- Email: [email protected]
Magnetic depth profiles in strained nickel thin films measured by polarized neutron reflectometry
Journal of Magnetismand Magnetic Materials 165 (1997) 475-478
~4
ELSEVIER
Journalof magnetism and magnetic materials
Magnetic depth profiles in strained nickel thin films measured by polarized neutron reflectometry F. Otta,*,
C. Fermon
b
a Laboratoire L~on Brillouin, CEA/CNRS Saclay, 91191 Gif-sur-Yvette Cedex, France b DRECAM/SPEC, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
Abstract We investigated the modifications of the magnetostrictive properties of nickel thin films due to relaxation strains at the substrate/film and film/vacuum interfaces. The in-plane magnetization rotation induced by a mechanical applied strain varies with the depth in the film. In nickel thin films submitted to strains of 3 × 10 -4 (expressed in relative deformation) the magnetization rotation is shown to be of 55° at the vacuum/film and substrate film interfaces whereas it goes up to 65 ° in the middle of the film. These magnetic depth profiles were measured by polarized neutron reflectometry with polarization analysis. Keywords: Neutron reflectometry;Thin films; Strain; Magnetostfiction;Magnetoelastics
1. Introduction When applying a strain to magnetic materials, the magnetization rotates either along the applied strain or perpendicular to it, depending on the sign of the magnetostriction coefficient (positive for NixFe I -x with x < 0.8 and negative for x > 0.8) [l]. Recent studies [2] have shown that in such films the magnetoelastic (ME) coefficients can increase dramatically for very thin films (below l0 nm) even for the permalloy composition in which the bulk ME coefficients are essentially zero. Results are interpreted as a bulk contribution plus a surface contribution decreasing as the inverse of the film thickness Beff(Z) = Bbulkq-Bsurf/(Z- Z0). This suggests that in thicker films, there must exist a gradient of the ME coefficient. If this B ( z ) profile exists, one must observe an inhomogeneous rotation of the magnetization in a thin film submitted to strains. So to separate the effect of each interface and evaluate the propagation of surface effects throughout the film, we have determined magnetic depth profiles by neutron reflectometry on thick films (20 to 100 nm).
2. The measurement technique By measuring the specular reflectivity of a neutron beam (or X-rays beam) as a function of the incident angle,
* Corresponding author. Email: [email protected]; fax: + 33-1-6908-8786.
the internal structure of a thin film can be determined [3]. As the magnetic scattering amplitude of neutrons is large, working with polarized neutrons beams enables one to determine in-plane vectorial magnetic depth profiles even in rather complex multilayered structures [4-6]. Considering a beam having two polarisation states (up and down), the reflectivity curves of neutrons keeping their polarization after reflection (incident up (resp. down), reflected up (resp. down)) give information about the magnetization along the neutron quantization axis (i.e. the external field direction). The reflectivity curves of the neutron flipping after reflection (incident up (resp. down), reflected down (resp. up)) is related to the magnetization perpendicular to the quantization axis. The experiments were made at the Laboratoire L~on Brillouin, Centre d'Etudes de Saclay, on the reflectometer G2-2.
3. Experimental procedure and results We studied nickel thin films deposited by RF sputtering on a glass or a silicon substrate. The films were deposited at room temperature under an argon pressure of 5 × 10 -3 bar at a rate of 25 nm per minute. The film's thickness varied from 20 nm to 80 nm. The experimental study consisted in applying mechanical stresses to magnetic thin films and then observing their magnetization state. The strains were obtained by mechanically bending the glass or the silicon substrates. Strains will further be expressed in relative deformation. For
0304-8853/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0304-8853(96)00596-3
476
F. Ott, C. Fermon /Journal of Magnetism and Magnetic Materials 165 (1997) 475-478
~--~--
Contraction Unstrained Elongation
288 336
ppm ppm
0,04
0.02
\ S.
