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Magneto-optic constants of thin cobalt films
Thin Solid Films, 51 (1978) 251-255 Elsevier Sequoia S.A., Lausanne
Printed in the Netherlands
251
M A G N E T O - O P T I C C O N S T A N T S OF T H I N C O B A L T F I L M S R. CAREY, 1.). M. NEWMAN AND B. W. J. THOMAS
Department of Applied Physics, Lanchester Polytechnic, Prioo" St., Covent O" CVI 5FB (Gt. Britain) (Received November 9, 1977; accepted November 30, 1977)
The transverse Kerr effect was measured for thin cobalt films (of thickness 13-108 nm) at three angles of incidence over the visible and near infrared wavelength range. A new technique is introduced for the evaluation o f the magneto-optic constants Q~ and Q2 (Q = QI +iQ2) by using these measurements together with previously determined optical constants. Both Q1 and Q2 are found to be thickness dependent. For a fixed thickness, Q1 is found to be fairly uniform over the wavelength range considered but a marked resonance occurs in Q2 at approximately 1.1 eV.
1. INTRODUCTION Most magneto-optic investigations are concerned with either the ultimate device potential of specific materials or the study of the basic atomic structure of magnetic materials. In both cases any systematic approach demands a detailed knowledge of both the complex parameters r~and Q for the range of wavelengths to be discussed. With thin film materials it becomes more difficult to establish these parameters because of the need to include the effect of multiple internal reflections in their evaluation. The use of photometric techniques to measure the parameter r~ for thin film material has already been discussed by several authors (see, for example, ref. 1). Furthermore, a detailed computational study of the sensitivity of such techniques for the study of thin films 2 has established that very accurate results may be obtained (for n and k) when the experimental arrangement is carefully optimized. The utilization of basically similar experimental techniques to obtain the parameter Q is not new for bulk material 3'4. In such experiments the values of Q1 and Q 2 a r e obtained from photometric measurement of the transverse Kerr effect. A further sensitivity study 5 indicates that, provided the experimental s e t - u p is optimized, accurate values of Q may be obtained from such measurements. For thin films, although the basic experimental techniques and measurements are essentially the same as for bulk materials (and are therefore not described in detail), the evaluation of the parameters ~ and Q from the experimental measurements is far more complex. In this paper we discuss the evaluation of Q from measurements of the fractional reflectivity difference 4 of the transverse Kerr effect for a group of thin cobalt films.
252 2.
R. ('AREY, D. M. NEWMAN, B. \V. J. THOMAS
EVALUATION OF fi AND Q FOR THIN FILM MATERIALS
The evaluation ofn and k from photometric measurements follows the method given in ref. 2 and is described in outline since the method forms a basis for the subsequent evaluation of Q. Measured Rp/R~ ratios for two angles of incidence together with a separate independent film thickness measurcmcnl are used to determine n and k. A matrix of n,k values is used to generate computed Rp/R~ ratios by' utilizing the explicit expressions for Rp and R~ for a thin film {' at the separate angles of incidence 01 and (12. The values chosen for (l 1 and (1, are in accordance with the results of the sensitivity studies referred to above. Using simple iterative techniques a set of n, k values at (1~ for which the computed Rp/Rs is within a predetermined range of the experimental value is obtained. A further set of values is obtained at 0 2, and finall3, the n, k values for the film are obtained by direct comparison of these two sets o1" Rp/R~ values. To avoid spurious solutions the measured Rp/R~ at some third angle is compared with the value calculated by using the computed result for n, k. A similar technique was developed for the evaluation of the magneto-optic