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The effect of stress bias on themagnetic and magnetomechanicalproperties of tbxho1-nfe1.9, 0 < x < 0.2Simon Charles Busbridge aa Department of Mathematical Sciences , University of Brighton ,Lewes Road, Moulsecoomb, Brighton, BN2 4GJPublished online: 07 Mar 2011.

To cite this article: Simon Charles Busbridge (1996) The effect of stress bias on the magnetic andmagnetomechanical properties of tbxho1-nfe1.9, 0 < x < 0.2, Ferroelectrics, 187:1, 141-152, DOI:10.1080/00150199608244850

To link to this article: http://dx.doi.org/10.1080/00150199608244850

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Ferruelecfrics. 1996. Vol. 187. pp. 141-152 Reprints available directly from the publisher Photocopying permitted by licensc only

8 1996 OPA (Overseas Publishers Association) Amsterdam B V. Published in The Netherlands

under license by Gordon and Breach Science Publishers SA

Printed in Malaysia

THE EFFECT OF STRESS BIAS ON THE MAGNETIC AND MAGNETOMECHANICAL PROPERTIES OF TbsHoI-sFel 9.0 < x < 0.2

SIMON CHARLES BUSBRIDGE Department of Mathematical Sciences, University of Brighton, Lewes Road, Moulsecoomb, Brighton, BN2 4GJ

(Received August 31. 1995)

Abstract The quasi-static magnetic and magnetomechanical properties of Tb,Hol.,Fel.9 have been studied at room temperature, as a function of stress bias, over the composition range 0 < x < 0.2, within which the easy axis changes between <loo> and < I 1 I> . In both easy axis regimes, the saturation strain increases with increasing stress bias, and the saturation magnetisation is independent of stress bias. In the <111> easy regime, the magnetisation process changes from a mixture of domain wall motions followed by rotation with no applied stress, to a single 180° wall motion followed by rotation when stress is applied. In the <loo> easy regime, applied stress levels < 20 MPa favour the movement of 90' walls and produce increased negative magnetostriction. Stress values > 70 MPa produce only positive magnetostriction. Unlike the < I 1 I > easy regime, the shape of the magnetisation curves is invariant under stress bias because the value of magnetisation at which rotation commences is constant.

I"

TbsHol-sFel.9 is potentially useful as a transducer material because TbFel.9 and HoFe1,9 both have large XI 1 1 magnetostriction constants and opposite signs for the K1 anisotropy constant1. Anisotropy compensation occurs at room temperature when x = 0.14. Development of this material for transducer applications has been overshadowed by advances in the properties of Tbo.27Dy0.7jFe1.9. principally because the saturation magnetostrain of Terfenol-D is approximately 2.5 times that of Tbo.l~Hoo.86Fel.9~. Interest in this material remains because K2 takes the opposite sign to that for Terfenol-D, allowing the possibility for a quaternary composition in which both the K 1 and K2 anisotropy constants are close to zero3.

In this paper the effect of stress bias, in the range 0 MPa to 80 MPa, on the magnetic and magnetomechanical properties for compositions of Tb,Hol-,Fe1,9 (0 < x < 0.2) at + 20 OC for which K I < 0 (and the easy direction of magnetisation is

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142 SIMON C BUSHIIICXE

< I 1

reported. The measurements are compared with calculations of the sum of the magnetoelastic and magnetocrystalline anisotropy energies (i.e. the total energy at remanence). Three dimensional plots obtained with a computer program, similar to that developed by Jiles', show this energy as a function of crystallographic direction as a height above a stereographic projection plane.

cum$, WdM, allows the magnetisation process to be investigated as a function of applied field and stress bias.

and for which K1> 0 (and the easy direction of magnetisation is <loo>), is

The model, together with use of the slope of the strain vs. magnetisation

Quasi-static measurements were made on rods of arc melted and vertical zone refined material using a standard 4" Newport electromagnet. The bias field, H, was measured with a Hall probe. The magnetostrain, A, was measured by a series of strain gauges placed at 60' intervals around the centre of the samples. This was essential to check and correct for any bending of the rods. The magnetisation, M, was measured with a two coil induction technique.

pneumatic aluminium cap sealed to one of the electromagnet pole pieces by means of "0" rings. An excess pressure of 0.81 Ib in-2 resulted in a stress of 1 MPa being applied to the ends of the sample. The demagnetising field at the centre of the sample was found to be less than 1% of the applied field, and was therefore not corrtcted for.

which x = 0.00,O. 10,0.13,0.15 and 0.20 directly onto an X-Y plotter. A chamber surrounding the sample maintained it at a constant temperature of + 20 O C .

