Relaxation and magnetic clusters in mictomagnetic copper-manganese alloys

Journal of the Less Common Metals, 43 (1975) 69 - 82 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands

RELAXATION AND MAGNETIC CLUSTERS COPPER-MANGANESE ALLOYS*

*, R. D. SHULL

A. K. MUKHOPADHYAY*

University of Illinois, Urbana, Ill 61801 (Received

February

27,

and PAUL

69

IN MICTOMAGNETIC

A. BECK

(U.S.A.)

197 5)

Summary

Quantitative data were obtained on the average giant moment and the concentration of the magnetic clusters in Cu-Mn alloys. For aged CuT5Mnz5 the magnitude of the giant moment is consistent with the size of the small, atomically-ordered regions, determined by Sato et al. by means of nuclear diffuse neutron scattering. Contrary to an early model, the results do not indicate that the concentration of giant moments is measurably affected either by cooling in a magnetic field or by isothermally increasing the applied magnetic field. The relaxation of the giant moments in the applied field is responsible for most of the alternating low field susceptibility at its peak and this relaxation also gives rise to the “quasi-viscous” time-dependence of the steady field magnetization in a certain temperature range below the peak. At very low temperatures, where the relaxation effects are frozen out, it is the “quasi-elastic” response of the giant moments that is responsible for the exceedingly high steady field susceptibility.

Introduction

It is now well known that in mictomagnetic Cu-Mn alloys below a certain temperature, Tr, the spin orientations are frozen without long range spin order [l] and that, at temperatures above T1, these alloys are paramagnetic with giant moments [ 2, 11. The present work was undertaken in order to study the magnitude and the concentration of the giant moments in the paramagnetic state, and their role in the mictomagnetic state below Tf. Ihperimental

procedures

Alloys with 9,16.7, and 25 at.% Mn were prepared by induction melting under an argon atmosphere. The specimens were homogenized by means * Dedicated

to Professor

** Present address: Steel Plant, Durgapur,

Dr. E. Raub in celebration

c/o Chief Metallurgist, W. Bengal, India.

Research

of his 70th and Control

birthday. Laboratory,

Alloy

of two, consecutive, severe plastic deformation and annealing sequences, ground to spherical or ellipsoidal shape, and quenched from 850 “C into cold water. After completion of the magnetic measurements in the quenched state, the specimens were aged for three weeks at 100 “C and magnetic measurements were then made in the aged condition. Steady-field magnetic measurements were made in fields up to 12.7 kOe by means of the Faraday method in the temperature range between 4.2 and 300 K. Alternating lowfield measurements were made in a field of approximately 4 Oe rms, using a differential transformer, a 0.5 - 2000 Hz primary current of constant amplitude and a vector voltmeter lock-in amplifier, giving both the component in-phase with the primary current and the quadrature component of the differential transformer output voltage. The output of the lock-in amplifier was corrected by subtracting from it, vectorially, the output with the specimen removed from the transformer. The quadrature component of the difference, divided by the frequency and by the mass of the specimen, was used as an approximate index, in arbitrary units, of the alternating low-field susceptibility. Results and interpretation Figure 1 shows the reciprocal initial susceptibility (in steady field) us. temperature for CuaIMns and CursMnas in both the quenched and the aged condition. Quenched CusIMns obeys the Curie-Weiss law above about 180 K. Calculated from the Curie constant between 180 and 300 K, the dipole moment per Mn atom is very close to 4 pg (Table I), in agreement with earlier work on dilute alloys [ 31. It may be concluded that in this temperature range the dipoles in quenched CuarMna are individual Mn moments, thermally flipping independently of one another. The deviation from the CurieWeiss law below about 180 K suggests that, at lower temperatures, the magnetic structure of this alloy changes. The nature of the change can be studied by means of magnetization, (I, us. internal field, H, isotherms (Fig. 2). The isotherms were fitted with the sum of a susceptibility term and a Srillouin function term : 0 = XH + wB[ct,

= XH + W{(P

H+h(o-xH) ~ +

+ lktnh[b

I

+ 1) (

- ctnh (

N+X(a

--$I)