constants Q1 and Q2. A matrix OfQl, Q2 values is used to generate 6 valucs for the thin film specimen at two angles of incidence 04 and 05. The expression used for 6 is that reported recently 7 for a thin film specimen and wherever possible the angles are close to those shown in ref. 5 to be optimum for the determination of Q from transverse Kerr effect measurements for bulk specimens. Calculated values 0t'~5 are compared with experimental values in an iterativc computation to give a set of values of Q1 and Q2, and (Q,, Q2)O,, and (Qj, Q2)0s. for the thin film specimen. The ultimate values of Q~ and Q2 for the thin film are those given by the point of intersection of the functions (Q1, Q2)04 and (QI- Q2)0s • Measurement of?i at a third angle of incidence again provides a useful check on the accuracy' of the Q values obtained. 3. EXPERIMENTAL DETAILS
All the films examined were prepared by' vacuum deposition in background pressures of better than 5 × 10 ~ Tort. The films, on glass substrates, were polycrystalline with crystallites between 2.5 and 7.5 nm in diameter and had thicknesses within the range 10- 110 nm (nine thicknesses were prepared). To determine the optical constants the optimized reflection technique 2 was used with Rp/R s measured at three angles of incidence. & measured by using a phaselocked system with the sample switching from - M s to + Ms at 62 Hz. was also determined at three angles of incidence. Miller and Taylor 2 have pointed out that, for acceptable accuracy of the optical constants obtained from photometric measurements in reflection, optimization of the angles of incidence is essential. Accordingly, for the measurement of Rp/R s the angles of incidence selected were (Ij = 5 8 and 02 = 8 4 , with an associated error in 0 of not greater than 0.1'. R p / R s ratios were measured over the spectral range 0.49 ~m ~< 2 ~< 1.25/am with an accuracy of ± 0.5 I},,. Interferometric thickness measurements have associated errors of less than _+3 nm. The values o f n and k so evaluated are typically estimated to be within _+0.1. The third angle fit at
253
MAGNETO-OPTIC CONSTANTS OF THIN CO FILMS
0 3 = 76.7 °, obtained by comparing Rp/R s calculated by using these values ofn and k with the experimentally determined Rp/R s, was in all cases better than + l ~ . These values of n and k were subsequently used in the generation of the (Q1, Q2)04 and (Q1, Q2)05functions referred to in Section 2. The sensitivity of the evaluation of Q from 6 measurements also is optimum for well-defined angles of incidence for bulk material 5. The angles chosen here for measurements on thin film specimens were close to those suggested in ref. 5 wherever possible. For most measurements the angles were 04 = 65 ° and 05 = 84":. (For very thin films 04 = 45 ° and 05 = 70°.) In each case a third angle check was carried out at 06 -- 45 °. These angles of incidence were set to within + 0.1°, and the ultimate 6 value was determined with a typical accuracy of + 1 ~,i. The values of Qt and Q2 obtained are in most cases better than + 10% for Q1 and + 5 ~o for Q2.
4. RESULTS The results presented in this section are confined to the magneto-optic measurements and the determination of Q1 and Q2. Detailed discussion of the measured optical constants will be presented elsewhere. Figure 1 shows a typical wavelength variation of 6 for the three angles of incidence, and Fig. 2 shows the variation of Q1 and Q2 for three films for energies in the 1.0-2.2 eV range. (Q1 and Q2 for bulk cobalt 3 are shown for comparison.) 12
10
8
6 o
4 ( x l O "3 )
2
i
400
600
i
i
,
l
800
wavelength
( prn
*
1000 )
i
I
|
1200
Fig. I. The wavelength dependence oft~ for a thin (d = 22 nm) cobalt film at three angles of incidence.
254
R. ('AREY, D. M. NEVeMAN. B. ~'. J. THOMAS
35' QI ( xlO -3 )
\
'Q7
N
k 30
~
-
.
~
o
_.
o -..
~ 6 n m
\
~
Q, " Q''O
25
"'~ \\\ 2c
,, i
15'
•/ ~
/
\\
\
"',~
\\,oo
~
-,,o~
I
i
.i
1-0
1-5
2.0
eV Fig. 2. T h e d e p e n d e n c e of Q~ and Q2 oil incident radiation energy for thin c o b a h fihns : . film.
