- Email: [email protected]
Magnetooptic depth sensitivity in a simple ultrathin film structure
Journal of Magnetismand Magnetic Materials 165 (1997) 92-95
ELSEVIER
~H ~H ~H
journalof magnetism and magnetic materials
Magnetooptic depth sensitivity in a simple ultrathin film structure J. Ferr~
a,*, p. Meyer a, M. Nyvlt b, S. Visnovsky b, D. Renard c
a Laboratoire de Physique des Solides, associ£ au CNRS, Bat. 510, Universit[ Paris-Sud, 91405 Orsay Cedex, France b Institute of Physics, Charles University, Ke Karlovu 5, 12116 Prague 2, Czech Republic c lnstitut d'Optique Th£orique et Appliqu£e, associ£ au CNRS, Bat. 503, Universit£ Paris-Sud, 91405 Orsay Cedex, France
Abstract Polar magnetooptics (MO) is able to probe the magnetization depth profile in ultrathin magnetic film structures on a nanometer scale. This information can be deduced by modelling the MO effects in the considered layered medium when performing MO experiments with a compensator or changing the wavelength of the incident light beam. Spectroscopic MO measurements are then helpful for analysing this phenomenon in detail. The in-depth selectivity of MO effects for magnetization is demonstrated for a simple ultrathin film structure consisting of two magnetic Co layers with perpendicular anisotropy separated by a non-magnetic Au spacer layer. The individual magnetic contributions of the two Co layers may be observed directly when performing MO Kerr measurements at selected compensator phase shifts or photon energies. The experimental data are interpreted by MO calculations in both cases. Keywords: Magnetooptics;Ultrathin films; Kerr effect
1. Introduction The interesting properties of magnetic ultrathin film structures, such as magnetoresistance, magnetooptical effects, etc., are very sensitive to the homogeneity of the magnetization inside the specimen. In particular, it is known that the magnetic moment departs from the bulk value close to perfect surfaces or interfaces. Atomic interdiffusion and stresses can obviously affect the magnetization even at larger distances. Therefore, it is important to be able to obtain information on the in-depth magnetization profile, especially near buried interfaces, in multilayer ultrathin film structures. Surface magnetic sensitive techniques, such as electron microscopy with spin polarization analysis [1-3], already give invaluable information on the upper magnetic layervacuum interface. On the other hand, only a few promising techniques, such as neutron reflectometry with polarization analysis [4] and the magnetooptical (MO) Kerr effect [5-7], are available at the moment to probe the in-depth magnetization profile on a nanometer scale. As first shown by Hubert et al. [5,6], magnetooptics in laterally uniform layered structures is magnetically depth sensitive. It has recently been shown that the MO contribution of an ultrathin magnetic element lying inside the film structure can be eliminated using a compensator [8] or, in
* Correspondingauthor. Email: [email protected].
specific cases, by choosing the photon energy [7] of the incident light beam.
2. Experimental To check these predictions we performed polar MO Kerr measurements in a simple magnetic cobalt bilayer structure with perpendicular anisotropy, [Au(5 nm)/Co(1.2 nm)/Au(3 nm)/Co(0.8 nm)/Au(111)(25 nm)], deposited on a float glass (1 mm) substrate. A pertinent application of the electromagnetic model for calculating MO effects may be derived for this C o / A u system since it exhibits very abrupt interfaces and no Co-Au interdiffusion, as previously demonstrated for A u / C o / A u sandwiches [9,10]. The Au (3 nm) spacer layer was thin enough to demonstrate the selectivity of the method for isolating the magnetic effect of one or other Co layer. We chose two different Co layer thicknesses to identify MO hysteresis loop contributions due to different coercivities. A sensitive modulation technique [11] was used to measure the polar Kerr effect. The experimental setup is depicted in Fig. 1; the modulation of the state of polarization of the light is realized by a photoelastic modulator (MOD) working at a frequency of f = 50 kHz. Without compensator (COMP) it allows accurate measurements of either the polar Kerr ellipticity (PKE), detected at frequency f, or the polar Kerr rotation (PKR), detected at frequency 2 f [11,12]. The light is provided either by a high pressure xenon lamp associated with a monochro-
0304-8853/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PI1 S0304-885 3(96)00479-9
93
J. Ferrd et al. / Journal of Magnetism and Magnetic Materials 165 (1997) 92-95 ANAL PMf . ~ 0 >
80
-'
I
I
m .-.,
L~g~cte
POL (oc= 45°, 0)
MOD ~P (0, 80 sin 2 g ft ) (0, q~)
40 SAMPLE!
Fig. 1. Schematic diagram of the experimental arrangement for MO Kerr measurements. The azimuth of each optical element and the introduced phase shift are indicated in parentheses. The angle of incidence 3' was chosen as small as possible (3' -~ 5°) to preserve the nearly normal incidence.