)Z

T

(1) It is assumed here that in P = gS, g = 2, and that S is not required to be an integer multiple of %. The attempt of fitting in the entire temperature range from 50 to 300 K was not successful, even with the interaction between the dipoles and their magnetic environment allowed for in the molecular field approximation (through the adjustable molecular field coefficient, X). However, this type of lea&squares fitting was successfully accomplished for pairs of adjacent

71

i

0

200

100

300

T 1°K)

Fig. 1. Reciprocal initial susceptibility us. temperature the quenched and in the aged condition.

for CugIMn9

and Cu,&fn25

in

isotherms from 50 to 140 K. The best fitting parameter values are shown in Table 1. It is seen that the average moment, p, of the dipoles increases, whilst their concentration, c, decreases with decreasing temperature ,:Fig. 3), and that the field-independent susceptibility, x’, taking the place of x in eqn. (l), is also a function of the temperature, Under the heading PC in Table 1 the saturated paramagnetic magnetization from all dipoles contributing to the Brillouin term in eqn. (1) is given for each pair of isotherms. It is interesting to note that PC decreases with decreasing temperature in spite of the increase of P. The simplest interpretation is that the average giant moment of the magnetic clusters decreases with increasing temperature by dissociating into smaller clusters and individual atomic moments, as thermal agitation overcomes the overall ferromagnetic exchange coupling locally weakened by the admixture of parasitic antiferromagnetism, while the ferromagnetic spin alignment within the magnetic clusters is improving. The increase of the positive molecular field coefficient, h, with increasing temperature (Table l), indicates that the exchange interaction of the giant moments with their magnetic environment also becomes more ferromagnetic as the temperature increases, presumably because of a gradual decrease in the antiferromagnetic component of this exchange interaction. As seen in Fig. 1, quenched Cu,5Mn25 shows a Curie-Weiss-type behavior in the temperature range between 209 and 298 K. However, the average moment per Mn atom, calculated from the Curie constant in that temperature range is only 3.4 pg. Similar results were previously obtained by Kouvel [4], who interpreted them as a result of antiferromagnetic interactions, which persist up to about room temperature. In a somewhat higher temperature range, Kouvel found a higher Curie constant, giving a moment per manganese atom of approximately 4.5 p B. For quenched Cu,5Mn25, the observed low average moment would require approximately 15% of the Mn atoms to be antiferromagnetically coupled to each other in the temperature

1

Tf= 124 K

CwiWs

A

Q

A

Tf= 112 K

cu75M”25

Tf= 46 K

%rlh%

Tf==46K

%lM% Q

Alloy and metallurgical condition

140,160 160,180 180,202 202,225 225,249 249,274 274,296

120,140 140,160 160,180 180,200 209 - 298

50,60 60,80 80,100 100,120 120,140

236 168 137 136 132 136 148

73.3 46.0 29.7 17.05 3.42

112 85.0 57.8 29.3 17.1

92.2 78.6 48.8 25.8 16.5 4.06

@B)

(K)

5060 60,81 81,101 101,120 12O,i40 179 - 300

/J

Isotherms

0.345 0.495 0.569 0.508 0.483 0.429 0.374

0.311 0.670 1.159 2.57 250

0.393 0.747 1.63 3.57 5.24

0.360 0.716 1.636 5.35 9.49 90.0

cx lo3 (atomic fraction)

3356 5396 8081 10,336 12,634 14,906 15,440

26,362 36,730 58,896 88,006

3406 3411 4290 10,502 27,005

5141 3498 5595 6971 11,742

(--> emu

0e.g

x

lo6

208 188 181 159 139 122 98.6

107 87.6 78.4 68.1 0

186 98.9 23.4 32.5 42.3

140 58.8 19.95 2.55 6.69 0

(emu/g)

x’x

0.0814 0.0832 0.0780 0.0690 0.0640 0.0583 0.0554

0.0228 0.0308 0.0344 0.0438 0.855

0.0440 0.0635 0.094 1 0.10.47 0.1101

0.0332 0.0562 0.0799 0.1379 0.1566 0.3654

(I,cn/alloy

/&

atom)

0.0662

0.0193

0.0335

0.0239

Gc at 4.2 K

0.0265 0.0252 0.025 1 0.0 204 0.0192 0.0177 0.0138

0.0104 0.0113 0.0086 0.0169 -

0.0192 0.0185 0.0099 0.0096 0.0443

0.0194 0.0168 0.0094 0.0110 0.0056 -

RMSFD

Parameters obtained from least-squares fitting of eqn (1) to pairs of adjacent isotherms for CuglMn9 and Cu&Una in the quenched (Q) or aged (A) condition. The average moment per Mn atom for the quenched condition in the highest temperature range was calculated from the Curie constant.

