Transition metal alloys

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Transition metal alloys

W.M. Lomer

To cite this version:

W.M. Lomer. Transition metal alloys. J. Phys. Radium, 1962, 23 (10), pp.716-720. �10.1051/jphys-

rad:019620023010071601�. �jpa-00236668�

[5] ^SUHL (H.), ^Low temperature physics, ^{cours de l’École}

des Houches, ¹⁹⁶¹ (Gordon ^{et Breach,} New-York), p. 321.

[6] ^BARDEEN (J.), ^COOPER (L. N.) ^et SCHRIEFFER (S.), Phys. Rev., 1957,108, ^1175.

[7] ^{GOR’ KOV} (L. P.), ^J. Exp. ^Theor. Phys., ^{U. R. S.} S., 1959, 36, 1918 ; ^Soviet Physics (J. ^{E. T.} P.), 1959, 9,1364.

[8] ^{Pour une revue de ces} méthodes, dues essentiellement à EDWARDS (S. F.), ^ABRIKOSOV (A.) ^{et GOR’KOV} (L. P.), ^{voir par} exemple Rickayzen, ^{cours de}

l’école d’été de Bergen, 1960.

[9] ^HEBEL (L. C.) ^{et SLICHTER} (C. P.), Phys. Rev., 1957, 107, 401 ^et Phys. Rev., 1959, 113, ^{1503. REDFIELD} (A. G.), Phys. ^Rev. Letters, 1959, 3, ^{85. Pour une} mise au point ^{récente sur} l’aluminium, voir MASUDA

(Y.), Phys. Rev., 1962, 126, 1271.

[10] ^ABRIKOSOV (A.) ^{et GOR’KOV} (L. P.), J. E. T. P., U. R. S. S.,19t9, 36, 319 ; 1960, 39, 1781.

[11] FRIEDEL (J.), ^{Adv. in} Physics, 1954, 3, ^446.

[12] GINSBURG (V. L.) ^{et LANDAU} (L. D.), ^{J. E. T. P.,}

U. R. S. S.,1959. 20, 1064.

TRANSITION METAL ALLOYS

By ^{W. M.} LOMER,

A. E. R. E., Harwell, Didcot, ^Berks.

Résumé.

Une propriété intéressante des alliages de métaux de transition est actuellement l’existence de spins électroniques localisés. Il y a aussi, particulièrement ^{dans la} première période,

le problème ^{des états} magnétiques ordonnées. Des travaux récents ont établi _que les spins ^loca-

lisés peuvent disparaître dans les matériaux ayant ^une forte densité d’états au niveau de Fermi, par combinaison ^{de ces} états de conduction (qui ^sont également acceptés pour les ^deux directions de spin) avec l’état localisé favorisé par l’atome d’impureté. Cependant la densité d’états n’est pas ^un paramètre ^assez déterminant, ^{et des} propriétés additionnelles, telles que la forte suscep-

tibilité, dans le cas du palladium par exemple, jouent ^{un rôle} important dans la stabilisation des états atomiques magnétiques. ^{Dans le} modèle des bandes, ^le ferromagnétisme ^est favorisé par

une grande ^densité d’états, ^{venant de la bande d.} Cependant ^une forte densité d’états de conduc- tion supprime le moment de spin ^sur les atomes d’impuretés, ^en élargissant considérablement les états d et en favorisant des populations égales ^de spin. ^{Il est done} particulièrement intéressant d’étudier les propriétés ^des alliages ^aux concentrations où commence à apparaitre ^le comportement ferromagnétiques, ^par exemple ^{V-Fe entre 15} % ^{et 25} % ^{de fer.}

Abstract.

A particular interest in the properties of transition metal alloys ^{at the} present

time is the problem ^{of the} occurrence of localised electron spins. ^{There is} also, particularly ⁱⁿ

the ^first period, ^the problem of ordered magnetic ^states. Recent work has established that

suppression of localised spin ^{may occur} in materials with a high density of states at the Fermi level, through ^the agency of combining those conduction states (with their balanced spin ^occu- pation) with the local state favoured by ^the impurity ^{atom. The} density ^of states, however, ^is

not a sufficient discriminating parameter, ^and additional properties, ^{such as the} high suscepti- bility ^of e.g. Pd, play ^an important ^{role in} stabilising magnetic atomic states. Ferromagnetism

on the band model is favoured by ^a high density ^{of states,} originating from the d-band. A high density of conduction states, however, suppresses spin ^{moment on impurity atom,} by broadening

the d-states considerably and favouring ^equal spin occupation. Very particular interest, ^there- fore, ^{attaches to the} properties ^of alloys at concentrations where ferromagnetic ^behaviour begins, such as vanadium-iron between 15 % ^{and 25} % ^Fe.

LE JOURNAL

PHYSIQUE ^{ET LE RADIUM TOME} 23, ^OCTOBRE 1962,

Introduction.

The last few _years have seen some notable advances in our knowledge ^{of the}

Fermi surfaces of simple ^metals [1], ^{and now there}

are; ^over the last few months, reports ^{of measu-}

rements of de Haas van Alphen [2], magnetoresis-

tance [3], cyclotron ^resonance [4] ^{and ultrasonic} absorptions [5] ⁱⁿ Cr, Mo, ^{W. At the same} time,

some fairly convincing ^band theory computations

have been carried for transition metals [6] (see fige 1)

and it seems as though ^{we must} expect ^to get

more and more detailed information, ^which may

even prove ^as informative as that on copper.