20
=
"".
",
0
~ -40 M
-
0
mator in the case of photon energy dependent measurements, or by a red H e - N e laser ( E = 1.96 eV) for phase shift dependent experiments. In the latter case the phase q~ of the incoming modulated light polarization is modified by a Babinet-Soleil compensator (COMP) inserted just in front of the sample. The incident light penetrates into the film structure through the Au(5 nm) overlayer. Polarimetric measurements were carried out between the polariser (POL) and analyser (ANAL). The relative orientation of the optical elements are shown in Fig. 1.
3. Photon energy dependent Kerr measurements We limited our investigations to PKE measurements in the Co bilayer structure described above. Its PKE hysteresis loop, measured at E = 1.96 eV (Fig. 2), can be decomposed into two contributions coming from the Co(1.2 nm) and Co(0.8 nm) layers, the smallest coercivity being exhibited by the thickest Co(1.2 nm) layer. In this case the photon energy lies far from the value E 0, corresponding to the cancellation of the total PKE signal 0 K, so that the relative magnitude of the two MO contributions is close to the ratio between the cobalt thicknesses [7]. This property is no longer valid when E tends towards E 0 since the PKE dispersion with photon energy differs for each individual Co layer, as a consequence of their different optical environments. This may be checked directly from calculations of the PKE contribution of each Co layer (Fig. 3) using the set of optical and magnetooptical parameters for Au and Co
• --80
J
I
,
2
I
3 Energy
,
I
~
4 [eV]
"1""
5
Fig. 3. Polar Kerr ellipticity spectra of the Co bilayer structure: individual contributions of the lower Co(0.8 nm) (---) and upper Co(1.2 nm) ( - - ) layers. The PKE of the full film structure is also shown (. • .). Inset: details in the vicinity of the PKE cancellation.
reported in Ref. PKE dispersion data [9,10]. As principle, valid
[10]. The general shape of these calculated curves coincides well with experimental a consequence of the MO superposition for ultrathin film structures, one strictly
10
.,~
!
0
~-5
a) -10 -2
i
I
-1 Magnetic field [kOe] I
20 ¸
I
-~ 10 80
s
i
i
"~ 0
~..~
_£J
c~ ~
~ -lO
0
-8o -2
I I -1. 1 Magnetic field [kOe]
Fig. 2. Polar Kerr ellipticity hysteresis loop of the Co bilayer structure measured at photon energy E = 1.96 eV.
-20 -2
b) !
-1
J
I
1 Magnetic field [kOe]
Fig. 4. Polar Kerr ellipticity hysteresis loops of the Co bilayer structure measured at photon energies (a) E I = 2.510 eV and (b) E 2 = 2.454 eV. The two loops correspond to magnetization reversal of the 0.8 and 1.2 nm thick cobalt layers.
