7. Physical Review Letters, 101(22):227204, November 2008.