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Magnetic behaviour of ferromagnetics at high frequencies
P h y s i c a X V , no I - 2
A p r i l 1949
MAGNETIC BEHAVIOUR OF FERROMAGNETICS AT H I G H F R E Q U E N C I E S b y H. J. VAN L E E U W E N Laboratorium voor Technische Physica der Technische Hogesehool, Delft
In the last few years we h a v e tried in the l a b o r a t o r y of Delft to get some f u r t h e r i n f o r m a t i o n on the b e h a v i o u r of the ferromagnetics in the high f r e q u e n c y region. A l r e a d y in 1903 it was k n o w n f r o m the e x p e r i m e n t s of H a g e n and R u b e n s 1) on infrared reflection t h a t in this w a v e l e n g t h region (30 #) the p e r m e a b i l i t y of iron was 1. E x p e r i m e n t s of L i n d m a n 3) in 1938 with d a m p e d oscillations on a single iron wire and on a s y s t e m of two parallel wires gave a fall of the p e r m e a b i l i t y from 100 to 10 in the region b e t w e e n 50 and 15 cm. M a x w e 11 3) m e a s u r e d a p e r m e a b i l i t y in a wave guide for a w a v e l e n g t h of 1,25 cm in 1946. Mr. J. S m i d t of our l a b o r a t o r y , now in Bandoeng, m e a s u r e d the p e r m e a b i l i t y of a pure iron wire in the region b e t w e e n 83 and 52 cm and found a v e r y steep descent from 60 to 1 at 63 cm wavelength 4). T h e m e t h o d of m e a s u r e m e n t was not new, b u t it was not used before at so small wavelengths t h a t the p e r m e a b i l i t y decreased till 1. I t consisted in the main in the measuring of the difference of w a v e l e n g t h of u n d a m p e d oscillations on two concentric L e c h e r systems, one of which had a f e r r o m a g n e t i c wire as an inner conductor, the o t h e r one a non f e r r o m a g n e t i c wire.The w a v e l e n g t h measured on the f e r r o m a g n e t i c line is smaller t h a n on the non ferromagnetic and the r e s o n a n t peaks b r o a d e r on the first t h a n on the last. T h e difference of w a v e l e n g t h is a measure of the inner self-inductance of the ferromagnetic wire and so of its permeability. T h e steep descent of the p e r m e a b i l i t y of the iron wire sets in at a wavelength, which depends on the t e m p e r a t u r e and the foregoing heat t r e a t m e n t of the wire, as is shown in fig. 1. I t occurs in the region where B e c k e r and D 6 r i n g predicted the descent on their t h e o r y 5). This t h e o r y - -
2 5 8
I
259
MAGNETIC BEHAVIOUR OF FERROMAGNETICS
was based on the idea, t h a t the front of a Weiss d o m a i n in travelling t h r o u g h the metal, gives rise to F o u c a u 1 t currents which in their t u r n exercise a force on the front opposite to its m o t i o n and p r o p o r t i o n a l to its velocity. T h e front m o t i o n has, on account of this force, a smaller elongation at higher frequencies t h a n at lower. This would be the cause of the decrease of the p e r m e a b i l i t y with increasing frequency. T h o u g h we know from the e x p e r i m e n t s of S i x t u s and T o n k s 6) on materials with large Weiss domains t h a t t.heir [J tn e . m . u 80-
60-
3
AT ABOUT-40"C.
4
AT ABOU'i" 15°C
~,
.
o
,--o
-
| °
AT ABOUT 20°C, ANNEALEDAT 800 "C AND COOLEDIN A MA6NETIC FIELD ,o-
_
_ :_
,:
,_v0_,_v'_c_
°
)t |
.
AT ABOUT 20=C,ANNEALED AT 800% 20:- .o-..o.---o-..--o=
o
I
I
BO
75
~', 70
I
65
60
:
I
55
cm
Fig. 1. T h e p e r m e a b i l i t y of iron as a f u n c t i o n of t h e w a v e - l e n g t h in v a c u o .
fronts do not t r a v e l as flat planes, as was supposed b y B e c k e r and D 5 r i n g and t h a t the viscous force on the front, which limits the elongation, depends on the form of the front ~), the basis of the t h e o r y of B e c k e r and D 6 r i n g is essentially certain and correct, and the region where the decrease of the p e r m e a b i l i t y is predicted b y t h e m also. I t depends however on the dimensions of the Weiss domains and the form of the fronts. Of the dimensions only the order of m a g n i t u d e is known, the form of the front is unknown, from which the conclusion m u s t be derived t h a t the form of the curve which gives the p e r m e a b i l i t y as a function of the f r e q u e n c y rests indeterminate. S m i d t gives the curve t h a t is best a d a p t e d to his m e a s u r e m e n t s if all the domains of Weiss should have the same length. T h e experim e n t a l curve is m u c h steeper t h a n this theoretical curve.