J. Ferr£ et al. /Journal of Magnetism and MagneticMaterials 165 (1997) 92-95
94
reproduces (within an accuracy of the order of 10 - 6 degrees) the calculated PKE dispersion curve of the full structure by adding the MO contributions for the two Co layers (Fig. 3). The calculated PKE of Co(1.2 nm) and Co(0.8 nm) layers vanish at photon energies E~ = 2.414 eV and E 2 = 2.371 eV, respectively. Consistent with these calculations we measured the hysteresis loops of the Co(0.8 nm) and Co(1.2 nm) layers selectively at E l = 2.510 eV and E 2 = 2.454 eV, respectively (Fig. 4). The associated PKE signs and magnitudes measured at saturation are consistent with the calculations (Figs. 3 and 4). The slight discrepancy between the experimental and calculated values of E 1 (2.510 and 2.414 eV), E 2 (2.454 and 2.371 eV) and their difference ( E 1 - E 2) (0.056 and 0.043 eV) comes from the uncertainties on the optical constants of gold. 4. Phase shift dependent Kerr measurements
The experimental arrangement shown in Fig. 1 equipped with a compensator, giving an additional phase shift q~, is then used. The Sf and S2f ac signals measured respectively at frequency f and 2 f are linear combinations of the PKR and PKE of the sample, OK and eK: S f = 4J1(60) [ - O K sin ¢p+ e K cos ~p],
S2f--4J2(6o)[ 0 K cos q~+ e K sin q~],
(1)
where J1(8o) and J2(8o) are the first and second order Bessel function values corresponding to the photoelastic modulation amplitude 8 o. When the compensator phase shift is adjusted to 90 ° (the compensator acts as a quarter wave plate) the PKR and PKE are measured at frequencies f and 2f, respectively, i.e. the opposite of the results
obtained without compensator. Expressing the complex Kerr effect ~ K as: ~K = OK -- ieK = g-2ei~,
(2)
where g2 is the modulus and ~ the argument, Eq. (1) can be rewritten as: Sl-- - 4 Y 1 ( 6 o ) O sin(cp + ~ ) ,
S2f ~- 4 J 2 ( 8 o ) O cos(~p + ~ ).
(3)
The calculated variations of the total Sf and S2f signals with the compensator phase shift ~p are shown in Fig. 5. Experimental data fit these variations well. Therefore, one deduces that: Sf and S2f are harmonic functions of the compensator phase shift q~, Sf vanishes when q~ is adjusted to the values q~= q~o(f) = nTr - ~, where n = 0 , _ 1,_ 2 ..... This shows the significance of the argument ~ of the complex Kerr effect in phase shift dependent experiments. Considering again the Co bilayer sample, the individual Kerr effect contributions of the two Co(1.2 nm) and Co(0.8 nm) layers provide different values of the Kerr argument ~1 and ~2. This is expected since, as we have seen above, the photon energy dependence of OK and e K differs for the two Co layers. Restricting ourselves to the interval - ~ r / 2 < q~o(f or 2 f ) < 7r/2 we calculated the corresponding phase shifts of the compensator to cancel one of the MO contributions:for the Co(1.2 nm) layer q ~ ( f ) = - 4 4 . 3 °,
~o~(2f) = 45.7 °,
for the Co(0.8 nm) layer
q~g(f) = - 4 0 . 2 °,
q~o2(2f) = 49.8 °.
On the other hand, we found experimentally:
~
Sf
~'"~ 0 ~
"
&
m
q~ol(f) = - 4 6 . 7 ___0.5 °,
~p~(2f) = 42.0 ___0.5 °,
¢poZ(f) = - 4 1 . 0 + 0.5 °,
q~2(2f) = 48.0 _ 0.5 °.
Fixing these compensator phase shift values we have access to the magnetization of only one Co layer, as depicted in Fig. 6, for example, for the MO signal detected at frequency f. The agreement between experimental and calculated values of q~o is again reasonably good taking into account the inaccuracy of the optical and MO constants of gold and cobalt.
8f 5. Conclusion
-!
-901....
01 i i i 19|0i i i 1189
P h a s e s h i f t [deg]
Fig. 5. Calculated Sf and S2f variation as a function of the compensator phase shift q~ (E = 1.96 eV) using the values of the total complex Kerr effect of the Co bilayer structure. (0, • ) Experimental data.
