MAGNETIC STRUCTURE OF DISORDERED Au-Mn ALLOYS

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MAGNETIC STRUCTURE OF DISORDERED Au-Mn ALLOYS

R. Cohen, K. West

To cite this version:

R. Cohen, K. West. MAGNETIC STRUCTURE OF DISORDERED Au-Mn ALLOYS. Journal de

Physique Colloques, 1971, 32 (C1), pp.C1-781-C1-782. �10.1051/jphyscol:19711273�. �jpa-00214105�

JOURNAL DE PHYSIQUE Colloque C 1, suppldment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - ⁷⁸¹

MAGNETIC STRUCTURE OF DISORDERED Au-Mn ALLOYS

by R. L. COHEN and K. W. WEST

Bell Telephone Laboratories, Incorporated Murray Hill, New Jersey, 07974

R6sum6. - Nous discutons ici la structure hyperfine Mossbauer de Au197 dans les alliages Au-Mn comprenant moins de 20 % Mn. Nous avons dkveloppk un modkle, conceptuellement simple, qui reussit a expliquer la structure hyperfine compliqu6e obtenue pour l'alliage B 20 % Mn. Avec des parametres rkduits par une Bchelle approprike, la structure hyper- h e obtenue est bien prkdite pour les alliages comprenant moins de Mn. Des calculs fond& sur d'autres modeles plausi- bles ne reproduisent pas les spectres observes.

Abstract. - This article discusses the Mossbauer hfs of Au197 in magnetically ordered crystallographically dis- ordered Au-Mn alloys containing up to 20 % Mn. A conceptually simple model is developed which is successful in explai- ning the complex hfs observed in the 20 % alloy. With appropriately scaled parameters, the hfs observed in alloys with smaller Mn concentrations is also predicted. Calculations based on a nymber of other plausible models fail to reproduce the observed hfs.

Previous studies by Meyer [I] of the susceptibility and magnetization of the crystallographically ordered (bct) and disordered (random substitutional fcc) phases of Au4Mn have shown that both have a susceptibility of about 4.8 p, per Mn ion above their magnetic ordering points. The ordered phase of Au,Mn has a low temperature magnetization of - ^{4.2 I*, per Mn,}

corresponding to the ferromagnetic alignment of the Mn ions, but the disordered phase shows a much smaller magnetization [I]. This suggests that the magnetic properties of the Au-Mn systems arise from local moments on the Mn ions, but that antiferro- magnetic coupling among the Mn ions can reduce the net moment of the disordered system. This is not surprising, since the Ruderman-Kittel oscillating spin density mechanism provides an exchange interaction which changes sign with distance. A wide range of magnetic structures appears in Au-Mn intermetallic compounds [2, 3, 4, 5, 6, 71 showing a strong correla- tion with the Mn-Mn nearest neighbor distance (see Table I).

TABLE I

Manganese NN distances and couplings in ordered Au-Mn intermetallics

Formula Mn NN Dist. Coupling Ref.

- - -

Au4Mn 3 . 9 8 ~ FM

Au,Mn 2.86 AFM P I

Au5Mn, 2.91 131

AFM 14 , 51

Au,Mn 3.37 FM

AuMn 3.25 FM [61

AuMn 3.15 AFM 171

~ 7 1 The Mossbauer spectrum of A u ' ~ ~ in the ordered Au4Mn shows a well resolved hyperfine spectrum [8,9], arising from an effective field, Hi,,, at the gold nucleus, coming from the contact interaction with spin- polarized conduction electrons. The hfs of the disorder- ed phase material, though, shows a broad spectrum with the lines only poorly resolved. This presumably results from the range of environments for the gold atoms, caused by the random alloy statistics. It would at first appear to be almost impossible to construct a microscopic model describing the origins of the hfs in this random alloy. However, with the aid of a number

of assumptions described below, it is possible to develop a model which reproduces the observed hfs very closely. The successful duplication of the experi- mental hfs is not a guarantee that the model is correct.

However, calculations based on a number of other plausible models yield quite different results from those obtained experimentally. The success of the model in predicting the observed hfs in other (random fcc) alloys with less Mn also suggests that the calculation described below does describe the microscopic magne- tic structure of these materials.

We make the following assumptions :

1. We assume that the alloys are random, with no short range order.

2. The isomer shift (IS) is assumed to be increased by 0.63 mm/s by each Mn NN to a gold (this value is determined from the well resolved spectrum of the ordered phase Au4Mn).

3. The hf field, Hi,,, at a gold atom is assumed to come from the linear superposition of H,,,, from the Mn NN' s, and Ifdist, a cr long-range D term which lumps together the effects of all the magnetic ions outside the NN shell.

4. Quadrupole hfs is neglected. (This is suggested by the negligible quadrupole coupling [8] in ordered Au,Mn and in ordered and disordered [8] Au4V.)

5. Each Mn ion contributes a fixed amount, HNN, to H,,,, but it can either add to or substract from H,,, depending on its spin direction.

