The temperature dependence of the coercive field of Co5Sm magnets

Journal of Magnetism and Magnetic Materials 4 (1977) 1-7 © North-Holland Publishing Company

S E S S I O N 1: P E R M A N E N T

MAGNETS

THE TEMPERATURE DEPENDENCE OF THE COERCIVE F I E L D OF C o s S m MAGNETS R. KUTTERER, H.-R. HILZINGER and H. KRONMI/LLER Max-Planck-lnstitut ffdr Metallforschung, lnstitut ffftr Physik, Biisnauer Strasse 1 71, D-7000 Stuttgart 80, Fed. Rep. Germany Received 29 April 1976

The temperature dependence of the coercive field H c of CosSm has been investigated between 4.2 and 300 K. In magnets with high coercive fields a strong dependence of the magnitude of H c on the heat treatment is found, whereas the temperature dependence of H c remains unaffected. The coercive field is attributed to the expansion of small reversed domains and to the pinning of domain walls at planar defects. In low coercive materials and in well-annealed CosSm single crystals we find a considerably stronger temperature dependence of H c which is quantitatively explained by pinning of two-dimensionally vaulted domain walls at randomly distr~uted defects. Below 100 K the Peierls potential of the narrow domain walls plays a significant role whereas its influence is smeared out at higher temperatures by thermally activated Bloch-wall diffusion.

1. Introduction The strong magnetic anisotropy and the high saturation magnetization predestinate the intermetallic compound C o s S m as a suitable material to produce permanent magnets. Exceedingly high coercive forces are actually obtained b y use o f powder metallurgy [1,2]. The coercive field o f these sinter magnets, however, is found to depend strongly on the heat treatment [3]. The largest values for H c are obtained after quenching the sample from about 900°C. A heat treatment at 700°C or sintering above 1150°C on the other hand cause a strong decrease of the coercive field. It is generally accepted that magnetization reversal occurs b y the nucleation o f small reversed domains and subsequent displacement of domain walls [4]. The coercive field o f this combined process has been determined in a previous paper [5]. In a further paper [6] it has been shown that in CosSm point defects and disorder effects play an important role for the pinning o f domain walls. It is the object o f this paper to clarify the nature o f the processes which determine the coercive field after different thermal treatments. For this purpose we have measured the temperature dependence of H e

in the range between 4.2 K and r o o m temperature. It is assumed in this experiment that different mechanisms exhibit different temperature dependences and may thus be identified.

2. Experimental procedure We started with sinter magnets and single crystals of an average composition corresponding to 63.5 wt% Co, 35.9 wt% Sm and 0.6 wt% oxygen. This material was spark-cut to spherical and cubic samples o f 3 m m dia. in size. In a first step the sample was successively heated for 20 rain at different temperatures between 200 and 960°C. After each heat treatment the sample was quenched and the coercive field was measured at 4.2 K. The variation of the coercive field with the temperature of the heat treatment exhibits the well-known behaviour [3], including the typical minimum at 750°C. In a second stage a cubic sample was heated at the following temperatures: (a) 2 hr at 960°C (Hc4.2 K = 43 kOe); (b) 1 hr at 750°C ( H c = 4.3 kOe); (c) 3 hr at 750°C ( H e = 586 Oe);

2

R. Kiitterer et al./Temperature dependence of the coercive field o f Co sSm

(d) 6 hr at 1200°C (H c = 274 Oe). (The given coercive fields all refer to 4.2 K.) At temperatures up to 1000°C the heat treatment was performed in He-atmosphere, whereas at more elevated temperatures, the sample was encapsuled in a quartz tube under Ar-atmosphere. After quenching the sample we measured the temperature dependence of H c in the temperature range between 4.2 and 300 K. The magnetic measurements were carried out with a Foner vibrating magnetometer with superconducting solenoids. For measuring the anisotropy constant K 1 we used a specimen which consisted of two monocrystalline domains tilted by an angle of 5° against each other. K 1 was determined by extrapolating the magnetization curve in the direction perpendicular to the easy axes of both domains. Up to the maximum available field of 50 kOe the magnetization curve was linear and reversible.

