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Invar behaviour in crystalline and amorphous alloys
Journal of Magnetism and Magnetic Materials 10 (1979) 120-125 o North-Holland Publishing Company
INVAR BEHAVIOUR
E.P. WOHLFARTH
IN CRYSTALLINE
AND AMORPHOUS ALLOYS
*
Abteilung fiir Physik, Ruhr-Universitiit, Bochum,
Fed. Rep. Germany
A review is given of the wide range of ferromagnetic materials which exhibit Invar characteristics. It is proposed to illustrate the thesis that Invar behaviour is very general among such materials and does not necessarily demand the following conditions to be satisfied: (1) presence of iron; (2) incipient antiferromagnetism; (3) heterogeneous alloying; (4) closeness to a martensite transformation. For most but not all of the materials discussed weak itinerant ferromagnetism accompanies and causes Invar characteristics. An example counter to this behaviour is FesPt. Here, Pettifor and Roy proposed as the origin of Invar behaviour a more general itinerant electron instability than is characteristic of weak itinerancy.
1. Introduction The present subject
matter
report
is deliberately
has only very recently
succinct
success in the last 10 years in almost all instances. Only recently have some cases arisen where Invar characteristics occur although the magnetism is strong or almost strong. This is the case for ordered Fe3Pt [6] and perhaps amorphous Fe-B alloys [7]. The number of such cases is thus still small, but this counter example to our original proposal [S] clearly demands an explanation. This was promptly provided in the wotk of Pettifor and Roy [8] who find the following, with specific reference to ordered Fe3Pt: Invar characteristics occur near an alloy concentration where the magnetic moment is unstable as a result of the Stoner criterion. For Fe,Pt this instability occurs very suddenly due to the particular disposition of the Fermi energies in the density of states curve. For weak itinerant ferromagnetism the instability is gradual and occurs where the Stoner criterion naturally demands the existence of a critical concentration for ferromagnetism. The latter effect is clearly more easily attainable since it is in essence a second order transition. The situation for Fe3Pt demands peculiarities in the density of states leading to a first order transition. This is a rarer event which recalls the phenomenon of itinerant electron metamagnetism which we had previously proposed for paramagnetic and antiferromagnetic materials [9]. Both cases are covered by the occurrence of an instability which has as its naturally occurring consequence the well-known phenomena of Invar, such as large high field susceptibilities, an accompanying large volume magnetostriction, etc. In neither case is any facet of
since the
been reviewed
by us [l-4]. It suffices, therefore, to present clearly the philosophical motivation for this report and to illustrate the experimental evidence behind this motivation as briefly as possible using some very recent data as well as some older ones. During the recent history of the Invar problem, there has arisen what we have previously described as a folklore [ 11: “The observed anomalies demand the presence of iron. Antiferromagnetism, already established in pure y-Fe, is as a result present also in fee Invar alloys, if only “incipiently”. The magnetization of the alloys is inhomogeneous due to a fluctuation of the alloy concentration. This effect is particularly marked near a martensitic phase transition.” While not denying that all or some of these effects may well sometimes accompany Invar anomalies we have long felt that these anomalies are much more general and may arise even where none of the facets of this folklore manifest themselves. A simple unique recipe for Invar anomalies was thus proposed (for the first time in ref. [5]) that weak itinerant ferromagnetism is a necessary and sufficient condition for the effect to occur. The proposal has had considerable * Permanent address: Department of Mathematics, Imperial College, London SW7, England. 120
E.P. I¢ohlfarth / Invar behaviour in crystalline and amorphous alloys the above mentioned folklore strictly necessary, although electronic effects of the present type can clearly contribute to a martensitic phase transition. The rest of this report lists crystalline and amorphous alloys showing Invar characteristics. This list is remarkable for its wide range showing that the phenomena are indeed very general. The report is to be read in the context of many of the other papers presented at this, the world's first international symposium on the Invar problem.
2. Annotated list of materials showing lnvar
phenomena 2.1. Fe-Ni, Fe-Pd, Fe-Pt Disordered alloys near 30-35% Ni, Pd, Pt show all properties associated with this phenomena [1,10], namely relatively low Curie temperatures and saturation magnetizations, large high field susceptibilities, relatively fiat magnetization versus temperature curves, high volume magnetostrictions, large negative linear thermal expansions at low temperature (giving low expansions at higher temperatures), large negative pressure derivatives of the Curie temperature and saturation magnetization and characteristic elastic phenomena, including negative AE effects at Te. Special attention should be paid to the following phenomena which have arisen after the main stream of data had been established: (1) The pressure derivatives of Tc of all three alloy series follow very well the relation dTc _ dP
rTc
--~c'
(1)
where K is the compressibility and ot a constant fully discussed, for example, in ref. [3]. The first term in eq. (1) is negligibly small here and a has the approximate value [11] 2050 K2/kbar. The coincidence of the pressure derivatives for all three alloy systems is surprising since a rigid band behaviour is not expected to be very good. (2) The Arrott plots (giving M 2 " H/M), described, for example, in ref. [12], have been found to be well behaved for Fe-Ni, i.e. to be parallel and linear in fields up to about 100 kOe [13]. At higher fields Hatta et al. [14] have found rather sudden positive deviations which might again be manifes.