H. ]. V A N LEEUWEN
260
If the domains of Weiss should have different lengths, the discrepance should be still larger. There exists another theoretical approach to the problem of the dispersion of the permeability, made by K i t t e 1 s). It faces quite another aspect of the phenomenon. While B e c k e r and D 6r i n g fix their attention to the measure in which the front motion can develop at different wavelengths, they neglect a possible influence of discontinuities by passing from one of the domains of Weiss to another. In the fine wires of the experiments the front travels perpendicular to the length of the wire and tangential in the cross-section of the wire. K i t t e 1 discusses the circumstance that at these high frequencies the depth of penetration in the wire is of the same order of magnitude as the dimensions of a domain of Weiss. ~. in e.m.u.. 102 _ _ • %%m
_MEASURED CURVE AT ABOUT 45"C
~'~',,.,..THEORETICAL CURVE FROM ~C,, BECKER AND DORING
40
~¢,,_THEORE TICAL CURVE I OF KITTEL
4
i
'108
i
~'
: ',
t0 9
,
t
I
i /
1040 Hz
Fig. 2. T h e e x p e r i m e n t a l and t w o t h e o r e t i c a l c u r v e s g i v i n g t h e p e r m e a b i l i t y of iron as a f u n c t i o n of t h e f r e q u e n c y .
While B e c k e r and D 6 r i n g assume the magnetization to follow the field in each point of a radiusvector of the cross-section independently of other points, K i t t e 1 assumes the motion of points in different depth beneath the surface, but all in the first Weiss domain to be identical and for all frequencies this motion and thus the magnetization the same for the same field strength. He omits also the Foucault-damping, which is a shortcoming of his
MAGNETIC BEHAVIOUR OF FERROMAGNETICS
261
theory 9). That the magnetization is in his theory independent of the depth beneath the surface alters the usual equations for the skin effect and in order to get the same value for the irrfpedance of the wire as from the usual equations, from which the permeability is derived, he has to make the permeability a definite function of the frequency with only one parameter, the length of a domain of Weiss. With this parameter adapted to the measurements the theoretical curve of K i t t e 1 also is much less steep than the experimental one (fig. 2). A third explanation of high frequency dispersion of permeability has been given by S n o e k 10), who takes a handing over of the spin direction from spin to spin in the layer between two Weiss domains as the basis of the phenomenon. This theory too expects a ,~ IQ
cm
,,~
fO-
temp..17°C+-1 J
5-
0
?0
Cm
- - ¢ ~ . .
k
0
5-
fOF i g . 3. T h e w a v e l e n g t h d i f f e r e n c e o n t w o l i n e s w i t h r e s p e c t i v i l y a c o p p e r a n d i r o n - n i c k e l wire a s a n i n n e r c o n d u c t o r a s a f u n c t i o n of t h e w a v e l e n g t h in v a c u o .
fall of the permeability in the din-region of wavelengths. Because the explanation of B e c k e r and D 6 r i n g depends directly on the coefficient of conduction of the material, that of K i t t e 1 only indirectly and that of S n o e k not, we planned measurements with
262
H.J. V A N L E E U W E N
materials of a lower coefficient of conduction which is the case for alloys. The expectation was that the fall of the permeability could be more or less displaced. It was therefore t h a t Mr. A. W i e b e r d i n k 11) has measured nearly in the same way as mentioned before the difference of wavelength on lines with a copper and an iron-nickel central wire. Beyond expectation the difference of wavelength offered the picture of fig. 3. ~1.
col
.
.10-
,<
.t
I +5.
. . . . . ,
is
8o Ext~rhqJ
5,
Curve Pfagnehzohon
Z 7rr
-10'
l 1
None fO0 0ersted A/let
/ I
8'5 !/ temp. f7 ° C
20OC 20oC
~'o: Wavelength on Cu . • Ni-Fe (35-65)
/
I 9'o
II
cm
I
~
I
~ ~
[ i
II ~,1
Fig. 4. T h e w a v e l e n g t h d i f f e r e n c e on t w o lines w i t h r e s p e c t i v i l y a c o p p e r a n d a n i r o n - n i c k e l wire as a n i n n e r c o n d u c t o r as a f u n c t i o n of t h e w a v e l e n g t h in v a c u o , c u r v e I w i t h o u t s t a t i c m a g n e t i c field, c u r v e I I in a s t a t i c m a g n e t i c field of I00 O p a r a l l e l t o t h e wire, c u r v e I I I a f t e r t h e s t a t i c m a g n e t i c field of curve II has been removed.
