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Ferro-acoustic resonance in nickel single crystals
Journal of Magnetism and Magnetic Materials 2 (1976) 296-299 0 North-Holland Publishing Company
FERRO-ACOUSTIC RESONANCE IN NICKEL SINGLE CRYSTALS G. DIETZ, HJ. L6SCH and G. WIELP6TZ II. Physikalisches Institut der Universitlt zu Kiiln, W. Germany Received 6 June 1975
Peaks of ultrasound absorption as a function of magnetic induction are observed under conditions similar to those for ferromagnetic resonance. The peaks are attributed to a resonance phenomenon which must be different from the ferroacoustic resonance in insulators.
1. Introduction and experimental results.
2. Discussion of the results
The absorption coefficient of ultrasound in ferromagnetic materials usually decreases with increasing average magnetization to a value at or below magnetic saturation and does not alter in a further increasing magnetizing field [l] . Few authors have reported on an absorption maximum larger than the value measured in the demagnetized state [2,3]. We have investigated the absorption of longitudinal and transversal sound waves between 5 and 100 MHz, (in some cases up to 150 MHz) in nickel single crystals using the pulse echo technique. The samples have been cylinders with axes parallel to UOO),(1 lo), or (111) and coercivities smaller than 0.1 Oe. They have been magnetized by an electromagnet perpendicular to their axes. With the aid of special pole pieces the spatial fluctuations of the magnetic induction inside the samples has been kept below 7% of the average value. Figures 1,2,3 show typical results of the logarithmic decrement versus magnetic induction. No peak was observed if an easy direction or the vibration direction of the sound was parallel to the mag netizing field (fig. 3). In some cases the maxima were so large that we were not able to measure the logarithmic decrement. The peaks are shifted to higher intensities of magnetic inductions if the temperature is lowered (fe. 4), but they remain at the same place if the frequency is varied (figs. 1,2).
The peak is most pronounced, if the field is parallel to a (1OO)direction and perpendicular to the vibration
1
oj
02
03
0.L
05
f
magnetic induction 0 -
Fig. 1. Magnetic part of the absorption coefTicient of transversnl sound waves in a nickel single crystal versus magnetic induction. Propagation direction [ 1011, polarization [lOO] , direction of the external field [ 0011.
297
G. Dietz et al./Ferro-acoustic resonance in nickel single crystals
L23 K -r-*r,
db I 30.1ci2..
x\ L13K O-4,
11,
= 6Mttz = 15MHz = 25MHz = 35MHz
x
0 d _
G 2
::
1\ 1%
x
5.
9 ,”
0.1 0.2 0.3 0.4 OS 0.6 0.7 0.6 magnetic
0.1
0.5 T 0.6 a2 a3 0.L magnetic induction 8 -
Fig. 2. Magnetic part of the absorption coefficient of longitudinal sound waves in a nickel single crystal versus magnetic induction. Propagation direction [ 1011, direction of external field [OOl].
direction of the sound wave. This configuration is similar to that used in ferromagnetic resonance. The alternating field is produced by the sound wave as a result of magnetoelastic coupling. The effective steady field flz which satisfies the resonance condition
x 5MHz 0 13.3 MHz I 25 MHz
L.. T ;d 0
3.. 6-x= -2.b--_b=
:
I x-x-q_ --bz&b %, -q:x, ‘h
1..
0.1
a2
OJ
magnetic
-+ W&
35 MHz
.
L+ a5 T CL6 induction B --+
0.4
Fig. 3. Magnetic part of the absorption coefficient of transversal sound waves in a nickel single crystal versus magnetic induction. Propagation direction [ 1011, polarization [ lOO], direction of external field [ 1001.
induction B _
Fig. 4. Magnetic part of the absorption coefficient of longitudinal sound waves in a nickel single crystal versus magnetic induction at different temperatures. Frequency 5 MHz, prop agation direction (1011, direction of the external field [OOl] .