121
tations of first order transitions driven by the band structure [8,9].
2.2. Fe3Pt The experimental data [6,15] show the following particularly interesting features: (1) The magnetization is high, about 2.7 It B per Fe atom, as already discussed. An interpretation of Invar behaviour in terms of an approach to an instability was introduced by Pettifor and Roy [8] as already mentioned. (2) The AE effect is unusually large [15], the observed relative change of the Young's modulus between the Curie point and low temperatures being as much as about 70%. The explanation given in ref. [8] is that the instability of the magnetization is also responsible for the observed magnetoelastic anomalies for this material. If a large change of magnetization at this instability implies a large AE effect the reverse should also be true. The above division of Invar materials into rare ones showing first order transitions and more common ones showing second order transitions implies that the latter should have small AE effects. This is indeed observed, for Ni-Fe Invar alloys have relatively small AE effects compared to FeaPt and, for example, for NiaA1 an even smaller anomally [16] was observed.
2.3. F e - N i - M n A series of measurements on this alloy system was reported by Nakamura et al. [17]. The following results are noteworthy: (1) The volume magnetostriction varies as T 2 as expected for weak itinerant ferromagnetism; this effect is even carried over into the antiferromagnetic phase! (2) The pressure dependence of Tc and the magnetization at low pressures is related to the high field susceptibility as given in ref. [23], based on the same model. (3) Another noteworthy result concerns the pressure dependence of Te at higher pressures where relation (1) gives Tc (P) = To(0) (1 - PIPe)1/2,
(2)
where Pc = T2e(O)/2ct. This parabolic law is sometimes observed [18] and sometimes not [19]. This result is surely rather less exciting than it is sometimes considered to be; it has been suggested [3,20] as arising from alloy heterogeneities which can also lead to deviations of Arrott plots from linearity.
E.P. Wohlfarth / Invar behaviourin crystallineand amorphous alloys
122
2.4. Ni-Pt Invar characteristics have been observed in many binary nickel alloys, but the N i - P t system is particularly interesting [21,22]. None of the features of the above-mentioned folklore are present, but weak itinerant ferromagnetism with a very homogeneous magnetization near a naturally occurring critical concentration, is clearly observed. All Invar characteristics listed above have been observed, with the exception of flat magnetization, temperature curves and of AE effects. The following results are particularly noteworthy: (1) The underlying theory predicts the following relationship between the saturation magnetization M, Curie temperature To, high field susceptibility ×, concentration c, its critical value Co and Stoner parameter i = IN(EF), where I is the interaction energy and N(EF) the density of states at the Fermi energy: M 2 ~ rc2
~
X -1
~
(I-
-
1) ~ (c - Co).
(3)
Pressure derivatives of M, T c and X agree well [21] with these predictions and enable those o f / and c o to be measured. (2) The magnetic contribution to the volume thermal expansion coefficient is [ 1 ] tiM
=
--
(2 KCM2/Tae) T,
(4)
where K is the compressibility and C the magnetoelastic coupling coefficient. Kortekaas and Franse [22] showed clearly that this result applies to N i - P t alloys and that this magnetic contribution vanishes very rapidly near the critical concentration Co = 42% Ni.
2.5. NisAI The several results for this material have already been summarized [1,3]. It suffices to note that the coefficient C, to which a in relation (1) is closely related, can be obtained from the measurements [22] and that even its temperature dependence, as T 2 [23], is observed. The values of a for N i - P t and for NiaA1, about 36 and 28 K2/kbar, are very similar as are almost all other properties of these two systems. The value of ct for ZrZn 2 is also of this order, namely about 39 K2/kbar [1 ]. This material has also been reviewed several times already [3]. Very recent measurements [24] of Arrott plots in fields higher than before show that up to 170 kOe these and the earlier results persist in
showing that the magnetization is very homogeneous in the specimens investigated. The similarity of this material to N i - P t and NiaAl is very striking; it shows clearly the very general nature of Invar behaviour in the absence of iron.