The fact that the wavelength on the ferromagnetic line is in a small interval between 86 and 88 cm larger than on the non-ferromagnetic one means a negative and even a complex value of the permeability, corresponding with an extreme broadening of the resonant peaks. It will not be until the resistance of the wire has been measured too, which is not yet the case, that the value of the permeabilit.y itself can be deduced.
MAGNETIC B E H A V I O U R OF FERROMAGNETICS
263
On proposal of Prof. K r o n i g who gave the theoretical interpretation of the phenomenon 12) the same measurements were done by Mr. W i e b e r d i n k in a static magnetic field of 100 0 in the direction of the wire. The peculiar phenomenon of fig. 3 is thereby obviously disturbed, as is to be seen from fig. 4. The fall of the permeability of iron, which is steeper than on the proposed theories might correspond to an effect of a similar kind, which is not fully developed.
REFERENCES 1) 2) 3) 4) 5) 6)
7) 8) 9) 10) 11) 12)
E. H a g e n enH. Rubens, Ann. d. P h y s . ( I V ) 1 1 , 8 7 3 , 1903. K . F . L i n d m a n, Z. techn. Phys. 19, 158, 1938. E. M a x w e l l , M.I.T. Rad. Lab. Rep. 854, 1946. J. S m i d t , Appl. sei. Res. B 1, 127, 1948. R. B e c k e r u . W . D 6 r i n g, Ferromagnetismus. J. Springer, 234, 1939. K.J. Sixtus a.L. Tonks, Phys. Rev. 37,930, 1931;39,357, 1932; 42,419, 1932;43,70,931, 1933. K. J. S i x t u s , Probleme der technischen Magnetisierungskurve, 14, 15, 1938. H.J. van Leeuwen, Physica ! ! , 3 5 , 1944. C. K i t t e l , Phys. Rev. 70,281, 1946. H.J. van Leeuwen, Appl. sci. Rev. B 1 , 135, 1948. J . L . S n o e k, New developments in ferromagnetic materials, ElsyPubl. C 63, 1947. A. W i e b e r d i n k , Nature 162, 527, 1948. R. K r o n i g , Nature 162, 527, 1948.
A p r i l 1949
MAGNETIC BEHAVIOUR OF FERROMAGNETICS AT H I G H F R E Q U E N C I E S b y H. J. VAN L E E U W E N Laboratorium voor Technische Physica der Technische Hogesehool, Delft
In the last few years we h a v e tried in the l a b o r a t o r y of Delft to get some f u r t h e r i n f o r m a t i o n on the b e h a v i o u r of the ferromagnetics in the high f r e q u e n c y region. A l r e a d y in 1903 it was k n o w n f r o m the e x p e r i m e n t s of H a g e n and R u b e n s 1) on infrared reflection t h a t in this w a v e l e n g t h region (30 #) the p e r m e a b i l i t y of iron was 1. E x p e r i m e n t s of L i n d m a n 3) in 1938 with d a m p e d oscillations on a single iron wire and on a s y s t e m of two parallel wires gave a fall of the p e r m e a b i l i t y from 100 to 10 in the region b e t w e e n 50 and 15 cm. M a x w e 11 3) m e a s u r e d a p e r m e a b i l i t y in a wave guide for a w a v e l e n g t h of 1,25 cm in 1946. Mr. J. S m i d t of our l a b o r a t o r y , now in Bandoeng, m e a s u r e d the p e r m e a b i l i t y of a pure iron wire in the region b e t w e e n 83 and 52 cm and found a v e r y steep descent from 60 to 1 at 63 cm wavelength 4). T h e m e t h o d of m e a s u r e m e n t was not new, b u t it was not used before at so small wavelengths t h a t the p e r m e a b i l i t y decreased till 1. I t consisted in the main in the measuring of the difference of w a v e l e n g t h of u n d a m p e d oscillations on two concentric L e c h e r systems, one of which had a f e r r o m a g n e t i c wire as an inner conductor, the o t h e r one a non f e r r o m a g n e t i c wire.The w a v e l e n g t h measured on the f e r r o m a g n e t i c line is smaller t h a n on the non ferromagnetic and the r e s o n a n t peaks b r o a d e r on the first t h a n on the last. T h e difference of w a v e l e n g t h is a measure of the inner self-inductance of the ferromagnetic wire and so of its permeability. T h e steep descent of the p e r m e a b i l i t y of the iron wire sets in at a wavelength, which depends on the t e m p e r a t u r e and the foregoing heat t r e a t m e n t of the wire, as is shown in fig. 1. I t occurs in the region where B e c k e r and D 6 r i n g predicted the descent on their t h e o r y 5). This t h e o r y - -
2 5 8
I
259
MAGNETIC BEHAVIOUR OF FERROMAGNETICS
was based on the idea, t h a t the front of a Weiss d o m a i n in travelling t h r o u g h the metal, gives rise to F o u c a u 1 t currents which in their t u r n exercise a force on the front opposite to its m o t i o n and p r o p o r t i o n a l to its velocity. T h e front m o t i o n has, on account of this force, a smaller elongation at higher frequencies t h a n at lower. This would be the cause of the decrease of the p e r m e a b i l i t y with increasing frequency. T h o u g h we know from the e x p e r i m e n t s of S i x t u s and T o n k s 6) on materials with large Weiss domains t h a t t.heir [J tn e . m . u 80-
60-
3
AT ABOUT-40"C.
