- Email: [email protected]
Generalized magneto-optical ellipsometry in ferromagnetic metals
Thin Solid Films 455 – 456 (2004) 39–42
Generalized magneto-optical ellipsometry in ferromagnetic metals ¨ G. Neuber*, R. Rauer, J. Kunze, J. Backstrom, M. Rubhausen ¨ Angewandte Physik und Zentrum fur ¨ Mikrostrukturforschung, Universitat ¨ Hamburg, Jungiusstraße 11, D-20355, Hamburg, Germany Institut fur
Abstract We present spectral generalized magneto-optical ellipsometry as an optical tool to investigate magnetic and electronic properties of ferromagnetic materials. The advantage of the simultaneous observation of the dielectric and the magnetic responses within one measurement procedure is crucial for materials with coupled degrees of freedom near a phase transition or during annealing procedures to improve the film quality by removing grain boundaries. Moreover, we show the implementation of this technique within an UHV-cryostat for a temperature range between 4.2 and 800 K and fields up to 40 mT. Examplary measurements on iron and Permalloy demonstrate the comfortable application of this technique. 䊚 2003 Elsevier B.V. All rights reserved. Keywords: Ellipsometry; Ferromagnetic metals; Dielectric function; Magnetic permeability
1. Introduction In many important materials like Permalloy, the Heusler alloys, and the ferromagnetic manganites the simultaneous study of electronic and magnetic properties for enhanced spin-polarized transport and for magnetoresistive devices is required. Usually this is done by a combination of several different experimental techniques such as optical spectroscopy, nuclear magnetic resonance, or neutron scattering. However, the combination of Kerr spectroscopy and spectroscopic ellipsometry uses the fact that the refractive index n is given as n 2s m´ with the magnetic permeability m, and the dielectric function ´ corresponding to the response of a medium to an externally applied electric and magnetic field, respectively. This allows an optical analysis of electronic and magnetic properties w1,2x. Nevertheless, a technique permitting the simultaneous determination of electronic and magnetic susceptibilities within one measurement procedure provides complementary information under exactly the same measurement conditions. This is of importance in materials that show a high sensitivity to local strain effects, grain boundaries or the exact spot temperature. 2. Experimental set-up We use a SENTECH SE 850 ellipsometer and a modified CRYOVAC UHV-cryostat equipped with a *Corresponding author. Tel.yfax: q49-40-482-92-6233.
custom Helmholtz solenoid made from high purity copper as shown in Fig. 1a–c. The magnetic field homogeneity was better than 0.025 in strength and direction over the maximum sample area of 1 by 1 cm2 in the symmetry center of the solenoid. The maximum field strength in this configuration is 40 mT and limited by the heat transfer to the actively cooled heat shield of the cryostat. The light passes a calcite polarizer P1 in the left arm of the SE 850 and is then incident with an angle of 708 on the surface of the sample placed inside the solenoid shown in Fig. 1c. The additional opening of the solenoid that faces the sample serves as an alignment help. After reflexion, the light passes the calcite analyzer P2 in the right arm of the SE 850 in Fig. 1a, is then dispersed by a grating, and detected by a photodiode line. The electric field at the detector ED is given within the Jones–Matrix formalism as a multiplication of 2 by 2 matrices with complex coefficients on the source field Es: EDsP2ŽQ2.ØRØP1ŽQ1.Es,
(1)
where P1(Q1) and P2(Q2) represent the two linear polarizers as a function of their respective polarization angles Q1 and Q2. As shown by Metzger et al., R describes the reflection matrix and includes the Voigt parameter QsQrqiQi w2x. The Voigt parameter represents the linear response of a material to an externally applied magnetic field, where the overall magneto-optic effect is directly proportional to the sample magnetiza-
0040-6090/04/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2003.12.069
40
G. Neuber et al. / Thin Solid Films 455 – 456 (2004) 39–42
Fig. 1. (a) Experimental set-up showing the schematic optical beam path from source to detector including the polarizer as well as analyzer and their corresponding angles. The lower panel shows the direction of the sample magnetization, (b) SE-850 with revolvable UHV cryostat. (c) Helmholtz solenoid with the two 708 windows and one alignment opening facing the sample surface.
