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The magnetostriction of aluminum substituted nickel ferrites
I. Phys. Chcm. Solids Vol. 41. pp. 925-928 Pergamon Press Ltd., 1980 Printed in Great Britain
THE
MAGNETOSTRICTION OF ALUMINUM NICKEL FERRITES
SUBSTITUTED
P. J. M. VAN DER STRATEN Department
of Chemistry,
Eindhoven University
of Technology, Eindhoven, The Netherlands
and TH. KWAAITAAL and W. M. M. M. VAN DEN
Department
of Electrical Engineering, Eindhoven University (Received
I2 October
1979; accepted
EIJNDEN
of Technology, 7 December
Eindhoven, The Netherlands 1979)
is determined for Abstract-The room temperature magnetostriction constant A ,t, of the system NiFez_,AI,04 0
INTRODUCTION
In a recent article[ I] it has been shown that in monocrystalline Ni(Fe, Alb04 films, grown in tension by liquid phase epitaxy (LPE) on (Ill)-ZnGa,O, substrates, a stress-induced uniaxial anisotropy is present. This uniaxial anisotropy K,” results from the stress u in the film and from the magnetostriction constant A,, , of the film: K.” = - 3/2A,,,u. In order to calculate Ku” for films with different values of u we must know At,, as a function of the aluminum content of NiFe,_.Al,O,. So far only data on hloo and A,, , for pure NiFe,04 [2] are known from literature, while only qualitative information is available for the aluminum substituted nickel ferrites as regards the saturation magnetostriction constants [3]. In this article the room-temperature magnetostriction constant A,, , is determined as a function of the aluminum content in NiFe,_,AI,O, single crystals, using an interferometric method[4]. THEGROWHOFNICKELFERRITE-ALUMINATESINGLE CRYSTALS
Single crystals were grown from a PbO-BzO, flux by slow cooling. The melt composition 1 PbO-0.32 B,O,0.23 NiFez_,Al,Oa (moles), contains considerably more BzO, than the one used by Rybal’skaya et a1.[5] for the growth of pure NiFezOc that is 1 PbO-0.07 B20&23 NiFe204 (moles). The saturation temperature of this melt is reported to be 1250°C. We have chosen a higher BzOj content in order to reduce the evaporation of PbO and to diminish the corrosion of the platinum crucibles. We have used melts with compositions of x = 0, 0.15, 0.30 and 0.45 in 25 ml platinum crucibles. By cooling these melts from 1300 to 800°C at a rate of 2”C/hr and after leaching away flux residues in a mixture of hot dilute acetic acid and nitric acid, octahedrally shaped crystals up to 4 mm in dimension along the edge (x = 0) were obtained. Since the dimensions of the crystals obtained from the melt with x = 0.45 were less than 1 mm we have also grown crystals from a PbzPzO, flux using the same growth procedure. A melt composition of 0.4 PbzPzOr PCSVol. 41. No.
9-A
0.6 NiFe,.4Alo60., was used. Single crystals with dimensions up to 3 mm were obtained. ANALYSISOFTHESINGLECRYSTALS
The composition, lattice constant and saturation magnetization of the nickel ferrite-aluminate crystals were analysed. The results are presented in Table I. The compositions were determined by electron microprobe analyses. The concentrations were calculated with the aid of a computing program using the measured intensities of pure Ni, Fe, Al and Pb as standards. On comparing the results thus obtained with sintered internal standards of NiFe,_,Al,04 with x = 0.0, 0.5 and I .O the degree of accuracy was found to be better than 0.02 atoms per formula unit. The crystals proved to be stoichiometric nickel ferritealuminate within the accuracy limit. The aluminum concentrations in the crystals are lower than expected from the A120,:Fez0, ratio in the melt. The largest deviation is found for the Pb2P,0, flux. The A1203:FezOx ratio in the melt is about twice as high as the ratio in the crystals. The Pb content of the crystals proved to be lower than 0.02 atoms per formula unit. Microprobe analyses showed no concentration gradients in the crystals, despite the fact that the AlzOx:Fe203 ratio of the melt increases during growth. A decrease of the segregation coefficient for Al, defined as the mole ratio kAl= ]Al/(Al+ F41cr,,taI/W/W + Wlm,lt with decreasing temperature and/or diffusion of Fe and Al in the growing crystal can explain the absence of concentration gradients. The lattice constants of the single crystals were determined by X-ray diffractometry, measuring the Bragg angles either from planes parallel to the (111) face, and giving a surface lattice constant, or from powdered samples, giving a bulk lattice constant. Using a SiOz standard the obtained accuracy was about 0.2pm (0.002 A). 925
926
P.J. M. VAN
DER STRATEN el al.