4
AT ABOU'i" 15°C
~,
.
o
,--o
-
| °
AT ABOUT 20°C, ANNEALEDAT 800 "C AND COOLEDIN A MA6NETIC FIELD ,o-
_
_ :_
,:
,_v0_,_v'_c_
°
)t |
.
AT ABOUT 20=C,ANNEALED AT 800% 20:- .o-..o.---o-..--o=
o
I
I
BO
75
~', 70
I
65
60
:
I
55
cm
Fig. 1. T h e p e r m e a b i l i t y of iron as a f u n c t i o n of t h e w a v e - l e n g t h in v a c u o .
fronts do not t r a v e l as flat planes, as was supposed b y B e c k e r and D 5 r i n g and t h a t the viscous force on the front, which limits the elongation, depends on the form of the front ~), the basis of the t h e o r y of B e c k e r and D 6 r i n g is essentially certain and correct, and the region where the decrease of the p e r m e a b i l i t y is predicted b y t h e m also. I t depends however on the dimensions of the Weiss domains and the form of the fronts. Of the dimensions only the order of m a g n i t u d e is known, the form of the front is unknown, from which the conclusion m u s t be derived t h a t the form of the curve which gives the p e r m e a b i l i t y as a function of the f r e q u e n c y rests indeterminate. S m i d t gives the curve t h a t is best a d a p t e d to his m e a s u r e m e n t s if all the domains of Weiss should have the same length. T h e experim e n t a l curve is m u c h steeper t h a n this theoretical curve.
H. ]. V A N LEEUWEN
260
If the domains of Weiss should have different lengths, the discrepance should be still larger. There exists another theoretical approach to the problem of the dispersion of the permeability, made by K i t t e 1 s). It faces quite another aspect of the phenomenon. While B e c k e r and D 6r i n g fix their attention to the measure in which the front motion can develop at different wavelengths, they neglect a possible influence of discontinuities by passing from one of the domains of Weiss to another. In the fine wires of the experiments the front travels perpendicular to the length of the wire and tangential in the cross-section of the wire. K i t t e 1 discusses the circumstance that at these high frequencies the depth of penetration in the wire is of the same order of magnitude as the dimensions of a domain of Weiss. ~. in e.m.u.. 102 _ _ • %%m
_MEASURED CURVE AT ABOUT 45"C
~'~',,.,..THEORETICAL CURVE FROM ~C,, BECKER AND DORING
40
~¢,,_THEORE TICAL CURVE I OF KITTEL
4
i
'108
i
~'
: ',
t0 9
,
t
I
i /
1040 Hz
Fig. 2. T h e e x p e r i m e n t a l and t w o t h e o r e t i c a l c u r v e s g i v i n g t h e p e r m e a b i l i t y of iron as a f u n c t i o n of t h e f r e q u e n c y .
While B e c k e r and D 6 r i n g assume the magnetization to follow the field in each point of a radiusvector of the cross-section independently of other points, K i t t e 1 assumes the motion of points in different depth beneath the surface, but all in the first Weiss domain to be identical and for all frequencies this motion and thus the magnetization the same for the same field strength. He omits also the Foucault-damping, which is a shortcoming of his
MAGNETIC BEHAVIOUR OF FERROMAGNETICS
261
theory 9). That the magnetization is in his theory independent of the depth beneath the surface alters the usual equations for the skin effect and in order to get the same value for the irrfpedance of the wire as from the usual equations, from which the permeability is derived, he has to make the permeability a definite function of the frequency with only one parameter, the length of a domain of Weiss. With this parameter adapted to the measurements the theoretical curve of K i t t e 1 also is much less steep than the experimental one (fig. 2). A third explanation of high frequency dispersion of permeability has been given by S n o e k 10), who takes a handing over of the spin direction from spin to spin in the layer between two Weiss domains as the basis of the phenomenon. This theory too expects a ,~ IQ
cm
,,~
fO-
temp..17°C+-1 J
5-
0
?0
Cm
- - ¢ ~ . .