tion. For optical frequencies the deviation of Q from zero is very small f10y3 and hardly affects the diagonal component of the reflexion matrix. Due to the strongly coupled nature of the electric and magnetic components in the Maxwell equations at high frequencies, Q is responsible for the existence of an off-diagonal contribution in the reflexion matrix and might be seen as difference between left and right circular charge motion creating a small magnetic moment that couples to the external magnetic field w3x. It can equivalently be seen as remaining response of the huge mf103 in a ferromagnetic material at vs0 that drops with increasing
frequencies by five to six orders of magnitude. The resulting intensities arc given as IDsEDE*D and can be calculated from, Eq. (1). Berger and Pufall w4x calculated the fractional intensity change (FIC) under inversion of a magnetic field, ≠ x dID ID yID s2 ≠ x , ID ID qID
(2)
x where I≠ D and ID denote the intensities at the detector with opposite magnetic fields. An example for the measured fractional intensity change for a fixed polarizer
Fig. 2. (a) Intensity spectra at Q1s708 as a function of y908-Q2-908 with 25 repetitve measurements for the two different magnetic field settings. The small difference in the curve-pairs represents the fractional intensity change, (b)–(c) Vanishing fractional intensity change according to Eq. (2) in paramagnetic Si and Au. Note the scale.
G. Neuber et al. / Thin Solid Films 455 – 456 (2004) 39–42
41
Fig. 3. (a)–(c) Refractive index, f, and Voigt parameter for Fe and Py at room temperature, n and k show a moderate impact on doping with Ni in Py, whereas the magnetic response becomes strongly modified, (d)–(e) Temperature study on Py at 300, 400, 500, 600 and 700 K. Note the jump in k above 500 K and the non-monotonic development of QR at 600 K.
angle of 708 and several analyzer positions is given in Fig. 2a. For a given frequency the vertical cut through the data gives the fractional intensity change of the order of 10y3 for a given polarizer angle Q1 as a function of the analyzer angle Q2. This allows extracting amplitude and phasing information. Hence, six parameters can be obtained from three sets of polarizer angles in order to determine n and k, the Voigt parameter, and the angle of the magnetization f w4x. In Fig. 2b we also display the fractional intensity change for different polarizer (Q1) and analyzer angles (Q2) as a function of wavelength in non-magnetic Si and Au. These are reference measurements in order to verify that the magnetic fields between 3 and 40 mT used in our measurement procedure are not causing artificial depolarization effects. The latter would severely affect the analysis of the data and could even terminate any useful information of the FIC. However, in ferromagnets and even super strong paramagnets the internal sample magnetic fields arc one to three orders of magnitude stronger than the applied external field (1–2 T compared to 3– 40 mT).
generalized magneto-optical ellipsometry (SGME) for the better characterization of the sample properties. A well-known material is Permalloy, Ni0.83Fe0.17, which is used for applications demanding a high degree of spin polarization in a metal. Fig. 3 shows Py and Fe in comparison. Whereas Fig. 3a shows a rather similar absorption coefficient and refractive index, (c) outlines the drastically different magnetic responses in Py compared to Fe. Fig. 3d–e displays the temperature dependence of the dielectric properties and the Voigt parameter in Py. They show rather weak temperature dependence up to 500 K, i.e. a slight enhancement of the absorption and a decrease of QR outlining an increased damping of the spin-polarized Drude response and the concomitant decrease of the spin orientation. However, above 500 K the absorption shows a clear jump and QR shows a sudden increase against the trend. This behavior is most likely connected to an annealing effect increasing the average size of the crystallite domains in the Py-film matrix leading to an increase of the carrier number due to a reduction of the crystallite boundaries trapping charges.
3. Ferromagnetic metals
4. Conclusions
As outlined in the previous section ferromagnetic materials provide a rich field to apply spectroscopic
The advantage of spectroscopic generalized magnetooptical ellipsometry is the simultaneous observation of
42
G. Neuber et al. / Thin Solid Films 455 – 456 (2004) 39–42
the dielectric function and the magnetic permeability within one measurement procedure. We have shown the implementation of this technique within an UHV-cryostat for a temperature range between 4.2 and 800 K and fields up to 40 mT. Exemplary measurements on Py and Fe show the impact of Ni-doping on the magnetic response. In Py films we observe an annealing effect above 500 K leading to an enlargement of the crystallites in the film matrix. Acknowledgments We thank J. Gancarz, T. Korn, C. Pels, G. Meier, and U. Merkt for many discussions and the supply of the Fe
and Py films. Special thanks to G. Dittmar, U. Wielsch, and U. Richter. We acknowledge financial support for this work via DFG Ru773y2-1 and Ru773y2-2 and the Graduiertcnkolleg ‘Physik nanostrukturierter ¨ Festkorper’. References w1x R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light, Elsevier, New York, 1999. w2x G. Metzger, P. Pluvinage, R. Torquet, Ann. Phys. 10 (1965) 5. w3x J.L. Erskine, E.A. Stern, Phys. Rev. B 12 (1975) 5016. w4x A. Berger, M.R. Pufall, Appl. Phys. Lett. 71 (1997) 965.