The in-depth selectivity of magnetooptics to magnetization is demonstrated here for the simple case of cobalt ultrathin layers separated by a non-magnetic spacer layer. The individual magnetic contributions of these two Co layers can be observed separately in MO Kerr measurements with a convenient adjustment of the compensator or
J. Ferr£ et al./ Journal of Magnetism and Magnetic Materials 165 (1997) 92-95
I
a) -1 -1500
i
i
1500 Magnetic field [Oe]
95
Fe overlayer of a F e / C r / F e ultrathin Cr wedge structure [8]. The author demonstrated unambiguously the occurrence of a biquadratic coupling in such a structure at selected Cr thicknesses. Such a method could be extended in the future to the study of in-depth magnetic domain structures and to show correlations between magnetically coupled layers in complex ultrathin film structures. Acknowledgements. This work was carded out in the framework of an HCM European project on 'Novel magnetic structures' extended through PECO to Eastern countries. Partial support from the Grant Agency for Education Development of the Czech Republic (FR 1002), the Grant Agency of Charles University (GAUK 165/95) and Konstruktis Praha, Inc. is gratefully acknowledged. References
40
- 1500
0 Magnetic field [Oe]
1500
Fig. 6. Polar Kerr loops of the Co bilayer structure measured at frequency f with compensator phase shifts (a) ~01(f)=- 46.7 ° and (b) q~02(f)= -41.0 °. The two loops correspond to magnetization reversal of the 0.8 and 1.2 nm thick cobalt layers.
at selected photon energies. These magnetooptical measurements therefore have potential for checking the magnetization of buried ultrathin layers on a nanometer scale. We demonstrate that cancellation of the MO contribution associated with the magnetization at a given depth is closely related to the corresponding argument ~ of the complex Kerr effect. We discuss this phenomenon here in the polar configuration, but similar arguments may be developed for the longitudinal case. The phase shift technique has been applied successfully to MO microscopy to distinguish between domain structures in the Fe wisker and
[1] J. Woods, A. Ushioda, M.M. Donovan, S.W. Sun, M. Tobise and R.C. O'Handley, J. Appl. Phys. 63 (1988) 3669. [2] H.P. Oepen, J. Magn. Magn. Mater. 93 (1991) 116; R. Allenspach, M. Stampanoni and A. Bischof, Phys. Rev. lett. 26 (1990) 3344. [3] E. Bauer, T. Duden, H. Pinkvos, H. Poppa and K. Wurm, J. Magn. Magn. Mater. 156 (1996) 1. [4] Felcher, R.O. Hilleke, R.K. Crawford, J. Haumann, R. Kleb and G. Ostrowski, Rev. Sci. Instr. 58 (1987) 609. [5] G. Traeger, L. Wenzel and A. Hubert, Phys. Status Solidi (a) 121 (1992) 201. [6] A. Hubert and G. Traeger, J. Magn. Magn. Mater. 124 (1993) 185. [7] G. P~nissard, P. Meyer, J. Ferr6 and D. Renard, J. Magn. Magn. Mater. 146 (1995) 55. [8] R. Sch~ifer, J. Magn. Magn. Mater. 148 (1995) 226. [9] S. Visnovsky, M. Nyvlt, V. Prosser, J. Ferr6, G. P6nissard, D. Renard and G. Sczigel, J. Magn. Magn. Mater. 128 (1993) 179. [10] S. Visnovsky, M. Nyvlt, V. Prosser, R. Lopusnik, R. Urban, J. FerrY, G. P6nissard, D. Renard and R. Krishnan, Phys. Rev. B 52 (1995) 1090. [11] J. Badoz, M. Billardon, J.C. Canit and M.F. Russel, J. Opt. (Pads) 8 (1977) 373. [12] K. Sato, Jpn. J. Appl. Phys. 20 (1981) 2403.