0.00
............ I
~D v
-0.02
-0.04
-40
-20
0
H
20
40
(gauss)
Fig. 1. Kerr loops obtained on a single 18 nm nickel layer deposited on silicon for three different applied strains. An elongation strain created a hard axis perpendicular to the direction of the applied strain. A contraction strain squared the cycle.
m - H loops let us derive a magnetoelastic coefficient using the method proposed in Ref. [7]. A determination of the absolute magnetization was obtained by neutron measurements which give the magnetization of the sample in ix B per atom. The anhysteretic parts of the m - H loops give a magnetoelastic coefficient of 1.2 X 106 (Jr- 20%) J m -3. This is lower than what is observed in bulk material but this is confirmed by neutron measurements. These magneto-optic measurements are surface selective. This selectivity can be described by expressing a
silicon the strain limit before substrate breaking was about 3 X 10 -4, for glass substrates the limit was about 6 x 10 -4. These values are far below the elastic limit of metallic films. Kerr loops were measured on a 18 nm nickel film deposited on a silicon substrate (cf. Fig. 1). In these measurements, the magnetic field was applied along the strain direction. For nickel films in which the M E coefficient is negative, an elongation strain creates an easy axis perpendicular to the applied strain and a contraction strain creates an easy axis parallel to the strain direction. These
ended sample
field~ O
X neutron UP
neutron D O W N Fig. 2. Scheme of the reflection geometry of a polarized neutron beam on a strained sample.
F. Ott, C. Fermon/ Journal of Magnetism and Magnetic Materials 165 (1997) 475-478 mean over the local values of B(z) through the thickness l of the film [2]:
and avoid domain formation which creates non-specular signals, we saturated the sample along a direction making 20° with the (Ox) axis and then decreased the field down to 6 G. The films were then strained by a mechanical bending of the glass substrate. The strains obtained were of about 3 X 10 -4 in either contraction or elongation along the (Oy) axis (see Fig. 2). The 6 G magnetic field was then realigned along the (Ox) axis. This 6 G field had to be applied on the sample to keep the neutron beam polarized. We measured reflectivity curves on a 18 nm nickel film deposited on a silicon substrate and on 40 nm and 80 nm nickel films deposited on a glass substrate. Fig. 3 shows the experimental results and the fitting results for the 40
ft g( z ) B ( z ) d z B(z)=
f'og(z)dz
'
477
(1)
where z is the depth in the film and g(z) is a weighting function which can be described by g(z) = e - z/a, where -- 20 nm is the skin depth. Thus magneto-optic measurements give only a surface or a mean value for the magnetoelastic coefficient. We made polarized neutron reflectivity measurements in order to determine a local ME coefficient profile (as a function of z). The experimental procedure was the following. In order to have a preferential direction of rotation
(a) 10000000
Up-Up O Down-Down []
1000000
~
,.j d
100000
~
¢,. ¢:
10000
I--fits
'
m
1000 100
I 0,5
0
I 1
1,5
2
0 (degrees)
(b) 10000000
~ ~ 1000000 o ~ ,~, o~ =. 100000 I o o ->',,, w
10000
_
Up-Up o Spin-flip o Down-Down
[]
, ~
~
~
~
t-
1000
-
100 10 0
' 0,2
q 0,4
L 0,6
I 0,8
I 1
I 1,2
1,4
e (degrees) Fig. 3. Reflectivitycurves measured on a iron-nickel film unstrainedand under a 3 × 10 - 4 elongationstrain. Fits are shown in continuous lines. Up-up and down-down denotes reflected neutrons that did not change of polarization state. Up-down denotes the neutrons having flipped after reflection. Spin-flipreflectivitywas very small in the unstrainedfilm.