TABLE

73

T,,,

1°K)

Fig. 2. Magnetization us internal field isotherms for quenched CuDIMng. Fig. 3. Moment and concentration of magnetic clusters us. temperature for quenched CuglMn9, obtained by analyzing pairs of adjacent isotherms.

range considered. The results shown in Table 1 for quenched Cu,sMnz5, as well as for both alloys in the aged condition, are similar in many respects to those described above in some detail for quenched CuaIMna. However, aged C&Mnz5 does not become Curie-Weiss-like, at least up to 300 K. As seen in Fig. 1, for aged CuslMns, the deviations from linearity between 180 and 300 K are rather small; the cr us. H isotherms in this temperature range are straight lines. For aged Cu,sMnss the isotherms are curved, even at 300 K. Least squares fitting of eqn. (1) to pairs of adjacent isotherms for this specimen shows that around room temperature the average dipole moment is 148 pg (Table 1). In agreement with the above observations, the initial susceptibility per Mn atom (Fig. 4) increases greatly on aging, particularly for C%Mn25. The low values and the rather small increase of the susceptibility per Mn atom with decreasing temperature for quenched Cu,5Mn25 (Fig. 4) are undoubtedly due to the relatively large concentration of nearestneighbor Mn pairs, interacting antiferromagnetically, as suggested by Kouvel [4] and by Sato et al. [ 61. The increase of the giant moments upon aging, which is particularly pronounced for Cu75Mn26, suggests that the magnetic clusters may correspond to small, atomically-ordered regions in these alloys. Recent neutron-scattering results [6, 71 indicate an increase of the short-range atomic order in Cu-Mn alloys on aging. Werner, Sato and Yessik [ 71 found, by neutron scattering from single crystals, that Cu7sMnz5, aged by very slow cooling, has atomically-ordered regions with linear dimensions of approximately three unit cell edge lengths. This would correspond, on the average, to approximately 27 Mn atoms per ordered region, or a giant moment at 300 K of approximately 108 pB, provided that all Mn moments within an ordered region are aligned parallel with each other. The average giant moment of 148 pg, obtained from the magnetic measurements near 300 K in the present work, represents a reasonably good agreement with the neutron scattering results

-

/ , 2.5

T

(‘K)

Fig. 4. Initial susceptibility per Mn atom for CuglMng and Cu75Mn25 in the quenched and in the aged condition. Fig. 5. Magnetization us. temperature for quenched Cu$In25 after field cooling, 0, and after cooiing in zero field, 0. Tf is the freezing temperature at the peak of the afternating low-field susceptibi~ty.

(particularly if the difference in the aging treatments used in the two investigations is taken into consideration), indicating that in aged Cu75Mn25 at 300 K the ferromagnetic alignment of the Mn moments within each atomically-ordered region is essentially complete. One can estimate that in aged Cu75Mns5 just below room temperature, the total number of Mn atoms in all magnetic clusters represents approximately 8.1% of the manganese content of the alloy. In quenched CuVSMns5 (and in both quenched and aged Cus,Mn,) the ferromagnetic spin alignment within the magnetic clusters is apparently less good, as suggested, for instance, by their far more extensive thermal degradation (Table 1). Because of this, and because of the lack of suitable neutron scattering data, it is difficult to make a reliable estimate of the fraction of the Mn atoms in magnetic clusters in these specimens. It is clear that the change in the magnetic structure, indicated by the low-temperature deviation from linearity in the reciprocal initial susceptibility us. temperature graphs (Fig. l), is characterized by a trend of increase of the giant moments and by a decrease of the positive molecular field coefficient, A, with decreasing temperature (Table 1). It is well known [ 81 that below a certain temperature, increasing with the Mn content, Cu-Mn alloys show drastic deviations from paramagnetic behavior. This has been recently demonstrated [9] for alloys with Mn contents down to at least 9 ppm, Typical u us. T curves are shown in Fig. 5 for quenched Cu75Mn25. Careful studies by Window [ 10,111, using Cu-Mn alloys containing small amounts of the isotopes 57Fe or ‘lgSn, established