ELSEVIER
~H ~H ~H
journalof magnetism and magnetic materials
Magnetooptic depth sensitivity in a simple ultrathin film structure J. Ferr~
a,*, p. Meyer a, M. Nyvlt b, S. Visnovsky b, D. Renard c
a Laboratoire de Physique des Solides, associ£ au CNRS, Bat. 510, Universit[ Paris-Sud, 91405 Orsay Cedex, France b Institute of Physics, Charles University, Ke Karlovu 5, 12116 Prague 2, Czech Republic c lnstitut d'Optique Th£orique et Appliqu£e, associ£ au CNRS, Bat. 503, Universit£ Paris-Sud, 91405 Orsay Cedex, France
Abstract Polar magnetooptics (MO) is able to probe the magnetization depth profile in ultrathin magnetic film structures on a nanometer scale. This information can be deduced by modelling the MO effects in the considered layered medium when performing MO experiments with a compensator or changing the wavelength of the incident light beam. Spectroscopic MO measurements are then helpful for analysing this phenomenon in detail. The in-depth selectivity of MO effects for magnetization is demonstrated for a simple ultrathin film structure consisting of two magnetic Co layers with perpendicular anisotropy separated by a non-magnetic Au spacer layer. The individual magnetic contributions of the two Co layers may be observed directly when performing MO Kerr measurements at selected compensator phase shifts or photon energies. The experimental data are interpreted by MO calculations in both cases. Keywords: Magnetooptics;Ultrathin films; Kerr effect
1. Introduction The interesting properties of magnetic ultrathin film structures, such as magnetoresistance, magnetooptical effects, etc., are very sensitive to the homogeneity of the magnetization inside the specimen. In particular, it is known that the magnetic moment departs from the bulk value close to perfect surfaces or interfaces. Atomic interdiffusion and stresses can obviously affect the magnetization even at larger distances. Therefore, it is important to be able to obtain information on the in-depth magnetization profile, especially near buried interfaces, in multilayer ultrathin film structures. Surface magnetic sensitive techniques, such as electron microscopy with spin polarization analysis [1-3], already give invaluable information on the upper magnetic layervacuum interface. On the other hand, only a few promising techniques, such as neutron reflectometry with polarization analysis [4] and the magnetooptical (MO) Kerr effect [5-7], are available at the moment to probe the in-depth magnetization profile on a nanometer scale. As first shown by Hubert et al. [5,6], magnetooptics in laterally uniform layered structures is magnetically depth sensitive. It has recently been shown that the MO contribution of an ultrathin magnetic element lying inside the film structure can be eliminated using a compensator [8] or, in
* Correspondingauthor. Email: [email protected].
specific cases, by choosing the photon energy [7] of the incident light beam.
2. Experimental To check these predictions we performed polar MO Kerr measurements in a simple magnetic cobalt bilayer structure with perpendicular anisotropy, [Au(5 nm)/Co(1.2 nm)/Au(3 nm)/Co(0.8 nm)/Au(111)(25 nm)], deposited on a float glass (1 mm) substrate. A pertinent application of the electromagnetic model for calculating MO effects may be derived for this C o / A u system since it exhibits very abrupt interfaces and no Co-Au interdiffusion, as previously demonstrated for A u / C o / A u sandwiches [9,10]. The Au (3 nm) spacer layer was thin enough to demonstrate the selectivity of the method for isolating the magnetic effect of one or other Co layer. We chose two different Co layer thicknesses to identify MO hysteresis loop contributions due to different coercivities. A sensitive modulation technique [11] was used to measure the polar Kerr effect. The experimental setup is depicted in Fig. 1; the modulation of the state of polarization of the light is realized by a photoelastic modulator (MOD) working at a frequency of f = 50 kHz. Without compensator (COMP) it allows accurate measurements of either the polar Kerr ellipticity (PKE), detected at frequency f, or the polar Kerr rotation (PKR), detected at frequency 2 f [11,12]. The light is provided either by a high pressure xenon lamp associated with a monochro-
0304-8853/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PI1 S0304-885 3(96)00479-9
93
J. Ferrd et al. / Journal of Magnetism and Magnetic Materials 165 (1997) 92-95 ANAL PMf . ~ 0 >
80
-'
I
I
m .-.,
L~g~cte
POL (oc= 45°, 0)
MOD ~P (0, 80 sin 2 g ft ) (0, q~)
40 SAMPLE!
Fig. 1. Schematic diagram of the experimental arrangement for MO Kerr measurements. The azimuth of each optical element and the introduced phase shift are indicated in parentheses. The angle of incidence 3' was chosen as small as possible (3' -~ 5°) to preserve the nearly normal incidence.
20
=
"".
",
0
~ -40 M
-
0
mator in the case of photon energy dependent measurements, or by a red H e - N e laser ( E = 1.96 eV) for phase shift dependent experiments. In the latter case the phase q~ of the incoming modulated light polarization is modified by a Babinet-Soleil compensator (COMP) inserted just in front of the sample. The incident light penetrates into the film structure through the Au(5 nm) overlayer. Polarimetric measurements were carried out between the polariser (POL) and analyser (ANAL). The relative orientation of the optical elements are shown in Fig. 1.
