Abstract

A novel technique, polarized neutron reflectometry with phase analysis (PNRPA), is suggested, in which not only the moduli of reflection matrix elements but also up to three phase differences are measured. It is realized in the scheme with two flippers and an analyzer, by reflection of neutrons with the spin, in succession, parallel and antiparallel to two inclined axes fixed to the sample. More detailed information about magnetic layered structures can be thus obtained. An adequate mathematical formalism is given.

Author Keywords: Polarized neutrons; Reflectometry; Neutron optics; Magnetic films

PACS classification codes: 61.12.Ha

Article Outline

1. Introduction

2. Full neutron reflectometry

3. Scheme with one analyzing axis

4. Scheme with two analyzing axes

5. Magnetically collinear layered structures

6. Summary

Acknowledgements

References

(4K)
Fig. 1. Geometrical representation of the spin states of the incident and reflected neutrons in terms of polarization vectors, respectively, P₀ ( and are its polar and axial angles) and P_r (the corresponding angles are and ) for an arbitrary quantization (Z) axis. The (X, Y, Z) reference frame is generally independent of the system of coordinates (x, y, z) related to the sample. Due to precession in the guide field, the phase difference of the opposite spin components (and, consequently, and ) is, generally, a function of the surface coordinates (x, y). The orientation of the polarization vector P_r at the sample surface is defined by interference of each pair (NSF and SF) of beams reflected in the same spin state and superposition of the two resultant coherent beams of neutrons in opposite spin states.

(2K)
Fig. 2. A structure model (three layers on a glass substrate). The z-axis is normal to the sample surface. Parameters of the model (i stands "for the ith layer"): d₁=z₁−z₀=50 nm, d₂=z₂−z₁=4 nm, d₃=d₁ (d_i is the thickness), V₁=V₃=100 neV, V₂=80 neV (V_i is the nuclear potential), M_1,in=M_3,in=10 kG, M₂=0 (M_i and M_i,in are the total and in-plane magnetization, respectively), ₁=₃=/6, (_i is the angle between M_i,in and the (y, z)-plane).

(35K)
Fig. 3. Reflectivities R₊₊, R₊₋, R₋₊, R₋₋ (left), the phases ₊₊, ₊₋, ₋₊, ₋₋ of the reflection matrix elements (center) and the phase differences Δ₊≡₋₊−₊₊, Δ₋≡₋₋−₊₋, Δ_NSF≡₋₋−₊₊, Δ_SF≡₋₊−₊₋ (right) are given as a function of the wave vector component normal to the sample surface, k_z. Since all reflectivities approach unity at small k_z, one can easily guess their absolute magnitudes (the curves are shifted to each other by an integer number of orders). Calculations (a, b, c) are for the structure model shown in Fig. 2. Calculations (d, e) are for the same structure, but when the magnetization in the third layer is parallel to that in the first layer. The quantization axis is always along the applied field which is either along the x-axis (a, e) or along the z-axis (b, c, d) (the coordinate system is defined in Fig. 2). The magnitude of the applied field H is assumed to be vanishing except for the case (c) when it is 0.2 T. The magnetic induction vector in the i-th layer is B_i=M_i,in+H (i=1, 2, 3).

(5K)
Fig. 4. The incident neutrons polarized ‘up’ the guide field (P₀||H) are assumed to be reflected in a state with the spins non-collinear to H. Since the spins of the reflected neutrons start precessing at different points of the sample surface, they are oriented identically (P_r=const) only in the beam cross sections parallel to the sample surface.

(3K)
Fig. 5. All magnetic fields (B) inside a stratified structure are assumed to be collinear. The unit vector b specifies one of the two opposite directions of B.