He, (T) Hc (4,2"K) 1.0 Q9 '

0#0,7,

x

x

%

X

O&O

Q6. O,5 0,4 Q3 C~2 O,t

3. Experimental results In fig. 1 we have represented the temperature dependence of the coercive field H c after different heat treatments. It is noteworthy that the heat treatment at 750°C (b), although reducing the absolute value of H c by an order of magnitude with respect to the heat treatment at 960°C (a), does not affect the temperature dependence of H c. This dependence agrees well with the curve reported by Benz and Martin [7]. Only a second, longer heat treatment at 750°C (c) produced a slight variation of the temperature dependence at very low temperatures whilst again H c is reduced by a large amount. Sintering the samples at 1200°C (d), however, causes a drastic variation of the temperature dependence of H c in the whole temperature range. The magnetic domain pattern of these sintered samples was investigated using the magneto-optical Kerr effect. We observed a multi-domain structure which extended across the grain boundaries. This points to the fact that nucleation effects and surface pinning no longer determine the coercive field. The grain size of these sintered samples was determined to 8 0 - 1 0 0 ~m. During this last sintering treatment growing of the grains must therefore have occurred on a large scale. This result corresponds to the observations of Huppmann and Adler [8].

Fig. 1. T e m p e r a t u r e dependence of the coercive field H c in C o s S m sinter magnets after different heat treatments: zx 2 hr at 960°C; o 1 ht at 750°C; X 3 ht at 750°C; o 6 hr at 1200°C; o single crystal.

In addition to the sinter material results the coercive field of a single crystal is represented in fig. 1. In the temperature range T > 100 K this sample exhibits a similar dependence as the sintered polycrystal. At low temperatures, however, a more pronounced increase of H e is observed. This difference in the temperature dependence indicates that obviously other mechanisms determine the coercive field than in the case of the high coercive magnets. To interpret the different temperature dependences we assume that the microstructure of the specimens remains unchanged during the magnetic measurements. The observed variation of the coercive field is then reduced to the temperature dependence of the micromagnetic parameters, i.e. anisotropy constant K1, exchange constant A and saturation magnetization I s. We have, therefore, measured K 1 and I s of the single crystal in dependence of the temperature (fig. 2). The saturation magnetization in good approximation obeys a T 3/2 law

R. Kiitterer et al./Temperature dependence o f the coercive field o f CosSm

3

K293K = 1.71 X 108 erg/cm 3 , fit(T) H c (T) Kt (4.2"K) ; /'/c ('~.2°K) j

J~ iT) -Is (4,2*K)

lie just between those reported by Klein and Menth [10, 11 ] and Ermolenko [15], whereas the temperature dependence is in good agreement with these authors. It is interesting, however, to note that K 1 remains constant below 80 K. The dispersion o f K 1 seems to be caused by different qualities of the single crystals as well as by the insufficient values of the available magnetic fields (cf. Korolev et al. [16]).

0.9 o,o 0,7 0.6

05

4. Theory and discussion

0,4 4.1. H ~ h coercive magnets 0,3 Q2

0.1

o,2

0.3

T/Tc

Fig. 2. Temperature dependence of saturation magnetization Is(×), anisotropy constant K l (o) and coercive field H c (zx, t~) of CosSm. - - - theoretical coercive field according to eq. (7).

Is(T) = I s (0) [1-0.4(T/Tc)3/2].