Generalized magneto-optical ellipsometry in ferromagnetic metals ¨ G. Neuber*, R. Rauer, J. Kunze, J. Backstrom, M. Rubhausen ¨ Angewandte Physik und Zentrum fur ¨ Mikrostrukturforschung, Universitat ¨ Hamburg, Jungiusstraße 11, D-20355, Hamburg, Germany Institut fur
Abstract We present spectral generalized magneto-optical ellipsometry as an optical tool to investigate magnetic and electronic properties of ferromagnetic materials. The advantage of the simultaneous observation of the dielectric and the magnetic responses within one measurement procedure is crucial for materials with coupled degrees of freedom near a phase transition or during annealing procedures to improve the film quality by removing grain boundaries. Moreover, we show the implementation of this technique within an UHV-cryostat for a temperature range between 4.2 and 800 K and fields up to 40 mT. Examplary measurements on iron and Permalloy demonstrate the comfortable application of this technique. 䊚 2003 Elsevier B.V. All rights reserved. Keywords: Ellipsometry; Ferromagnetic metals; Dielectric function; Magnetic permeability
1. Introduction In many important materials like Permalloy, the Heusler alloys, and the ferromagnetic manganites the simultaneous study of electronic and magnetic properties for enhanced spin-polarized transport and for magnetoresistive devices is required. Usually this is done by a combination of several different experimental techniques such as optical spectroscopy, nuclear magnetic resonance, or neutron scattering. However, the combination of Kerr spectroscopy and spectroscopic ellipsometry uses the fact that the refractive index n is given as n 2s m´ with the magnetic permeability m, and the dielectric function ´ corresponding to the response of a medium to an externally applied electric and magnetic field, respectively. This allows an optical analysis of electronic and magnetic properties w1,2x. Nevertheless, a technique permitting the simultaneous determination of electronic and magnetic susceptibilities within one measurement procedure provides complementary information under exactly the same measurement conditions. This is of importance in materials that show a high sensitivity to local strain effects, grain boundaries or the exact spot temperature. 2. Experimental set-up We use a SENTECH SE 850 ellipsometer and a modified CRYOVAC UHV-cryostat equipped with a *Corresponding author. Tel.yfax: q49-40-482-92-6233.
custom Helmholtz solenoid made from high purity copper as shown in Fig. 1a–c. The magnetic field homogeneity was better than 0.025 in strength and direction over the maximum sample area of 1 by 1 cm2 in the symmetry center of the solenoid. The maximum field strength in this configuration is 40 mT and limited by the heat transfer to the actively cooled heat shield of the cryostat. The light passes a calcite polarizer P1 in the left arm of the SE 850 and is then incident with an angle of 708 on the surface of the sample placed inside the solenoid shown in Fig. 1c. The additional opening of the solenoid that faces the sample serves as an alignment help. After reflexion, the light passes the calcite analyzer P2 in the right arm of the SE 850 in Fig. 1a, is then dispersed by a grating, and detected by a photodiode line. The electric field at the detector ED is given within the Jones–Matrix formalism as a multiplication of 2 by 2 matrices with complex coefficients on the source field Es: EDsP2ŽQ2.ØRØP1ŽQ1.Es,
(1)
where P1(Q1) and P2(Q2) represent the two linear polarizers as a function of their respective polarization angles Q1 and Q2. As shown by Metzger et al., R describes the reflection matrix and includes the Voigt parameter QsQrqiQi w2x. The Voigt parameter represents the linear response of a material to an externally applied magnetic field, where the overall magneto-optic effect is directly proportional to the sample magnetiza-
0040-6090/04/$ - see front matter 䊚 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2003.12.069
40
G. Neuber et al. / Thin Solid Films 455 – 456 (2004) 39–42
Fig. 1. (a) Experimental set-up showing the schematic optical beam path from source to detector including the polarizer as well as analyzer and their corresponding angles. The lower panel shows the direction of the sample magnetization, (b) SE-850 with revolvable UHV cryostat. (c) Helmholtz solenoid with the two 708 windows and one alignment opening facing the sample surface.