75

the fact that, on cooling below a certain temperature, increasing with the Mn content, the Mossbauer spectrum for either nuclide rather abruptly develops hyperfine splitting. These observations indicate the freezing of the spin orientations at the temperatures in question. Figure 6 shows the freezing temperature, Tf, as a function of the Mn content. As first found by Cannella, Mydosh and Budnick for Au-Fe alloys [ 121, the alternating low-field susceptibility of mictomagnetic alloys has a sharp peak at the same temperature where the hyperfine splitting in the Mossbauer spectrum indicates freezing of the spin orientations. Accordingly, in Fig. 6, the Tf us. Mn content curve for Cu-Mn alloys was drawn through the Miissbauer effect hyperfine split ting temperatures [ 10, 111, as well as through the temperatures defined by the alternating low-field susceptibility peaks (Cannella [ 131, and this investigation). As seen in Fig. 5 for quenched Cu,sMnz5, Tf (given here on the basis of the low alternating field susceptibility peak) is not very different from T,,,, the broad maximum of the high, steady field magnetization measured at increasing temperature after the specimen has been cooled to 4.2 K in zero field (H, = 0). Figure 5 also shows that, below a temperature near T,,,, the magnetization values measured at decreasing temperatures with the specimen cooled in the magnetic field, are considerably higher than those for the zerofield cooled state. Such thermomagnetic history effects are typical for CuMn and for other mictomagnetic alloys [ 1, 81. Also typical for mictomagnets is the time-dependence of the magnetization in a certain temperature range [14, 1, 81. It has been suggested [ 151 that these “magnetic visbelow T,,, cosity” effects in mictomagnetic alloys may be described in terms of a potential barrier, E, resulting from the interaction between the giant moment of a magnetic cluster and the Mn moments in the surrounding matrix. This potential barrier tends to prevent a change in the orientation of the giant moments, p, but its effect may be overcome by the joint action of an applied field, H, and of thermal agitation. As a result, the giant moment can be turned in small, consecutive, thermally-activated steps [ 151 at a rate proportional to exp[-(E - pH)/kT] . This explains the initial increase in the magnetization with increasing temperature after zero-field cooling, Fig. 5. Figure 7 shows, for quenched CuslMn9, that this initial increase and, as a result, to some extent also T,,, are shifted to higher temperatures as the applied field decreases. At temperatures above Tf, where the alloy is paramagnetic, the o/H us. T curves for different fields tend to superimpose on one another and, of course, the superposition becomes quantitative (i.e., u /H becomes independent of H) at high temperatures, where the magnetization is proportional to the field. This limits the shifting of the paramagnetic high-temperature branch of the curves in Fig. 7 with decreasing field. Accordingly, the maximum of the o/H VS. T curve is becoming narrower and Tmax is approaching Tf with decreasing field, Fig. 7. Thus, the sharp peak of the alternating lowfield susceptibility appears to be but an extrapolation of the steady field o/H us. T maxima to a field of about 4 Oe.

76

loooL_$---’

40

60

80

7 f’Kf

Fig. 6. Tf from Mijssbauer effect hyperfine splitting with 57Fe [ 11 J or ll’Sn [lo]. X, from alternating low-field susceptibility peak [ 131, x , and the present work, X ; TEAR [20], l, [21], o, [22], e;T,[23], *, [24],~, 141, l, us. Mncontent. Fig. 7. o/H, vs. temperature, after zero-field cooling, for quenched CugrMng. The maxima are marked by arrows. Tf from the alternating low-field susceptibility peak.