(1)

From eq. (1) the exchange constant A may be derived [9, 14]. In general, limited to ferromagnetic materials (i.e. only 1 magnetic sublattice), this method may also be applied to CosSm, since the magnetization of CosSm mainly results from the Co sublattice. This is supported by the apparent conformity of the Is(T) curves in Co5 Sm and CO5 Y [10, 11 ]. Keeping in mind that this method yields a lower limit of A, the exchange constant A in CosSm is determined to be A ~> 0.8 X 10 -6 erg/cm in accordance with the values derived from the specific wall energy of CosSm [12, 13] (withK 1 = 1.71 X 108 erg/cm 3 and 3~= 57 erg/cm 2 [13] we getA = 1.2 X 10 -6 erg/cm). For T < T e the temperature dependence of the exchange constant A is given by that of I s [14] A(T) ~ I s ( T ) . Our absolute values of the anisotropy constant K1, K4.2K = 2.62 × 108 erg/cm 3

(2)

The heat treatment reduces the coercive field of the high coercive samples by almost two orders of magnitude without changing the temperature dependence of H c. This indicates that the same mechanism determines the coercive field before and after the heat treatment or that different mechanisms cause just the same temperature dependence. To obtain a quantitative description of the magnetization processes which determine H c we consider 3 models. 4.1.1. Nucleation o f reversed domains

Reversed domains in hard magnetic materials are preferentially formed at disturbed lattice regions. The nucleation field thus strongly depends on the kind of defect. It is generally accepted that in CosSm sinter magnets a heat treatment at 750°C facilitates the nucleation process [17, 18]. This is attributed to an eutectoidal decomposition of the CosSm phase below 800°C according to 20Co5Sm -> 3CO17Sm 2 + 7Co7Sm 2 . As Kronmuller and I-lilzinger [5] have shown, in this case of incoherent nucleation the coercive field is determined either by the nucleation of reversed domains in the magnetically soft phase Col7Sm 2 or by the expansion of these reversed domains into the magneticaUy hard matrix CosSm. In both cases H c is approximately given by

and tl e ~ Iq /I s .

(3)

4

R. Ki~tterer et al./Temperature dependence of the coercive field of Co sSm

In the first case, however, we have to insert into eq. (3) the anisotropy of the perturbed region (e.g. K 1 of Co17Sm2), whereas in the second case K 1 means the anisotropy constant of the matrix Co 5 Sin. 4.1.2. Pinning o f domain walls at planar defects Den Broeder and Zijlstra [18] and Huppmann and Adler [8] have suggested to relate the coercive force in Co5Sm sinter magnets to the pinning of domain wails at grain boundaries. A similar effect as grain boundaries show antiphase boundaries in ordered alloys [19-21 ]. The magnetic perturbation of these defects originates in the modification of the anisotropy and exchange energy thus leading to a pinning force on the domain wall. It is expedient [22] to distinguish two cases corresponding to the thickness D of the grain boundary with respect to the wall width ~B = 7r~0" For weak and thin defects the coercive field is given by

H c - 3 x / 3 Is

g0

-K-

(D'~60)"

(4)

Provided the relative variations A'M and K ' / K of exchange and anisotropy energy at the grain boundary are independent of T, the temperature dependence of H c follows from eq. (4) as H c (T) "~ (K/Is) 3/2.

(5)

For extended defects we find a dependence according to [22] Hc(T) "~K/1 s

(D >> 80).

(6)

4.1.3. Pinning o f domain walls by atomic disorder (small wall area) The domain walls in CosSm are extremely narrow due to the large magnetic anisotropy. Kronmiiller and Hilzinger [6] have pointed out that in such materials, atomic defects act as effective pinning centres. In fact, atomic defects (Co vacancies or Co interstitials) may be present in high concentrations in Co 5 Sm already at small deviations from the stoichiometric composition [23, 28]. In the case of a large number of randomly distributed defects the pinning force is caused by statistical fluctuations of the defect density on a microscopic scale. These fluctuations are effective especially at small wall areas which for instance are present in the beginning of the expansion of reversed

domains. Even if the nucleation is assumed to be easy the expansion of the reversed domains nevertheless is suppressed due to the strong pinning forces of the defects. The temperature dependence of H c, following from this mechanism, is derived as [6] Hc(T ) ~ I2s (KIIs)514 .