Table I. Data on comoosition. lattice constant and magnetization for NiFe, 1AI,O, single crystals grown from a PbO-BzO1flux (A-D) and from a Pb2PZ0, flux (E)
A
0
0
B
0.15
0.09
c
0.30
0.22
D
0.45
0.38
0.60
0.29
E
I
Whereas the bulk and surface lattice constants for pure NiFe>O, are about the same, the surface lattice constants for the nickel-ferrite aluminates are up to 0.4 pm higher than the bulk lattice constants. This means that the Al content on the surface can be up to 0.03 atoms per formula unit higher than in the bulk although a slightly higher Pb content on the surface can also be responsible for this. From literature it is known that Pb incorporation is higher at lower temperatures [6], resulting in a Pb concentration gradient in the crystals. The relation between Al content and bulk lattice constants is plotted in Fig. 1. The straight line represents the Vegard relation in the NiFez_,AI,Od system[7]. The saturation magnetization M, of the crystals was determined using a Faraday balance. The variation in M, within a batch of single crystals grown from the same melt is of the same order as the accuracy obtained, this being about ? 5 x 10’ Am-’ ( ‘- 5 emu/cm’). The relation between MS and Al content is plotted in Fig. 2. The results are somewhat lower than the values calculated from the data of Blasse and Gorter[S] using X-ray densities. For pure NiFezO, we find 2.29x IO'Am-' (229 emu/cm3), which is very close to the 2.35 x IO5Am-’ (235 emu/cm’), obtained for LPE-grown nickel ferrite films on (11I)-MgO substrates. For polycrystalline NiFe204, sintered at 1250°C in oxygen, we find 2.65 x 10’ Am-’ (265 emu/cm’) a little higher than reported by Blasse and Gorter, that is 2.58 x 10’ Am--’ (258 emu/cm’).
F c 0.832
0
0.10 atoms
020 Al
0.30 per
0.40
form&-tnnt
Fig. 1. Bulk lattice constant vs aluminium content x in NiFe?_,Al,Oa. Straight line represents results of Schulkes and Blasse [7].
0
0.10 a20 0.30 2
atoms
Al
per
formula
x unit
Fig. 2. Saturation magnetization vs aluminium content x in
NiFez_xAl,04.Straight line represents results of Blasse and Garter [8]. MAGNETOSTRICTION MEASUREMENTS
The standard strain gauge techniques used in magnetostriction measurements are not applicable here, owing to the small dimensions of the ferrite crystals available. An unconventional magnetostriction-measuring system[4] was used for the striction measurements. As this system is treated in detail in Ref. [4], we confine ourselves to a brief description of the principle. In this method the sample is placed in a magnetic field Ho, which is slowly increased from 0 to 2 Tesla. A small a.c. modulating field H, of the order of 100Am-' is superposed on this field. The frequency f, of the modulating field is of the order of 1OOHz.Two strictions will arise out of these fields, a slowly changing A, corresponding to the field Ho, and an a.c. striction A, corresponding to the field H,. This situation is presented in Figs. 3(a and b). We now measure A, as a function of Ho with constant amplitude of HI and it is easy to show that AI/HI equals the derivative of the ho-Ho curve so that, upon integration of this quantity with respect to H,, the original curve is restored. The measurement of A, is done with a Michelson interferometer. Its sensitivity is stabilized against temperature changes and acoustic vibrations, except those with the frequency f, of the modulating field. This results in a sensitivity to vibrational amplitudes of frequency f, as low as 10-‘4m. This is sufficient to determine magnetostriction in very small samples. We must, however, be careful when interpreting the
The magnetostriction
of aluminum substituted nickel ferrites
921
II. = {I t N(/& - l)}Hi
