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Nucleation of magnetisation reversal in iron whiskers
PHYSICS
Volume 6, number 3
NUCLEATION
OF
15 September 1963
‘LETTERS
MAGNETISATION
REVERSAL
IN IRON
WHISKERS
*
A. AHARONI and E. NEEMAN Department
of Electronics,
The Weizmann Institute
of Science,
Rehovoth,
Israel
Received 23 August 1963
Theoretically the nucleation field for magnetisation reversal in a smooth, elongated iron single crystal is -560 Oe l). Experimental results approaching this value were first obtained by De Blois and Bean I), in certain parts of a few out of several hundredwhiskers studied. In other parts, the nucleation field was numerically much smaller, indicating that the theory applies only to the most perfect regions of the crystals. Later De Blois 2) observed that the nucleation field is very sensitive to electropolishing or corrosion of the surface, so that the difference between theoretical and experimental value is mainly due to surface roughness. However, no quantitative data were given for the dependence of nucleation field on surface roughness. A first attempt to obtain such a quantitative dependence will be reported here. The experimental set-up was essentially as described by De Blois 2), the main difference being that we could not make the magnetising coil as small as he did. Our coil was 0.5 mm diameter and 0.5 mm long, made of 5 turns of 0.05mm copper enameled wire, with a one turn pick-up coil at one of its ends. The iron whiskers ** were put in a protective quartz tube, 0.2 mm in diameter, which was glued to a fine screw arrangement to move it, on a calibrated scale, inside the magnetising coil. The whole set-up was in a dC magnetic field of lOOOe, which saturated the whisker along its long axis. Some measurements were done in other fields, up to 500 Oe, and the change in the external field was found to add to the apparent nucleation field. These measurements served mainly as a calibration of the current pulse through the magnetising coil in terms of magnetic field, thus eliminating the uncertainty in the coil dimensions. The current pulse through the magnetising coil, and the output of the pick-up coil were observed simultaneously on a Tektronix double beam oscilloscope. This yields the nucleation field, which is defined, for the purpose of this experiment 51, as the value of the magnetising field at the time when there starts a pick-up signal. * Part of an M.Sc. thesis by E. Neeman submitted to the Hebrew University, Jerusalem. ** Kindly supplied by R. W. De Blois.
The rise time of the magnetising current pulse was about 1 psec, and could be changed somewhat by adjusting the pulse height. We found that the value of the nucleation field depended on the slope of the magnetising pulse, especially for low slopes. Such a time dependence is not surprising, in view of the high frequency used, where eddy currents and other types of viscosity delay the nucleation. Time dependence of nucleation field has also been observed in thin iron-nickel film 4). We, therefore, took a double set of readings at each point on the whisker, one at the highest slope, and one for the pulse height adjusted so that the pick up appeared at the wide maximum of the pulse. In the latter case, the field is applied for a relatively long time, and the pick up appears as “flickering” signal, which seems better applicable to the definition of nucleation. However, since the two sets of values gave almost parallel graphs and only differences are used in the following, either set could be used. Typical results of nucleation field for one of the whiskers are plotted in fig. 1. Similar graphs I I I I I I
Fig. 1. Nucleation field along part of whisker No. 1. The circles are for high slope magnetising pulse and the triangles for a pick-up flickering on the flat maximum of the pulse.
