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Normal magnetization in nickel
1354 NORMAL MAGNETIZATION IN NICKEL R.R. BIRSS and D.G. LORD Department of Pure and Applied Physics, University of Salford, Salford, M5 4WT, U.K. Measurements are reported of the variation of the normal component of magnetization with applied magnetic field obtained from nickel single crystal spheres, by rotating sample magnetometry, in both (100) and (110) planes at 300 K. Together with observations of the differential normal susceptibility, these measurements are compared with theoretical magnetization models.
1. Introduction
In the case of cubic ferromagnetic single crystals, theories developed by N6el [1], Lawton and Stewart [2] and Birss and Hegarty [3] have shown that the process of magnetization occurs, in general, in four modes. Minimization of the sum of the magnetocrystalline anisotropy energy and the interaction energy with the internal field indicate that transitions between different modes should be exhibited as distinct changes in slope of the magnetization curve at various critical values of applied flux density for particular orientations of the crystal with respect to the applied flux density. Previous measurements of the magnetization, both the parallel and normal components, of a nickel ellipsoid by Kaya [4] have shown rather poor agreement with theoretical prediction, especially with respect to the sharpness of the slope discontinuities. Reasonable agreement between theory and experiment has been obtained by using reflection magneto-optical techniques by Birss et al. [5] from both bulk single crystal nickel discs and thin films. This paper reports measurements obtained by rotating sample magnetometry of the variation of the normal component of magnetization with applied flux density from a nickel single crystal sphere at 300 K. These measurements, together with observations of the normal differential susceptibility, are compared with the theoretical models. 2. Experimental
The specimen used, a 15 mm diameter nickel single crystal sphere of 4N purity, was attached securely to one end of a rotation shaft with the particular crystallographic plane under investigation [the (100) or the (110)] being aligned normal to within ½degree of the rotation shaft axis by back reflection Laue photography. The Physica 86-88B (1977) 1354-1356 ~ North-Holland
vertical rotation axis, defined by two Teflon bearings, was arranged such that the specimen was located at the centre of the pole gap of a 7 inch Newport electromagnet. A pair of measuring coils were connected in series addition and aligned on either side of the specimen with their axes mutually parallel and normal to the horizontal magnetic flux density direction. 2.1. Magnetization measurement
The induced voltage, V~, generated in the measuring coils on rotation of the specimen at a rotation speed of to radians s 1 in a particular applied magnetic flux density B0 is given (see Flanders [6]) by Vl(J~0) =
C d[M sin (O - ~b)]/dt = Co~ dMN/d~b,
(1) where C is a constant for a particular system, M is the specimen magnetization, M N is the component of M normal to B0, and ~b and 0 are the angles made by B0 and M respectively to a particular reference direction in the crystal, the (100) direction in this work. Data from ten rotations of the specimen were recorded sequentially for each of several values of applied flux density between 0.1 and 0.6 T. Each data set from a particular field was averaged to reduce non-coherent noise and Fourier analysed up to the sixteenth harmonic. The resulting harmonics of V1 were then integrated for each field value to produce, from eq. (1), values of M N at 5 degree intervals of ~b from the (100) direction for each plane under investigation. 2.2 Susceptibility measurement The differential normal susceptibility was measured using a ripple-field technique for
1355 various static orientations, 4), of the crystal. A pair of Helmholtz coils was used to provide a sinusoidal ripple flux density of 5 x 10-4T peakto-peak amplitude and of frequency 27Hz, parallel to the electromagnet field. The electromagnet field was ramped linearly from zero to ---0.7 T at a rate of 0.1 T min -1, and the component of the sinusoidal induced voltage in the measuring coils in phase with the ripple field was plotted using phase sensitive detection as a function of applied flux density. 3. Results and discussion
The values of M~ for a particular value of ~b, collated from the integration procedure, have been plotted as a function of applied flux density as shown in fig. 1. The experimental data have been fitted to the theoretically predicted variations for nickel of Birss and Hegarty [3] by normalising the values of MN obtained at flux densities of both 0.5 T and 0.6 T. For all $, the ratio of theoretical to experimental values of MN for these two fields was constant to within 0.8%.