where N is the demagnetizing factor and pcL,is the relative magnetic permeability. This permeability however, depends on the kind of field and is a function of the fieldstrength. For d.c. fields we must use the normal permeability, defined as (9) CL,,,= (l/p,,)(B,/H,) and for a.c. fields the reversible permeability plr = ( I//.L~) x (&/HI)B~.H~, where p,, = 47r x lo-’ Vs A-’ m-’ is the permeability of free space. It is obvious that the depenFig. 3. (a) The arrangement of the sample between the poles of the electromagnet and the modulation coils. (b) The relation dence of CL,., and CL,.,, on the field must be known to perform between the striction A, and AI and the fields H,,and H,, the conversion and the proper integration. In the case of respectively. our samples the demagnetizing factor was about 0.2 and the dependence of CL,., and CL,,,on the field was taken from strictions measured by this method. Three problems can Smit and Wijn[ 1I]. A numerical estimate of the correction arise. as well as a comparison with the literature value for x = 0 (i) As we measure the change in dimensions going show that the correction was less than about 10% in this from zero field upwards until the sample is saturated, and case. stating that the accompanying striction is identical with (iii) A third complication can arise from the homothe saturation striction h,(or Aloo,A,,,, etc. in the case of geneity of the magnetic fields. A material in an incrystals) we assume that the sample is in an ideal homogeneous field is subjected to a force. If the sample demagnetized state if it is put between the poles ‘of the is clamped at one end this force will cause a striction Ai magnet. We did, in fact, take some precautions to ensure of the material. An expression for this striction can be this assumption to be correct. The striction of the as derived from the force dF, in the x-direction, i.e. the grown crystals was determined the first time they were direction of the fields HI and Ho in Fig. 3(a) on a small put into the magnetic field. There was a tendency of the sample in a field H: measured striction to be lower at the second and third measurements. After the magnetic field Ho was run several times we tried to demagnetize the samples with an a.c. field that slowly decreased in amplitude. This brought the measured striction back to a higher value but in general not to the value found from the first where du is the volume of the sample and x its susceptibility. From this it follows that the strain A(x) in a measurement. cylindrical sample with its axes along the x-direction and (ii) A second complication arises from the difference in clamped at one end at x = 0 is given by fieldstrength Hi in and H. outside the sample. The saturation striction can be calculated by integrating the curve of A, vs the internal field Hi,whereas the A(x)=~dH2x 2E ax measurements give the relation between A, and the external field H..The necessary conversion between internal and external fields is given by the relation (9) where E is Young’s modulus of the sample. Integration
Table 2. Results of magnetostriction measurements of NiFez_,Al,04 conpositionx
0.0
magnatostriction
mean
constant
23.3
AllI
value
of
hill
standard deviation
ill’ 21.9
1.4
20.9
0.7
17.4
0.5
16.1
0.3
20.5 0.10
21.0 22.0 19.9 20.3 21.3
0.23
17.9 16.9
0.28
16.2 15.7 15.9 16.5
0
928
P. J. M. VAN DER STRATEN
et al. CONCLUSIONS
atoms Fig. 4. The saturation
Al
per
formula
magnetostriction A,, x in NiFez_,Al,04.
un!t
-X
, vs aluminium
content
over the whole sample (length I) leads to
A,,=u
2E
H
aH,+H,aH,,
* ax
ax
considering that the field H is a superposition of H,,and HI while only terms with the frequency of the modulating field are measured. We calculated this striction assuming field gradients of 10” and 103Am-* for (dH,/dx) and (aH,/dx) resp.; a value of the susceptibility of x = 100, the Young’s modulus value of IO” Nrn-‘, a sample length of I mm and a fieldstrength of Ho = 10" Am-’ and H, = IO“Am- ‘, and found a striction A = 1.2 x 10e9. It is obvious that this effect is negligible for our samples (CL,< IO@),but in materials with a high permeability and a low magnetostriction it could have an influence on the measurements. The results of the magnetostriction measurements are given in Table 2 and Fig. 4. The strictions given are the results on virgin materials. The mean value of hII, was calculated from the values found from different samples of each composition. The standard deviation (T is tabulated to give an impression of the spread of the results.
