THE ONSET OF MAGNETIC ORDER IN DISORDERED ALLOYS AS REVEALED BY THEIR TRANSPORT PROPERTIES

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THE ONSET OF MAGNETIC ORDER IN

DISORDERED ALLOYS AS REVEALED BY THEIR TRANSPORT PROPERTIES

B. Coles

To cite this version:

B. Coles. THE ONSET OF MAGNETIC ORDER IN DISORDERED ALLOYS AS REVEALED BY

THEIR TRANSPORT PROPERTIES. Journal de Physique Colloques, 1974, 35 (C4), pp.C4-203-C4-

205. �10.1051/jphyscol:1974436�. �jpa-00215627�

JOURNAL DE PHYSIQUE Colloque

C4, suppliment

au no

5 ,

tome

35, Mai _1974,

page

C4-203

THE ONSET OF MAGNETIC ORDER IN DISORDERED ALLOYS AS REVEALED BY THEIR TRANSPORT PROPERTIES

B. R. COLES

Imperial College, London SW7, U. K.

RBsum6. ^-

Dans plusieurs alliages de substitution AB oh

A

est non magnktique, bien qu'il n'y ait apparemment pas de moment sur les atomes B lorsque l'alliage est dilue (c.4-d. i faible concen- tration de

B),

on observe cependant un ordre magnktique au-dessus d'une certaine concentration critique. Les mesures magnktiques conventionnelles sont souvent delicates i interprkter, alors que celles de propriktks de transport ont Btk une source importante &information dans beaucoup de systemes. On discute de l'application de ces mesures et l'on degage une comparaison entre les resultats de telles mesures et ceux obtenus par d'autres techniques. Le r61e du type de solute et celui des interactions entre proches voisins sera considerk.

Abstract. -

There are a number of random substitutional alloys of the type

AB

where A is non-magnetic, where in the dilute limit (small concentration of B) there appears tobe no magnetic moment on B atoms at low temperatures, and yet magnetic order sets in above some critical concen- tration. Conventional magnetic measurements are often difficult to interpret, but transport pro- perty measurements have been a valuable source of information in many systems. Their application will be surveyed and a comparison made between the results of such measurements and those of other techniques. The role of the character of the solvent and that of near neighbour interactions will be considered.

1 . Introduction.

-

The simplest example of the manifestation in the electrical resistance of the onset of magnetic order is the Curie point anomaly in pure gadolinium

; the most recent single crystal data of

Nigh et al. [I] even show critical scattering effects.

Other effects can also be seen in resistivity-tempera- tures curves (for example the onset of the antiferro- magnetic super-zone in chromium, manganese and dysprosium) and in retrospect it is obvious that the electrical resistivity of iron was trying many years ago to tell us of the presence of local moment character above the Curie point.

Questions of particular interest to this conference are-associated with the onset of magnetic order in random solid solutions. It has tacitly been assumed that the ferromagnetic ordering of a Ni-Co alloy or even the antiferromagnetic ordering of a Cr-Mn alloy present no greater problems conceptually than does the ordering in the pure component metals.

Even if that is true for those systems, it cannot be so for the solid solutions of iron in gold, nickel in palladium, cobalt in rhodium, etc., where there is evidence that there exist boundaries of some sort between regimes of temperature and concentration where magnetic order of some sort exists and those where it does not. In the region of the phase diagrams rich in the 3d element no great problems exist (even

and the situation is much as it is in the 3d-3d alloys.

In the dilute (with respect to 3d element) region however the situation is much more complicated.

2. Resistivity behaviour in the dilute limit.

-

It is essential to our discussion to recall that in no system does a well defined local moment persist in the dilute limit to arbitrarily low temperatures, and an attempt at a classification of alloy systems in terms of some characteristic temperature T* has been given elsewhere [2]. For our present purposes, where we are considering mainly the resistive behaviour we can distinguish two main categories.

2.1 Systems where no marked resonance in the band structure is produced by the solute but local exchange enhancement on solute sites gives rise to scattering by local spin fluctuations as discussed by Lederer and Mills [3] and Kaiser and Doniach [4].