-)
, bulk :
5. DISCUSSION
The significant features that arise from these results are as fbllows. (1) The values o f 6 for the thin films (22 nm in Fig. 1) are similar to previously reported results 8 for a 50 nm cobalt film. 6 is positive for angles of incidence o f 45 and 65 ' and is negative for 8 4 . (2) Q1 shows litfle variation with the energy o f the incident radiation over the range covered. (3) Q2 shows a marked resonance for all films in the region o f I. 1 eV. (4) The values o f Q1 a n d Q , are thickness dependent. Intermediate calculations (i.e. the variation o f 6 with Q2 for a fixed Qt) indicate that the choice o f angles o f incidence o f 65' and 8 4 for the measurement o f 6 is satisfactory for thin films as well as for bulk 5.
MAGNETO-OPTIC CONSTANTS OF THIN CO FILMS
255
It is clear from Fig. 2 that that the constants for the thin films are quite different from those for bulk (thick film) cobalt. Hence if any material is to be properly assessed from a magneto-optic point of view, it is essential that the constants of the film material are measured rather than are assumed to be those of the bulk material. Apart from the obvious advantage of using similar photometric procedures, and therefore essentially the same apparatus, to measure both the optical and the magneto-optical properties of the films, the use of the transverse Kerr effect as a suitable experiment for the evaluation of magneto-optic constants has proved to be relatively simple and accurate. REFERENCES 1 P.B. Johnson and R. W. Christy, Phys. Rev., Sect. B, 9 (1974) 5056. 2 R . F . Miller and A, J. Taylor, J. Phys. D, 4 (1971) 1419. 3 G.S. Krinchik and R. D. Nuraliyeva, Fiz. Met. Metalloved., 5 (1959) 694. 4 D . H . Martin, K. F. Neal and T. J. Dean, Proc. Phys. Soc., London, 86 (1965) 605. 5 W. Hasan, R. B. Inwood and R. F. Miller, J. Phys. D, 8 (1975) 2090. 6 L . N . Hadley and D. M. Dennison, J. Opt. Soc. Am., 37 (6) (1947) 451.
7 8
R. Carey, D.M. NewmanandB. W.J. Thomas, J. Appl. Phys. D, lO(1977) L131. R. Carey, E. D. Isaac and B. W. J. Thomas, J. Phys. D, 1 (1968) 945.
Printed in the Netherlands
251
M A G N E T O - O P T I C C O N S T A N T S OF T H I N C O B A L T F I L M S R. CAREY, 1.). M. NEWMAN AND B. W. J. THOMAS
Department of Applied Physics, Lanchester Polytechnic, Prioo" St., Covent O" CVI 5FB (Gt. Britain) (Received November 9, 1977; accepted November 30, 1977)
The transverse Kerr effect was measured for thin cobalt films (of thickness 13-108 nm) at three angles of incidence over the visible and near infrared wavelength range. A new technique is introduced for the evaluation o f the magneto-optic constants Q~ and Q2 (Q = QI +iQ2) by using these measurements together with previously determined optical constants. Both Q1 and Q2 are found to be thickness dependent. For a fixed thickness, Q1 is found to be fairly uniform over the wavelength range considered but a marked resonance occurs in Q2 at approximately 1.1 eV.
1. INTRODUCTION Most magneto-optic investigations are concerned with either the ultimate device potential of specific materials or the study of the basic atomic structure of magnetic materials. In both cases any systematic approach demands a detailed knowledge of both the complex parameters r~and Q for the range of wavelengths to be discussed. With thin film materials it becomes more difficult to establish these parameters because of the need to include the effect of multiple internal reflections in their evaluation. The use of photometric techniques to measure the parameter r~ for thin film material has already been discussed by several authors (see, for example, ref. 1). Furthermore, a detailed computational study of the sensitivity of such techniques for the study of thin films 2 has established that very accurate results may be obtained (for n and k) when the experimental arrangement is carefully optimized. The utilization of basically similar experimental techniques to obtain the parameter Q is not new for bulk material 3'4. In such experiments the values of Q1 and Q 2 a r e obtained from photometric measurement of the transverse Kerr effect. A further sensitivity study 5 indicates that, provided the experimental s e t - u p is optimized, accurate values of Q may be obtained from such measurements. For thin films, although the basic experimental techniques and measurements are essentially the same as for bulk materials (and are therefore not described in detail), the evaluation of the parameters ~ and Q from the experimental measurements is far more complex. In this paper we discuss the evaluation of Q from measurements of the fractional reflectivity difference 4 of the transverse Kerr effect for a group of thin cobalt films.