tion. For optical frequencies the deviation of Q from zero is very small f10y3 and hardly affects the diagonal component of the reflexion matrix. Due to the strongly coupled nature of the electric and magnetic components in the Maxwell equations at high frequencies, Q is responsible for the existence of an off-diagonal contribution in the reflexion matrix and might be seen as difference between left and right circular charge motion creating a small magnetic moment that couples to the external magnetic field w3x. It can equivalently be seen as remaining response of the huge mf103 in a ferromagnetic material at vs0 that drops with increasing
frequencies by five to six orders of magnitude. The resulting intensities arc given as IDsEDE*D and can be calculated from, Eq. (1). Berger and Pufall w4x calculated the fractional intensity change (FIC) under inversion of a magnetic field, ≠ x dID ID yID s2 ≠ x , ID ID qID
(2)
x where I≠ D and ID denote the intensities at the detector with opposite magnetic fields. An example for the measured fractional intensity change for a fixed polarizer
Fig. 2. (a) Intensity spectra at Q1s708 as a function of y908-Q2-908 with 25 repetitve measurements for the two different magnetic field settings. The small difference in the curve-pairs represents the fractional intensity change, (b)–(c) Vanishing fractional intensity change according to Eq. (2) in paramagnetic Si and Au. Note the scale.
G. Neuber et al. / Thin Solid Films 455 – 456 (2004) 39–42
41
Fig. 3. (a)–(c) Refractive index, f, and Voigt parameter for Fe and Py at room temperature, n and k show a moderate impact on doping with Ni in Py, whereas the magnetic response becomes strongly modified, (d)–(e) Temperature study on Py at 300, 400, 500, 600 and 700 K. Note the jump in k above 500 K and the non-monotonic development of QR at 600 K.
angle of 708 and several analyzer positions is given in Fig. 2a. For a given frequency the vertical cut through the data gives the fractional intensity change of the order of 10y3 for a given polarizer angle Q1 as a function of the analyzer angle Q2. This allows extracting amplitude and phasing information. Hence, six parameters can be obtained from three sets of polarizer angles in order to determine n and k, the Voigt parameter, and the angle of the magnetization f w4x. In Fig. 2b we also display the fractional intensity change for different polarizer (Q1) and analyzer angles (Q2) as a function of wavelength in non-magnetic Si and Au. These are reference measurements in order to verify that the magnetic fields between 3 and 40 mT used in our measurement procedure are not causing artificial depolarization effects. The latter would severely affect the analysis of the data and could even terminate any useful information of the FIC. However, in ferromagnets and even super strong paramagnets the internal sample magnetic fields arc one to three orders of magnitude stronger than the applied external field (1–2 T compared to 3– 40 mT).
generalized magneto-optical ellipsometry (SGME) for the better characterization of the sample properties. A well-known material is Permalloy, Ni0.83Fe0.17, which is used for applications demanding a high degree of spin polarization in a metal. Fig. 3 shows Py and Fe in comparison. Whereas Fig. 3a shows a rather similar absorption coefficient and refractive index, (c) outlines the drastically different magnetic responses in Py compared to Fe. Fig. 3d–e displays the temperature dependence of the dielectric properties and the Voigt parameter in Py. They show rather weak temperature dependence up to 500 K, i.e. a slight enhancement of the absorption and a decrease of QR outlining an increased damping of the spin-polarized Drude response and the concomitant decrease of the spin orientation. However, above 500 K the absorption shows a clear jump and QR shows a sudden increase against the trend. This behavior is most likely connected to an annealing effect increasing the average size of the crystallite domains in the Py-film matrix leading to an increase of the carrier number due to a reduction of the crystallite boundaries trapping charges.
3. Ferromagnetic metals
4. Conclusions
As outlined in the previous section ferromagnetic materials provide a rich field to apply spectroscopic
The advantage of spectroscopic generalized magnetooptical ellipsometry is the simultaneous observation of
42
G. Neuber et al. / Thin Solid Films 455 – 456 (2004) 39–42
the dielectric function and the magnetic permeability within one measurement procedure. We have shown the implementation of this technique within an UHV-cryostat for a temperature range between 4.2 and 800 K and fields up to 40 mT. Exemplary measurements on Py and Fe show the impact of Ni-doping on the magnetic response. In Py films we observe an annealing effect above 500 K leading to an enlargement of the crystallites in the film matrix. Acknowledgments We thank J. Gancarz, T. Korn, C. Pels, G. Meier, and U. Merkt for many discussions and the supply of the Fe
and Py films. Special thanks to G. Dittmar, U. Wielsch, and U. Richter. We acknowledge financial support for this work via DFG Ru773y2-1 and Ru773y2-2 and the Graduiertcnkolleg ‘Physik nanostrukturierter ¨ Festkorper’. References w1x R.M.A. Azzam, N.M. Bashara, Ellipsometry and Polarized Light, Elsevier, New York, 1999. w2x G. Metzger, P. Pluvinage, R. Torquet, Ann. Phys. 10 (1965) 5. w3x J.L. Erskine, E.A. Stern, Phys. Rev. B 12 (1975) 5016. w4x A. Berger, M.R. Pufall, Appl. Phys. Lett. 71 (1997) 965.