2.6. FexCOl_xTi This interesting alloy series with two critical concentrations x ~ 0.4 and 0.8 has been investigated for Invar characteristics by Hilscher et al. [25] and by Beille and Towfiq and Beille et al. [26]. A prediction [27] of a critical pressure in the sense of relation (2) was based on an assumed analogy with the Si containing materials (see below) leading to a value of a about 40 K2/kbar at x ~ 0.5 (again close to the above values) and a critical pressure about 45 kbar where all ferromagnetism ceases. The data of [25] and [26] agree well with this prediction. In ref. [26] it was found that for materials with x ~< 0.5 Arrott plots remain well behaved under pressure but that there is a different behaviour for x ~> 0.5 which is not clearly defined. Where the weak itinerant model applies, the pressure derivatives of M and Tc continue to follow approximately relations (3) in that d In M/dP
d ha Tc/dP. 2. Z FexCOl_xSi Invar and weak itinerant characteristics were observed by Bloch et al. [28]. It was found that there were many similarities with the Ti alloys. The two crit. ical concentrations are about x ~- 0.2 and 0.8. The Arrott plots for the alloy with x = 0.5 are closely linear and parallel. The ratio of magnetic moments above and below Tc fits into the scheme of ref. [2], and the moment at 0 K is 0.17/~B per formula unit. The logarithmic derivative of the saturation magnetization, - 1 . 2 6 × 10 -2 kbar -1 f o r x = 0.5, fits in with the observations for N i - P t [21,22] and ZrZn2 [3]. For neither the Ti nor the Si containing alloys are there as yet any other data of relevance, such as of thermal expansion.
2.8. Zr(Fez_xCox) 2 This material has been investigated for x = 0.68 0.74 by Franse et al. [29]. It was found that dTcldP
E.P. Wohlfarth / Invar behaviour in crystalline and amorphous alloys was large and negative but did not obey relation (1) with a constant value of a. It is thus not clear how far these materials are weakly itinerant and if the negative pressure derivative alone allows them to be Classified as Invar materials.
2.9. Y6 (Fe1-xMnx)23 This material was investigated in refs. [25] and [29]. It has two critical concentrations x = 0.4 and 0.7 between which no ferromagnetism has been observed. Although purely magnetic measurements point somewhat to weak itinerancy the pressure derivative of Tc is small and positive. The result may point to strong heterogeneities of the magnetization and indeed there is evidence for spin glass behaviour. The material recalls Sc3In for which we have also suggested overriding heterogeneity effects [2]. Neither seem, as a result, to be good Invars.
2.10. MnSi This material has been found to be a weak itinerant ferromagnet beyond a region of helical spin ordering which is removed in a field of 6 kOe [30]. The logarithmic pressure derivative o f - 1.15 × 10 -2 kbar -1 for the magnetization is close to the value for F e - C o Si [28] but it differs from that for T c, - 3 . 9 × 10 -2 kbar -1, as would be expected from eq. (3). Magnetic excitations in this system have been studied very successfully by Ishikawa et al. [31] who clearly describe it as weakly itinerant as a result.
2.11. Zro. 7Nbo.3Fe 2 This material was studied by Alfieri et al. and by Shiga [32] who found that a large volume magnetostriction and a large negative pressure derivative of T e (-3.3 K/kbar at Tc = 382 K, i.e. a = 1260 K2/kbar) accompanies flat magnetization, temperature curves, a T 2 dependence of the magnetization and a ratio of magnetic moments above and below Te in line with ref. [2]. This Laves phase compound is surely one of many showing the effects being discussed here, another example being ZrZn 2.
2.12. MnB This material was studied by Shigematsu et al. [33] who found that a large positive volume magnetostric-
123
tion occurs which varies as M 2 far below To. This result follows from the analysis of ref. [23], for example. The Curie temperature, 570 K, is rather high. However, many other borides of Mn, Fe and Co in the crystalline state have been suggested [2] to show weak itinerant ferromagnetism very readily. The table in this reference contains magnetic data for many of these materials.
2.13. M n - A s - S b Nakamura [10] makes full reference to early measurements of K/Sster and Braun [34] who observed the Invar characteristics of large positive volume magnetostriction and negative thermal expansion below To. Edwards and Bartel [35] since found that where solid solutions with second order transitions were investigated (As content between 0 and 90%) the pressure derivative of Tc is large and negative and obeys well relation (1) with a "" 1800 K2/kbar, i.e. close to the value for the classical Invar alloys containing iron. These authors use the present philosophy to discuss also the first order transition for the As rich compounds.
2.14. Rare earth-iron and cobalt compounds A wide range of these compounds has been investigated for magnetovolume effects and summaries of these measurements have been given by Buschow [36] and Buschow et al. [37] for iron and cobalt containing compounds. Jaakkola et al. [38] discussed their measurements on nickel compounds which are similar. The data tend to support very strikingly the theoretical formula (1): Compounds such as Gd2Col7 and YFe 2 which have high Tc values have small positive pressure derivatives of Tc while others, such as GdCo2 and Th2 Fe 17 have low Curie points and large negative pressure derivatives. The values of ol in eq. (1) are of the same order (about 1000 for the iron and 2000 K2/kbar for the cobalt compounds) as for F e - N i Invars. Only a brief report has been given [39] of the observed thermal expansion anomalies and the data have not yet been fully analyzed in terms of the coupling constants C. Buschow [36] also refers to recent work on hydrogen absorption in some of these materials. Those with a pronounced pressure dependence of T c should also mutatis mutandis have Curie temperatures sensitive to hydrogen (equivalent to a negative pressure [40]).