3. Photon energy dependent Kerr measurements We limited our investigations to PKE measurements in the Co bilayer structure described above. Its PKE hysteresis loop, measured at E = 1.96 eV (Fig. 2), can be decomposed into two contributions coming from the Co(1.2 nm) and Co(0.8 nm) layers, the smallest coercivity being exhibited by the thickest Co(1.2 nm) layer. In this case the photon energy lies far from the value E 0, corresponding to the cancellation of the total PKE signal 0 K, so that the relative magnitude of the two MO contributions is close to the ratio between the cobalt thicknesses [7]. This property is no longer valid when E tends towards E 0 since the PKE dispersion with photon energy differs for each individual Co layer, as a consequence of their different optical environments. This may be checked directly from calculations of the PKE contribution of each Co layer (Fig. 3) using the set of optical and magnetooptical parameters for Au and Co
• --80
J
I
,
2
I
3 Energy
,
I
~
4 [eV]
"1""
5
Fig. 3. Polar Kerr ellipticity spectra of the Co bilayer structure: individual contributions of the lower Co(0.8 nm) (---) and upper Co(1.2 nm) ( - - ) layers. The PKE of the full film structure is also shown (. • .). Inset: details in the vicinity of the PKE cancellation.
reported in Ref. PKE dispersion data [9,10]. As principle, valid
[10]. The general shape of these calculated curves coincides well with experimental a consequence of the MO superposition for ultrathin film structures, one strictly
10
.,~
!
0
~-5
a) -10 -2
i
I
-1 Magnetic field [kOe] I
20 ¸
I
-~ 10 80
s
i
i
"~ 0
~..~
_£J
c~ ~
~ -lO
0
-8o -2
I I -1. 1 Magnetic field [kOe]
Fig. 2. Polar Kerr ellipticity hysteresis loop of the Co bilayer structure measured at photon energy E = 1.96 eV.
-20 -2
b) !
-1
J
I
1 Magnetic field [kOe]
Fig. 4. Polar Kerr ellipticity hysteresis loops of the Co bilayer structure measured at photon energies (a) E I = 2.510 eV and (b) E 2 = 2.454 eV. The two loops correspond to magnetization reversal of the 0.8 and 1.2 nm thick cobalt layers.
J. Ferr£ et al. /Journal of Magnetism and MagneticMaterials 165 (1997) 92-95
94
reproduces (within an accuracy of the order of 10 - 6 degrees) the calculated PKE dispersion curve of the full structure by adding the MO contributions for the two Co layers (Fig. 3). The calculated PKE of Co(1.2 nm) and Co(0.8 nm) layers vanish at photon energies E~ = 2.414 eV and E 2 = 2.371 eV, respectively. Consistent with these calculations we measured the hysteresis loops of the Co(0.8 nm) and Co(1.2 nm) layers selectively at E l = 2.510 eV and E 2 = 2.454 eV, respectively (Fig. 4). The associated PKE signs and magnitudes measured at saturation are consistent with the calculations (Figs. 3 and 4). The slight discrepancy between the experimental and calculated values of E 1 (2.510 and 2.414 eV), E 2 (2.454 and 2.371 eV) and their difference ( E 1 - E 2) (0.056 and 0.043 eV) comes from the uncertainties on the optical constants of gold. 4. Phase shift dependent Kerr measurements
The experimental arrangement shown in Fig. 1 equipped with a compensator, giving an additional phase shift q~, is then used. The Sf and S2f ac signals measured respectively at frequency f and 2 f are linear combinations of the PKR and PKE of the sample, OK and eK: S f = 4J1(60) [ - O K sin ¢p+ e K cos ~p],
S2f--4J2(6o)[ 0 K cos q~+ e K sin q~],
(1)
where J1(8o) and J2(8o) are the first and second order Bessel function values corresponding to the photoelastic modulation amplitude 8 o. When the compensator phase shift is adjusted to 90 ° (the compensator acts as a quarter wave plate) the PKR and PKE are measured at frequencies f and 2f, respectively, i.e. the opposite of the results
obtained without compensator. Expressing the complex Kerr effect ~ K as: ~K = OK -- ieK = g-2ei~,
(2)
where g2 is the modulus and ~ the argument, Eq. (1) can be rewritten as: Sl-- - 4 Y 1 ( 6 o ) O sin(cp + ~ ) ,
S2f ~- 4 J 2 ( 8 o ) O cos(~p + ~ ).