10
For all flux density values greater than about 0.17 T, and for all values of 4), the experimental curves of MN lie below the theoretical curves for rotation in both the crystallographic planes investigated. The critical values of flux density for mode transitions, indicated clearly by discontinuities in slope, are found experimentally to occur, for all ~b, at slightly higher values than predicted. These findings are both consistent with the hypothesis [3] that imperfections present in the sample would tend to reduce MN. For flux densities of less than about 0.17T, experimental values of MN greater than predicted are observed for some particular values of 4). In particular for the (100) plane results, depicted in fig. 2, this discrepancy is seen to increase as d~ approaches 45 degrees. For applied flux density directions at small angles to a (110) direction, a non-zero MN implies magnetization occupancy of the two out of plane (111) easy directions normal to this (110) direction. That the values of Ms found at both 4) = 40° and ~b = 50° are both larger than the theoretical prediction for these low flux densities is thought to arise from a fundamental difficulty imposed in fitting together an acceptable total domain pattern. A particular consequence of the method of rotating sample magnetometry used here is the (b)
(o)
tO"
z"
o
"
:z
5' o
• = 40"
0.1
C-15
0"2 MAGNETIC FLUX
0"25 DENSITY, E~(T )
(}1
¢~=60"
0,3
Fig. 1. Normal component of magnetization variation with applied field for three field directions in the (100) plane of a nickel sphere obtained with a rotation speed of to = 0.3 rad s ~. Full line from theory 3; open circles experimental points for the given ~b; closed circles for ~b = 50 °.
0-2
MAGNETIC
FLUX
DENSITY, 13,(T )
Fig. 2. Differential normal susceptibility variation with applied field for three field directions in (a) (100) plane and (b) (110) plane of nickel sphere.
1356 angular asymmetry found in the (100) plane for rotation through the (110) directions as shown in fig. 1. Though essentially a hysteretic phenomenon, the asymmetry is closely related to domain nucleation mechanisms and should thus be dependent on the crystal microstructure. The results obtained from measurement of the differential susceptibility in both the (100) and (110) planes are shown in fig. 2. The curves obtained compare favourably with differentials of the theoretical predictions, and the critical fields for the various mode changes are clearly defined. 4. Conclusions
Measurements of the normal component of magnetization of a single crystal nickel sphere by rotating sample magnetometry have revealed clear experimental evidence for well defined
transitions between individual modes of magnetization. Measurements of the normal differential susceptibility confirm these results and discrepancies between experiment and theory, observed in some particular field directions in both the (100) and (110) planes are thought to arise from domain configuration constraints and crystal imperfections. References [1] L. N6el, J. Phys. Radium 5 (1944) 241. [2] H. Lawton and K.H. Stewart, Proc. Roy. Soc. A193 (1948) 72. [3] R.R. Birss and B.C. Hegarty, Brit. J. appl. Phys. 17 (1966) 1241. R.R. Birss, B.C. Hegarty and P.M. Wallis, Brit. J. appl. Phys. 18 (1967) 459. [4] S. Kaya, Sci. Rep. Res. Inst. Tohoku Univ. 17 (1928) 639. [5l R.R. Birss, D.G. Lord, D.J. Martin, S.M.N. Momen and M.R. Parker, Phys. Stat. Sol. (a) 32 (1975) 157. [6] P.J. Flanders, Rev. Sci. Inst. 41 (1970) 697.
1. Introduction
In the case of cubic ferromagnetic single crystals, theories developed by N6el [1], Lawton and Stewart [2] and Birss and Hegarty [3] have shown that the process of magnetization occurs, in general, in four modes. Minimization of the sum of the magnetocrystalline anisotropy energy and the interaction energy with the internal field indicate that transitions between different modes should be exhibited as distinct changes in slope of the magnetization curve at various critical values of applied flux density for particular orientations of the crystal with respect to the applied flux density. Previous measurements of the magnetization, both the parallel and normal components, of a nickel ellipsoid by Kaya [4] have shown rather poor agreement with theoretical prediction, especially with respect to the sharpness of the slope discontinuities. Reasonable agreement between theory and experiment has been obtained by using reflection magneto-optical techniques by Birss et al. [5] from both bulk single crystal nickel discs and thin films. This paper reports measurements obtained by rotating sample magnetometry of the variation of the normal component of magnetization with applied flux density from a nickel single crystal sphere at 300 K. These measurements, together with observations of the normal differential susceptibility, are compared with the theoretical models. 2. Experimental
The specimen used, a 15 mm diameter nickel single crystal sphere of 4N purity, was attached securely to one end of a rotation shaft with the particular crystallographic plane under investigation [the (100) or the (110)] being aligned normal to within ½degree of the rotation shaft axis by back reflection Laue photography. The Physica 86-88B (1977) 1354-1356 ~ North-Holland
vertical rotation axis, defined by two Teflon bearings, was arranged such that the specimen was located at the centre of the pole gap of a 7 inch Newport electromagnet. A pair of measuring coils were connected in series addition and aligned on either side of the specimen with their axes mutually parallel and normal to the horizontal magnetic flux density direction. 2.1. Magnetization measurement