478
F. Ott, C. Fermon / Journal of Magnetism and Magnetic Materials 165 (1997) 475-478
Table 1 Summary of the fitting results for a 18 nm and a 40 nm nickel layer. The magnetization is expressed in Bohr magneton by atom. c~ is the angle the magnetization makes with the direction of application of the strain. The samples were submitted to strains of 3.6 X 10 - 4 in relative deformation
Alloy layer 1st nickel layer 2nd nickel layer 3rd nickel layer 4th nickel layer Surface layer
18 nm nickel layer deposited on a silicon substrate
40 nm nickel layer deposited on a glass substrate
Thickness (,~)
rn (izB)
a (deg)
Thickness (/k)
m (IXn)
ot (deg)
26 35 38 38 35 15
0.2 0.53? 0.53 0.53 0.53 0.37
56 62 65 64 57 41
40 100 100 100 94.5 31.3
0.177 0.53 0.53 0.53 0.53 0.5
62.3 61.7 70 74.4 75.3 56.7
nm nickel film. The first step was to fit the reflectivity curves on the unstrained and saturated samples in order to determine its magnetic parameters, particularly to determine an alloy layer between the substrate and the film and a surface layer. These layers characterize the roughness of the film interfaces. The second step consisted in dividing the layer in five sublayers and letting the magnetization direction vary in each of these layers to fit the refiectivity curves on the strained sample. The fitting results are summarized in Table 1. For the 80 nm nickel film the experimental resolution did not allow us to determine an accurate magnetic profile. The results must not be considered as absolute values but should be read as relative values. There are several reasons: the magnetic field can have been misaligned with the strain direction and the applied strain is only determined with a 10% accuracy. The most important point to note is that in both cases we observed magnetic rotation gradients which go up to 10 degrees between the film surfaces and the middle of the film.
4. Interpretation and conclusion In order to describe these features, one can introduce a ME coefficient B ( z ) depending on the depth in the film. This dependence can be linked to surface relaxation or misfit strains [7]. Other groups [8] demonstrated that thin films always present rather high internal strain gradients. These gradients are very dependent on the deposition technique and the deposition conditions. Our measurements are an indirect measurements and consequences of these effects. A simple evaluation of a B ( z ) profile in the films can be done by introducing the total energy of the system and minimizing it with respect to the measured magnetization profile. There are four energy terms: the Zeeman interaction E z = - M H o cos(~0(z) - 0me), the magnetoelastic energy Em~ = e B ( z ) sin2(q~(z) - 0m~), the exchange energy Eex = A ( a ~ o ( z ) / a z ) 2, the anisotropy energy E a = K sin2(~b(z)). In these expressions q~(z) is the direction of the magnetization at the depth z in the film, 0m¢ is the
direction of the easy axis created by the strain, H o is the extemal applied field. One of the problems is that it is difficult to take into account non-reversible processes such as coercivity losses. So we were yet not able to derive reliable values of the M E coefficients. W e can only say that there must be important strain gradients in the films. These measurements show that surface effects (especially at the f i l m / v a c u u m interface) are not limited very near to the surface. One can introduce a N t e l model of the form Bell(Z) = Bbulk + Bsuff/(Z - t o) tO describe the behavior of very thin films [2], the effective M E coefficient being the sum of a bulk contribution and a surface contribution, z is the thickness of the film, z0 is a shift which could be due to chemical mixing with the substrate. The measurements of an effective M E coefficient on very thin films gave an average over the films thicknesses. It showed rather drastic changes with the film thicknesses, showing a strong departure from the bulk behavior for thickness varying from 4 to 10 nm, depending of the substrate. In our case the effect has a lengthscale of about 20 nm. The difference may be due to the film deposition process: a crystalline growth induces a shorter relaxation length than an amorphous growth. These problems are very important for engineering thin films with homogeneous magnetic properties.
References [1] R.M. Bozorth, Ferromagnetism (Van Nostrand, Princeton, NJ, 1951) p. 619. [2] O. Song, C.A. Ballentine and R.C. O'Handley, Appl. Phys. Lett. 64 (1994) 2593. [3] J. Lekner, Theory of Reflection (Martinus Nijhoff, Dordrecht, 1987). [4] G.P. Felcher, R.O. Hilleke, R.K. Crawford, J. Haumann, R. Kleb and G. Ostrowski, Rev. Sci. Instr. 58 (1987) 609. [5] S.J. Blundell and J.A.C. Bland, Phys. Rev. B 46 (1992) 3391. [6] C. Fermon, Physica B 213/214 (1995) 910. [7] R.C. O'Handley, Oh-Sung Song and C.A. Ballentine, J. Appl. Phys. 74 (1993) 6302. [8] M. Boutry, A. Bosseboeuf and J.P. Grandchamp, private communication.