(3)
The calculated variations of the total Sf and S2f signals with the compensator phase shift ~p are shown in Fig. 5. Experimental data fit these variations well. Therefore, one deduces that: Sf and S2f are harmonic functions of the compensator phase shift q~, Sf vanishes when q~ is adjusted to the values q~= q~o(f) = nTr - ~, where n = 0 , _ 1,_ 2 ..... This shows the significance of the argument ~ of the complex Kerr effect in phase shift dependent experiments. Considering again the Co bilayer sample, the individual Kerr effect contributions of the two Co(1.2 nm) and Co(0.8 nm) layers provide different values of the Kerr argument ~1 and ~2. This is expected since, as we have seen above, the photon energy dependence of OK and e K differs for the two Co layers. Restricting ourselves to the interval - ~ r / 2 < q~o(f or 2 f ) < 7r/2 we calculated the corresponding phase shifts of the compensator to cancel one of the MO contributions:for the Co(1.2 nm) layer q ~ ( f ) = - 4 4 . 3 °,
~o~(2f) = 45.7 °,
for the Co(0.8 nm) layer
q~g(f) = - 4 0 . 2 °,
q~o2(2f) = 49.8 °.
On the other hand, we found experimentally:
~
Sf
~'"~ 0 ~
"
&
m
q~ol(f) = - 4 6 . 7 ___0.5 °,
~p~(2f) = 42.0 ___0.5 °,
¢poZ(f) = - 4 1 . 0 + 0.5 °,
q~2(2f) = 48.0 _ 0.5 °.
Fixing these compensator phase shift values we have access to the magnetization of only one Co layer, as depicted in Fig. 6, for example, for the MO signal detected at frequency f. The agreement between experimental and calculated values of q~o is again reasonably good taking into account the inaccuracy of the optical and MO constants of gold and cobalt.
8f 5. Conclusion
-!
-901....
01 i i i 19|0i i i 1189
P h a s e s h i f t [deg]
Fig. 5. Calculated Sf and S2f variation as a function of the compensator phase shift q~ (E = 1.96 eV) using the values of the total complex Kerr effect of the Co bilayer structure. (0, • ) Experimental data.
The in-depth selectivity of magnetooptics to magnetization is demonstrated here for the simple case of cobalt ultrathin layers separated by a non-magnetic spacer layer. The individual magnetic contributions of these two Co layers can be observed separately in MO Kerr measurements with a convenient adjustment of the compensator or
J. Ferr£ et al./ Journal of Magnetism and Magnetic Materials 165 (1997) 92-95
I
a) -1 -1500
i
i
1500 Magnetic field [Oe]
95
Fe overlayer of a F e / C r / F e ultrathin Cr wedge structure [8]. The author demonstrated unambiguously the occurrence of a biquadratic coupling in such a structure at selected Cr thicknesses. Such a method could be extended in the future to the study of in-depth magnetic domain structures and to show correlations between magnetically coupled layers in complex ultrathin film structures. Acknowledgements. This work was carded out in the framework of an HCM European project on 'Novel magnetic structures' extended through PECO to Eastern countries. Partial support from the Grant Agency for Education Development of the Czech Republic (FR 1002), the Grant Agency of Charles University (GAUK 165/95) and Konstruktis Praha, Inc. is gratefully acknowledged. References
40
- 1500
0 Magnetic field [Oe]
1500
Fig. 6. Polar Kerr loops of the Co bilayer structure measured at frequency f with compensator phase shifts (a) ~01(f)=- 46.7 ° and (b) q~02(f)= -41.0 °. The two loops correspond to magnetization reversal of the 0.8 and 1.2 nm thick cobalt layers.
at selected photon energies. These magnetooptical measurements therefore have potential for checking the magnetization of buried ultrathin layers on a nanometer scale. We demonstrate that cancellation of the MO contribution associated with the magnetization at a given depth is closely related to the corresponding argument ~ of the complex Kerr effect. We discuss this phenomenon here in the polar configuration, but similar arguments may be developed for the longitudinal case. The phase shift technique has been applied successfully to MO microscopy to distinguish between domain structures in the Fe wisker and
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