Uniaxial stress was applied along the rod axis by means of a sturdy

Plots of L vs. H. M vs. H and A vs. M were made with compositions for

~ < 1 1 1 > ~

The dependence of 1 on H for Tb015H~.85Fe1.g (in which < I 1 I > is easy at room temperature) at different, constant, applied stress bias values is shown in Figure 1. The saturation magnetostrain, AM. increases monotonically with increasing stress bias. The strain at smaller values of H, however, initially shows an increase with increasing stress bias, but this trend reverses as the stress is further increased. This

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THE EFFECT OF STRESS BIAS ON THE PROPERTIES OF TbxHol-xFel,g 143

&kct is presumably due to the additional stress-induced anisotropy. Similar curves have been obtained for Tbo.1d-b0.87Fe1.9 and Tbo.2oHoo.mFe1.9.

0 50 loo 150 200 250 300 350 406 4m

HIM m-’

FIGURE 1 Strain vs. H for Tbo.1sHoo.8sFe1.9 under various applied stresses

FIGURE 2 M vs. H far Tbo.~sH~.8sFe1.9 under various applied stresses

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144 SIbNiN C RUSBRIDGE

The magnetisation vs. H curves for Tbo.lsHoo.~~Fe1.9, shown in Figure 2, change shape with changing stress bias, although the saturation magnetisation, Mat, is independent of applied stress. At high values of applied stress, the curves become divided into two regions: a straight, high slope region at low values of H and a variable slope region up to the saturation magnetisation at higher values of H. The two regions are separated by a "knee", which becomes more pronounced the higher the applied stress. There is a small amount of hysteresis (not shown in Figure 2) at values of H < 20 kA m-1, i.e. below the knee. Similar magnetisation curves were obtained for the other compositions whose easy direction of magnetisation is <11 I>.

<loo> Figure 3 shows the dependence of li on H, at different applied stress values, for HoFe1.9, which is <loo> easy. The appearance of negative magnetostriction before dUdH becomes positive is due to a combination of 90' wall motion and a negative value for hloo6. As the applied stress bias is increased, the amount of negative magnetostrain first increases, and then decreases, before being completely eliminated at high stress values

0 50 100 150 200 250 300 350 400 450

H ~ A m-'

FIGURE 3 Strain vs. H for HoFe1.9 under various applied stresses

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THE EFFECT OF STRESS BIAS ON THE PROPERTIES OF Tb,Hol-,Fel.g 145

The slope of the X vs. H curves when dWdH is positive decreases with increasing stress bias, as in the < I 1 I > easy regime. The value of k,t increases with increasing stress bias; this was verified by cooling Tbo. 1oHoo.goFel.g (which has less magnetocrystalline anisotropy than HoFe1.g) to below its spin re-orientation temperature (approximately - 40 "C).

The shape of the magnetisation curve, shown in figure 4, does not change with different values of stress bias. We have previously shown7 that the "knee" in this curve separates domain wall motion at small values of H from rotation at larger values of H.

m m 600.0

500.0

400.0

300.0

200.0

1 00.0

0.0 0 50 100 150 200 250 300 350 400 450

HkA rn-'

FIGURE 4 M vs. H for HoFe1.g irrespective of applied stress

In order to obtain a better understanding of the magnetisation process under stress bias, the free energy in the ideally demagnetisated state has been calculated as a function of crystallographic direction. The magnetostriction along the length of the rod is given by k:

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146 SIMON C R1JSRRIIX;E

where the zone refining process is assumed to perfectly produce <112> preferential orientation*, and I . m and n are the usual direction cosines. Since the stress bias is also applied along the rod length, the magnetoelastic energy, Erne, is given by:

where a is the applied stress. The magnetocrystalline anisotropy energy, Em, is given by:

Em = K, (I2m2 + m2n2 + n2I2) + K2 ( I2m2n2) (3)

The total contribution to the free energy, Etot, is the sum of Em and Emc.

projection plane looking down on [Ool]. Figures S(a)-(c) show the < I 1 I > easy regime, whilst figures S(d)-(e) show the <loo> easy regime. The following values were used in the calculationsl. In the < I 11> easy case, K1 = -100 kJ m-3, K2 = 10 kJ m-3, 511 1 = 500 ppm and Xloo = -50 ppm. In the <loo> easy case, K1 = 150 kJ m-3, K2 = 15 kJ m-3, 51 I 1 = 180 ppm and Xi00 = -60 ppm.