References

1. G.S. Krinchik, V.E. Zubov and L.V. Nikitin. Poverkhnost' 1 (1982), p. 22.

2. G.S. Krinchik, Physics of Magnetic Phenomena. , Moscow State University, Moscow (1985).

3. S. Alvarado, M. Campanga and H. Hopster. Phys. Rev. Lett. 48 (1982), p. 51. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

4. G.P. Felcher. Physica B 192 (1993), p. 137. Abstract | Abstract + References | PDF (794 K)

5. H. Zabel. Physica B 198 (1994), p. 156. Abstract | Abstract + References | PDF (531 K)

6. O. Schärpf and H. Strothmann. Phys. Scripta T 24 (1988), p. 58. Abstract-INSPEC   | $Order Document

7. G.P. Felcher. Phys. Rev. B 24 (1981), p. 1595. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

8. R.M. Moon, T. Riste and W. Koehler. Phys. Rev. 181 (1969), p. 920. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

9. C.F. Majkrzak, S. Satija, D.A. Neumann, J.F. Ankner, NIST reactor: summary of activities, July 1989–June 1990, in: C. O'Connor (Ed.), NIST Technical Note 1285, Washington, DC, US Government Printing Office, p. 55, 1990.

10. N.K. Pleshanov. Z. Phys. B 94 (1994), p. 233. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

11. V.M. Pusenkov, N.K. Pleshanov, V.G. Syromyatnikov, V.A. Ul'yanov and A.F. Schebetov. J. Magn. Magn. Mater. 175 (1997), p. 237. SummaryPlus | Full Text + Links | PDF (857 K)

12. V.K. Ignatovich, Physics of Ultracold Neutrons. , Nauka, Moscow (1988).

13. G.P. Felcher, S. Adenwalla, V.O. De Haan and A.A. Van Well. Nature 377 (1995), p. 409. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

14. N.K. Pleshanov. Z. Phys. B 100 (1996), p. 423. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

15. N.K. Pleshanov. Physica B 234–236 (1997), p. 516. SummaryPlus | Full Text + Links | PDF (174 K)

16. A.I. Okorokov, V.V. Runov, V.I. Volkov and A.G. Gukasov. Zh. ETP 69 (1975), p. 590. Abstract-INSPEC   | $Order Document

17. M.Th. Rekveldt, J. Van Woesik and J. Meijer. Phys. Rev. 181 (1977), p. 920.

18. N.K. Pleshanov, Phys. Lett. A (1998) submitted for publication.

19. P. Böni, D. Clemens, H.A. Grimmer, H. Van Swyygenhoven, Annual Report 1994, Annex F3A, PSI Condensed Matter Research and Material Sciences.

20. D.A. Korneev, Neutron optical devices and applications, in: C.F. Majkrzak, J.L. Wood (Eds.), Proceedings of the SPIE, vol. 1738, 1992, p. 477.

21. N.K. Pleshanov, Preprint PNPI-2131, 1996.

22. K. Chadan and P.C. Sabatier, Inverse Problems in Quantum Scattering Theory. , Springer, New York (1977).

23. R. Lipperheide, G. Reiss, H. Leeb and S.A. Sofianos. Physica B 221 (1996), p. 514. Abstract | PDF (314 K)

24. C.F. Majkrzak and N.F. Berk. Physica B 221 (1996), p. 520. Abstract | PDF (250 K)

25. V.O. de Haan, A.A. van Well, P.E. Sacks, S. Adenwalla and G.P. Felcher. Physica B 221 (1996), p. 524. Abstract | PDF (513 K)

26. G. Reiss. Physica B 221 (1996), p. 533. Abstract | PDF (243 K)

27. N.K. Pleshanov. Physica B 198 (1994), p. 70. Abstract | Abstract + References | PDF (130 K)

28. N.K. Pleshanov and V.M. Pusenkov. Z. Phys. B 100 (1996), p. 507. Abstract-INSPEC   | $Order Document | Full Text via CrossRef

Corresponding author. Tel.: +7-812-71-46973; Fax: +7-81271-39053; email: pnk@hep486.pnpi.spb.zu