The data in Table I suggest that the coupling between Mn ions is antiferromagnetic if they are less than - ^3.2 apart and ferromagnetic if they are further apart 141. Applying this picture to a sample cell of the fcc structure (Fig. 1) shows that if two Mn ions are NN' s, they should be antiferromagnetically coupled, and if they are further apart, but still within the same cell, they should be coupled with spins parallel. The application of this algorithm leads to a self-consistent spin configuration for each possible local arrangement of Mn ions.

The calculation of the hfs on this model proceeds by the following stages : First, for each possible number of Mn ions in the cell shown, the spin configuration is

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711273

R. L. COHEN AND K. W. WEST

FIG. 1. - An example of the random fcc cell used in the ana- lysis. The circles without arrows represent gold atoms. This particular cell contains 4 Mn ions as Au NN's, with the Mn ions coupled using the algorithm described in the text, so that 3 have spin up and 1 has spin down. The Au atom (solid circle) at the center of the cell sees HI,,

~ H N N for this particular spin

configuration.

worked out for various possible positions of the Mn ions. This calculation is facilitated by the use of equivalence classes and a simplified Monte-Carlo approach. For 4 Mn nearest neighbors to the gold, for example, H,,, can be 0,2, or 4 x Hm, with a probability depending on the (random) distribution of Mn ions at the 12 possible sites. The hfs for the gold cr test atom D

shown at the center of the cell in figure 1 is then calcu- lated by using an IS determined from the total number of Mn nearest neighbors, and Hint = Hdist.+ HI,,.

Because the number of Mn NN' s is determined by random alloy statistics, and the HI,, for a particular number of Mn ions can also take on a number of values, the calculation is complex, but straightforward.

Because the IS per Mn NN can be estimated from the ordered phase Au,Mn, the only free parameters in the model are HNN and ITdi,, ; the remainder of the calcula- tion is determined by the probability distributions.

The calculated hfs, shown by the solid line in figure 2, is in good agreement with the observed spectrum for the 20 % alloy, with the parameter values HNN = 105 kOe and HdiSt = 425 kOe. To calculate the spectra for the other alloys, the model requires that the IS and HNN values should stay the same, and that only the Hdi,, values should be changes. A severe test of the model's validity is to determine H,,,, for alloys with < 20 % Mn from the value providing the best fit to the data for the 20 % alloys, taking account of the reduced concentration of Mn ions, and the relatively

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FIG. 2. -Experimental spectra of the disordered fcc alloys at 4 OK. The solid line is in all cases the model described in the text. The dashed lines for the 20 and 10 % alloys were obtained by setting HNN

0, equivalent to the assumption that all the magnetic hfs comes from relatively long-range interactions, with all Au nuclei having the same Hi0 (570 kOe for the 20 % alloy and 350 kOe for the 10 % alloy). The dotted lines for the 20 % and 15 % alloys were calculated assuming that the Mn- Mn coupling is always ferromagnetic, so that HI,, is propor- tional to the number of Mn NN's to a gold

= 0, HNN = 210 kOe). The model described in the text is seen to be in much better agreement with the experimental results than are the

alternate descriptions shown here.

greater proportion of ferromagnetically coupled Mn ions. This leads to the result (for 15, 10, and 3.5 % Mn) Hdist = 350,260, 110 kOe, and those values have been used to calculate the solid lines in figure 2 (Somewhat better agreement with the experimental hfs can be obtained with slightly smaller values of H,,,,.)

The success of the theory, with no arbitrary adjus- table parameters, in fitting the observed spectra for the more dilute alloys suggests that the model on which the calculations is based is a meaningful descrip- tion of the sources of the hfs in the Au-Mn disordered alloys.

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and 1957, 244, 2028 ; J. Phys. Radium, 1959, 20, 430.

KUSSMAN (A.) and RAUB (E.), 2. Metallk, 1956,47,9.

SATO (K.), HIRONE (T.), WATANABE (H.), MAEDA (S.) and ADACHI (K.), J. Phys. SOC. Jap., 1962,17 (Supp. Bl), 160 ; JACOBS (I. S.), KOUVEL (J. S.), LAWRENCE (P. E.), ibid, 157.

INOUB (K.), NAKAMURA (Y.), YAMAMOTO (K.) and MARWAMA (S.), J. Phys. Soc. Jap., 1968, 24, 646.

SMITH ,. (J. H.)

and WELLS (P.), J. Phys. (C) Ser. 2, 1969,

[6] FERROMAGNETIC coupling between Mn ions lying 3.31 A apart on square planar lattice. Overall magnetic structure is flat spiral. HERPIN (A.), MERIEL (P.) and VILLAIN (J.), Compt. Rend., 1959, 249, 1334.

[7] Slightly distorted from CsCl structure. Overall magne- tic structure is antiferromagnetic. BINDLOSS (W.), J. Phys. Chem. Sol., 1968, 29, 225.

[8] COHEN (R. L.), WERNICK (J. H.), WEST (K. W.), SHERWOOD (R. C.) and CHIN (G. Y.), Phys.

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[9] PATTERSON @. O.), THOMSON (J. O.), HURAY (P. G.)

and ROBERTS (L. D.), Phys. Rev. B, Sept. 1,1970.