EXPERIMENTS TO TEST « PARAMAGNON THEORIES » : ELECTRICAL RESISTIVITY, LOW TEMPERATURE SPECIFIC HEAT AND MAGNETIZATION MEASUREMENTS ON Ni3Al AND Ni3Ga REVIEWED

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EXPERIMENTS TO TEST “ PARAMAGNON THEORIES ” : ELECTRICAL RESISTIVITY, LOW

TEMPERATURE SPECIFIC HEAT AND

MAGNETIZATION MEASUREMENTS ON Ni3Al AND Ni3Ga REVIEWED

P. de Chatel, F. de Boer, W. de Dood, J. Fluitman, C. Schinkel

To cite this version:

P. de Chatel, F. de Boer, W. de Dood, J. Fluitman, C. Schinkel. EXPERIMENTS TO TEST

“ PARAMAGNON THEORIES ” : ELECTRICAL RESISTIVITY, LOW TEMPERATURE SPE- CIFIC HEAT AND MAGNETIZATION MEASUREMENTS ON Ni3Al AND Ni3Ga REVIEWED.

Journal de Physique Colloques, 1971, 32 (C1), pp.C1-999-C1-1001. �10.1051/jphyscol:19711356�. �jpa- 00214392�

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JOURNAL DE PHYSIQUE Colloque C I, supplkment au no 2-3, Tome 32, Fivrier-Mars 1971, page C 1 - ⁹⁹⁹

EXPERIMENTS TO TEST PARAMAGNON THEORIES >> : ELECTRICAL RESISTIVITY, LOW TEMPERATURE SPECIFIC HEAT

AND MAGNETIZATION MEASUREMENTS ON Ni3Al AND Ni3Ga REVIEWED

P. F. De CHATEL, F. R. De BOER, W. De DOOD, J. H. J. FLUITMAN and C. J. SCHINKEL

Natuurkundig Laboratorium der Universiteit van Amsterdam, the Netherlands

Rksumk. - On passe en revue les experiences qui appuient les theories du paramagnon. La resistivite electrique a basse temperature prksente des effets de paramagnon prononces tandis que les mesures de chaleur spMfique ne sont pas en accord avec la thkorie. On s'attend B ce que les effets sur I'aimantation a basse temperature soient trop petits pour btre observables dans les systemes Ni3Al et Ni3Ga.

Abstract. - A review of some experiments which can support paramagnon theories is given. The electrical resistivity at low temperatures shows pronounced paramagnon effects, whereas the specific heat measurements are not unambiguously supporting the theory. The effects in low temperature magnetization measurements are expected to be too small to be observable in the Ni3A1 and Ni3Ga systems.

I. Introduction. - In strongly paramagnetic sys- results taken on three paramagnetic Ni3A1 alloys. The tems, where the magnetic susceptibility is enhanced data between 1.2 and 6 ^O^Khave been analyzed in terms over x,, the value calculated from the band density of of the theoretically expected temperature depen- states, persistent spin fluctuations (paramagnons) are dence [2]

expected to lead to important effects. Some of the

predicted effects become singularly large as D, the C(T) = Y * T + P T ~ + ^A

(a31n:

^- ⁽¹⁾

enhancement factor, defined as the ratio of the T = 0

susceptibility and x,, approaches infinity. Alloy sys- where Y* involves the mass adxtncement tems, in which D varies with concentration reaching co _m*

- - 9 D at a critical concentration c,, where the alloys become 1 = -1n-

m 2 3 (2)

ferromagnetic, are very suitable to the experimental

investigation of paramagnon effects. However, in the and in the last term, which gives rise t o the characte- disordered systems studied so far, the observation of the ristic ⁽⁽upturn ⁾⁾in the CIT vs T~ plots, Tsf is the spin predicted mass enhancement [I] and low temperature fluctuation temperature ; k~ _Ts,= EFID. The para- specific heat anomaly [2] has been hampered either by meters found in the analysis with P chosen independent the extreme smallness of the effect (Pd-Ni [3, 4]), or by of concentration are listed in the first half of table I.

the formation of ferromagnetic clusters [5] ( ~ i - ~ u Y* is found to be linear in In D, but the proportionality [6, 7, 81 and Ni-Rh [9]), which can give rise to a factor is by a factor of 40 smaller than given by eq. (2).

constant specific heat at low temperatures over a The fact that Tsf comes out a constant makes the relatively wide temperature range [lo]. interpretation of the cr upturn D in terms of para- The measurement of the specific heat, electrical magnon effects questionable, and leads us to suspect resistivity and low temperature magnetization on a these systems as well of containing clusters. When we number of alloys in the vicinity of the Ni3AI and Ni3Ga subtract a << normal ⁾⁾term y T ^fP T ~ from the specific stoichiometric compositions has been undertaken with heat, the low temperature anomaly appears as a peak the expectation that these systems are free from the in C vs Tlocated, for all concentrations, at 2.5 OK. The complications caused by clusters. The measurement height of the peak changes but slightly and not syste- of the bulk magnetic properties 111, 121 encouraged matically with concentration. A closer analysis [I51 this expectation, as it gave agreement [13] with the shows that the customarily assumed constant contri- Stoner theory as applied to very weak itinerant ferro- bution to the specific heat results only from the pre- magnets by Edwards and Wohlfarth [14] and no sence of fairly large clusters (2 S + 1 -- loo), and for discontinuity was found at the stoichiometric composi- small values of the cluster momentum a peak is t o be tion in the parameters used in the description. expected in the specific heat. Identifying this with the experimentally found peak, we can give an estimate for 11. Specific heat. - Our specific heat measure- the number of clusters, which is given in the last two merits being in a preliminary stage, we report only columns of table I. The resulting concentrations are not

Ni conc. D Y* T s f Number of clusters

(at. %I (vJIK2 g ) (K) ( P

J;/K.