Figure 5 shows several plots of Etot as a height above the stereographic

-<Ill>- In figure 5(a) the energies are calculated for Q = 0. The minima occur for (I1 = Iml= In1 = 1/43, i.e. the expected eight 4 1 I > easy directions. The maxima occur in the <loo> directions. In figure 5(b). u has been increased to 50 MPa. The values of I, m and n at the minima are no longer equal to Il/d31. The minimum closest to [ I IT] has deepened whilst the minimum closest to [ 11 I ] is less pronounced. Further increases in o cause the minimum closest to [ I 1 I ] to vanish, followed by the minima closest to [TI 11 and []TI], with the minimum closest to [ 1 IT] continuing to deepen. At the same time, the maximum that was located at [OOI] increases and shifts along the [ IT01 zone in the general direction of 6. As Q tends to -, one minimum, located at I = m = -0.4405, n = 0.7823, and one maximum, located at I =

m = 0.5531. n = 0.6230. remain, as shown in figure 5(c). The angle between the minimum and the maximum is W', but the angle between the minimum and [ I 121 is 74'. Hence the application of stress does not produce alignment of the direction of magnetisation perpendicular to the rod axis, assuming that it is necessary to apply sufficient stress to reach the condition described by figure S(c) in order to exclude all other types of domains. The change in strain in figure 5(c) from the ideally

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THE EFFECT OF STRESS BIAS ON THE PROPERTIES OF Tb,HoI-,Fel 147

FIGURE 5 Free energy surfaces in cylindrical co-ordinates with H = 0 under varying applied stress biasses in each easy axis regime (a = 0 (a), 50 MPa (b), - (c); < I 11> easy; a = 0 (d), 300 MPa (e), - (0; <loo> easy}

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148 SIMON C UIJSRRIDGE

demagnetised state is -0.613 hi 1 1 . Hence the observed magnetostrain under stress bias increases in comparison to that without stress bias.

& 4 1 OO> F,av R ~ $ m g Figure 5(d) shows this case for o = 0. This time the minima occur in the expected six <loo> easy directions with the maxima being in 41 1 I>. In figure 5(e). o has been increased to 300 MPa. As in the <111> easy regime, the minima no longer lie exactly in the <loo> directions. The maximum nearest to [ l 1 11 has increased, whilst the minimum nearest to [IOO] has deepened. The minima in the [loo] and [OlO] directions vanish first with increasing o, followed by the minima in [TOO] and [OTO]. The minimum in [OOl] shifts along the [ IT01 zone away from the general direction of o, whilst the maximum in [ 1 1 11 direction remains in the same position. As s tends to infinity, the situation depicted in figure 5 ( f ) develops, with one minimum located at I = m = -0.4087, n = 0.816, (i.e. at [T2]) , and one maximum located 90' away at [ 1 1 I]. The change in strain in figure 5 ( f ) from the ideally demagnetised state is -0.666 A1 1 1

discussed in the next section. The large values of o required to bring about these changes in the model are

MAGTjEUSATION PROCESSES

The normalised strain vs. normalised magnetisation curves and their slopes can be used to infer information about particular domain wall motion and rotation processes responsible for the magnetisation of the specimen.

Figure 6 shows two such curves for Tb0.20Ho0.80Fe1.9, which is 41 11> easy. The solid line represents the following theoretical magnetisation curve from the ideally demagnetised state: 180' wall motion between domains with magnetisation in [TIT] and [ l l l ] , and [TTl] and [ I IT], followed by 71' wall motion between domains with magnetisation in [TIT] and [Tll], [ITTI and [ITl], and [IIT] and [11 I], followed by magnetic rotation simultaneously from [ITI], [TI 11 and [111] into [ 1121. This sequence of processes fits the experimental data quite well (an even better fit can be achieved if the 71 ' wall motion is mixed with some 109' wall motions, as the latter have a lower value of dli/dM) with zero stress, however the fit breaks down when stress is applied. This is because the easy directions of magnetisation have now become confined to [l IT] and [TTl]. The magnetisation

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I f I E EFFECT 01- STIIESS HIAS ON T H E PROPERTIES OF Tb,Hol-xl-el.c) 149

process is then likely to consist of some 180" wall motion followed by rotation over most of the 90" into [ 1 121

%I

1.2

1 l. ' .o I 0.9 0

0 0

0 ,,d 0 Experimental 0. I

0,

?' 0.4

0.2 model

0.1 0.0

0.3 ' Theoretical

_. . 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

M'Msat

FIGURE 6 Normalised strain vs. magnetisation for Tbo.2oHoo.goFe1.9

Figure 7 shows the equivalent curve for HoFel.9, which is <loo> easy At zero applied stress, the theoretical magnetisation process consisting of 180" wall motion between domains with magnetisation in [OOT] and [OOl], followed by 90'

wall motion between domains with magnetisation in PO01 and [OOl], and [OTO] and [OOI], followed by magnetic rotation from [loo], [OlO] and [OOI] to [112], produces a good fit to the experimental data. At low applied stress values, the amount of negative strain increases, suggesting that 90" wall motion is favoured. This is substantiated by the second theoretical magnetisation process, in which wall motion between domains with magnetisation in [IOO] and [OOI], and [OIO] and [OOI], which have larger Jdh/dMI values than the 90' wall motion used in the first

model, have been included. Rotation now appears to take place solely from [OOI] into [ 1121. At higher values of applied stress, the amount of negative magnetostrain decreases, and is completely eliminated when Q = 70 MPa. There is some experimental evidence to suggest that its sign reverses for Q > 70 MPa. It is not possible to account for the flat region of the h vs. M curve at high stress values

with just 180' wall motion, because this process alone cannot achieve a high enough magnetisation. However, if the easy directions of magnetisation are no

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150

0.7

0.6

0.5

0.4

0.2

0.1

SIMON C BIJSBRIDGE

- Points: experimental data

: Lines: theoretical plots

.