~4
ELSEVIER
Journalof magnetism and magnetic materials
Magnetic depth profiles in strained nickel thin films measured by polarized neutron reflectometry F. Otta,*,
C. Fermon
b
a Laboratoire L~on Brillouin, CEA/CNRS Saclay, 91191 Gif-sur-Yvette Cedex, France b DRECAM/SPEC, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France
Abstract We investigated the modifications of the magnetostrictive properties of nickel thin films due to relaxation strains at the substrate/film and film/vacuum interfaces. The in-plane magnetization rotation induced by a mechanical applied strain varies with the depth in the film. In nickel thin films submitted to strains of 3 × 10 -4 (expressed in relative deformation) the magnetization rotation is shown to be of 55° at the vacuum/film and substrate film interfaces whereas it goes up to 65 ° in the middle of the film. These magnetic depth profiles were measured by polarized neutron reflectometry with polarization analysis. Keywords: Neutron reflectometry;Thin films; Strain; Magnetostfiction;Magnetoelastics
1. Introduction When applying a strain to magnetic materials, the magnetization rotates either along the applied strain or perpendicular to it, depending on the sign of the magnetostriction coefficient (positive for NixFe I -x with x < 0.8 and negative for x > 0.8) [l]. Recent studies [2] have shown that in such films the magnetoelastic (ME) coefficients can increase dramatically for very thin films (below l0 nm) even for the permalloy composition in which the bulk ME coefficients are essentially zero. Results are interpreted as a bulk contribution plus a surface contribution decreasing as the inverse of the film thickness Beff(Z) = Bbulkq-Bsurf/(Z- Z0). This suggests that in thicker films, there must exist a gradient of the ME coefficient. If this B ( z ) profile exists, one must observe an inhomogeneous rotation of the magnetization in a thin film submitted to strains. So to separate the effect of each interface and evaluate the propagation of surface effects throughout the film, we have determined magnetic depth profiles by neutron reflectometry on thick films (20 to 100 nm).
2. The measurement technique By measuring the specular reflectivity of a neutron beam (or X-rays beam) as a function of the incident angle,
* Corresponding author. Email: [email protected]; fax: + 33-1-6908-8786.
the internal structure of a thin film can be determined [3]. As the magnetic scattering amplitude of neutrons is large, working with polarized neutrons beams enables one to determine in-plane vectorial magnetic depth profiles even in rather complex multilayered structures [4-6]. Considering a beam having two polarisation states (up and down), the reflectivity curves of neutrons keeping their polarization after reflection (incident up (resp. down), reflected up (resp. down)) give information about the magnetization along the neutron quantization axis (i.e. the external field direction). The reflectivity curves of the neutron flipping after reflection (incident up (resp. down), reflected down (resp. up)) is related to the magnetization perpendicular to the quantization axis. The experiments were made at the Laboratoire L~on Brillouin, Centre d'Etudes de Saclay, on the reflectometer G2-2.
3. Experimental procedure and results We studied nickel thin films deposited by RF sputtering on a glass or a silicon substrate. The films were deposited at room temperature under an argon pressure of 5 × 10 -3 bar at a rate of 25 nm per minute. The film's thickness varied from 20 nm to 80 nm. The experimental study consisted in applying mechanical stresses to magnetic thin films and then observing their magnetization state. The strains were obtained by mechanically bending the glass or the silicon substrates. Strains will further be expressed in relative deformation. For
0304-8853/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PII S0304-8853(96)00596-3
476
F. Ott, C. Fermon /Journal of Magnetism and Magnetic Materials 165 (1997) 475-478
~--~--
Contraction Unstrained Elongation
288 336
ppm ppm
0,04
0.02
\ S.