The induced voltage, V~, generated in the measuring coils on rotation of the specimen at a rotation speed of to radians s 1 in a particular applied magnetic flux density B0 is given (see Flanders [6]) by Vl(J~0) =
C d[M sin (O - ~b)]/dt = Co~ dMN/d~b,
(1) where C is a constant for a particular system, M is the specimen magnetization, M N is the component of M normal to B0, and ~b and 0 are the angles made by B0 and M respectively to a particular reference direction in the crystal, the (100) direction in this work. Data from ten rotations of the specimen were recorded sequentially for each of several values of applied flux density between 0.1 and 0.6 T. Each data set from a particular field was averaged to reduce non-coherent noise and Fourier analysed up to the sixteenth harmonic. The resulting harmonics of V1 were then integrated for each field value to produce, from eq. (1), values of M N at 5 degree intervals of ~b from the (100) direction for each plane under investigation. 2.2 Susceptibility measurement The differential normal susceptibility was measured using a ripple-field technique for
1355 various static orientations, 4), of the crystal. A pair of Helmholtz coils was used to provide a sinusoidal ripple flux density of 5 x 10-4T peakto-peak amplitude and of frequency 27Hz, parallel to the electromagnet field. The electromagnet field was ramped linearly from zero to ---0.7 T at a rate of 0.1 T min -1, and the component of the sinusoidal induced voltage in the measuring coils in phase with the ripple field was plotted using phase sensitive detection as a function of applied flux density. 3. Results and discussion
The values of M~ for a particular value of ~b, collated from the integration procedure, have been plotted as a function of applied flux density as shown in fig. 1. The experimental data have been fitted to the theoretically predicted variations for nickel of Birss and Hegarty [3] by normalising the values of MN obtained at flux densities of both 0.5 T and 0.6 T. For all $, the ratio of theoretical to experimental values of MN for these two fields was constant to within 0.8%.
10
For all flux density values greater than about 0.17 T, and for all values of 4), the experimental curves of MN lie below the theoretical curves for rotation in both the crystallographic planes investigated. The critical values of flux density for mode transitions, indicated clearly by discontinuities in slope, are found experimentally to occur, for all ~b, at slightly higher values than predicted. These findings are both consistent with the hypothesis [3] that imperfections present in the sample would tend to reduce MN. For flux densities of less than about 0.17T, experimental values of MN greater than predicted are observed for some particular values of 4). In particular for the (100) plane results, depicted in fig. 2, this discrepancy is seen to increase as d~ approaches 45 degrees. For applied flux density directions at small angles to a (110) direction, a non-zero MN implies magnetization occupancy of the two out of plane (111) easy directions normal to this (110) direction. That the values of Ms found at both 4) = 40° and ~b = 50° are both larger than the theoretical prediction for these low flux densities is thought to arise from a fundamental difficulty imposed in fitting together an acceptable total domain pattern. A particular consequence of the method of rotating sample magnetometry used here is the (b)
(o)
tO"
z"
o
"
:z
5' o
• = 40"
0.1
C-15
0"2 MAGNETIC FLUX
0"25 DENSITY, E~(T )
(}1
¢~=60"
0,3
Fig. 1. Normal component of magnetization variation with applied field for three field directions in the (100) plane of a nickel sphere obtained with a rotation speed of to = 0.3 rad s ~. Full line from theory 3; open circles experimental points for the given ~b; closed circles for ~b = 50 °.
0-2
MAGNETIC
FLUX
DENSITY, 13,(T )
Fig. 2. Differential normal susceptibility variation with applied field for three field directions in (a) (100) plane and (b) (110) plane of nickel sphere.
1356 angular asymmetry found in the (100) plane for rotation through the (110) directions as shown in fig. 1. Though essentially a hysteretic phenomenon, the asymmetry is closely related to domain nucleation mechanisms and should thus be dependent on the crystal microstructure. The results obtained from measurement of the differential susceptibility in both the (100) and (110) planes are shown in fig. 2. The curves obtained compare favourably with differentials of the theoretical predictions, and the critical fields for the various mode changes are clearly defined. 4. Conclusions
Measurements of the normal component of magnetization of a single crystal nickel sphere by rotating sample magnetometry have revealed clear experimental evidence for well defined
transitions between individual modes of magnetization. Measurements of the normal differential susceptibility confirm these results and discrepancies between experiment and theory, observed in some particular field directions in both the (100) and (110) planes are thought to arise from domain configuration constraints and crystal imperfections. References [1] L. N6el, J. Phys. Radium 5 (1944) 241. [2] H. Lawton and K.H. Stewart, Proc. Roy. Soc. A193 (1948) 72. [3] R.R. Birss and B.C. Hegarty, Brit. J. appl. Phys. 17 (1966) 1241. R.R. Birss, B.C. Hegarty and P.M. Wallis, Brit. J. appl. Phys. 18 (1967) 459. [4] S. Kaya, Sci. Rep. Res. Inst. Tohoku Univ. 17 (1928) 639. [5l R.R. Birss, D.G. Lord, D.J. Martin, S.M.N. Momen and M.R. Parker, Phys. Stat. Sol. (a) 32 (1975) 157. [6] P.J. Flanders, Rev. Sci. Inst. 41 (1970) 697.