The sharp, low-field susceptibility peak was originally interpreted by Cannella [ 131 as a result of the onset of long-range antiferromagnetic spin order in Cu-Mn. However, none of the neutron diffraction studies [ 16 - 18 J done so far indicates any long-range antiferromagnetic spin order in Cu-Mn alloys containing less than 60% Mn. The above interpre~tion of the maxima in the steady field o/H us. T graphs (for a zero-field cooled specimen) clearly shows that by far the largest part of the o/H value at the maximum must be due to the reorientation of the giant moments. This suggests that the sharp, alternating low-field susceptibility peaks, such as those shown in Fig. 8, are also due to the reorientation of the giant moments of magnetic clusters. Figure 9 shows the variation of the magnitude of the susceptivity index* at its peak with the frequency for Cuss3Mn16.7 in both the quenched and the aged conditions. The effect of aging in increasing the peak value of the susceptibility index by a factor of about 5.5, in the entire frequency range explored, shows the importance of the magnitude of the cluster moment, P, in regard to the rate of response to an external magnetic field. The sharp increase of the susceptib~i~ index at low frequencies clearly indicates a slow relaxation effect, akin to the “quasi-viscous” phenomena described above. * The “susceptibility index”, as defined in the Section on Experimental Procedures, could not be translated into accurate susceptibility values because of insufficient homogeneity of the field at the specimen location. However, the susceptibility index values are reproducible and they certainly may serve as ~miquantitative indicators of the large effects of frequency and of aging. The calculated skin depth, even for the highest frequency used (2 kHz) and for the lowest temperatures of measurement and the lowest Mn content, is larger than the specimen radius (2.5 mm), so that the results are free from skin effect distortions.

77

T PK)

O’ 0.5

5

50 Y

(Hz)

500

5000

Fig. 8. Alternating low-field susceptibility index us temperature for quenched Cu83.3Mn16_7 at frequencies from 0.5 to 2000 Hz. Fig. 9. Alternating low-field susceptibility index peak values us. frequency for quenched

(Q) and for aged(A) Cuss.sMn16.7. The large effect of aging and the strong frequency dependence, both shown in Fig. 9, further support the interpretation given above that most of the alternating field susceptibility at the peak arises from the “quasi-viscous” relaxation of the giant moments of magnetic clusters. The independence of the temperature of the susceptibility peak from the frequency (Fig. 8), and the fact that this temperature changes very little, or not at all, on aging, shows clearly that it is determined, not by the magnitude of the giant moments, but by the freezing of the spin orientations in the matrix surrounding the clusters. The magnetic behavior of quenched CuT5MnB at very low temperatures is shown in Fig. 10, giving the magnetization us. applied field at 4.2 K both after zero-field cooling .and after cooling in a 12.7 kOe field. The unidirectional remanence obtained after field cooling, umC*, represents the sum of all giant moments aligned by the cooling field and frozen in this orientation. The giant moments frozen in random orientations upon zero-field cooling are clearly not undergoing any major reorientation at 4.2 K in fields up to 12.7 kOe. If the giant moments are aligned with one another by field cooling, however, they can be turned around collectively at 4.2 K by a reversed field of only 1.95 kOe. Kouvel found 143 that, by decreasing the cooling field, the unidirectional remanence can be considerably decreased and that the displacement of the loop to a reversed field of Hn is then increased in such a way that the product of the remanence and of the displacement remains constant. *%x was measured as remanence at 4.2 K for quenched Cu,5Mn25; for aged Cu7&In25 and for CugIMne in both the quenched and the aged conditions, U, was obtained by extrapolation to H = 0 of the high-field, straight line portion of the u us. H isotherm, measured at 4.2 K after field cooling (“extrapolated remanence”).