0.00
............ I
~D v
-0.02
-0.04
-40
-20
0
H
20
40
(gauss)
Fig. 1. Kerr loops obtained on a single 18 nm nickel layer deposited on silicon for three different applied strains. An elongation strain created a hard axis perpendicular to the direction of the applied strain. A contraction strain squared the cycle.
m - H loops let us derive a magnetoelastic coefficient using the method proposed in Ref. [7]. A determination of the absolute magnetization was obtained by neutron measurements which give the magnetization of the sample in ix B per atom. The anhysteretic parts of the m - H loops give a magnetoelastic coefficient of 1.2 X 106 (Jr- 20%) J m -3. This is lower than what is observed in bulk material but this is confirmed by neutron measurements. These magneto-optic measurements are surface selective. This selectivity can be described by expressing a
silicon the strain limit before substrate breaking was about 3 X 10 -4, for glass substrates the limit was about 6 x 10 -4. These values are far below the elastic limit of metallic films. Kerr loops were measured on a 18 nm nickel film deposited on a silicon substrate (cf. Fig. 1). In these measurements, the magnetic field was applied along the strain direction. For nickel films in which the M E coefficient is negative, an elongation strain creates an easy axis perpendicular to the applied strain and a contraction strain creates an easy axis parallel to the strain direction. These
ended sample
field~ O
X neutron UP
neutron D O W N Fig. 2. Scheme of the reflection geometry of a polarized neutron beam on a strained sample.
F. Ott, C. Fermon/ Journal of Magnetism and Magnetic Materials 165 (1997) 475-478 mean over the local values of B(z) through the thickness l of the film [2]:
and avoid domain formation which creates non-specular signals, we saturated the sample along a direction making 20° with the (Ox) axis and then decreased the field down to 6 G. The films were then strained by a mechanical bending of the glass substrate. The strains obtained were of about 3 X 10 -4 in either contraction or elongation along the (Oy) axis (see Fig. 2). The 6 G magnetic field was then realigned along the (Ox) axis. This 6 G field had to be applied on the sample to keep the neutron beam polarized. We measured reflectivity curves on a 18 nm nickel film deposited on a silicon substrate and on 40 nm and 80 nm nickel films deposited on a glass substrate. Fig. 3 shows the experimental results and the fitting results for the 40
ft g( z ) B ( z ) d z B(z)=
f'og(z)dz
'
477
(1)
where z is the depth in the film and g(z) is a weighting function which can be described by g(z) = e - z/a, where -- 20 nm is the skin depth. Thus magneto-optic measurements give only a surface or a mean value for the magnetoelastic coefficient. We made polarized neutron reflectivity measurements in order to determine a local ME coefficient profile (as a function of z). The experimental procedure was the following. In order to have a preferential direction of rotation
(a) 10000000
Up-Up O Down-Down []
1000000
~
,.j d
100000
~
¢,. ¢:
10000
I--fits
'
m
1000 100
I 0,5
0
I 1
1,5
2
0 (degrees)
(b) 10000000
~ ~ 1000000 o ~ ,~, o~ =. 100000 I o o ->',,, w
10000
_
Up-Up o Spin-flip o Down-Down
[]
, ~
~
~
~
t-
1000
-
100 10 0
' 0,2
q 0,4
L 0,6
I 0,8
I 1
I 1,2
1,4
e (degrees) Fig. 3. Reflectivitycurves measured on a iron-nickel film unstrainedand under a 3 × 10 - 4 elongationstrain. Fits are shown in continuous lines. Up-up and down-down denotes reflected neutrons that did not change of polarization state. Up-down denotes the neutrons having flipped after reflection. Spin-flipreflectivitywas very small in the unstrainedfilm.