252 2.
R. ('AREY, D. M. NEWMAN, B. \V. J. THOMAS
EVALUATION OF fi AND Q FOR THIN FILM MATERIALS
The evaluation ofn and k from photometric measurements follows the method given in ref. 2 and is described in outline since the method forms a basis for the subsequent evaluation of Q. Measured Rp/R~ ratios for two angles of incidence together with a separate independent film thickness measurcmcnl are used to determine n and k. A matrix of n,k values is used to generate computed Rp/R~ ratios by' utilizing the explicit expressions for Rp and R~ for a thin film {' at the separate angles of incidence 01 and (12. The values chosen for (l 1 and (1, are in accordance with the results of the sensitivity studies referred to above. Using simple iterative techniques a set of n, k values at (1~ for which the computed Rp/Rs is within a predetermined range of the experimental value is obtained. A further set of values is obtained at 0 2, and finall3, the n, k values for the film are obtained by direct comparison of these two sets o1" Rp/R~ values. To avoid spurious solutions the measured Rp/R~ at some third angle is compared with the value calculated by using the computed result for n, k. A similar technique was developed for the evaluation of the magneto-optic constants Q1 and Q2. A matrix OfQl, Q2 values is used to generate 6 valucs for the thin film specimen at two angles of incidence 04 and 05. The expression used for 6 is that reported recently 7 for a thin film specimen and wherever possible the angles are close to those shown in ref. 5 to be optimum for the determination of Q from transverse Kerr effect measurements for bulk specimens. Calculated values 0t'~5 are compared with experimental values in an iterativc computation to give a set of values of Q1 and Q2, and (Q,, Q2)O,, and (Qj, Q2)0s. for the thin film specimen. The ultimate values of Q~ and Q2 for the thin film are those given by the point of intersection of the functions (Q1, Q2)04 and (QI- Q2)0s • Measurement of?i at a third angle of incidence again provides a useful check on the accuracy' of the Q values obtained. 3. EXPERIMENTAL DETAILS
All the films examined were prepared by' vacuum deposition in background pressures of better than 5 × 10 ~ Tort. The films, on glass substrates, were polycrystalline with crystallites between 2.5 and 7.5 nm in diameter and had thicknesses within the range 10- 110 nm (nine thicknesses were prepared). To determine the optical constants the optimized reflection technique 2 was used with Rp/R s measured at three angles of incidence. & measured by using a phaselocked system with the sample switching from - M s to + Ms at 62 Hz. was also determined at three angles of incidence. Miller and Taylor 2 have pointed out that, for acceptable accuracy of the optical constants obtained from photometric measurements in reflection, optimization of the angles of incidence is essential. Accordingly, for the measurement of Rp/R s the angles of incidence selected were (Ij = 5 8 and 02 = 8 4 , with an associated error in 0 of not greater than 0.1'. R p / R s ratios were measured over the spectral range 0.49 ~m ~< 2 ~< 1.25/am with an accuracy of ± 0.5 I},,. Interferometric thickness measurements have associated errors of less than _+3 nm. The values o f n and k so evaluated are typically estimated to be within _+0.1. The third angle fit at
253
MAGNETO-OPTIC CONSTANTS OF THIN CO FILMS
0 3 = 76.7 °, obtained by comparing Rp/R s calculated by using these values ofn and k with the experimentally determined Rp/R s, was in all cases better than + l ~ . These values of n and k were subsequently used in the generation of the (Q1, Q2)04 and (Q1, Q2)05functions referred to in Section 2. The sensitivity of the evaluation of Q from 6 measurements also is optimum for well-defined angles of incidence for bulk material 5. The angles chosen here for measurements on thin film specimens were close to those suggested in ref. 5 wherever possible. For most measurements the angles were 04 = 65 ° and 05 = 84":. (For very thin films 04 = 45 ° and 05 = 70°.) In each case a third angle check was carried out at 06 -- 45 °. These angles of incidence were set to within + 0.1°, and the ultimate 6 value was determined with a typical accuracy of + 1 ~,i. The values of Qt and Q2 obtained are in most cases better than + 10% for Q1 and + 5 ~o for Q2.