At low temperatures this resistivity will vary as (TIT*)', like other electron-electron scattering effects.

I t is understandable that alloys between elements in the same column of the Periodic Table should belong to this category e. g. PdNi, RhCo ; it is slightly more surprising that ~ t ~ o T ~ h ~ c a n d even PtFe [5] are similar

(I),

but-6-like resonances in d-bands should not be narrow.

-

in Cu-Mn the can probably be regarded

₍₁₎

The observation of such behaviour

in

a system of even as replacing Mn atoms in all sub-lattices at random more widely separated elementsEtMn has recently

been made in

rather as Zn atoms do in MnF2-ZnF, solid solutions) the author's laboratory by

Mr.

Sarkissian.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1974436

C4-204 B. R. COLES

2.2 Systems where resonant scattering dominates and local spin fluctuations effectively narrow the range of energy over which a large change of phase shift occurs. The first explicit recognition of this effect was by Caplin and Rizzuto for the AI-Mn system, but it is probably the most useful approach for a number of systems including Au-V, Th-U and Rh-Cr.

Here the resistivity varies as 1 -(T/T.")~ at ~ o w % & ~ e - ratures, a form that has even been urged by Star [6]

for the canonical Kondo system

-

Cu-Fe in the dilute limit.

Rivier and Zlatic [7, 81 have adopted a formalism capable of treating both types of system and yielding the physically reasonable result of a temperature- independent (Kasuya) resistance of a simple spin- disorder type when the local spin fluctuations can effectively be treated as good local moments and Curie- Weiss behaviour is found in the susceptibility.

3. The effect of interactions. -

In both types of system as the solute concentration increases the local spin fluctuations will interact via the electrons of the host, lowering co-operatively their characteristic temperatures, and sooner (CuMn, PtCo) or later (C_uNi, RhCo) yielding a statein which indi- vidual solute moments, or clusters thereof, have frozen on cooling into a ferromagnetic or spin glass structure.

These effects are very clearly revealed in the electrical resistivity. For simple hosts and modest solute concen- trations the interaction will be of the oscillatory RKKYIcharacter and a spin glass will be found.

For systems in which special features such as host enhancement (PdFe) or small Fermi wave-vector ( G e ~ e - M n ~ e [91) displace any change in sign of the coupling to very large distances from a solute atom ferromagnetism will be found down to very small solute concentrations.

Of the simple solvent spin glasses the archetypes are CuMn and AuFe where the resistivity maximum at temperatures (K) of the order of 10 times the atomic percentage of solute was the first experimental mani- festation of the spin glass. A recent aspect of interest is the demonstration with such methods by Laborde and Radhakrishna [lo] of the low concentration cut-off of the AuFe spin glass when its characteristic temperature ( ~ T f a l l s below the Kondo temperature.

For larger values of T, the detailed temperature depen- dence of the resistivity together with specific heat data should throw some light on the difficult problem of the excitations in spin glasses.

On PdFe the Curie temperature is very strikingly revealed[11] in the resistivity

;

measurements at lower temperatures and concentrations may prove the existence of oscillating tails in the matrix polarization by yielding spin glass behaviour.

Dilute alloy measurements show rather a low value of T* for RhFe and this should therefore be a candi- date for spin glass stabilization with a non-resonant solute. This was found to be the case in the suscep-

tibility measurements of Murani [12], but the most striking demonstration of the critical composition is afforded by a plot against concentration (Fig. 1) of the low temperature local spin fluctuation term in the resistivity that has recently been measured by Dr. R. Rusby of the National Physical Laboratory.

Moment stabilization (to yield ferromagnetism) in a highly polarizable host had been demonstrated earlier by a similar type of plot by Tari [13], the critical composition being in excellent agreement with later measurements of the low field magnetization beha- viour.

FIG. 1. - The temperature dependent spin-fluctuation term

(PZK - PO.~K) in the low temperature resistivity of dilute e - F e alloys. (10s plmicrohm cm).

4.