124
E.P. l¢ohlfarth /Invar behaviour in crystalline and amorphous alloys
2.15. Amorphous ferromagnets
Acknowledgements
Invar characteristics in amorphous ferromagnets are a natural consequence of weak itinerancy where this occurs [4]. It is therefore not surprising that such effects are now beginning to be observed, as first signalled by Mizoguchi [41 ]. More recently Invar behaviour has been investigated by Fukamichi et al. [ 4 2 44] and b y Hiroyoshi et al. [45]. The scattered data given by Mizoguchi concern the observed large negative pressure derivatives o f the Curie temperature and the saturation magnetization of Metglas-like materials such as ( F e - M n or Cr)aoP10Blo . Large positive volume magnetostrictions have been observed for amorphous F e - B alloys with a maximum effect at about 11.5% B. The data [44] were transformed (by means which we can not fully accept!) into a dTc/dP versus Tc curve which fitted well relation (1) with ct = 3500 K2/kbar. The Curie temperature corresponding to the above maximum effects is about 520 K and the saturation magnetization about 2.1/a 8 per iron atom. Hence, amorphous F e - B alloys m a y well form a second example of Invar behaviour where the phenomena are related to a more general type o f instability than is demanded by the presence o f a critical concentration, i.e. F e - B may be similar to Fe3Pt [8]. However, such critical concentrations Co are definitely present in some other amorphous alloys, in particular N i - Y (Co = 16.7% Y [46]), N i - P ( c o = 1 7 - 1 8 % P [ 4 7 ] ) a n d F e - G e (Co --~ 75% Ge [48]). Weak itinerancy has been established in all three systems and a negative pressure derivative o f the magnetization, in line with values for N i - P t , for F e - G e . There is thus a clear prediction of Invar behaviour in N i - Y , N i - P , F e - G e and other similar amorphous alloys.
I wish to acknowledge the many helpful communications I have had from M. Shimizu and also from Y. Nakamura, with whose review [10] the present briefer one has much in common.
3. Conclusion The annotated list and the philosophical background given here are intended to show that a simple discussion is possible of a wide range o f materials and phenomena. Where the philosophy appears weak this weakness is only deceptive and is in fact a sign o f the strength which must surely underlie any virile branch of science, with its ever changing and ever new aims and boundaries. The Invar problem appears clearly to be such a branch and thus fit and proper for further research, leading perhaps to a second symposium!
References [1 ] E.P. Wohlfarth, IEEE Trans. Magnetics 11 (1975) 1638. [2] E.P. Wohlfarth, J. Magn. Magn. Mat. 7 (1978) 113. [3] E.P. Wohlfarth, Honda Memorial Series 3 (1978) 327. [4] E.P. Wohlfarth, IEEE Trans. Magnetics 14 (1978) 933. [5] J. Mathon and E.P. Wotdfarth, Phys. Stat. Sol. 30 (1968) K131. [6] K. Sumiyama et al., J. Phys. F8 (1978) 1281. [7] K. Fukamichi et al., Solid State Commun. 23 (1977) 955; H. Hiroyoshi et al., Phys. Lett. 65A (1978) 163. [8] D.G. Pettifor and D.M. Roy, J. Phys. F8 (1978). [9] E.P. Wohlfarth and P. Rhodes, Phil. Mag. 7 (1962) 1817; E.P. Wohlfarth, Phys. Lett. 4 (1963) 83; D. Bloch et al., J. Phys. F5 (1975) 1217; D. Gignoux et al., Physica 86-88B (1977) 165. [10] Y. Nakamura, IEEE Trans. Magnetics 12 (1976) 278. [ 11 ] G.T. Dubovka and Y.G. Ponyatovsky, Phys. Metal. MetaUog. 33 (1972) 179. [12] E.P. Wohlfarth, Physica 91B (1977) 305. [13] O. Yamada et al., Physica 91B (1977) 298. [14] S. Hatta et al., J. Phys. Soc. Japan 43 (1977) 451. [15] G. Hausch, J. Phys. Soc. Japan 37 (1974) 819,824. [16] J.J.M. Franse et al., Physica 86-88B (1977) 317. [17] Y. Nakamura et al., J. Phys. Soc. Japan 30 (1971) 720, 729. [18] G.T. Dubovka et al., Phys. Stat. Sol. 32 (1975) 301. [19] L.C. Bartel et al., AlP Conf. Proc. 5 (1972) 482. [20] J.M. Leger and C. Susse-Loriers, Phys. Rev. B6 (1972) 4250. [21] H.L. Alberts et al., Phys. Rev. B9 (1974) 2233. [22] T.F.M. Kortekaas and J.J.M. Franse, J. Phys. F6 (1976) 1161. [23] E.P. Wohlfarth, J. Phys. C2 (1969) 68. [24] P.G. Mattocks and D. Melville, J. Phys. F8 (1978) 1291. [25] G. Hilscher et al., Physica 91B (1977) 170. [26] J. Beille and F. Towfiq, J. Phys. F8 (1978); J. Beille et al., Solid State Commun. 25 (1978) 57. [27] E.P. Wohlfarth, EPS Conf. Abstr. 1A (1975) 30. [28] D. Bloch et al., Phys. Lett. 51A (1975) 362; J. Beille et al., AlP Conf. Proc. 29 (1976) 123. [29] J.J.M. Franse et al., Physica 86-88B (1977) 283,319; AIP Conf. Proc. 29 (1976) 288. [30] D. Bloch et al., Phys. Lett. 51A (1975) 259. [31 ] Y. Ishikawa et al., Phys. Rev. B16 (1977) 4956. [32] M. Shiga, Phys. Lett. 53A (1975) 319; G.T. Alfieri et al., J. Appl. Phys. 40 (1969) 1322.