;

.

longer exacrly < I OO>, the amount of negative magnetostrain will decrease, and then change sign, because lIllll>> IIlool. This mechanism could radically alter the shape of the I vs. M curve without affecting the magnetisation process. Further evidence for this exists in the fact that the value of W S a t at which rotation commences is independent of applied stress, suggesting that the onset of rotation occurs at the same value of magnetisation. This is probably why the M vs. H curves do not change shape with applied stress bias.

0.7

0.6

0.5

0.4

0.2

0.1

- Points: experimental data

: Lines: theoretical plots

.

;

.

-0.0

-0.2 ' . . 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

sat

FIGURE 7 Nonnalised strain vs. magnetisation for HoFe1.9 under various values of applied stress bias

.

There is a considerable discrepancy between the values of applied stress required to affect the measured magnetic and magnetomechanical properties, and the values required to eliminate all but the dominant energy minimum in the model. This suggests that relatively small perturbations of the value of the free energy at the minima can have a considerable impact on the distribution of domains, both at remanence and with an applied field. This is perhaps not surprising, since an applied stress of 10 MPa represents a stored elastic energy of - 500 J m-3, which is comparable with the magnetostatic energy of a 180' domain pattern magnetised perpendicular to the rod axis. This energy, for a coplanar strip domain structure, is given by?

-0.0 .

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THE EFFECT OF STRESS BIAS ON THE PROPERTIES OF TbsHol-sFel.g 151

3 . 5 x 105 wM& E = d (4)

where w is the width of the domain strips and d the diameter of the rod. Using w =

10 pm and d = 7.5 mm gives E - 500 J m-3. Hence a redistribution of the population of the easy directions of magnetisation is possible without first requiring that any of these easy directions are eliminated.

CONCLUSIONS

The effect of uniaxial stress bias on the magnetic and magnetomechanical properties of TbsH~1-sFel.9 has been studied in both the < I 1 I > and <loo> easy regimes. The following conclusions may be drawn from this work: 1.

2.

3 .

4.

5 .

6.

In both easy axis regimes, the saturation strain increases with increasing stress bias, and the saturation magnetisation is independent of stress bias. In the <11 I> easy regime, the magnetisation process changes from a mixture of domain wall motions followed by rotation with no applied stress, to a single 180' wall motion followed by rotation when stress is applied. The magnetisation curve changes to reflect the changes in the magnetisation process In the <loo> easy regime, low values of applied stress favour the movement of 90' domain walls and produce increased negative magnetostrain. Higher stress values produce only positive magnetostrain. The magnetisation curve is invariant under applied stress because the value of M at which rotation commences is constant. The energy calculations predict that similar magnetomechanical behaviour will be observed in both easy axis regimes at very large applied stress values, irrespective of the value of the magnetocrystalline anisotropy constants. The predicted values of stress required to do this are higher than those observed, suggesting that it is not necessary to eliminate energy minima before domains with magnetisation directions in those minima are depopulated. When stress is applied, the easy directions of magnetisation no longer necessarily coincide with the crystallographic axes. The observed behaviour and interpretation of the magnetisation process based on the energy calculations is consistent with our previous use of the normalised strain vs. normalised magnetisation curves.

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152 SlblON C IWSRRIDGE

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1. A. E. Clark, Y. S . Na vv . Journal of Underwater A c o w ' , u, 109 (1977).

2. N. C. Koon, C. M. Williams and B. N. Das., -, JQQ, 173

(1991).

3. N. C. Koon and C. M. Williams, U. S. Navv Jour nal of Underwater A c o h , 22, 127 (1977).

5. A. R. Piercy, S. C. Busbridge and D. Kendall, L&gL&s, 76, 7006 (1 994).

6. R. Abbundi. A. E. Clark and N. C. Koon, J , A d . PhvL, 2, 1671 (1979)

7. S . C. Busbridgeand A. R. Piercy, -, 140-144, 817, (1995).

8. J. D. Verhoeven. E. D. Gibson, 0. D. McMasters and H. H. Baker, Met. TranS. A, m, 223 (1 987).

4. J. B. Thoelke and D. C. Jiles, M y . 104-10Z, 1453 (1992).

9. R. M. Bozorth, ' (D. Van Nostrad, 1959), p. 814.

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