78 TABLE

2

Unidirectional remsnence, urn,_,and loop displacement, H,, us.temperature of the start of field cooling, Ta, for quenched Cu75Mns Trc (K)

*mc (emu/g)

295.6

1.76 1.76 1.76 1.76 1.76 1.76 1.72 1.66 1.09 0.39 0.13

248.0 178.2 160.2 140.2 120.4 69.7 60.2 40.2 20.1 10.1

HD (koe) 1.95 1.95 1.95 1.95 1.95 1.95 2.00 2.07 3.05 9.55 ~12.7

amc x HD (emu - kOe/g) 3.43 3.43 3.43 3.43 3.43 3.43 3.43 3.44 3.32 3.72 -

Fig. 10. Magnetization vs. applied field at 4.2 K, for quenched Cu7&Inz5 after field cooling, o and l . Curve shows unidirectional remanence and displacement from origin. Sequence of measurements is indicated by arrows. Magnetization us applied field at 4.2 K after zero-field cooling is a straight line through the origin, a and A.

Table 2 shows the result of an experiment in which the magnitude of the cooling field was kept constant at 12.7 kOe, but the temperature of the start of field cooling, Tfo at which the cooling field was turned on during. cooling from room temperature to 4.2 K, was varied. As seen in Table 2, both u,, and the loop displacement, H,, are constant, while Tfc remains within the temperature range from 296 to 120 K. However, if Tf, is decreased to 70 K, or below, ume decreases while H, increases and, as in Kouvel’s experiments [4], umc X H,-, remains constant. The susceptibility at 4.2 K of zero-field cooled CuT5Mn2s in the quenched condition, corresponding to line 0 in Fig. 10, is 5050 X 10m6 emu/g mole, an unusually large value. If the quenched specimen is subsequently aged at 100 oC, the corresponding value is larger still by a factor of 2.6. The effect of aging in increasing the susceptibility at 4.2 K in the zero-field cooled state is similar at other Mn concentrations; the increase for the 16.7% Mn alloy is by a factor of 2.9 and for the 9% Mn alloy by a factor of 1.3. The

79

large increase of the susceptibility on aging suggests that these very high susceptibilities result mainly from the response of the giant.moments to the applied field. This conclusion is strongly supported by the fact that the total cluster magnetization, as measured by the unidirectional remanence at 4.2 K after cooling in a field of 12.7 kOe, increases on aging in nearly the same ratio as the susceptibility. The cluster magnetization ratios for the three alloys are 3.4, 2.9, and 1.4, respectively. Discussion The detailed model proposed by Kouvel [ 191 for explaining the lowtemperature magnetic behavior of mictomagnetic alloys, as revealed by his pioneering studies [ 4, 51, assumes the presence in such alloys of “ensembles”, each consisting of two ferroma~eti~ and two ~tife~omagnetic “domains”. The model further requires each ferromagnetic “domain” to be coupled tightly to one of the antiferromagnetic “domains”, and the two ferromagnetic-antiferromagnetic pairs to interact with one another in such a way that, in the ground state of an ensemble, the giant moments of the two ferromagnetic “domains” are antiparallel. Thus, in the ground state, each ensemble has a zero net moment, When a efficiently large field is applied at high temperatures, the interaction between the two ferromagnetic-antiferromagnetic pairs is overcome, and both giant moments are then turned in the direction of the applied field. During field cooling, this higher energy configuration is retained, according to the model, by virtue of the effect of the magnetoc~s~lline anisotropy on the ~tife~oma~etic “domains”; the latter, being strongly coupled with their respective associated fe~om~etic “domains”, keep the giant moments of the latter in their parallel alignment. In this model, the increase of the unidirectional remanence, umc, with increasing cooling field was explained 1191 by assuming a distribution of interaction strengths in the various ensembles present, so that, with increasing applied field, an increasing number of en~mbles are raised to the higher energy state, forming an increasing number of giant moments. It should be noted (Table 1) that the total cluster magnetization value, PC, derived from paramagnetic data for temperatures just above Tf, agrees well within a factor of 1.5 with the total cluster magnetization, urn,, measured as unidirectional remanence at 4.2 K after field cooling. It appears then that the giant moments, observed after field cooling to very low temperatures, are essentially the same as identified in the paramagnetic state, above the freezing temperature. Field cooling could only increase the concentration (or the moment) of the magnetic clusters by a factor of less than 1.5. In order to detect the possible formation of giant moments by the action of high fields on ensembles ohginally in the ground state above the freezing temperature, Tf,the magnetization values for quenched CualMn, at 50 and 60 K, obtained after zero-field cooling and with the specimens exposed only to the measuring fields of 100 and 200 Oe, were compared