^g) ^{per gram} per formule

- unit

- - - - -

74 23 179 10.2 159 5.8 x 10'' 3.0 x

74.3 47 187 11.0 169 8.2 5.1

74.5 115 198 9.5 176 8.2 5.1

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711356

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C 1 - ¹⁰⁰⁰ ^P.^F.DE CHATEL, F. R. D E BOER, W. DE DOOD, J. H. J. FLUITMAN AND C. J. SCHINKEL unreasonable, but the origin of an internal field or

anisotropy of the order of 2.5 ^{O K}is not understood.

111. Electrical resistivity. - The paramagnon theory predicts a relatively strong temperature dependence of the electrical resistivity at low temperatures due to scattering of the conduction electrons by paramagnons. This effect was first studied by Mills and Lederer [16]. The functional variation of the tempe- rature dependent part of the resistivity Ap with tempe- rature and with enhancement factor D can serve to make a choice between three theoretical models.

a) Rice [17, 181 uses a model function to approxi- mate the uniformly enhanced dynamical susceptibility

~ ( 4 , ^0).

He predicts a rather complex variation of Ap with temperature T , in the low temperature limit given by A p = B T ~ . The dependence of the coefficient B on the enhancement factor D should also be a bit complex : B K D~ for small D going to B cc for large D, implying a singularity at the critical concentration c,,.

b) Mathon [19], using an analytic approximation to ~ f q , o) finds a finite Ap cc T5I3 for a critical alloy, and using a model function approximation finds Ap = AT^ with A cc D1" for alloys with finite D.

c) Finally the local exchange enhancement model of Lederer and Mills [20] also leads to Ap = AT2, with A proportional to D, however. The experimental results [21] for 1.2 < T c 4 OK can be analyzed according to Rice's calculations, resulting in A p o=DO.' for 5 < D < 50 in good agreement with the theory (table IT). Going to higher temperatures Ap increases faster with temperature than predicted by theory.

When we represent the data for 1.2 < T < 4 OK simply by A p = A T , x is found to vary from 2 for the off-critical alloys to 1.5 for alloys in the critical region (table 111). The variation of A with D _{for 5}< D < 50 does not fit the predicted expression A cc D ' I ~ (table 111). This Mathon type of analysis also leads to theoretical curves which deviate from the experimental data at higher temperatures.

Ni3A1 Ni,Ga

Ni conc. D B D B

n Ohm cm n Ohm cm

Ni conc.

(at. %) - 73 73.5 74 74.5 75 75.5 76

IV. Low temperature susceptibility. - BCal-Monod et al. [22] calculated the temperature dependence of the susceptibility in the paramagnon model. Retaining the same terms as in the calculation of the specific heat 121, they arrive at the result that the temperature depen- dence expected from molecular field theory [14], x - I ( T ) = ~ - ' ( 0 ) ( 1 + D F T ~ ) should be enhanced as for temperatures T < T, D - ~ / ~ . The validity of this result being interrelated with that of the predictions regarding the specific heat, and the latter being over- shadowed by clustering effects, it would be of interest to try a check on this result. However, even for a relatively weakly paramagnetic alloy as Ni,,.,Ga,,., (D = 7 , TF

-

⁴⁰⁰^OK) the validity of relation (3) is restricted to T 4 22 OK. Moreover, the variation of the susceptibility going from 0 to 4 OK, according to (3), still would be as little as 0.7 %. Contributions to the low temperature magnetization due to the presence of 10 ppm iron and perhaps the clusters discussed in relation with the specific heat measurements will be much larger.

V . Conclusion. - Except for the resistivity, for which we found an effect in good agreement with theory exceeding by an order of magnitude all pre- viously found similar low temperature effects, we have to draw the conclusion that in the Ni3A1 and Ni,Ga systems paramagnon effects, if present, are much smaller than theoretically expected. The correct dependence of the mass enhancement on D is pro- bably significant, but the ⁽⁽upturn ⁾⁾in C / T vs T2 due to paramagnons is at the best a weak background behind the more intense clustering contribution. The effect in the low temperature susceptibility is not observable and this, together with the examples quoted in the introduction, leads to the rather general conclusion that in alloy systems uncontrollable concentrations of magnetic impurities and/or clusters are likely to blurr the picture and conceal paramagnon effects, which seem to be over-estimated by theory.

References

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[2] DONIACH (S.) and ENGLESBERG (S.), Phys. Rev. Let- [5] HAHN (A.) and WOHLFARTH (E. P.), Helvetia Physica

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[3] SCHINDLER (A. I.) and MACKLIET (C. A.), ^Phys. ^[6]GUPTA (K. P.), CHENG (C. H.) and BECK (P. A.), Rev. Letters, 1968, 20, 15. Phys. Rev., 1964, 133, A 203.

[4] FAWCETT (E.), BUCHER (E.), BRINKMAN (W. F.)

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EXPERIMENTS TO TEST ⁽⁽PARAMAGNON THEORIES ^>)ELECTRICAL RESISTIVITY, LOW TEMPERATURE C 1 - ¹⁰⁰¹

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1 QfiQ

*> ">.

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