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Polarization analysis of neutron reflectometry on non-magnetic structures deposited on a magnetic layer
Physica B 276}278 (2000) 642}643
Polarization analysis of neutron re#ectometry on non-magnetic structures deposited on a magnetic layer R.W.E. van de Kruijs *, H. Fredrikze , M.Th. Rekveldt Interfacultair Reactor Instituut, Delft University of Technology, Mekelweg 15, 2629 JB Delft, Netherlands
Abstract We present polarized neutron re#ectometry calculations for a non-magnetic bilayer on top of a substrate with a thin magnetic "lm. In contrast to non-magnetic and collinear magnetic re#ectivities, the spin-#ipped re#ectivities from a non-collinear system are shown to be very sensitive to small changes in the non-magnetic scattering length densities. 2000 Elsevier Science B.V. All rights reserved. PACS: 61.12.Ha; 75.70.Ak Keywords: Re#ectometry; Polarized neutrons; Polarization analysis; Noncollinear structures; Thin "lms
Because of the inverse problem in re#ectometry data analysis [1], it is impossible to obtain a unique scattering length density pro"le directly from experimental data. Clever use can be made of contrast variation (neutrons) and the use of di!erent wavelengths close to and far from the substrate absorption edge (X-rays) to reduce pro"le ambiguities by simultaneous "tting of data sets. Several authors have commented that polarized neutrons can also be used to facilitate the data analysis of non-magnetic thin "lm structures [2]. Adding a thin magnetic "lm to the substrate and using a spin-polarized incident neutron beam yields two separate re#ectivity curves. Scattering length density pro"le models with a common non-magnetic part and a magnetic part depending on the polarization of the neutron beam are then "tted simultaneously to both sets of re#ectivity data. It is well-known that a non-collinear orientation of magnetization vectors results in spin-#ipped neutron re#ectivities. For a buried magnetic thin "lm (magnetization perpendicular to applied "eld) in a non-magnetic matrix, the amount of spin-#ip re#ection depends on the
* Corresponding author. Tel.: #31-0-15-2786775; fax: #310-15-2786442. E-mail address: [email protected] (R.W.E. van de Kruijs)
neutron probability density inside the magnetic layer. This probability density is determined by neutron wave function boundary conditions between magnetic "lm and
Fig. 1. Non-magnetic neutron re#ectivities as a function of the perpendicular component of the incident neutron wave vector k show only small changes resulting from di!erent X scattering length densities. The modeled system consists of a bilayer (d "50 nm, C "5.0;10\ nm\, d "10 nm, C "2.0, 2.5, 3.0;10\ nm\) on top of a substrate (C "4.5;10\ nm\) with a thin magnetic "lm (d "0.5 nm, C "3.0;10\ nm\). In all model calcu lations 5% resolution was included.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 7 5 9 - 7
R.W.E. van de Kruijs et al. / Physica B 276}278 (2000) 642}643
Fig. 2. Polarized neutron re#ectivities on a non-collinear system (B "0.01T, B "1.6 T, other parameters equal to Fig. 1.) X V show large peak intensity variations in the spin-#ipped re#ectivity for changing C .
643
non-magnetic matrix, linking the spin-#ip intensity with the non-magnetic matrix scattering density pro"le C(z)"4p1nb2. To investigate the sensitivity of spin-#ipped neutrons to changes in C(z), we have performed model calculations on a system of a non-magnetic bilayer on a substrate with a thin magnetic layer. Non-polarized re#ectivity curves (Fig. 1) show little response to small variations of C(z). Although polarized neutron re#ectometry (PNR) without re#ected polarization analysis may reduce ambiguities by simultaneous "tting of data sets, calculations show that detailed changes in C(z) are still di$cult to observe. Fig. 2 shows PNR calculations with polarization analysis for a non-collinear system. Although non-spin-#ipped curves are similar to the case without polarization analysis, spin-#ipped re#ectivities show much larger sensitivity to small changes in C(z). Calculations for the same system with a di!erent second non-magnetic layer thickness again show large sensitivity (Fig. 3). Both peak position and peak intensity change dramatically when model parameters are changed. For systems with all magnetization vectors in one plane only three diwerent re#ectivity curves can be obtained because R,R [3]. A technically more challenging setup would be a system with two thin magnetic layers on top of the substrate, with magnetizations perpendicular to each other and perpendicular to the incident polarization, resulting in four di!erent re#ectivity curves, further enhancing the spin-#ip sensitivity.
References
Fig. 3. Polarized neutron re#ectivities on a non-collinear system (d "50 nm, other parameters equal to calculations shown in Fig. 2.) show large peak position variations in the spin-#ipped re#ectivity for changing C .
[1] K. Chadan, P.C. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer, New York, 1977. [2] W.D. Dozier, J.M. Carpenter, G.P. Felcher, Bull. Am. Phys. Soc. 36 (1991) 772. [3] H. Fredrikze, R.W.E. van de Kruijs, in preparation.