80

with the magnetization values calculated from eqn. (l), using the parameter values derived by lea&squares fitting to data measured at fields up to 12.6 kOe (Table 1). It was found that the low-field data fitted well with the values calculated from data up to high fields. The rootmean-square fractional deviation (RMSFD) for the low-field data was 0.0117, as compared with 0.0194 for all data up to 12.6 kOe. Furthermore, two pairs of isotherms for quenched CusiMns, measured at 50 and 60 K in the one case, and at 81 and 101 K in the other, were analyzed assuming a field-independent dipole concentration, c, or, alternatively, assuming c to vary with H according to c = pH, c = qH*, or c = rdH. The best fits obtained with these four assumptions gave RMSFD values of 0.0194 (at c = 0.360 X 10m3), 0.103 (atp = 0.141 X lo-‘), 0.0957 (at q = 0.155 X lo-“), and 0.267 (at r = 0.134 X 10e4), respectively, for the 50 and 60 K isotherms. Similarly, for the 81 and 101 K isotherms the RMSFD values obtained were 0.00787 (at c = 0.163 X lo-*), 0.0668 (atp = 0.236 X lo-*), 0.165 (at q = 0.534 X lO_ll), and 0.321 (at r = 0.669 X 10e5). Since, for both pairs of isotherms, the calculation with a field-independent giant moment concentration gave by far the lowest RMSFD value, these results certainly do not indicate that any ensembles with initially zero net moment are acquiring giant moments upon increasing the applied field up to 12.6 kOe at the temperatures used. Since both the alternating low-field susceptibility at around T,, and the steady-field susceptibility at 4.2 K after zero-field cooling, are attributable mainly to the giant dipole moments of the magnetic clusters, as shown above, it is clear that the formation of these giant moments does not require exposure to, or cooling in, a high magnetic field. Thus, the assumption of pairwise cancellation of the giant moments within each ensemble upon zerofield cooling [ 191 no longer appears justifiable. The absence of remanence at 4.2 K after zero-field cooling could be, instead, attributed to the essentially random orientation of the giant dipole moments under such conditions. ESR measurements by various investigators with Cu-Mn alloys [20 221 indicate that, below a reasonably well-defined temperature, the proportionality of the resonance line width with the temperature (Korringa relationship) ceases to hold. Also, below this temperature, the reasonance, which at higher temperatures corresponds nearly to g = 2, shifts to higher fields. It would be quite natural to consider whether or not this “ESR tranto the onset of antiferromagnetic sition temperature”, TEsR, corresponds spin order. As shown in Fig. 6, T ESR is, over a wide range of Mn concentrations, considerably higher than Tt. Not only is there no long-range antiferromagnetism at TESR, there is clearly no freezing of the spin orientations in a static sense. It is, however, possible that the interactions, which do give rise to spin freezing at Tt, may cause the spins to be in a “kinematical” sense frozen at TEsR with respect to the frequency used in the measurements. If this is true, one may expect TEsR to vary with the frequency. It is known that the component of the electrical resistivity of Cu-Mn alloys attributable to the Mn solute has a maximum at a temperature, T,, which increases with the Mn content [23, 241 as shown in Fig. 6. It has been