ares = r*Hg does not only arise from the field of the electromagnet but also from demagnetizing fields due to the shape of the sample, to remaining inhomogenities of the average magnetization, and to the spatial variation of the phase of its precession about an equilibrium orientation. According to possible configurations of such fields one estimates a few oersteds or less for the resonance field q:. On the other hand the crystal anisotropy in nickel is equivalent to a field of about 170 Oe corresponding to a resonance frequency of more than 500 MHz (natural resonance). The resonance frequency, as Artman [4] has calculated, is first lowered by an external field parallel to a (1OO)direction in nickel, goes to zero at saturation, and increases again with further increasing field. Thus the resonance frequency should meet our sound frequency twice. But the curves of Artman depend strongly on the angle between effective field and easy direction. Because of the remaining inhomogenity and a possible misorientation of the sample of 2” during preparation and mounting between the pole pieces the resonance frequencies of different parts of the sample are different and do not reach zero or reach it at different values of the external field. Thus the two resonance peaks are broadened resulting in one ob-
298
G. Dietz et al./Ferrosmustic
servable peak. We should have found it near saturation [4]. Because of the uncertainty (mentioned above on how to calculate the effective field) we can not yet discuss the deviation of our measurements (fii. 4) from this calculated condition. If the external field is parallel to an easy direction it intensifies the effective steady field and thus the resonance frequency increases from the outset and does not coincide with our sound frequency. Since we interpret the absorption maxima as shown in figs. 1 and 2 as resonance phenomena, their positions should be dependent on frequency in contradiction with our measurements. The reason is that in our frequency region the effective resonance field is small in comparison with the magnetic induction at the maxima and so are possible shifts, which cannot be resolved by our apparatus in the present state. The shift of the maxima as function of temperature (fig. 4) can be qualitatively understood. The field necessary to turn the magnetization from an easy into a hard direction increases with decreasing temperature because the value of the constant K1 of the crystalline anisotropy becomes greater. Therefore the maxima appear at greater values of magnetic induction. Let us now look at former experiments performed on a polycrystalline alloy of 65% nickel and 35% iron. After annealing at 700 K for 100 hours in a magnetic field of 20 Oe the samples had an easy axis. Provided *at the external field is perpendicular to the easy axis the ultrasound absorption had a pronounced maximum below saturation, if the vibration direction of the sound wave was parallel to the easy axis. It was reduced by nearly a factor l/a, if vibration and field made an angle of 45’, and it was missed: if they were parallel with each other. This comes about because only the vibration component at right angle to the field maintains the precessions of the magnetic moments about the steady field. The average easy direction in this material is composed by the easy directions of the crystallites, the orientations of which are distributed over a certain region. Therefore the maxima in absorption are broader than those in nickel single crystals with well-defined easy directions [2] . One effect observed in polycrystalline magneticab ly isotrop material [2,5] can be attributed to ferracoustic resonance, too. There are no maxima in the
resonance in nickel single crystals
absorption coefficients as functions of magnetization, but the damping is greatest if the vibration direction is perpendicular, and smallest if it is parallel to the external field. The difference between these two curves shows a maximum below saturation. It is very broad because there are no preferred orientations of the crystal&es and their easy directions.
3. Final remarks According to our investigations three effects contribute to the coupling between an ultrasound wave and the magnetic structure: 1. a pressure acting on the domain walls and a torque acting on the magnetization due to the modulation of the density of magnetoelastic energy by the sound wave [6] corresponding to calculations of Mason and D8ring [7], 2. an additional pressure on the domain walls by the following mechanism; dislocations are caused to move by the sound wave and because of their coupling with domain walls they cause viirations of domain walls or parts of then [8], 3. a ferro-acoustic resonance. The absorption peaks in nickel cannot be attributed to an interaction between sound waves and spin waves, as can be done for the ferro-acoustic resonance in insulators [9]. In nickel there are no spin waves with the wavelength of the sound of about 1 mm at 5 MHz. Owing to eddy currents the skin depth of magnetic oscillations is smaller than l/20 mm. Further, more quantitative investigations must show whether damping by eddy currents is sufficient to describe the steep maxima in figs. 1 and 2.
Acknowledgements The measurements have been supported by Deutsche Forschungsgemeinschaft. The authors wish to thank Dr. H. Seiger for some of the experimental results and helpful discussions.
References (11 G.
Dietz and I. Jaumann, Z. Angew. Phys. 14 (1962) 222.
G. Dietz et al./Ferro-acoustic resonance in nickel single crystals
PI H. Db’ker and G. Dietz, Z. Angew. Phys. 32 (1971) 143. [31V.F. Taborov, Sov. Phys.-Acoustics 10 (1964) 209; V.F. Taborov and V.F. Tarasov, IEEE Trans. Son. Ultrason. SU-14 (1967). I41J.O. Artman, Proc. IRE 44 (1956) 1284. 151G. Dietz, Z. Angew. Phys. 27 (1969) 82. (61H. Seiger and G. Dietz, Int. J. Magnetism 5 (1973) 5.
299
[71 W.P. Mason, Phys. Rev. 83 (1951) 683; Rev. Mod. Phys. 25 (1953) 136; W. D&ing, Ber. Oberhess. Ges. Natur- u. Heilk., Naturw. Abt. 29 (1958) 580. G. Dietz and N. Rasche, Phys. Stat. Sol. (a) 21 (1974) K13. B. Lathi and F. Oertle, Phys. kondens. Materie 2 (1964) 99.
