- Email: [email protected]
Quantitative empirical correlation between coercivity and uniaxial anisotropy
Journal of Magnetism and Magnetic Materials 160 (1996) 25-26
N ELSEVIER
~H Journalof magnetism and magnetic materials
Quantitative empirical correlation between coercivity and uniaxial anisotropy G. V&tesy a,*, I. Tomfi~ b ~' Research Institute for Materials Science, Hungarian Academy of Sciences, P.O.B. 49, H-1525 Budapest, Hungao, b Institute of Physics, Academy of Sciences of the Czech Republic, Na Slocance 2, 180 40 Prague 8, Czech Republic
Abstract An experimental method is presented in which the quantitative relation between the domain wall coercive field and uniaxial anisotropy can be determined for epitaxially grown magnetic garnet films. A linear relationship was found between coercivity and anisotropy. The result also makes it possible to obtain the experimental shapes of the correlations between the domain wall coercive field and the domain wall parameters. Keywords: Anisotropy; Coercivity; Magnetic garnets
A large number of theories exists (for a review, see Ref. [1]) which attempt to calculate the coercivity from the material and wall parameters and an assumed a n d / o r estimated model distribution of defects. The models are based on more or less strongly simplifying assumptions about the structure and distribution of the imperfections and a priori it is not clear if these assumptions do not affect the theoretical conclusions excessively. Because of this a reliable comparison is important. It is possible to obtain experimental results for the dependence of the domain wall coercive field on material and domain wall parameters [2], but it is difficult and sometimes even questionable. If a series of similar samples is used, many parameters change from sample to sample and, in particular, the structure of imperfections can vary without control. The same is true for a series of measurements on a single sample at different temperatures. The experiment described below presents a useful method. The domain wall coercive field, Hew, was measured in a single sample of material, modifying the properties of the domain walls by decreasing the existing stresses in the material. An epitaxial magnetic garnet film (YSmCa)3(FeGe)50~2 was chosen for the investigation. The sample exhibited large uniaxial anisotropy with the easy axis of magnetization perpendicular to the film plane. The film was grown by liquid-phase epitaxy on a (111) oriented gadoliniumgallium-garnet substrate. The parameters of the film were measured by standard methods [3]: film thickness, h = 5.0
* Corresponding vert@ ra.atki.kfki.hu.
author.
Fax:
+36-1-1550694;
email:
/~m; saturation magnetization, 47rM~ = 210 G; characteristic material length, l = 0.55 /xm; and uniaxial material quality factor, Q = 4.4. The domain wall coercive field was measured using the low frequency (200 Hz) oscillation method [4]: the amplitude of an ac magnetic field oriented along the easy axis was increased linearly from zero and the onset of domain wall motion was detected photoelectrically. The accuracy of the H~w measurement was 0.05 Oe. The uniaxial anisotropy was measured using a magnetooptical method with an accuracy of 100 e r g / c m 3 [3]. The effect of mechanical stress due to lattice distortion was measured earlier on epitaxial magnetic garnet films [5]. A significant effect of mechanical stress was found on the uniaxial anisotropy and on the domain wall parameters. The stress dependence of these quantities are used in the present work to modify the magnetic properties of the same sample. Lattice distortion is caused by the different lattice constants of the substrate and the epitaxial film. Reducing the thickness of the substrate relaxes the misfit strains in the epitaxial film, and the stress-dependent magnetic parameters, such as the domain wall coercive field, H~w, and the uniaxial anisotropy constant, K u, are modified. The substrates of the films were thinned from the backside in several steps by mechanical polishing. Polishing of the substrate was performed with special care to ensure that no microscratches a n d / o r other defects were introduced into the substrate crystal lattice. In each polishing step about 100 /xm was removed from the substrate. After each step the magnetic parameters were remeasured. Both Hew and K u were found to decrease with de-
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. Pll S 0 3 0 4 - 8 8 5 3 ( 9 6 ) 0 0 0 9 2 - 3
26
G. Vdrtesy. I. Tom6,~/ Journal o[Magnetism and Magnetic Materials 160 (1996) 25 26 ID 0
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creasing substrate thickness, as can be seen in Figs. 1 and 2, respectively. Each point in these figures represents the average of five independent measurements. The effect became more distinct after attaining a substrate thickness of 150 /_tm. The other parameters of the film do not depend on the substrate thickness. Measuring the pairs of H~,, and K , values belonging to the same substrate thickness, we can determine their correlation. A linear relationship was found between H~,,. and K u, as can be seen in Fig. 3. This correlation is believed to be characteristic for the given material. The slope of the line was found to be 0.00124 O e c m 3 erg 1 in the case of the epitaxial film investigated. Further measurements are necessary to prove the generality of this relationship in the case of epitaxial garnets. In agreement with the theoretical model the experiment showed that, at least for epitaxial films of magnetic garnets with high uniaxial anisotropy, the domain wall coercive field, as measured by the wall oscillation method, depends significantly on the uniaxial anisotropy. The slope of this linear function, which largely represents the intrinsic coercivity of the sample, makes a good start for subsequent
6 4 0 0 -
6200-
~"
iii
6000-
II
I
i
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Fig. 1. Domain wall coercive field, //~,,., as a function of the substrate thickness.