81

suggested [ 241 that the decrease of the resistivity above T, may be connected with the gradual disappearance of the magnetic clusters. The present results show that this explanation must now be retracted. For quenched Cu,sMnz5, the magnetic clusters disappear at around 209 K, while T, is approximately 300 K. Another earlier interpretation [25], clearly also wrong, would connect the maximum of the resistivity with the static freezing of the spin orientations. The following explanation may be suggested tentatively for the decrease of the solute resistivity at temperatures below T,. If the magnetic component of the resistivity depends on spin flip scattering, a Mn moment must be able to flip within the period of time of the passage of a conduction electron in its vicinity. If the “kinematic freezing” of the Mn moments prevents flipping for the duration of the passage time and, as a result, the encounter does not give rise to “thermally assisted spin flip scattering”, one would expect to see a decrease of this resistivity component with decreasing temperature. A rough order-of-magnitude estimate of the “passage time” (with a Fermi velocity of lO”cm/s and an effective scattering radius of 10h8 cm) gives - lo-l8 s. Since th e corresponding relevant period of time in the ESR measurements discussed above is of the order of 1O-1os, one may expect T, > TESR, which agrees with the experimental results shown in Fig. 6. The above ideas on “thermally assisted spin flip scattering” may well be related to the theories of Silverstein [26] , of Harrison and Klein [27] , and of Loram, Whall and Ford [28] for dilute alloys. Acknowledgements This work was supported by grants from the NSF and the AEC. We wish to thank M. Salamon for performing the ESR measurements with a quenched CuT5Mnz5 specimen and for permission to use his unpublished results. One of us (P. A. B.) wishes to acknowledge gratefully the very helpful discussions he enjoyed with J. Bardeen, A. Arrott and M. Salamon. References 1 P. A. Beck, Metall. Trans., 2 (1971) 2015. 2. B. V. Znamenskiy and I. G. Fakidov, Fiz. Met. Metalloved., 14 (1962) 391. (English tr.: Phys. Met. Metallogr., 14 3 (1962) 61. 3 C. M. Hurd, J. Phys. Chem. Solids, 30 (1969) 539. 4 J. S. Kouvel, J. Phys. Chem. Solids, 21 (1961) 57. 5 J. S. Kouvel, J. Appl. Phys., 31 (1960) 142s. 6 H. Sato, S. A. Werner and R. Kikuchi, J. Phys. (Paris), 35 (1974) C4 - 25. 7 S. A. Werner, H. Sato and M. Yessik, Am. Inst. Phys. Conf. Proc., 10 (1972) 679. 8 P. A. Beck, Mictomagnetism in alloys, in P. A. Beck and J. T. Waber (eds.), Magnetism in Alloys, Met. Sot. AIME, New York, 1972, p. 211. 9 E. C. Hirschkoff, 0. G. Symko and J. C. Wheatley, J. Low Temp. Phys., 5 (1972) 155. 10 B. Window, J. Phys. C, 2 (1969) 2380. 11 B. Window, J. Phys. C, 3 (1970) 922. 12 V. Cannella, J. A. Mydosh and J. I. Budnick, J. Appl. Phys., 42 (1971) 1689.

82 13 V. CanneUa, Low field magnetic susceptibility of dilute alloys: are dilute Cu-Mn and in H. 0. Hooper and A. M. de Graaf (eds.), Amorphous Au-Mn magnetically ordered? Magnetism, Plenum Press, New York, 1973, p. 195. 14 R. Street, J. Appf. Phys., 31 (1960) 3105. 15 P. A. Beck, J. Less-Common Met., 28 (1972) 193. 16 P. Wells and J. H. Smith, J. Phys. F, 1 (1971) 763. 17 E. R. Vance, J. H. Smith and T. M. Sabine, J. Phys. C, 1 (1970) 334. 18 G. E. Bacon, I. W. Dunmur, J. H. Smith and R. Street, Proc. R. Sot. London, Ser. A, 241 (1957) 223. 19 J. S. Kouvel, J. Phys. Chem. Solids, 24 (1963) 795. 20 D. Griffiths, Proc. Phys. Sot. London, 90 (1967) 707. 21 Unpublished work by M. SaIamon, Univ. Illinois, Urbana, III. 23 A. Nakamura and N. Kinoshita, J. Phys. Sot. Jpn., 27 (1969) 382. 24 P. A. Beck and D. J. Chakrabarti, in H. 0. Hooper and A. M. de Graaf (HIS.), Amorphous Magnetism, Plenum Press, New York, 1973, p. 273. 25 D. Jha and M. H. Jericho, Phys Rev. B, 3 (197 1) 147. 26 S. D. Silverstein, Phys Rev. Lett., 16 (1966) 466. 27 R. J. Harrison and M. W. Klein, Phys. Rev., 154 (1967) 540. 28 J. W. Loram, T. E. Whail and P. J. Ford, Phys. Rev. B, 3 (1971) 953.