Polarization analysis of neutron re#ectometry on non-magnetic structures deposited on a magnetic layer R.W.E. van de Kruijs *, H. Fredrikze , M.Th. Rekveldt Interfacultair Reactor Instituut, Delft University of Technology, Mekelweg 15, 2629 JB Delft, Netherlands
Abstract We present polarized neutron re#ectometry calculations for a non-magnetic bilayer on top of a substrate with a thin magnetic "lm. In contrast to non-magnetic and collinear magnetic re#ectivities, the spin-#ipped re#ectivities from a non-collinear system are shown to be very sensitive to small changes in the non-magnetic scattering length densities. 2000 Elsevier Science B.V. All rights reserved. PACS: 61.12.Ha; 75.70.Ak Keywords: Re#ectometry; Polarized neutrons; Polarization analysis; Noncollinear structures; Thin "lms
Because of the inverse problem in re#ectometry data analysis [1], it is impossible to obtain a unique scattering length density pro"le directly from experimental data. Clever use can be made of contrast variation (neutrons) and the use of di!erent wavelengths close to and far from the substrate absorption edge (X-rays) to reduce pro"le ambiguities by simultaneous "tting of data sets. Several authors have commented that polarized neutrons can also be used to facilitate the data analysis of non-magnetic thin "lm structures [2]. Adding a thin magnetic "lm to the substrate and using a spin-polarized incident neutron beam yields two separate re#ectivity curves. Scattering length density pro"le models with a common non-magnetic part and a magnetic part depending on the polarization of the neutron beam are then "tted simultaneously to both sets of re#ectivity data. It is well-known that a non-collinear orientation of magnetization vectors results in spin-#ipped neutron re#ectivities. For a buried magnetic thin "lm (magnetization perpendicular to applied "eld) in a non-magnetic matrix, the amount of spin-#ip re#ection depends on the
* Corresponding author. Tel.: #31-0-15-2786775; fax: #310-15-2786442. E-mail address: [email protected] (R.W.E. van de Kruijs)
neutron probability density inside the magnetic layer. This probability density is determined by neutron wave function boundary conditions between magnetic "lm and
Fig. 1. Non-magnetic neutron re#ectivities as a function of the perpendicular component of the incident neutron wave vector k show only small changes resulting from di!erent X scattering length densities. The modeled system consists of a bilayer (d "50 nm, C "5.0;10\ nm\, d "10 nm, C "2.0, 2.5, 3.0;10\ nm\) on top of a substrate (C "4.5;10\ nm\) with a thin magnetic "lm (d "0.5 nm, C "3.0;10\ nm\). In all model calcu lations 5% resolution was included.
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 9 9 ) 0 1 7 5 9 - 7
R.W.E. van de Kruijs et al. / Physica B 276}278 (2000) 642}643
Fig. 2. Polarized neutron re#ectivities on a non-collinear system (B "0.01T, B "1.6 T, other parameters equal to Fig. 1.) X V show large peak intensity variations in the spin-#ipped re#ectivity for changing C .
643
non-magnetic matrix, linking the spin-#ip intensity with the non-magnetic matrix scattering density pro"le C(z)"4p1nb2. To investigate the sensitivity of spin-#ipped neutrons to changes in C(z), we have performed model calculations on a system of a non-magnetic bilayer on a substrate with a thin magnetic layer. Non-polarized re#ectivity curves (Fig. 1) show little response to small variations of C(z). Although polarized neutron re#ectometry (PNR) without re#ected polarization analysis may reduce ambiguities by simultaneous "tting of data sets, calculations show that detailed changes in C(z) are still di$cult to observe. Fig. 2 shows PNR calculations with polarization analysis for a non-collinear system. Although non-spin-#ipped curves are similar to the case without polarization analysis, spin-#ipped re#ectivities show much larger sensitivity to small changes in C(z). Calculations for the same system with a di!erent second non-magnetic layer thickness again show large sensitivity (Fig. 3). Both peak position and peak intensity change dramatically when model parameters are changed. For systems with all magnetization vectors in one plane only three diwerent re#ectivity curves can be obtained because R,R [3]. A technically more challenging setup would be a system with two thin magnetic layers on top of the substrate, with magnetizations perpendicular to each other and perpendicular to the incident polarization, resulting in four di!erent re#ectivity curves, further enhancing the spin-#ip sensitivity.
References
Fig. 3. Polarized neutron re#ectivities on a non-collinear system (d "50 nm, other parameters equal to calculations shown in Fig. 2.) show large peak position variations in the spin-#ipped re#ectivity for changing C .
[1] K. Chadan, P.C. Sabatier, Inverse Problems in Quantum Scattering Theory, Springer, New York, 1977. [2] W.D. Dozier, J.M. Carpenter, G.P. Felcher, Bull. Am. Phys. Soc. 36 (1991) 772. [3] H. Fredrikze, R.W.E. van de Kruijs, in preparation.