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We have investigated the properties of thermal entanglement in a triangular spin ring of the single molecular magnet (SMM) Na9[Cu3Na3(H2O)9 (α-AsW9O33)2]·26H2O in a magnetic field, and the pairwise concurrences of arbitrary two Cu2+ ion qubits are calculated numerically, hereafter abbreviated as C12, C23 and C13, respectively. Results show that the magnitude and direction of magnetic field as well as temperature have important effects on the pairwise thermal entanglement. Moreover, C12, C23 and C13 have difference variations with the change of the parameters. We also plot the changes of the critical temperatures Tc of C12, C23 and C13 with the magnetic fields along three different directions, and from the critical temperature-magnetic field phase diagrams one can obtain the ranges of parameters in which the pairwise thermal entanglement in a triangular spin ring of the SMM exists. Therefore, the pairwise entanglement can be controlled and enhanced in the SMM by choosing appropriate magnitude and direction of magnetic field and temperature.
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Keywords:
- pairwise entanglement /
- single molecular magnet /
- triangular spin ring
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[1] Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901
[2] Wang X G 2001 Phys. Rev. A 64 012313
[3] Wang X G 2001 Phys. Lett. A 281 101
[4] Wang X G 2002 Phys. Rev. A 66 034302
[5] Zhang G F, Li S S 2005 Phys. Rev. A 72 034302
[6] Sun Y, Chen Y, Chen H 2003 Phys. Rev. A 68 044301
[7] Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese) [张英丽, 周斌 2011 60 120301]
[8] Xi X Q, Chen W X, Liu Q, Yue R H 2006 Acta Phys. Sin. 55 3026 (in Chinese) [惠小强, 陈文学, 刘起, 岳瑞宏 2006 55 3026]
[9] Cao M, Zhu S Q 2005 Phys. Rev. A 71 034311
[10] Wu K D, Zhou B, Cao W Q 2007 Phys. Lett. A 362 381
[11] Cao M, Zhu S Q 2006 Chin. Phys. Lett. 23 2888
[12] Li D C, Wang X P, Cao Z L 2008 J. Phys.: Condens. Matter 20 325229
[13] Pan H Z, Kuang L M 2004 Chin. Phys. Lett. 21 424
[14] Xi X Q, Chen W X, Yue R H 2002 Chin. Phys. Lett. 19 1044
[15] Lu P, Wang J S 2009 Acta Phys. Sin. 58 5955 (in Chinese) [卢鹏, 王顺金 2009 58 5955]
[16] Ren J Z, Shao X Q, Zhang S, Yeon K H 2010 Chin. Phys. B 19 100307
[17] Zhou L, Song H S, Guo Y Q, Li C 2003 Phys. Rev. A 68 024301
[18] Zhang T, Xi X Q, Yue R H 2004 Acta Phys. Sin. 53 2755 (in Chinese) [张涛, 惠小强, 岳瑞宏 2004 53 2755]
[19] Wang Y H, Xia Y J 2009 Acta Phys. Sin. 58 7479 (in Chinese) [王彦辉, 夏云杰 2009 58 7479]
[20] Hu Z N, Yi K S, Park K S 2007 J. Phys. A: Math. Theor. 40 7283
[21] Luczak J, Bulka B R 2012 J. Phys.: Condens. Matter 24 375303
[22] Zhou B 2011 Int. J. Mod. Phys. B 25 2135
[23] Hou J M, Du L, Ding J Y, Zhang W X 2010 Chin. Phys. B 19 110313
[24] Qin M, Tian D P, Tao Y J 2008 Acta Phys. Sin. 57 5395 (in Chinese) [秦猛, 田东平, 陶应娟 2008 57 5395]
[25] Zheng Q, Zhang X P, Zhi Q J, Ren Z Z 2009 Chin. Phys. B 18 3210
[26] Thomas L, Lionti F, Ballou R, Gatteschi D, Sessoli R, Barbara B 1996 Nature 383 145
[27] Wernsdorfer W, Sessoli R 1999 Science 284 133
[28] Kortz U, Nellutla S, Stowe A C, Dalal N S, Rauwald U, Danquah W, Ravot D 2004 Inorg. Chem. 43 2308
[29] Stowe A C, Nellutla S, Dalal N S, Kortz U 2004 Eur. J. Inorg. Chem. 19 3792
[30] Choi K Y, Matsuda Y H, Nojiri H, Kortz U, Hussain F, Stowe A C, Ramsey C, Dalal N S 2006 Phys. Rev. Lett. 96 107202
[31] Bogani L, Wernsdorfer W 2008 Nature Mater. 7 179
[32] Leuenberger M N, Loss D 2001 Nature 410 789
[33] Zhou B, Tao R B, Shen S Q, Liang J Q 2002 Phys. Rev. A 66 010301
[34] Meier F, Levy J, Loss D 2003 Phys. Rev. B 68 134417
[35] Troiani F, Ghirri A, Affronte M, Carretta S, Santini P, Amoretti G, Piligkos S, Timco G, Winpenny R E P 2005 Phys. Rev. Lett. 94 207208
[36] Lehmann J, Gaita-Ariño A, Coronado E, Loss D 2007 Nature Nanotech. 2 312
[37] Trif M, Troiani F, Stepanenko D, Loss D 2008 Phys. Rev. Lett. 101 217201
[38] Kortz U, Al-Kassem N K, Savelieff M G, Kadi N A A, Sadakane M 2001 Inorg. Chem. 40 4742
[39] Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022
[40] Wootters W K 1998 Phys. Rev. Lett. 80 2245
[41] Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306
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