,
i
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,
~
5800
,
i
5900
,
i
6000
,
i
6100
,
i
6200
Uniaxial anisotropy, erg/cm 3
Fig. 3. The determined empirical correlation between the uniaxial anisutropy constant. K., and the domain wall coercive field, H,,,,,. quantitative evaluations of the relevance of various theoretical models of domain wall coercivity to currently investigated materials. However, the revealed correlation does not mean that by measuring the uniaxial anisotropy constant of a sample its coercivity can be calculated. The relation of the coercivity to the magnetic parameters is only one side of the coin. The coercivity of a sample also depends significantly on the structure of the material (material imperfections, etc.), and samples with very similar magnetic parameters (anisotropy, saturation magnetization, exchange stiffness, etc.) can have very different coercive properties. This shows the very complex character of coercive properties. The importance of the above-described quantitative correlation between H,.w and K, is to show the type of function between these quantities. The results of the above experiment also make it possible to obtain the experimental shapes of the correlations between the domain wall coercive field and the wall parameters (domain wall energy density a n d / o r domain wall width). Acknowledgement: The authors are indebted to Dr. B. Keszei for the growth of the sample. Financial support from CEC Joint Research Project No. ERB 3510 PL 92 3369 and from project No. 2 0 2 / 9 5 / 0 0 2 2 of the Grant Agency of the Czech Republic is appreciated. References
5800-
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5600i
100
,
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'[50
,
i
200
,
~
250
,
i
,
300
~
350
,
i
400
Substrate thickness, #m
Fig. 2. Uniaxial anisotropy constant, K u, as a function of the substrate thickness.
[1] [2] [3] [4]
M. Pardavi-Horvfith, IEEE Trans. Magn. 21 (1985) 1694. R. Raasch and J. Reck, J. Appl. Phys. 74 (1993) 1229. R.M. Josephs, AIP Conf. Proc. 10 (1972) 286. J.A. Seitchik, G.K. Goldberg and W.D. Doyle, J. Appl. Phys. 42 (1971) 1272. [5] G. V6rtesy, Elsevier Studies in Applied Electromagnetics in Materials 4, ed. L. Lanotte (Elsevier, Amsterdam, 1993) p. 57.
N ELSEVIER
~H Journalof magnetism and magnetic materials
Quantitative empirical correlation between coercivity and uniaxial anisotropy G. V&tesy a,*, I. Tomfi~ b ~' Research Institute for Materials Science, Hungarian Academy of Sciences, P.O.B. 49, H-1525 Budapest, Hungao, b Institute of Physics, Academy of Sciences of the Czech Republic, Na Slocance 2, 180 40 Prague 8, Czech Republic
Abstract An experimental method is presented in which the quantitative relation between the domain wall coercive field and uniaxial anisotropy can be determined for epitaxially grown magnetic garnet films. A linear relationship was found between coercivity and anisotropy. The result also makes it possible to obtain the experimental shapes of the correlations between the domain wall coercive field and the domain wall parameters. Keywords: Anisotropy; Coercivity; Magnetic garnets
A large number of theories exists (for a review, see Ref. [1]) which attempt to calculate the coercivity from the material and wall parameters and an assumed a n d / o r estimated model distribution of defects. The models are based on more or less strongly simplifying assumptions about the structure and distribution of the imperfections and a priori it is not clear if these assumptions do not affect the theoretical conclusions excessively. Because of this a reliable comparison is important. It is possible to obtain experimental results for the dependence of the domain wall coercive field on material and domain wall parameters [2], but it is difficult and sometimes even questionable. If a series of similar samples is used, many parameters change from sample to sample and, in particular, the structure of imperfections can vary without control. The same is true for a series of measurements on a single sample at different temperatures. The experiment described below presents a useful method. The domain wall coercive field, Hew, was measured in a single sample of material, modifying the properties of the domain walls by decreasing the existing stresses in the material. An epitaxial magnetic garnet film (YSmCa)3(FeGe)50~2 was chosen for the investigation. The sample exhibited large uniaxial anisotropy with the easy axis of magnetization perpendicular to the film plane. The film was grown by liquid-phase epitaxy on a (111) oriented gadoliniumgallium-garnet substrate. The parameters of the film were measured by standard methods [3]: film thickness, h = 5.0
* Corresponding vert@ ra.atki.kfki.hu.
author.