4. RESULTS The results presented in this section are confined to the magneto-optic measurements and the determination of Q1 and Q2. Detailed discussion of the measured optical constants will be presented elsewhere. Figure 1 shows a typical wavelength variation of 6 for the three angles of incidence, and Fig. 2 shows the variation of Q1 and Q2 for three films for energies in the 1.0-2.2 eV range. (Q1 and Q2 for bulk cobalt 3 are shown for comparison.) 12
10
8
6 o
4 ( x l O "3 )
2
i
400
600
i
i
,
l
800
wavelength
( prn
*
1000 )
i
I
|
1200
Fig. I. The wavelength dependence oft~ for a thin (d = 22 nm) cobalt film at three angles of incidence.
254
R. ('AREY, D. M. NEVeMAN. B. ~'. J. THOMAS
35' QI ( xlO -3 )
\
'Q7
N
k 30
~
-
.
~
o
_.
o -..
~ 6 n m
\
~
Q, " Q''O
25
"'~ \\\ 2c
,, i
15'
•/ ~
/
\\
\
"',~
\\,oo
~
-,,o~
I
i
.i
1-0
1-5
2.0
eV Fig. 2. T h e d e p e n d e n c e of Q~ and Q2 oil incident radiation energy for thin c o b a h fihns : . film.
-)
, bulk :
5. DISCUSSION
The significant features that arise from these results are as fbllows. (1) The values o f 6 for the thin films (22 nm in Fig. 1) are similar to previously reported results 8 for a 50 nm cobalt film. 6 is positive for angles of incidence o f 45 and 65 ' and is negative for 8 4 . (2) Q1 shows litfle variation with the energy o f the incident radiation over the range covered. (3) Q2 shows a marked resonance for all films in the region o f I. 1 eV. (4) The values o f Q1 a n d Q , are thickness dependent. Intermediate calculations (i.e. the variation o f 6 with Q2 for a fixed Qt) indicate that the choice o f angles o f incidence o f 65' and 8 4 for the measurement o f 6 is satisfactory for thin films as well as for bulk 5.
MAGNETO-OPTIC CONSTANTS OF THIN CO FILMS
255
It is clear from Fig. 2 that that the constants for the thin films are quite different from those for bulk (thick film) cobalt. Hence if any material is to be properly assessed from a magneto-optic point of view, it is essential that the constants of the film material are measured rather than are assumed to be those of the bulk material. Apart from the obvious advantage of using similar photometric procedures, and therefore essentially the same apparatus, to measure both the optical and the magneto-optical properties of the films, the use of the transverse Kerr effect as a suitable experiment for the evaluation of magneto-optic constants has proved to be relatively simple and accurate. REFERENCES 1 P.B. Johnson and R. W. Christy, Phys. Rev., Sect. B, 9 (1974) 5056. 2 R . F . Miller and A, J. Taylor, J. Phys. D, 4 (1971) 1419. 3 G.S. Krinchik and R. D. Nuraliyeva, Fiz. Met. Metalloved., 5 (1959) 694. 4 D . H . Martin, K. F. Neal and T. J. Dean, Proc. Phys. Soc., London, 86 (1965) 605. 5 W. Hasan, R. B. Inwood and R. F. Miller, J. Phys. D, 8 (1975) 2090. 6 L . N . Hadley and D. M. Dennison, J. Opt. Soc. Am., 37 (6) (1947) 451.
7 8
R. Carey, D.M. NewmanandB. W.J. Thomas, J. Appl. Phys. D, lO(1977) L131. R. Carey, E. D. Isaac and B. W. J. Thomas, J. Phys. D, 1 (1968) 945.