241
Volume 6, number 3
PHYSICS
were plotted for several carefully selected whiskers some of which could not be used later because the whiskers were damaged when removed from the quartz tube to be inspected, or when photographed under the microscope. Only four whiskers remained for which fig. 1 and similar graphs could be related to observation of the surfaces under a microscope (Wild M 20). Qualitatively it can be stated that whenever a major surface defect could be seen in at least one of the 4 surfaces of a whisker, therealwaysappeared a minimum in the nucleation field. The opposite was not always true and some minima were found where the surface seemed rather smooth. As has been remarked by De Blois 2), these are possibly voids or inclusions within the whisker. In some cases minima were due to a collection of a large number of minor defects whose volume could not be measured, and these were discarded. In other cases the minima were very asymmetrical, so that is was impossible to define the effect of the particular defect observed, and these were discarded too. We have looked particularly for minima like 6.3 in fig. 1. At that place, where the whisker is 9.0 1 wide, a large cylinderlike defect was seen on the surface, whose volume was estimated at 785 p3, with no other defects in the near vicinity. The minimum there is rather symmetrical as is seen from fig. 1 and it can be estimated from that figure that that particular defect caused a reduction of 310 Oe from the values on both sides of the minimum. Similarly, at 7.1 in fig. 1 the whisker is 10 /J wide and an imperfection was observed, that when assumed to be an ellipsoid, its volume was 160 ~3. Another ellipsoid, 80 p3 in volume, was observed at 7.2, which presumably causes the shoulder in fig. 1. Since our coil is rather long, covering essentially both defects, we assumed that the combined volume was responsible for the difference of 125 Oe between the minimum and the maximum at 7.3 or 6.8, ignoring the change between 6.8 and 7.2, which is due to some other minor defect. In a similar way, all definable points were selected on the other 3 whiskers, yielding the results plotted in fig. 2. The abscissa in fig. 2 is the volume of the defect (or combination of defects) devided by the cube of the whisker width, to get a dimensionless quantity. The volumes were taken as those of the nearest geometrical form : parallelepipeds, cylinders, ellipsoids, or cones, with the appropriate dimension. *****
242
LETTERS
15 September 1963
Fig. 2. Reduction in nucleation field with respect to the vicinity as a function of defect volume, V, in terms of the cube of whisker width, a, at the defect. Boxes : whisker No. 1 (4.9 mm long, 9-10 & wide) ; crosses : whisker No. 2 (6 mm long, 9-11 u wide) ; circles : whisker No. 3 (5.6 mm long, 9.3-14.2 p wide) ; triangle : whisker No. 4 (5.4 mm long, 8.2 u wide). The widths given are at the regions from which points were taken for the graph.
This implied a rather high uncertainty in the volumes, as marked on the figure. However, the points on the graph seem tofollow a regular smooth curve. Although the number of points is rather small to draw conclusions, it seems that it is mainly the volume of the defect that counts. Attempts to draw the nucleation field as a function of either one of the dimensions of the defect gave scattered points, with no apparent tendency to form a regular curve. No distinction is made in fig. 2 between surface defects in the form of pits and those projecting out of the surface. There is no reason to believe that their different effect might be different. We are greatly indebted to Dr. R. W. De Blois for supplying the whiskers, and for many valuable discussions on the details of the experimental setup, and to Dr. D. Treves for help in the electronics.
References 1) R.W.De Blois andC.P.Bean, J.Appl.Phys. 30 (1959) 225 S. 32 (1961) 1561. 2) R.W.De Blois, J.Appl.Phys. 3) A. Aharoni, Revs. Modern Phys. 34 (1962) 227. 4) F.Schuler, J.Appl.Phys. 33 (1962) 1845.
Volume 6, number 3
NUCLEATION
OF
15 September 1963
‘LETTERS
MAGNETISATION
REVERSAL
IN IRON
WHISKERS
*
A. AHARONI and E. NEEMAN Department
of Electronics,
The Weizmann Institute
of Science,
Rehovoth,
Israel
Received 23 August 1963
Theoretically the nucleation field for magnetisation reversal in a smooth, elongated iron single crystal is -560 Oe l). Experimental results approaching this value were first obtained by De Blois and Bean I), in certain parts of a few out of several hundredwhiskers studied. In other parts, the nucleation field was numerically much smaller, indicating that the theory applies only to the most perfect regions of the crystals. Later De Blois 2) observed that the nucleation field is very sensitive to electropolishing or corrosion of the surface, so that the difference between theoretical and experimental value is mainly due to surface roughness. However, no quantitative data were given for the dependence of nucleation field on surface roughness. A first attempt to obtain such a quantitative dependence will be reported here. The experimental set-up was essentially as described by De Blois 2), the main difference being that we could not make the magnetising coil as small as he did. Our coil was 0.5 mm diameter and 0.5 mm long, made of 5 turns of 0.05mm copper enameled wire, with a one turn pick-up coil at one of its ends. The iron whiskers ** were put in a protective quartz tube, 0.2 mm in diameter, which was glued to a fine screw arrangement to move it, on a calibrated scale, inside the magnetising coil. The whole set-up was in a dC magnetic field of lOOOe, which saturated the whisker along its long axis. Some measurements were done in other fields, up to 500 Oe, and the change in the external field was found to add to the apparent nucleation field. These measurements served mainly as a calibration of the current pulse through the magnetising coil in terms of magnetic field, thus eliminating the uncertainty in the coil dimensions. The current pulse through the magnetising coil, and the output of the pick-up coil were observed simultaneously on a Tektronix double beam oscilloscope. This yields the nucleation field, which is defined, for the purpose of this experiment 51, as the value of the magnetising field at the time when there starts a pick-up signal. * Part of an M.Sc. thesis by E. Neeman submitted to the Hebrew University, Jerusalem. ** Kindly supplied by R. W. De Blois.