Homogeneous NiFer_,Al,04 single crystals (0 I ~5 0.38) were obtained from a PbO-B20-( and from a Pb,P,O, flux by slow cooling. The lattice constants, saturation magnetization and magnetostriction constant (A,, ,) decrease with increasing aluminum content. For pure NiFe204 very good agreement is found with the value ( - 21.6 x 10m6)given in literature [2]. This proves that laser interferometry is well suited for magnetostriction measurements in the case of small ferro- and ferrimagnetic crystals. In most experiments it is possible to cope with the complications arising from sample shape, demagnetized state and from the two kinds of permeability. Since the decrease of AllI is less than that of M.,with increasing aluminum content, monocrystalline (I I I)NiFe2_,Al,04 films grown in tension upon a suitable substrate [I] will have a stress-induced anisotropy energy exceeding the demagnetization energy. By using an external magnetic field perpendicular to the film plane, stable isolated cylindrical domains (bubbles) can be generated in these films. Details on this subject will be published separately.
REFERENCES R., Mat Res. Bull. 13, 1143 (1978). Smith A. B. and Jones R. V.. J. Appl. Phys. 37, 100 (1%6). Bleil D. F. and Butz A. R., Phys. Rev. 94, 1440 (1954). Kwaaitaal Th., .I. Mugn. Mugn. Mat 6, 290 (1977). Rybal’skaya E. V., Petrov T. G. and Titova A. G., SOIL Phys. Crystallog. 15, 958 (1971). Davies J. E., Giess E. A., Kuptsis J. D. and Reuter W., J. Cryst. Growth 36, I91 (1976). Schulkes J. A. and Blasse G.. J. Phys. Chem. Solids 24, 1651 (1%3). Blasse G. and Gorter E. W., J. Phys. Sot. Japan 17, Suppl. BI. 176 (1%2). Bozorth R. M., Ferromagnelism, 6th Edn., p. 6. van Nostrand, New York (1956). Kwaaitaal Th., Thesis, Eindhoven University of Technology (1980).
I. van der Straten 2. 3. 4. 5. 6. 7. 8. 9. IO.
P. J. M. and Metselaar
THE
MAGNETOSTRICTION OF ALUMINUM NICKEL FERRITES
SUBSTITUTED
P. J. M. VAN DER STRATEN Department
of Chemistry,
Eindhoven University
of Technology, Eindhoven, The Netherlands
and TH. KWAAITAAL and W. M. M. M. VAN DEN
Department
of Electrical Engineering, Eindhoven University (Received
I2 October
1979; accepted
EIJNDEN
of Technology, 7 December
Eindhoven, The Netherlands 1979)
is determined for Abstract-The room temperature magnetostriction constant A ,t, of the system NiFez_,AI,04 0
INTRODUCTION
In a recent article[ I] it has been shown that in monocrystalline Ni(Fe, Alb04 films, grown in tension by liquid phase epitaxy (LPE) on (Ill)-ZnGa,O, substrates, a stress-induced uniaxial anisotropy is present. This uniaxial anisotropy K,” results from the stress u in the film and from the magnetostriction constant A,, , of the film: K.” = - 3/2A,,,u. In order to calculate Ku” for films with different values of u we must know At,, as a function of the aluminum content of NiFe,_.Al,O,. So far only data on hloo and A,, , for pure NiFe,04 [2] are known from literature, while only qualitative information is available for the aluminum substituted nickel ferrites as regards the saturation magnetostriction constants [3]. In this article the room-temperature magnetostriction constant A,, , is determined as a function of the aluminum content in NiFe,_,AI,O, single crystals, using an interferometric method[4]. THEGROWHOFNICKELFERRITE-ALUMINATESINGLE CRYSTALS
Single crystals were grown from a PbO-BzO, flux by slow cooling. The melt composition 1 PbO-0.32 B,O,0.23 NiFez_,Al,Oa (moles), contains considerably more BzO, than the one used by Rybal’skaya et a1.[5] for the growth of pure NiFezOc that is 1 PbO-0.07 B20&23 NiFe204 (moles). The saturation temperature of this melt is reported to be 1250°C. We have chosen a higher BzOj content in order to reduce the evaporation of PbO and to diminish the corrosion of the platinum crucibles. We have used melts with compositions of x = 0, 0.15, 0.30 and 0.45 in 25 ml platinum crucibles. By cooling these melts from 1300 to 800°C at a rate of 2”C/hr and after leaching away flux residues in a mixture of hot dilute acetic acid and nitric acid, octahedrally shaped crystals up to 4 mm in dimension along the edge (x = 0) were obtained. Since the dimensions of the crystals obtained from the melt with x = 0.45 were less than 1 mm we have also grown crystals from a PbzPzO, flux using the same growth procedure. A melt composition of 0.4 PbzPzOr PCSVol. 41. No.