E.P. lCohlfarth / Invar behaviour in crystalline and amorphous alloys [33] T. Shigematsu et al., Phys. Lett. 53A (1975) 385. [34] W. KiSster and E. Braun, Ann. Phys. Leipzig 4 (1959) 66. [351 L.R. Edwards and L.C. Bartel, Phys. Rev. B5 (1972) 1064. [36] K.H.J. Buschow, Rept. Progr. Phys. 40 (1977) 1179. [37] K.H.J. Buschow et al., Physica 91B (1977) 261. [38] S. Jaakkola et al., Z. Phys. B20 (1975) 109. [39] M. Brouha et al., IEEE Trans. Magnetics 10 (1974) 182. [40] K.H.J. Buschow, private communication. [41] T. Mizoguchi, AlP Conf. Proc. 34 (1976) 286.
125
[42] K. Fukamichi et al., Solid State Commun. 23 (1977) 955. [43] K. Fukamichi et al., Sci. Rep. RITU 26A (1977) 225. [44] K. Fukamichi et al., Solid State Commun., 27 (1978) 405. [45] H. Hiroyoshi et al., Phys. Lett. 65A (1978) 163. [46] A. Li~nard and J.P. Rebouillat, J. Appl. Phys. 49 (1978) 1680. [47] A. Berrada et al., J. Phys. F8 (1978) 845. [48] Y. Endoh et al., Solid State Commun. 18 (1976) 735.
INVAR BEHAVIOUR
E.P. WOHLFARTH
IN CRYSTALLINE
AND AMORPHOUS ALLOYS
*
Abteilung fiir Physik, Ruhr-Universitiit, Bochum,
Fed. Rep. Germany
A review is given of the wide range of ferromagnetic materials which exhibit Invar characteristics. It is proposed to illustrate the thesis that Invar behaviour is very general among such materials and does not necessarily demand the following conditions to be satisfied: (1) presence of iron; (2) incipient antiferromagnetism; (3) heterogeneous alloying; (4) closeness to a martensite transformation. For most but not all of the materials discussed weak itinerant ferromagnetism accompanies and causes Invar characteristics. An example counter to this behaviour is FesPt. Here, Pettifor and Roy proposed as the origin of Invar behaviour a more general itinerant electron instability than is characteristic of weak itinerancy.
1. Introduction The present subject
matter
report
is deliberately
has only very recently
succinct
success in the last 10 years in almost all instances. Only recently have some cases arisen where Invar characteristics occur although the magnetism is strong or almost strong. This is the case for ordered Fe3Pt [6] and perhaps amorphous Fe-B alloys [7]. The number of such cases is thus still small, but this counter example to our original proposal [S] clearly demands an explanation. This was promptly provided in the wotk of Pettifor and Roy [8] who find the following, with specific reference to ordered Fe3Pt: Invar characteristics occur near an alloy concentration where the magnetic moment is unstable as a result of the Stoner criterion. For Fe,Pt this instability occurs very suddenly due to the particular disposition of the Fermi energies in the density of states curve. For weak itinerant ferromagnetism the instability is gradual and occurs where the Stoner criterion naturally demands the existence of a critical concentration for ferromagnetism. The latter effect is clearly more easily attainable since it is in essence a second order transition. The situation for Fe3Pt demands peculiarities in the density of states leading to a first order transition. This is a rarer event which recalls the phenomenon of itinerant electron metamagnetism which we had previously proposed for paramagnetic and antiferromagnetic materials [9]. Both cases are covered by the occurrence of an instability which has as its naturally occurring consequence the well-known phenomena of Invar, such as large high field susceptibilities, an accompanying large volume magnetostriction, etc. In neither case is any facet of
since the
been reviewed
by us [l-4]. It suffices, therefore, to present clearly the philosophical motivation for this report and to illustrate the experimental evidence behind this motivation as briefly as possible using some very recent data as well as some older ones. During the recent history of the Invar problem, there has arisen what we have previously described as a folklore [ 11: “The observed anomalies demand the presence of iron. Antiferromagnetism, already established in pure y-Fe, is as a result present also in fee Invar alloys, if only “incipiently”. The magnetization of the alloys is inhomogeneous due to a fluctuation of the alloy concentration. This effect is particularly marked near a martensitic phase transition.” While not denying that all or some of these effects may well sometimes accompany Invar anomalies we have long felt that these anomalies are much more general and may arise even where none of the facets of this folklore manifest themselves. A simple unique recipe for Invar anomalies was thus proposed (for the first time in ref. [5]) that weak itinerant ferromagnetism is a necessary and sufficient condition for the effect to occur. The proposal has had considerable * Permanent address: Department of Mathematics, Imperial College, London SW7, England. 120
E.P. I¢ohlfarth / Invar behaviour in crystalline and amorphous alloys the above mentioned folklore strictly necessary, although electronic effects of the present type can clearly contribute to a martensitic phase transition. The rest of this report lists crystalline and amorphous alloys showing Invar characteristics. This list is remarkable for its wide range showing that the phenomena are indeed very general. The report is to be read in the context of many of the other papers presented at this, the world's first international symposium on the Invar problem.