FERRO-ACOUSTIC RESONANCE IN NICKEL SINGLE CRYSTALS G. DIETZ, HJ. L6SCH and G. WIELP6TZ II. Physikalisches Institut der Universitlt zu Kiiln, W. Germany Received 6 June 1975
Peaks of ultrasound absorption as a function of magnetic induction are observed under conditions similar to those for ferromagnetic resonance. The peaks are attributed to a resonance phenomenon which must be different from the ferroacoustic resonance in insulators.
1. Introduction and experimental results.
2. Discussion of the results
The absorption coefficient of ultrasound in ferromagnetic materials usually decreases with increasing average magnetization to a value at or below magnetic saturation and does not alter in a further increasing magnetizing field [l] . Few authors have reported on an absorption maximum larger than the value measured in the demagnetized state [2,3]. We have investigated the absorption of longitudinal and transversal sound waves between 5 and 100 MHz, (in some cases up to 150 MHz) in nickel single crystals using the pulse echo technique. The samples have been cylinders with axes parallel to UOO),(1 lo), or (111) and coercivities smaller than 0.1 Oe. They have been magnetized by an electromagnet perpendicular to their axes. With the aid of special pole pieces the spatial fluctuations of the magnetic induction inside the samples has been kept below 7% of the average value. Figures 1,2,3 show typical results of the logarithmic decrement versus magnetic induction. No peak was observed if an easy direction or the vibration direction of the sound was parallel to the mag netizing field (fig. 3). In some cases the maxima were so large that we were not able to measure the logarithmic decrement. The peaks are shifted to higher intensities of magnetic inductions if the temperature is lowered (fe. 4), but they remain at the same place if the frequency is varied (figs. 1,2).
The peak is most pronounced, if the field is parallel to a (1OO)direction and perpendicular to the vibration
1
oj
02
03
0.L
05
f
magnetic induction 0 -
Fig. 1. Magnetic part of the absorption coefTicient of transversnl sound waves in a nickel single crystal versus magnetic induction. Propagation direction [ 1011, polarization [lOO] , direction of the external field [ 0011.
297
G. Dietz et al./Ferro-acoustic resonance in nickel single crystals
L23 K -r-*r,
db I 30.1ci2..
x\ L13K O-4,
11,
= 6Mttz = 15MHz = 25MHz = 35MHz
x
0 d _
G 2
::
1\ 1%
x
5.
9 ,”
0.1 0.2 0.3 0.4 OS 0.6 0.7 0.6 magnetic
0.1
0.5 T 0.6 a2 a3 0.L magnetic induction 8 -
Fig. 2. Magnetic part of the absorption coefficient of longitudinal sound waves in a nickel single crystal versus magnetic induction. Propagation direction [ 1011, direction of external field [OOl].
direction of the sound wave. This configuration is similar to that used in ferromagnetic resonance. The alternating field is produced by the sound wave as a result of magnetoelastic coupling. The effective steady field flz which satisfies the resonance condition
x 5MHz 0 13.3 MHz I 25 MHz
L.. T ;d 0
3.. 6-x= -2.b--_b=
:
I x-x-q_ --bz&b %, -q:x, ‘h
1..
0.1
a2
OJ
magnetic
-+ W&
35 MHz
.
L+ a5 T CL6 induction B --+
0.4
Fig. 3. Magnetic part of the absorption coefficient of transversal sound waves in a nickel single crystal versus magnetic induction. Propagation direction [ 1011, polarization [ lOO], direction of external field [ 1001.
induction B _
Fig. 4. Magnetic part of the absorption coefficient of longitudinal sound waves in a nickel single crystal versus magnetic induction at different temperatures. Frequency 5 MHz, prop agation direction (1011, direction of the external field [OOl] .