9-A
0.6 NiFe,.4Alo60., was used. Single crystals with dimensions up to 3 mm were obtained. ANALYSISOFTHESINGLECRYSTALS
The composition, lattice constant and saturation magnetization of the nickel ferrite-aluminate crystals were analysed. The results are presented in Table I. The compositions were determined by electron microprobe analyses. The concentrations were calculated with the aid of a computing program using the measured intensities of pure Ni, Fe, Al and Pb as standards. On comparing the results thus obtained with sintered internal standards of NiFe,_,Al,04 with x = 0.0, 0.5 and I .O the degree of accuracy was found to be better than 0.02 atoms per formula unit. The crystals proved to be stoichiometric nickel ferritealuminate within the accuracy limit. The aluminum concentrations in the crystals are lower than expected from the A120,:Fez0, ratio in the melt. The largest deviation is found for the Pb2P,0, flux. The A1203:FezOx ratio in the melt is about twice as high as the ratio in the crystals. The Pb content of the crystals proved to be lower than 0.02 atoms per formula unit. Microprobe analyses showed no concentration gradients in the crystals, despite the fact that the AlzOx:Fe203 ratio of the melt increases during growth. A decrease of the segregation coefficient for Al, defined as the mole ratio kAl= ]Al/(Al+ F41cr,,taI/W/W + Wlm,lt with decreasing temperature and/or diffusion of Fe and Al in the growing crystal can explain the absence of concentration gradients. The lattice constants of the single crystals were determined by X-ray diffractometry, measuring the Bragg angles either from planes parallel to the (111) face, and giving a surface lattice constant, or from powdered samples, giving a bulk lattice constant. Using a SiOz standard the obtained accuracy was about 0.2pm (0.002 A). 925
926
P.J. M. VAN
DER STRATEN el al.
Table I. Data on comoosition. lattice constant and magnetization for NiFe, 1AI,O, single crystals grown from a PbO-BzO1flux (A-D) and from a Pb2PZ0, flux (E)
A
0
0
B
0.15
0.09
c
0.30
0.22
D
0.45
0.38
0.60
0.29
E
I
Whereas the bulk and surface lattice constants for pure NiFe>O, are about the same, the surface lattice constants for the nickel-ferrite aluminates are up to 0.4 pm higher than the bulk lattice constants. This means that the Al content on the surface can be up to 0.03 atoms per formula unit higher than in the bulk although a slightly higher Pb content on the surface can also be responsible for this. From literature it is known that Pb incorporation is higher at lower temperatures [6], resulting in a Pb concentration gradient in the crystals. The relation between Al content and bulk lattice constants is plotted in Fig. 1. The straight line represents the Vegard relation in the NiFez_,AI,Od system[7]. The saturation magnetization M, of the crystals was determined using a Faraday balance. The variation in M, within a batch of single crystals grown from the same melt is of the same order as the accuracy obtained, this being about ? 5 x 10’ Am-’ ( ‘- 5 emu/cm’). The relation between MS and Al content is plotted in Fig. 2. The results are somewhat lower than the values calculated from the data of Blasse and Gorter[S] using X-ray densities. For pure NiFezO, we find 2.29x IO'Am-' (229 emu/cm3), which is very close to the 2.35 x IO5Am-’ (235 emu/cm’), obtained for LPE-grown nickel ferrite films on (11I)-MgO substrates. For polycrystalline NiFe204, sintered at 1250°C in oxygen, we find 2.65 x 10’ Am-’ (265 emu/cm’) a little higher than reported by Blasse and Gorter, that is 2.58 x 10’ Am--’ (258 emu/cm’).