Fax:
+36-1-1550694;
email:
/~m; saturation magnetization, 47rM~ = 210 G; characteristic material length, l = 0.55 /xm; and uniaxial material quality factor, Q = 4.4. The domain wall coercive field was measured using the low frequency (200 Hz) oscillation method [4]: the amplitude of an ac magnetic field oriented along the easy axis was increased linearly from zero and the onset of domain wall motion was detected photoelectrically. The accuracy of the H~w measurement was 0.05 Oe. The uniaxial anisotropy was measured using a magnetooptical method with an accuracy of 100 e r g / c m 3 [3]. The effect of mechanical stress due to lattice distortion was measured earlier on epitaxial magnetic garnet films [5]. A significant effect of mechanical stress was found on the uniaxial anisotropy and on the domain wall parameters. The stress dependence of these quantities are used in the present work to modify the magnetic properties of the same sample. Lattice distortion is caused by the different lattice constants of the substrate and the epitaxial film. Reducing the thickness of the substrate relaxes the misfit strains in the epitaxial film, and the stress-dependent magnetic parameters, such as the domain wall coercive field, H~w, and the uniaxial anisotropy constant, K u, are modified. The substrates of the films were thinned from the backside in several steps by mechanical polishing. Polishing of the substrate was performed with special care to ensure that no microscratches a n d / o r other defects were introduced into the substrate crystal lattice. In each polishing step about 100 /xm was removed from the substrate. After each step the magnetic parameters were remeasured. Both Hew and K u were found to decrease with de-
0304-8853/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. Pll S 0 3 0 4 - 8 8 5 3 ( 9 6 ) 0 0 0 9 2 - 3
26
G. Vdrtesy. I. Tom6,~/ Journal o[Magnetism and Magnetic Materials 160 (1996) 25 26 ID 0
2.4
i
24
2"32.2:
f 1 1
2.1 >~ .,~
f 1 1 f
2.0
1.8 ~
1.7 ~ .c::
1.6 -
E
1.5
o n
1.4
11
, 100
23
"1:5
2.2
21>~ 20~ 1.91.8-
1.9 ~ o C,
i~
c .
, 150
.
, 200
.
, 250
.
, 300
.
, 350
.
, 400
17-
16o 16-
Substrate thickness, ~tm
14
creasing substrate thickness, as can be seen in Figs. 1 and 2, respectively. Each point in these figures represents the average of five independent measurements. The effect became more distinct after attaining a substrate thickness of 150 /_tm. The other parameters of the film do not depend on the substrate thickness. Measuring the pairs of H~,, and K , values belonging to the same substrate thickness, we can determine their correlation. A linear relationship was found between H~,,. and K u, as can be seen in Fig. 3. This correlation is believed to be characteristic for the given material. The slope of the line was found to be 0.00124 O e c m 3 erg 1 in the case of the epitaxial film investigated. Further measurements are necessary to prove the generality of this relationship in the case of epitaxial garnets. In agreement with the theoretical model the experiment showed that, at least for epitaxial films of magnetic garnets with high uniaxial anisotropy, the domain wall coercive field, as measured by the wall oscillation method, depends significantly on the uniaxial anisotropy. The slope of this linear function, which largely represents the intrinsic coercivity of the sample, makes a good start for subsequent
6 4 0 0 -
6200-
~"
iii
6000-
II
I
i
5600
Fig. 1. Domain wall coercive field, //~,,., as a function of the substrate thickness.
,
i
5700
,
~
5800
,
i
5900
,
i
6000
,
i
6100
,
i
6200
Uniaxial anisotropy, erg/cm 3
Fig. 3. The determined empirical correlation between the uniaxial anisutropy constant. K., and the domain wall coercive field, H,,,,,. quantitative evaluations of the relevance of various theoretical models of domain wall coercivity to currently investigated materials. However, the revealed correlation does not mean that by measuring the uniaxial anisotropy constant of a sample its coercivity can be calculated. The relation of the coercivity to the magnetic parameters is only one side of the coin. The coercivity of a sample also depends significantly on the structure of the material (material imperfections, etc.), and samples with very similar magnetic parameters (anisotropy, saturation magnetization, exchange stiffness, etc.) can have very different coercive properties. This shows the very complex character of coercive properties. The importance of the above-described quantitative correlation between H,.w and K, is to show the type of function between these quantities. The results of the above experiment also make it possible to obtain the experimental shapes of the correlations between the domain wall coercive field and the wall parameters (domain wall energy density a n d / o r domain wall width). Acknowledgement: The authors are indebted to Dr. B. Keszei for the growth of the sample. Financial support from CEC Joint Research Project No. ERB 3510 PL 92 3369 and from project No. 2 0 2 / 9 5 / 0 0 2 2 of the Grant Agency of the Czech Republic is appreciated. References
5800-
•-'~
5600i
100
,
b
'[50
,
i
200
,
~
250
,
i
,
300
~
350
,
i
400
Substrate thickness, #m
Fig. 2. Uniaxial anisotropy constant, K u, as a function of the substrate thickness.
[1] [2] [3] [4]
M. Pardavi-Horvfith, IEEE Trans. Magn. 21 (1985) 1694. R. Raasch and J. Reck, J. Appl. Phys. 74 (1993) 1229. R.M. Josephs, AIP Conf. Proc. 10 (1972) 286. J.A. Seitchik, G.K. Goldberg and W.D. Doyle, J. Appl. Phys. 42 (1971) 1272. [5] G. V6rtesy, Elsevier Studies in Applied Electromagnetics in Materials 4, ed. L. Lanotte (Elsevier, Amsterdam, 1993) p. 57.