2. Annotated list of materials showing lnvar
phenomena 2.1. Fe-Ni, Fe-Pd, Fe-Pt Disordered alloys near 30-35% Ni, Pd, Pt show all properties associated with this phenomena [1,10], namely relatively low Curie temperatures and saturation magnetizations, large high field susceptibilities, relatively fiat magnetization versus temperature curves, high volume magnetostrictions, large negative linear thermal expansions at low temperature (giving low expansions at higher temperatures), large negative pressure derivatives of the Curie temperature and saturation magnetization and characteristic elastic phenomena, including negative AE effects at Te. Special attention should be paid to the following phenomena which have arisen after the main stream of data had been established: (1) The pressure derivatives of Tc of all three alloy series follow very well the relation dTc _ dP
rTc
--~c'
(1)
where K is the compressibility and ot a constant fully discussed, for example, in ref. [3]. The first term in eq. (1) is negligibly small here and a has the approximate value [11] 2050 K2/kbar. The coincidence of the pressure derivatives for all three alloy systems is surprising since a rigid band behaviour is not expected to be very good. (2) The Arrott plots (giving M 2 " H/M), described, for example, in ref. [12], have been found to be well behaved for Fe-Ni, i.e. to be parallel and linear in fields up to about 100 kOe [13]. At higher fields Hatta et al. [14] have found rather sudden positive deviations which might again be manifes.
121
tations of first order transitions driven by the band structure [8,9].
2.2. Fe3Pt The experimental data [6,15] show the following particularly interesting features: (1) The magnetization is high, about 2.7 It B per Fe atom, as already discussed. An interpretation of Invar behaviour in terms of an approach to an instability was introduced by Pettifor and Roy [8] as already mentioned. (2) The AE effect is unusually large [15], the observed relative change of the Young's modulus between the Curie point and low temperatures being as much as about 70%. The explanation given in ref. [8] is that the instability of the magnetization is also responsible for the observed magnetoelastic anomalies for this material. If a large change of magnetization at this instability implies a large AE effect the reverse should also be true. The above division of Invar materials into rare ones showing first order transitions and more common ones showing second order transitions implies that the latter should have small AE effects. This is indeed observed, for Ni-Fe Invar alloys have relatively small AE effects compared to FeaPt and, for example, for NiaA1 an even smaller anomally [16] was observed.
2.3. F e - N i - M n A series of measurements on this alloy system was reported by Nakamura et al. [17]. The following results are noteworthy: (1) The volume magnetostriction varies as T 2 as expected for weak itinerant ferromagnetism; this effect is even carried over into the antiferromagnetic phase! (2) The pressure dependence of Tc and the magnetization at low pressures is related to the high field susceptibility as given in ref. [23], based on the same model. (3) Another noteworthy result concerns the pressure dependence of Te at higher pressures where relation (1) gives Tc (P) = To(0) (1 - PIPe)1/2,
(2)
where Pc = T2e(O)/2ct. This parabolic law is sometimes observed [18] and sometimes not [19]. This result is surely rather less exciting than it is sometimes considered to be; it has been suggested [3,20] as arising from alloy heterogeneities which can also lead to deviations of Arrott plots from linearity.