Local environment effects. -

In the above

discussion the stabilization of moments and their

freezing at low temperatures has been, at least impli-

citly, ascribed to a long range coupling of a given

solute atom to many others. The work of the Grenoble

group, as Dr. Perrier's talk at this conference has

emphasized, has clearly shown the role of local envi-

ronment effects. In view of the significant 4-6 overlap

which will occur for nearest neighbour pairs of 3d

solutes in simple hosts one should perhaps have

expected these, and they can probably not be envisaged

as of RKKY origin. However the coupling of such

stabilized movements into a spin glass seems to yield

MAGNETIC ORDER I N DISORDERED ALLOYS AS REVEALED BY THEIR TRANSPORT PROPERTIES C4-205

behaviour rather like that of simpler systems at least in the Au-Co system. Just as for solute iron atoms, where moment stabilization required higher concen- trations in the non-resonant case (RhFe) than in the resonant case (AuFe), so for cobaltthe RhCo system requires ratherlarge solute concentrations before a spin glass is achieved [I41 but the local environment seems to play a role here also. The near neighbour couplings of the stabilized cobalt moments appear to be parallel (ferromagnetic) but the f. c. c. percolation limit for nearest neighbour coupling is passed without the appearance of long-range ferromagnetism (which is delayed to about 38 % Co). One might speculate that cobalt atoms without the adequate environment for moment stabilization break the percolation net.

In this system also measurements of the low tempe- rature resistivity provide the simplest indications of the onset of both spin glass and ferromagnetism.

In PdMn on the other hand long-range ferroma- gneticcoupling exists between manganese moments via the polarizable host at dilute concentrations but nearest neighbour solute couplings are antiparallel.

The consequences (observed in work to be published by Jamieson, Tari and the writer) are shown sche- matically in figure 2 where the boundaries of the

ferromagnetic phase have been defined by resistivity anomalies.

FIG. 2. - The magnetic phase diagram of the palladium- manganese alloys. p = paramagnetic ; f = ferromagnetic ; g = spin glass. Crosses indicate points from magnetization measurements, dots the temperatures of anomalies in dp/dT.

Acknowledgments. -

The author's thanks are due to Dr. Rusby, Dr. H. Jamieson, Dr. A. Tari and Mr. B. Sarkissian to quote results from their unpu- blished work.

References

[I] NIGH, H. E., LEGVOLD, S. and SPEDDING, F. H., Phys. Rev. [9] COCHRANE, R. W. and STROM-OLSEN, J. H. Proc. XIIIth

132 (1963) 1092. Low Temperature Conference. To be published.

P I

COLES, B. R., in Ainorphous Magnetism, ed. Hooper, H. 0. [lo] LABORDE, 0. and RADHAKRISHNA, P., Solid State Commun.

and de Graaf, A. M. (Plenum Press) 1973, p. 169. 9 (1971) 701.

r31

LEDERER9 P, and D. L., Phys. Rev. 165 837. [ i l l COLES, B. R., WASZINK, J. H. and LORAM, J. W., Proc. Inf.

[4] KAISER,

. .

A. B. and DONIACH, S., Znt. J. Magnetism 1 (1970) Magnetism Conference (Nottingham) Inst. of Physics

1 1 . and Physical Society (1964) p. 165.

[5] LORAM, J. W., WHITE, R. J., and GRASSIE, A. D. C., Phys.

Rev. 5B (1972) 3659. [12] MURANI, A. P. and COLES, B. R., J. Phys. C (Metal Physics r61 STAR. W. M. and NIEUWENHUYS. G. J., Phvs. Lett. A 30 Suppl.) 3 (1970) S 159.

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(1969) 22. [13] TARI, A. and COLES, B. R., J. Phys. F 1 (1971) L 69.

[7] RIVIER, N. and ZLATIC, V., J. Phys. F 2 (1972) L 87. [14] COLES, B. R., TARI, A. and JAMIESON, H. C., Proc. XIIIfh [8] RIVIER, N. and ZLATIC, V., J. Phys. F 2 (1972) L 99. Low Temp. Conf: To be published.