(7)

As may be seen from fig. 2 the experimental values of H c show a markedly stronger temperature dependence than K 1 or K 1/I s. We are therefore obliged to exclude the influence of extended grain boundaries (eq. 6) as well as the expansion of the reversed domains into the hard Co5 Sm phase (eq. 3) as the origin of the coercive field. On the other hand eq. (3) yields a good description of the experimental values if we take K 1 as the anisotropy constant of Co17Sm2 [24]. The remaining two models (wall pinning by thin grain boundaries [eq. (5)], and wall pinning by atomic disorder [eq. (7)]), however, exhibit a temperature dependence very similar to eq. (3). Representative for these three models we have additionally plotted in fig. 2 the theoretical dependence of H c as following from eq. (7), showing good agreement with the experiment. The difference in the temperature dependence between these three models is so small, however, that the present experiment does not allow a definite decision, which mechanism actually determines the coercive field of Co 5 Sm sir~ter magnets. If, in addition, the results of Den Broeder and Zijlstra [18] are considered then small grain boundaries may be favoured to have the principal influence on H c. This model in particular allows to explain the large influence of the thermal treatment on H c which is attributed to modifications of the exchange constant A ' and anisotropy constant K' in the grain boundary during the heat treatment [18]. This model is supported by the strong dependence of the magnetic anisotropy on small variations in composition of the sample, as reported by Korolev et al. [25]. It is possible, however, that the coercive field before and after the thermal treatments is determined by two different mechanisms yet with the same temperature dependence.

R. Kiitterer et al./Temperature dependence o f the coercive field o f CosSm 4.2. L o w coercive material

5

H~rrj t-/(293 K)

In constrast to the high coercive material the temperature dependence of the low coercive samples is much more pronounced, thus contradicting all of the above models. In particular, the first steep decrease o f H c corresponds to a temperature range where the anisotropy remains constant. To explain this temperature dependence we assume that H c is determined by volume pinning. This view is supported by the domain patterns revealing extended domain walls. The pinning forces are supposed to originate from statistically distributed defects. Due to the large wall area the statistical fluctuations o f the defect density are less important. Therefore lower coercive fields are expected than in comparable specimens with fimited walls. Moreover, an extended wall may respond to the interaction force of the defects, i.e. vaulting of the domain wall may occur. As outlined by Hilzinger and Kronmiiller [26, 27], in hard magnetic materials, such as CosSm the vaulting of the wall arises in two dimensions. In this case the coercive field is determined as n c = 1 X lO-2(E2p/Is7620),

(8)

where E 0 denotes the interaction energy of the wall with a single defect, p its volume density, 3' the specific wall energy and 6 B = rr60 the wall width. By inserting E 0 = 2 × 10 -14 erg and p = 1021 cm - 3 (corresponding to an atomic disorder of 1%), eq. (8) yields a coercive field o f about 10 Oe in good accordance with the experimental values (e.g. H c 293 K = 17 Oe in the case o f the single crystal). Since the interaction of the wall with the defect is caused by a local perturbation of anisotropy and exchange energy, we may assume that E 0 reveals the same temperature dependence as K 1 [6]. Eq. (8) then leads to a temperature dependence according to # c ( T ) ~ (K l/Is) 5/2 .