E.P. Wohlfarth / Invar behaviourin crystallineand amorphous alloys
122
2.4. Ni-Pt Invar characteristics have been observed in many binary nickel alloys, but the N i - P t system is particularly interesting [21,22]. None of the features of the above-mentioned folklore are present, but weak itinerant ferromagnetism with a very homogeneous magnetization near a naturally occurring critical concentration, is clearly observed. All Invar characteristics listed above have been observed, with the exception of flat magnetization, temperature curves and of AE effects. The following results are particularly noteworthy: (1) The underlying theory predicts the following relationship between the saturation magnetization M, Curie temperature To, high field susceptibility ×, concentration c, its critical value Co and Stoner parameter i = IN(EF), where I is the interaction energy and N(EF) the density of states at the Fermi energy: M 2 ~ rc2
~
X -1
~
(I-
-
1) ~ (c - Co).
(3)
Pressure derivatives of M, T c and X agree well [21] with these predictions and enable those o f / and c o to be measured. (2) The magnetic contribution to the volume thermal expansion coefficient is [ 1 ] tiM
=
--
(2 KCM2/Tae) T,
(4)
where K is the compressibility and C the magnetoelastic coupling coefficient. Kortekaas and Franse [22] showed clearly that this result applies to N i - P t alloys and that this magnetic contribution vanishes very rapidly near the critical concentration Co = 42% Ni.
2.5. NisAI The several results for this material have already been summarized [1,3]. It suffices to note that the coefficient C, to which a in relation (1) is closely related, can be obtained from the measurements [22] and that even its temperature dependence, as T 2 [23], is observed. The values of a for N i - P t and for NiaA1, about 36 and 28 K2/kbar, are very similar as are almost all other properties of these two systems. The value of ct for ZrZn 2 is also of this order, namely about 39 K2/kbar [1 ]. This material has also been reviewed several times already [3]. Very recent measurements [24] of Arrott plots in fields higher than before show that up to 170 kOe these and the earlier results persist in
showing that the magnetization is very homogeneous in the specimens investigated. The similarity of this material to N i - P t and NiaAl is very striking; it shows clearly the very general nature of Invar behaviour in the absence of iron.
2.6. FexCOl_xTi This interesting alloy series with two critical concentrations x ~ 0.4 and 0.8 has been investigated for Invar characteristics by Hilscher et al. [25] and by Beille and Towfiq and Beille et al. [26]. A prediction [27] of a critical pressure in the sense of relation (2) was based on an assumed analogy with the Si containing materials (see below) leading to a value of a about 40 K2/kbar at x ~ 0.5 (again close to the above values) and a critical pressure about 45 kbar where all ferromagnetism ceases. The data of [25] and [26] agree well with this prediction. In ref. [26] it was found that for materials with x ~< 0.5 Arrott plots remain well behaved under pressure but that there is a different behaviour for x ~> 0.5 which is not clearly defined. Where the weak itinerant model applies, the pressure derivatives of M and Tc continue to follow approximately relations (3) in that d In M/dP
d ha Tc/dP. 2. Z FexCOl_xSi Invar and weak itinerant characteristics were observed by Bloch et al. [28]. It was found that there were many similarities with the Ti alloys. The two crit. ical concentrations are about x ~- 0.2 and 0.8. The Arrott plots for the alloy with x = 0.5 are closely linear and parallel. The ratio of magnetic moments above and below Tc fits into the scheme of ref. [2], and the moment at 0 K is 0.17/~B per formula unit. The logarithmic derivative of the saturation magnetization, - 1 . 2 6 × 10 -2 kbar -1 f o r x = 0.5, fits in with the observations for N i - P t [21,22] and ZrZn2 [3]. For neither the Ti nor the Si containing alloys are there as yet any other data of relevance, such as of thermal expansion.
2.8. Zr(Fez_xCox) 2 This material has been investigated for x = 0.68 0.74 by Franse et al. [29]. It was found that dTcldP
E.P. Wohlfarth / Invar behaviour in crystalline and amorphous alloys was large and negative but did not obey relation (1) with a constant value of a. It is thus not clear how far these materials are weakly itinerant and if the negative pressure derivative alone allows them to be Classified as Invar materials.
2.9. Y6 (Fe1-xMnx)23 This material was investigated in refs. [25] and [29]. It has two critical concentrations x = 0.4 and 0.7 between which no ferromagnetism has been observed. Although purely magnetic measurements point somewhat to weak itinerancy the pressure derivative of Tc is small and positive. The result may point to strong heterogeneities of the magnetization and indeed there is evidence for spin glass behaviour. The material recalls Sc3In for which we have also suggested overriding heterogeneity effects [2]. Neither seem, as a result, to be good Invars.
2.10. MnSi This material has been found to be a weak itinerant ferromagnet beyond a region of helical spin ordering which is removed in a field of 6 kOe [30]. The logarithmic pressure derivative o f - 1.15 × 10 -2 kbar -1 for the magnetization is close to the value for F e - C o Si [28] but it differs from that for T c, - 3 . 9 × 10 -2 kbar -1, as would be expected from eq. (3). Magnetic excitations in this system have been studied very successfully by Ishikawa et al. [31] who clearly describe it as weakly itinerant as a result.