k
0
5-
fOF i g . 3. T h e w a v e l e n g t h d i f f e r e n c e o n t w o l i n e s w i t h r e s p e c t i v i l y a c o p p e r a n d i r o n - n i c k e l wire a s a n i n n e r c o n d u c t o r a s a f u n c t i o n of t h e w a v e l e n g t h in v a c u o .
fall of the permeability in the din-region of wavelengths. Because the explanation of B e c k e r and D 6 r i n g depends directly on the coefficient of conduction of the material, that of K i t t e 1 only indirectly and that of S n o e k not, we planned measurements with
262
H.J. V A N L E E U W E N
materials of a lower coefficient of conduction which is the case for alloys. The expectation was that the fall of the permeability could be more or less displaced. It was therefore t h a t Mr. A. W i e b e r d i n k 11) has measured nearly in the same way as mentioned before the difference of wavelength on lines with a copper and an iron-nickel central wire. Beyond expectation the difference of wavelength offered the picture of fig. 3. ~1.
col
.
.10-
,<
.t
I +5.
. . . . . ,
is
8o Ext~rhqJ
5,
Curve Pfagnehzohon
Z 7rr
-10'
l 1
None fO0 0ersted A/let
/ I
8'5 !/ temp. f7 ° C
20OC 20oC
~'o: Wavelength on Cu . • Ni-Fe (35-65)
/
I 9'o
II
cm
I
~
I
~ ~
[ i
II ~,1
Fig. 4. T h e w a v e l e n g t h d i f f e r e n c e on t w o lines w i t h r e s p e c t i v i l y a c o p p e r a n d a n i r o n - n i c k e l wire as a n i n n e r c o n d u c t o r as a f u n c t i o n of t h e w a v e l e n g t h in v a c u o , c u r v e I w i t h o u t s t a t i c m a g n e t i c field, c u r v e I I in a s t a t i c m a g n e t i c field of I00 O p a r a l l e l t o t h e wire, c u r v e I I I a f t e r t h e s t a t i c m a g n e t i c field of curve II has been removed.
The fact that the wavelength on the ferromagnetic line is in a small interval between 86 and 88 cm larger than on the non-ferromagnetic one means a negative and even a complex value of the permeability, corresponding with an extreme broadening of the resonant peaks. It will not be until the resistance of the wire has been measured too, which is not yet the case, that the value of the permeabilit.y itself can be deduced.
MAGNETIC B E H A V I O U R OF FERROMAGNETICS
263
On proposal of Prof. K r o n i g who gave the theoretical interpretation of the phenomenon 12) the same measurements were done by Mr. W i e b e r d i n k in a static magnetic field of 100 0 in the direction of the wire. The peculiar phenomenon of fig. 3 is thereby obviously disturbed, as is to be seen from fig. 4. The fall of the permeability of iron, which is steeper than on the proposed theories might correspond to an effect of a similar kind, which is not fully developed.
REFERENCES 1) 2) 3) 4) 5) 6)
7) 8) 9) 10) 11) 12)
E. H a g e n enH. Rubens, Ann. d. P h y s . ( I V ) 1 1 , 8 7 3 , 1903. K . F . L i n d m a n, Z. techn. Phys. 19, 158, 1938. E. M a x w e l l , M.I.T. Rad. Lab. Rep. 854, 1946. J. S m i d t , Appl. sei. Res. B 1, 127, 1948. R. B e c k e r u . W . D 6 r i n g, Ferromagnetismus. J. Springer, 234, 1939. K.J. Sixtus a.L. Tonks, Phys. Rev. 37,930, 1931;39,357, 1932; 42,419, 1932;43,70,931, 1933. K. J. S i x t u s , Probleme der technischen Magnetisierungskurve, 14, 15, 1938. H.J. van Leeuwen, Physica ! ! , 3 5 , 1944. C. K i t t e l , Phys. Rev. 70,281, 1946. H.J. van Leeuwen, Appl. sci. Rev. B 1 , 135, 1948. J . L . S n o e k, New developments in ferromagnetic materials, ElsyPubl. C 63, 1947. A. W i e b e r d i n k , Nature 162, 527, 1948. R. K r o n i g , Nature 162, 527, 1948.