(9)

Eq. (9) describes the experiments correctly above 100 K (fig. 3). Below this temperature, however, the pinning force of the defects approaches a constant value just like the anisotropy, whereas the experimentally determined coercive field strongly increases. This behaviour o f H c has a direct analogue in the temperature dependence o f the flow stress in bcc metals [28]. Just as in that case, the steep increase of H e originates

\ i

o,i

iJ

o,2

q'3 T/r~

Fig. 3. Temperature dependence of H c of a CosSm single crystal (o). - - - Theory: contribution of the lattice defects to H c (9). ----Theory: coercive field H c due to Peierls potential and lattice defects (18) (fit for H c Peierls (0 K) = I00 Oe). in the fact that at low temperatures the Peierls potential no longer may be disregarded. In magnetic materials the Peierls potential occurs since the energy of narrow domain walls periodically depends on the position of the wall centre with respect to the crystal lattice. Therefore the domain walls move in an intrinsic Peierls potential similar to the case of dislocations [29]. The theory of the magnetic Peierls effect has been elaborated by Van den Broek and Zijlstra [30], Egami and Graham [31] and Hilzinger and Kronmtiller [32, 33]. These latter authors in particular have treated the Peierls potential in CosSm and derived the following expression [32] Hco=l...2

20rr A exp 3 a2is

3

a

'

(10)

where a is the atomic spacing. The strong exponential dependence o f / / c o O n the domain wall width in eq. (10) results in the fact that the Peierls force is only important in materials with very large magnetocrystalline anisotropy. In the case of CosSm (~0 4.2K = 5 A, a = 2.5 )~) eq. (t0) yields a coercive field of

6

R. Kfttterer et aL/Temperature dependence of the coercive field of Co sSm

with

Hc4.2 K = 50...100 Oe. With increasing temperature (i.e. increasing wall width), however, the Peierls force drops down. The decrease is so extreme that at room temperature only a coercive field of 5 0 e results from eq. (10) though 50 has only increased by 20%. In addition to this exponential dependence, H e is affected by a thermally activated motion of the domain walls at finite temperatures. The Peierls potential is then overcome by thermally activated formation of planar domain wall kinks. According to Egami [ 3 4 - 3 6 ] , the nucleation rate of these kinks is given by (11)

v n = v(O) e x p ( - E e / k T ) .

The activation energy E c for the nucleation process in good approximation may be written as Ec-

rr 2

1-

.

(12)

In eq. (12), Hco denotes the coercive field given by eq. (10) in the absence of thermal activation and H i s the magnetic field acting on the wall. The nucleation and subsequent motion of the planar kinks produces a magnetization change A / o f the whole sample according to A / = I s (2a/LD) v n A t ,

(13)

where L D is the domain width. It is reasonable to assume a magnetization change A / o f about zMr---~ 1 (Hco/N),

(14)

in order to affect H e (N = demagnetization factor of the sample). From eqs. (11)-(14) follows E c / k T = In 4N ~

~D v(0) At

= const.

(15)

By inserting v(0)-At = 1012 sec -1 and alL D = 10 - 4 the constant in eq. (15) is evaluated as const = 23.5. Due to the logarithmical relation the constant is not influenced seriously by the inserted numerical values for the parameters of eq. (15), Eq. (12) is then easily solved as follows: n c ( T ) = n c o [ - T + (1 + ~2)1/2] ,

(16)

T = const. 7r2 k B T kBT - 14.516 7a 2 7a 2"

(17)

The Peierls potential is an intrinsic effect and thus independent of lattice defects in a first approximation. It therefore seems justified to add both pinning forces linearly Hctotal(T) = Hcdefects(T) + Hc Peierls(T).

(18)

The temperature dependence determined from eq. (18) is shown in fig. 3 together with the coercive field measured for the single crystal. The excellent agreement of the experimental and theoretical resuits indicates that both the two-dimensional domain wall vaulting as well as the intrinsic Peierls force, in fact, play an essential role in the low coercive Co5Sm samples. The effect of the Peierls potential is yet more important in the ternary compounds Sm(COl_xNix) 5 [37] and Sm(COl_xAlx) 5 [38] which at 0 K have a higher anisotropy energy and a lower T c than Co5Sm.

Acknowledgements

The authors are indebted to Dipl.-Phys. R. Herz for helpful discussions.

References

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