ares = r*Hg does not only arise from the field of the electromagnet but also from demagnetizing fields due to the shape of the sample, to remaining inhomogenities of the average magnetization, and to the spatial variation of the phase of its precession about an equilibrium orientation. According to possible configurations of such fields one estimates a few oersteds or less for the resonance field q:. On the other hand the crystal anisotropy in nickel is equivalent to a field of about 170 Oe corresponding to a resonance frequency of more than 500 MHz (natural resonance). The resonance frequency, as Artman [4] has calculated, is first lowered by an external field parallel to a (1OO)direction in nickel, goes to zero at saturation, and increases again with further increasing field. Thus the resonance frequency should meet our sound frequency twice. But the curves of Artman depend strongly on the angle between effective field and easy direction. Because of the remaining inhomogenity and a possible misorientation of the sample of 2” during preparation and mounting between the pole pieces the resonance frequencies of different parts of the sample are different and do not reach zero or reach it at different values of the external field. Thus the two resonance peaks are broadened resulting in one ob-
298
G. Dietz et al./Ferrosmustic
servable peak. We should have found it near saturation [4]. Because of the uncertainty (mentioned above on how to calculate the effective field) we can not yet discuss the deviation of our measurements (fii. 4) from this calculated condition. If the external field is parallel to an easy direction it intensifies the effective steady field and thus the resonance frequency increases from the outset and does not coincide with our sound frequency. Since we interpret the absorption maxima as shown in figs. 1 and 2 as resonance phenomena, their positions should be dependent on frequency in contradiction with our measurements. The reason is that in our frequency region the effective resonance field is small in comparison with the magnetic induction at the maxima and so are possible shifts, which cannot be resolved by our apparatus in the present state. The shift of the maxima as function of temperature (fig. 4) can be qualitatively understood. The field necessary to turn the magnetization from an easy into a hard direction increases with decreasing temperature because the value of the constant K1 of the crystalline anisotropy becomes greater. Therefore the maxima appear at greater values of magnetic induction. Let us now look at former experiments performed on a polycrystalline alloy of 65% nickel and 35% iron. After annealing at 700 K for 100 hours in a magnetic field of 20 Oe the samples had an easy axis. Provided *at the external field is perpendicular to the easy axis the ultrasound absorption had a pronounced maximum below saturation, if the vibration direction of the sound wave was parallel to the easy axis. It was reduced by nearly a factor l/a, if vibration and field made an angle of 45’, and it was missed: if they were parallel with each other. This comes about because only the vibration component at right angle to the field maintains the precessions of the magnetic moments about the steady field. The average easy direction in this material is composed by the easy directions of the crystallites, the orientations of which are distributed over a certain region. Therefore the maxima in absorption are broader than those in nickel single crystals with well-defined easy directions [2] . One effect observed in polycrystalline magneticab ly isotrop material [2,5] can be attributed to ferracoustic resonance, too. There are no maxima in the
resonance in nickel single crystals
absorption coefficients as functions of magnetization, but the damping is greatest if the vibration direction is perpendicular, and smallest if it is parallel to the external field. The difference between these two curves shows a maximum below saturation. It is very broad because there are no preferred orientations of the crystal&es and their easy directions.
3. Final remarks According to our investigations three effects contribute to the coupling between an ultrasound wave and the magnetic structure: 1. a pressure acting on the domain walls and a torque acting on the magnetization due to the modulation of the density of magnetoelastic energy by the sound wave [6] corresponding to calculations of Mason and D8ring [7], 2. an additional pressure on the domain walls by the following mechanism; dislocations are caused to move by the sound wave and because of their coupling with domain walls they cause viirations of domain walls or parts of then [8], 3. a ferro-acoustic resonance. The absorption peaks in nickel cannot be attributed to an interaction between sound waves and spin waves, as can be done for the ferro-acoustic resonance in insulators [9]. In nickel there are no spin waves with the wavelength of the sound of about 1 mm at 5 MHz. Owing to eddy currents the skin depth of magnetic oscillations is smaller than l/20 mm. Further, more quantitative investigations must show whether damping by eddy currents is sufficient to describe the steep maxima in figs. 1 and 2.
Acknowledgements The measurements have been supported by Deutsche Forschungsgemeinschaft. The authors wish to thank Dr. H. Seiger for some of the experimental results and helpful discussions.
References (11 G.
Dietz and I. Jaumann, Z. Angew. Phys. 14 (1962) 222.
G. Dietz et al./Ferro-acoustic resonance in nickel single crystals
PI H. Db’ker and G. Dietz, Z. Angew. Phys. 32 (1971) 143. [31V.F. Taborov, Sov. Phys.-Acoustics 10 (1964) 209; V.F. Taborov and V.F. Tarasov, IEEE Trans. Son. Ultrason. SU-14 (1967). I41J.O. Artman, Proc. IRE 44 (1956) 1284. 151G. Dietz, Z. Angew. Phys. 27 (1969) 82. (61H. Seiger and G. Dietz, Int. J. Magnetism 5 (1973) 5.
299
[71 W.P. Mason, Phys. Rev. 83 (1951) 683; Rev. Mod. Phys. 25 (1953) 136; W. D&ing, Ber. Oberhess. Ges. Natur- u. Heilk., Naturw. Abt. 29 (1958) 580. G. Dietz and N. Rasche, Phys. Stat. Sol. (a) 21 (1974) K13. B. Lathi and F. Oertle, Phys. kondens. Materie 2 (1964) 99.