478
F. Ott, C. Fermon / Journal of Magnetism and Magnetic Materials 165 (1997) 475-478
Table 1 Summary of the fitting results for a 18 nm and a 40 nm nickel layer. The magnetization is expressed in Bohr magneton by atom. c~ is the angle the magnetization makes with the direction of application of the strain. The samples were submitted to strains of 3.6 X 10 - 4 in relative deformation
Alloy layer 1st nickel layer 2nd nickel layer 3rd nickel layer 4th nickel layer Surface layer
18 nm nickel layer deposited on a silicon substrate
40 nm nickel layer deposited on a glass substrate
Thickness (,~)
rn (izB)
a (deg)
Thickness (/k)
m (IXn)
ot (deg)
26 35 38 38 35 15
0.2 0.53? 0.53 0.53 0.53 0.37
56 62 65 64 57 41
40 100 100 100 94.5 31.3
0.177 0.53 0.53 0.53 0.53 0.5
62.3 61.7 70 74.4 75.3 56.7
nm nickel film. The first step was to fit the reflectivity curves on the unstrained and saturated samples in order to determine its magnetic parameters, particularly to determine an alloy layer between the substrate and the film and a surface layer. These layers characterize the roughness of the film interfaces. The second step consisted in dividing the layer in five sublayers and letting the magnetization direction vary in each of these layers to fit the refiectivity curves on the strained sample. The fitting results are summarized in Table 1. For the 80 nm nickel film the experimental resolution did not allow us to determine an accurate magnetic profile. The results must not be considered as absolute values but should be read as relative values. There are several reasons: the magnetic field can have been misaligned with the strain direction and the applied strain is only determined with a 10% accuracy. The most important point to note is that in both cases we observed magnetic rotation gradients which go up to 10 degrees between the film surfaces and the middle of the film.
4. Interpretation and conclusion In order to describe these features, one can introduce a ME coefficient B ( z ) depending on the depth in the film. This dependence can be linked to surface relaxation or misfit strains [7]. Other groups [8] demonstrated that thin films always present rather high internal strain gradients. These gradients are very dependent on the deposition technique and the deposition conditions. Our measurements are an indirect measurements and consequences of these effects. A simple evaluation of a B ( z ) profile in the films can be done by introducing the total energy of the system and minimizing it with respect to the measured magnetization profile. There are four energy terms: the Zeeman interaction E z = - M H o cos(~0(z) - 0me), the magnetoelastic energy Em~ = e B ( z ) sin2(q~(z) - 0m~), the exchange energy Eex = A ( a ~ o ( z ) / a z ) 2, the anisotropy energy E a = K sin2(~b(z)). In these expressions q~(z) is the direction of the magnetization at the depth z in the film, 0m¢ is the
direction of the easy axis created by the strain, H o is the extemal applied field. One of the problems is that it is difficult to take into account non-reversible processes such as coercivity losses. So we were yet not able to derive reliable values of the M E coefficients. W e can only say that there must be important strain gradients in the films. These measurements show that surface effects (especially at the f i l m / v a c u u m interface) are not limited very near to the surface. One can introduce a N t e l model of the form Bell(Z) = Bbulk + Bsuff/(Z - t o) tO describe the behavior of very thin films [2], the effective M E coefficient being the sum of a bulk contribution and a surface contribution, z is the thickness of the film, z0 is a shift which could be due to chemical mixing with the substrate. The measurements of an effective M E coefficient on very thin films gave an average over the films thicknesses. It showed rather drastic changes with the film thicknesses, showing a strong departure from the bulk behavior for thickness varying from 4 to 10 nm, depending of the substrate. In our case the effect has a lengthscale of about 20 nm. The difference may be due to the film deposition process: a crystalline growth induces a shorter relaxation length than an amorphous growth. These problems are very important for engineering thin films with homogeneous magnetic properties.
References [1] R.M. Bozorth, Ferromagnetism (Van Nostrand, Princeton, NJ, 1951) p. 619. [2] O. Song, C.A. Ballentine and R.C. O'Handley, Appl. Phys. Lett. 64 (1994) 2593. [3] J. Lekner, Theory of Reflection (Martinus Nijhoff, Dordrecht, 1987). [4] G.P. Felcher, R.O. Hilleke, R.K. Crawford, J. Haumann, R. Kleb and G. Ostrowski, Rev. Sci. Instr. 58 (1987) 609. [5] S.J. Blundell and J.A.C. Bland, Phys. Rev. B 46 (1992) 3391. [6] C. Fermon, Physica B 213/214 (1995) 910. [7] R.C. O'Handley, Oh-Sung Song and C.A. Ballentine, J. Appl. Phys. 74 (1993) 6302. [8] M. Boutry, A. Bosseboeuf and J.P. Grandchamp, private communication.