9 values and in the opposite direction because of a special dependence of the Gibbs free energy on the field. This sort of hysteresis was observed experimentally in [4, 22] ( Fig.7b ). Numerical comparison between data presented at Fig.7b and Fig.7a shows that M ( T, H) ( Fig. 7a ) gives the qualitative description of the experimental data which obey the scaling rule: H exp 2 / H exp 1 ≃ H calc 2 / H calc 1 ≃ 5 / 2. For the quantitative description of the temperature and magnetic field dependence of the magnetic moment NS of structures, it will be important to take into account the exact spectrum of Andreev levels, the latter is sup- posedly possible within the framework of the Bogoliubov – de Gennes equations only. Note that our consideration was entirely based on the model of free electrons without account of strong electron-electron repulsion. numerical calculation shows that the nonlinearity of flux Φ (T , h) − field dependence ( T = constant ) ( Fig.6a ) gives rise to quite interesting features of M ( T, H). The magnetic moment in the N layer appears to be always dia- magnetic. The paramagnetic contribution to current (the paramagnetic reentrant effect) was not detected. How- ever, we have obtained the stepwise change in absolute value of the magnetic moment with increasing magnetic field ( Fig.7a ). This behavior can be interpreted as an appearance in the magnetic moment the paramagnetic additives. A behaviour of the NS structure changes from one stable state to another and the magnetic field pene- trates further into a bulk of the N layer. The new state has smaller absolute value of the diamagnetic moment, which is interpreted experimentally as an evidence of a paramagnetic addition in the system ( Fig.7b ). When the field grows further, | M (H) | increases again until its new value makes the system to jump to a next stable state with a smaller absolute value of the diamagnetic moment, and the magnetic field penetrates deeper inside the normal metal ( Fig.7a ). The number of the moment jumps depends on the number of Andreev levels in the NS structure. Under the isothermal condition, the values of the magnetic field at which jumps occur, do not coin- cide when the magnetic field changes from small to larger The authors thank A. N. Omelyanchouk, I. O. Kulik, I. V. Krive and G. I. Japaridze for useful discussions. IV. ACKNOWLEDGEMENT [1] A. D. Zaikin, Solid State Comm. 41 , 533 (1982). [2] A. C. Mota, P. Visani, and A. Pollini, J. Low Temp. Phys. 76 , 465 (1989). [3] P. Visani, A. C. Mota, and A. Pollini, Phys. Rev. Lett. 65 , 1514 (1990). [4] A. C. Mota, P. Visani, A. Pollini, and K. Aupke. Physica B 197 , 95 (1994). [5] C. Bruder, and Y. Imry, Phys. Rev. Lett. 80, 5782 (1998). [6] A. L. Fauchere, W. Belzig, and G. Blatter, Phys. Rev. Lett. 82 , 3336 (1999). [7] K. Maki and S. Haas, Physica C 341-348, 2667 (2000). [8] G. A. Gogadze, Fiz. Nizk. Temp. 31 ,120 (2005) [Low Temp. Phys. 31 , 94 (2005)]. [9] G. A. Gogadze, Fiz. Nizk. Temp. 32 , 716 (2006) [Low Temp. Phys. 32 , 546 (2006)]. [10] G. A. Gogadze, Fiz. Nizk. Temp. 34 , 225 (2008) [Low Temp. Phys. 34 , 173 (2008)]. [11] Y. Aharonov and D. Bohm, Phys. Rev. 115 , 485 (1959). [12] A. F. Andreev, Zh. Eksp. Teor. Fiz. 46 ,1823 (1964) [Sov. Phys. JETP 9 , 1228 (1964)] [13] E. N. Bogachek and G. A. Gogadze, Zh. Eksp. Teor. Fiz. 63 , 1839 (1972) [Sov.Phys.JETP 36 , 973 (1973)] [14] N. B. Brandt, E.N. Bogachek, N. D. Gitsu, G.A. Gogadze, I. O. Kulik, A. A. Nikolaeva, and Ya. G. Pono- marev, Fiz. Nizk. Temp. 8 , 718 (1982) [Sov. J. Low Temp. Phys. 8 , 358 (1982)] [15] J. B. Keller and S.I. Rubinow, Ann. Phys ( N. Y. ) 9 , 24 (1960) [16] G. A. Gogadze, R. I. Shekhter, and M. Jonson, Fiz. Nizk. Temp. 27 , 1237 (2001) [Low Temp. Phys. 27 , 913 (2001)]. [17] I. O. Kulik, Zh. Eksp. Teor. Fiz. 57 , 1745 (1969) [Sov. Phys. JETP 30 , 944 (1969)] [18] A. V. Galaktionov and A. D. Zaikin, Phys. Rev. B 67 ,184518 (2003). [19] W. Belzig, C. Bruder and A. L. Fauch`ere, Phys. Rev. B 58 , 14531 (1998). [20] W. Belzig, C. Bruder, and G. Schon, Phys. Rev. B 53 , 5727 (1996). [21] G. A. Gogadze S. N. Dolya, Fiz. Nizk. Temp. 35 , 932 (2009). [22] F. B. M¨ uller-Allinger, A. C. Mota, Phys. Rev. B 62 , 6120 (2000). [23] A. L. Fauch`ere G. Blatter, Phys. Rev. B 56 , 14102 (1997).