2.11. Zro. 7Nbo.3Fe 2 This material was studied by Alfieri et al. and by Shiga [32] who found that a large volume magnetostriction and a large negative pressure derivative of T e (-3.3 K/kbar at Tc = 382 K, i.e. a = 1260 K2/kbar) accompanies flat magnetization, temperature curves, a T 2 dependence of the magnetization and a ratio of magnetic moments above and below Te in line with ref. [2]. This Laves phase compound is surely one of many showing the effects being discussed here, another example being ZrZn 2.
2.12. MnB This material was studied by Shigematsu et al. [33] who found that a large positive volume magnetostric-
123
tion occurs which varies as M 2 far below To. This result follows from the analysis of ref. [23], for example. The Curie temperature, 570 K, is rather high. However, many other borides of Mn, Fe and Co in the crystalline state have been suggested [2] to show weak itinerant ferromagnetism very readily. The table in this reference contains magnetic data for many of these materials.
2.13. M n - A s - S b Nakamura [10] makes full reference to early measurements of K/Sster and Braun [34] who observed the Invar characteristics of large positive volume magnetostriction and negative thermal expansion below To. Edwards and Bartel [35] since found that where solid solutions with second order transitions were investigated (As content between 0 and 90%) the pressure derivative of Tc is large and negative and obeys well relation (1) with a "" 1800 K2/kbar, i.e. close to the value for the classical Invar alloys containing iron. These authors use the present philosophy to discuss also the first order transition for the As rich compounds.
2.14. Rare earth-iron and cobalt compounds A wide range of these compounds has been investigated for magnetovolume effects and summaries of these measurements have been given by Buschow [36] and Buschow et al. [37] for iron and cobalt containing compounds. Jaakkola et al. [38] discussed their measurements on nickel compounds which are similar. The data tend to support very strikingly the theoretical formula (1): Compounds such as Gd2Col7 and YFe 2 which have high Tc values have small positive pressure derivatives of Tc while others, such as GdCo2 and Th2 Fe 17 have low Curie points and large negative pressure derivatives. The values of ol in eq. (1) are of the same order (about 1000 for the iron and 2000 K2/kbar for the cobalt compounds) as for F e - N i Invars. Only a brief report has been given [39] of the observed thermal expansion anomalies and the data have not yet been fully analyzed in terms of the coupling constants C. Buschow [36] also refers to recent work on hydrogen absorption in some of these materials. Those with a pronounced pressure dependence of T c should also mutatis mutandis have Curie temperatures sensitive to hydrogen (equivalent to a negative pressure [40]).
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E.P. l¢ohlfarth /Invar behaviour in crystalline and amorphous alloys
2.15. Amorphous ferromagnets
Acknowledgements
Invar characteristics in amorphous ferromagnets are a natural consequence of weak itinerancy where this occurs [4]. It is therefore not surprising that such effects are now beginning to be observed, as first signalled by Mizoguchi [41 ]. More recently Invar behaviour has been investigated by Fukamichi et al. [ 4 2 44] and b y Hiroyoshi et al. [45]. The scattered data given by Mizoguchi concern the observed large negative pressure derivatives o f the Curie temperature and the saturation magnetization of Metglas-like materials such as ( F e - M n or Cr)aoP10Blo . Large positive volume magnetostrictions have been observed for amorphous F e - B alloys with a maximum effect at about 11.5% B. The data [44] were transformed (by means which we can not fully accept!) into a dTc/dP versus Tc curve which fitted well relation (1) with ct = 3500 K2/kbar. The Curie temperature corresponding to the above maximum effects is about 520 K and the saturation magnetization about 2.1/a 8 per iron atom. Hence, amorphous F e - B alloys m a y well form a second example of Invar behaviour where the phenomena are related to a more general type o f instability than is demanded by the presence o f a critical concentration, i.e. F e - B may be similar to Fe3Pt [8]. However, such critical concentrations Co are definitely present in some other amorphous alloys, in particular N i - Y (Co = 16.7% Y [46]), N i - P ( c o = 1 7 - 1 8 % P [ 4 7 ] ) a n d F e - G e (Co --~ 75% Ge [48]). Weak itinerancy has been established in all three systems and a negative pressure derivative o f the magnetization, in line with values for N i - P t , for F e - G e . There is thus a clear prediction of Invar behaviour in N i - Y , N i - P , F e - G e and other similar amorphous alloys.
I wish to acknowledge the many helpful communications I have had from M. Shimizu and also from Y. Nakamura, with whose review [10] the present briefer one has much in common.
3. Conclusion The annotated list and the philosophical background given here are intended to show that a simple discussion is possible of a wide range o f materials and phenomena. Where the philosophy appears weak this weakness is only deceptive and is in fact a sign o f the strength which must surely underlie any virile branch of science, with its ever changing and ever new aims and boundaries. The Invar problem appears clearly to be such a branch and thus fit and proper for further research, leading perhaps to a second symposium!
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