The rise time of the magnetising current pulse was about 1 psec, and could be changed somewhat by adjusting the pulse height. We found that the value of the nucleation field depended on the slope of the magnetising pulse, especially for low slopes. Such a time dependence is not surprising, in view of the high frequency used, where eddy currents and other types of viscosity delay the nucleation. Time dependence of nucleation field has also been observed in thin iron-nickel film 4). We, therefore, took a double set of readings at each point on the whisker, one at the highest slope, and one for the pulse height adjusted so that the pick up appeared at the wide maximum of the pulse. In the latter case, the field is applied for a relatively long time, and the pick up appears as “flickering” signal, which seems better applicable to the definition of nucleation. However, since the two sets of values gave almost parallel graphs and only differences are used in the following, either set could be used. Typical results of nucleation field for one of the whiskers are plotted in fig. 1. Similar graphs I I I I I I
Fig. 1. Nucleation field along part of whisker No. 1. The circles are for high slope magnetising pulse and the triangles for a pick-up flickering on the flat maximum of the pulse.
241
Volume 6, number 3
PHYSICS
were plotted for several carefully selected whiskers some of which could not be used later because the whiskers were damaged when removed from the quartz tube to be inspected, or when photographed under the microscope. Only four whiskers remained for which fig. 1 and similar graphs could be related to observation of the surfaces under a microscope (Wild M 20). Qualitatively it can be stated that whenever a major surface defect could be seen in at least one of the 4 surfaces of a whisker, therealwaysappeared a minimum in the nucleation field. The opposite was not always true and some minima were found where the surface seemed rather smooth. As has been remarked by De Blois 2), these are possibly voids or inclusions within the whisker. In some cases minima were due to a collection of a large number of minor defects whose volume could not be measured, and these were discarded. In other cases the minima were very asymmetrical, so that is was impossible to define the effect of the particular defect observed, and these were discarded too. We have looked particularly for minima like 6.3 in fig. 1. At that place, where the whisker is 9.0 1 wide, a large cylinderlike defect was seen on the surface, whose volume was estimated at 785 p3, with no other defects in the near vicinity. The minimum there is rather symmetrical as is seen from fig. 1 and it can be estimated from that figure that that particular defect caused a reduction of 310 Oe from the values on both sides of the minimum. Similarly, at 7.1 in fig. 1 the whisker is 10 /J wide and an imperfection was observed, that when assumed to be an ellipsoid, its volume was 160 ~3. Another ellipsoid, 80 p3 in volume, was observed at 7.2, which presumably causes the shoulder in fig. 1. Since our coil is rather long, covering essentially both defects, we assumed that the combined volume was responsible for the difference of 125 Oe between the minimum and the maximum at 7.3 or 6.8, ignoring the change between 6.8 and 7.2, which is due to some other minor defect. In a similar way, all definable points were selected on the other 3 whiskers, yielding the results plotted in fig. 2. The abscissa in fig. 2 is the volume of the defect (or combination of defects) devided by the cube of the whisker width, to get a dimensionless quantity. The volumes were taken as those of the nearest geometrical form : parallelepipeds, cylinders, ellipsoids, or cones, with the appropriate dimension. *****
242
LETTERS
15 September 1963
Fig. 2. Reduction in nucleation field with respect to the vicinity as a function of defect volume, V, in terms of the cube of whisker width, a, at the defect. Boxes : whisker No. 1 (4.9 mm long, 9-10 & wide) ; crosses : whisker No. 2 (6 mm long, 9-11 u wide) ; circles : whisker No. 3 (5.6 mm long, 9.3-14.2 p wide) ; triangle : whisker No. 4 (5.4 mm long, 8.2 u wide). The widths given are at the regions from which points were taken for the graph.
This implied a rather high uncertainty in the volumes, as marked on the figure. However, the points on the graph seem tofollow a regular smooth curve. Although the number of points is rather small to draw conclusions, it seems that it is mainly the volume of the defect that counts. Attempts to draw the nucleation field as a function of either one of the dimensions of the defect gave scattered points, with no apparent tendency to form a regular curve. No distinction is made in fig. 2 between surface defects in the form of pits and those projecting out of the surface. There is no reason to believe that their different effect might be different. We are greatly indebted to Dr. R. W. De Blois for supplying the whiskers, and for many valuable discussions on the details of the experimental setup, and to Dr. D. Treves for help in the electronics.
References 1) R.W.De Blois andC.P.Bean, J.Appl.Phys. 30 (1959) 225 S. 32 (1961) 1561. 2) R.W.De Blois, J.Appl.Phys. 3) A. Aharoni, Revs. Modern Phys. 34 (1962) 227. 4) F.Schuler, J.Appl.Phys. 33 (1962) 1845.