F c 0.832
0
0.10 atoms
020 Al
0.30 per
0.40
form&-tnnt
Fig. 1. Bulk lattice constant vs aluminium content x in NiFe?_,Al,Oa. Straight line represents results of Schulkes and Blasse [7].
0
0.10 a20 0.30 2
atoms
Al
per
formula
x unit
Fig. 2. Saturation magnetization vs aluminium content x in
NiFez_xAl,04.Straight line represents results of Blasse and Garter [8]. MAGNETOSTRICTION MEASUREMENTS
The standard strain gauge techniques used in magnetostriction measurements are not applicable here, owing to the small dimensions of the ferrite crystals available. An unconventional magnetostriction-measuring system[4] was used for the striction measurements. As this system is treated in detail in Ref. [4], we confine ourselves to a brief description of the principle. In this method the sample is placed in a magnetic field Ho, which is slowly increased from 0 to 2 Tesla. A small a.c. modulating field H, of the order of 100Am-' is superposed on this field. The frequency f, of the modulating field is of the order of 1OOHz.Two strictions will arise out of these fields, a slowly changing A, corresponding to the field Ho, and an a.c. striction A, corresponding to the field H,. This situation is presented in Figs. 3(a and b). We now measure A, as a function of Ho with constant amplitude of HI and it is easy to show that AI/HI equals the derivative of the ho-Ho curve so that, upon integration of this quantity with respect to H,, the original curve is restored. The measurement of A, is done with a Michelson interferometer. Its sensitivity is stabilized against temperature changes and acoustic vibrations, except those with the frequency f, of the modulating field. This results in a sensitivity to vibrational amplitudes of frequency f, as low as 10-‘4m. This is sufficient to determine magnetostriction in very small samples. We must, however, be careful when interpreting the
The magnetostriction
of aluminum substituted nickel ferrites
921
II. = {I t N(/& - l)}Hi
where N is the demagnetizing factor and pcL,is the relative magnetic permeability. This permeability however, depends on the kind of field and is a function of the fieldstrength. For d.c. fields we must use the normal permeability, defined as (9) CL,,,= (l/p,,)(B,/H,) and for a.c. fields the reversible permeability plr = ( I//.L~) x (&/HI)B~.H~, where p,, = 47r x lo-’ Vs A-’ m-’ is the permeability of free space. It is obvious that the depenFig. 3. (a) The arrangement of the sample between the poles of the electromagnet and the modulation coils. (b) The relation dence of CL,., and CL,.,, on the field must be known to perform between the striction A, and AI and the fields H,,and H,, the conversion and the proper integration. In the case of respectively. our samples the demagnetizing factor was about 0.2 and the dependence of CL,., and CL,,,on the field was taken from strictions measured by this method. Three problems can Smit and Wijn[ 1I]. A numerical estimate of the correction arise. as well as a comparison with the literature value for x = 0 (i) As we measure the change in dimensions going show that the correction was less than about 10% in this from zero field upwards until the sample is saturated, and case. stating that the accompanying striction is identical with (iii) A third complication can arise from the homothe saturation striction h,(or Aloo,A,,,, etc. in the case of geneity of the magnetic fields. A material in an incrystals) we assume that the sample is in an ideal homogeneous field is subjected to a force. If the sample demagnetized state if it is put between the poles ‘of the is clamped at one end this force will cause a striction Ai magnet. We did, in fact, take some precautions to ensure of the material. An expression for this striction can be this assumption to be correct. The striction of the as derived from the force dF, in the x-direction, i.e. the grown crystals was determined the first time they were direction of the fields HI and Ho in Fig. 3(a) on a small put into the magnetic field. There was a tendency of the sample in a field H: measured striction to be lower at the second and third measurements. After the magnetic field Ho was run several times we tried to demagnetize the samples with an a.c. field that slowly decreased in amplitude. This brought the measured striction back to a higher value but in general not to the value found from the first where du is the volume of the sample and x its susceptibility. From this it follows that the strain A(x) in a measurement. cylindrical sample with its axes along the x-direction and (ii) A second complication arises from the difference in clamped at one end at x = 0 is given by fieldstrength Hi in and H. outside the sample. The saturation striction can be calculated by integrating the curve of A, vs the internal field Hi,whereas the A(x)=~dH2x 2E ax measurements give the relation between A, and the external field H..The necessary conversion between internal and external fields is given by the relation (9) where E is Young’s modulus of the sample. Integration
Table 2. Results of magnetostriction measurements of NiFez_,Al,04 conpositionx
0.0
magnatostriction
mean
constant
23.3
AllI
value
of
hill
standard deviation
ill’ 21.9
1.4
20.9
0.7
17.4
0.5
16.1
0.3
20.5 0.10
21.0 22.0 19.9 20.3 21.3
0.23
17.9 16.9
0.28
16.2 15.7 15.9 16.5
0
928
P. J. M. VAN DER STRATEN
et al. CONCLUSIONS
atoms Fig. 4. The saturation
Al
per
formula
magnetostriction A,, x in NiFez_,Al,04.
un!t
-X
, vs aluminium
content
over the whole sample (length I) leads to
A,,=u
2E
H
aH,+H,aH,,
* ax
ax
considering that the field H is a superposition of H,,and HI while only terms with the frequency of the modulating field are measured. We calculated this striction assuming field gradients of 10” and 103Am-* for (dH,/dx) and (aH,/dx) resp.; a value of the susceptibility of x = 100, the Young’s modulus value of IO” Nrn-‘, a sample length of I mm and a fieldstrength of Ho = 10" Am-’ and H, = IO“Am- ‘, and found a striction A = 1.2 x 10e9. It is obvious that this effect is negligible for our samples (CL,< IO@),but in materials with a high permeability and a low magnetostriction it could have an influence on the measurements. The results of the magnetostriction measurements are given in Table 2 and Fig. 4. The strictions given are the results on virgin materials. The mean value of hII, was calculated from the values found from different samples of each composition. The standard deviation (T is tabulated to give an impression of the spread of the results.
Homogeneous NiFer_,Al,04 single crystals (0 I ~5 0.38) were obtained from a PbO-B20-( and from a Pb,P,O, flux by slow cooling. The lattice constants, saturation magnetization and magnetostriction constant (A,, ,) decrease with increasing aluminum content. For pure NiFe204 very good agreement is found with the value ( - 21.6 x 10m6)given in literature [2]. This proves that laser interferometry is well suited for magnetostriction measurements in the case of small ferro- and ferrimagnetic crystals. In most experiments it is possible to cope with the complications arising from sample shape, demagnetized state and from the two kinds of permeability. Since the decrease of AllI is less than that of M.,with increasing aluminum content, monocrystalline (I I I)NiFe2_,Al,04 films grown in tension upon a suitable substrate [I] will have a stress-induced anisotropy energy exceeding the demagnetization energy. By using an external magnetic field perpendicular to the film plane, stable isolated cylindrical domains (bubbles) can be generated in these films. Details on this subject will be published separately.
REFERENCES R., Mat Res. Bull. 13, 1143 (1978). Smith A. B. and Jones R. V.. J. Appl. Phys. 37, 100 (1%6). Bleil D. F. and Butz A. R., Phys. Rev. 94, 1440 (1954). Kwaaitaal Th., .I. Mugn. Mugn. Mat 6, 290 (1977). Rybal’skaya E. V., Petrov T. G. and Titova A. G., SOIL Phys. Crystallog. 15, 958 (1971). Davies J. E., Giess E. A., Kuptsis J. D. and Reuter W., J. Cryst. Growth 36, I91 (1976). Schulkes J. A. and Blasse G.. J. Phys. Chem. Solids 24, 1651 (1%3). Blasse G. and Gorter E. W., J. Phys. Sot. Japan 17, Suppl. BI. 176 (1%2). Bozorth R. M., Ferromagnelism, 6th Edn., p. 6. van Nostrand, New York (1956). Kwaaitaal Th., Thesis, Eindhoven University of Technology (1980).
I. van der Straten 2. 3. 4. 5. 6. 7. 8. 9. IO.
P. J. M. and Metselaar