One thing ^{which I am} always surprised ^{to find it}

necessary ^to repeat, ^{is that the} density ^{of states}

value _{for any} particular ^metal depends ^{on its}

structure, ^{and so there cannot be} any universal

curve of density ^{of states versus number of elec-}

trons per ^atom. Even within a single ^structure

there are many singularities ^{in a} density ^{of states}

curve, and they ^{cannot, be} correctly reproduced

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:019620023010071601

without proper inclusion of’ all states ; e.g. ^a tight binding calculation with d-states only ^{cannot be} good enough.

FIG. 1.

Energy ^vs. wavenumber relation in b. c. c.

iron in the (100) ^direction according ^{to Wood} [6].

FIG. 2. ’Density ^{of states in the} outer electron bands

according ^to Cornwell and ^Wohlfarth [7] ^{based on} Wood [6].

The curve derived by ^{Cornwell and Wolfarth} [7]

( fig. 2), shows what a strict deduction from Wood’s calculations leads to.

Perturbations of band structure and impurity

states.

The recent treatment (Clogston [8],

Anderson [9], ^Wolff [10]) ^{of the} problem ^{of local} spin polarised ^{states at dissolved atom sites in}

dilute alloys ^have explained much of the wide range of behaviour of diffeient alloy systems ^based

on simple ^{metals. While none of the treatments}

so far is strictly applicable ^to transition metal

alloys, ^the general viewpoint ^does extend into this field. The basic notion is that the conduction band functions are modified near the impurity atom, ^{in such a} way that ^a self-consistent charge density ^{is built} up. Spin polarisation ^{of this} charge density ^{then occurs if the} depression ^{of the}

centre of the virtual state, U, ^is greater ^{than the} width of the level A. In general ^terms this should still hold in the transition ^metals just ^{as in the}

formal treatment given ^for simpler ^cases (see fig. 3).

Fie. 3.

Occupation density of virtual levels split by self-polarisation (Anderson [9]).

FiG. 4.

Magnetic moment of iron dissolved in alloys ^of the second long period (Clogston ^{et al.} [11]).

Unfortunately, ^the density ^{of states is the} only

’ variable which we know at all accurately ; it pro-

bably does control the width of the virtual level,

so that these levels will be wide in V and Nb and

718

narrow in Cr and Mo. An explanation ^{of the}

results of Clogston ^{et al.} [11] (fig. 4) ^{on the} magnetism of Fe in second period metals, ^{may be} possible ^on these lines:

Another consequence of the general ^{form of}

the E - k curves for pure transition metals is that

throughout ^{the Brillouin} Zone, ^{at all k} values,

there will be occupied ^and unoccupied bands sepa- rated by only ^{a small} energy différence -perhaps

an electron volt or two. These levels will in

general ^be coupled together by ^a magnetic ^field, giving rise ^{to a Van Vleck} temperature-independent paramagnetism [12, 13]. ^{This will} probably ^fluc-

tuate less sharply than the electronic specific ^heat constant, y, with atomic number and with struc- ture (though ^{it will} normally ^be greater ^when y is

greater). ^{We therefore} expect ^a large temperature independent contribution _{to x} through ^induced

orbital moment, ^over and above that due to the

simple ^{Pauli term} xp TABLE

The Table demonstrates that this is ^so

The curves for the variation of _y and X ^across

the continuous b. c. c. disordered solutions of various metals are shown in figure ^{5 and 6} [14, 15].

FIG. 5.

Electronic specific heat of b. c. c. alloys (Cheng ^{et al.} [14]).

The solutions of Mn, Fe, Co, ^{Ni in V have also}

been studied and a suprisingly consistent plot against ^the electron/atom ratio has been found [16]

( fig. 7). ^{This has not been} adequately explained ;

the virtual levels arguments ^lead quickly ^{to the}

idea that the levels should be broad because of the

high density ^of states, ^{so that no} permanent para

FIG. 6.

Magnetic susceptibility ^{of b. c. c.} alloys

at room temperature (Taniguchi ^{et al.} [15]).

magnetic ^{moment should be} expected. ^{The for-}

mation of unpolarised ^{states below the} Fermi level may perhaps ^be regarded ^{as with} drawing ^states

from the top ^{of the} band, and from the region ^of

the Fermi surface, ⁱⁿ the way proposed by ^Friedel

to explain ^the persistence ^{of the} Hume-Rothery

rules in alloys ^{like Cu-Ge. It is not easy, however-}

to understand quantitatively ^the reduction in _sus,

719

ceptibility. ^{The absence of} polarised ^{local states}

is confirmed by ^{the absence of} serious line broa-

dening ^{in the} magnetic ^{resonance of the vanadium}

nuclei in the alloys [18]. ^At higher concentrations,

e.g. 20 % ^{Fe in} V, ferromagnetism ^sets in, ^{and the}

mechanism of the emergence of these polarised

states is not known.

FIG. 7.

Magnetic susceptibility of vanadium based alloys (Gardner ^{et al.} [16]).

The magnetic susceptibility ^{has been measured}

in a wider _{range of} alloys than has the low tempe-

rature spécifie heat. It is a pity, therefore, ^that

the complications associated with its interpretation preclude determination of the density ^{of states}

from it. The main terms are three ; ^{the basic}

Pauli term, ^{the Van Vleck} term, and the " exchange

enhancement " term, which functions as an un-

known multiplying ^{factor in front of the Pauli term.}

Nevertheless, ^{rise and fall} in X probably ^shows

FIG. 8.

Magnetic susceptibility ^of close-packed alloys (Taniguchi ^{et al.} [15]).

qualitatively ^{the nature of} the form of the density

of states. The results are shown for close packed

metals ⁱⁿ figure ⁸ [15].

Spin distribution in alloys.

^{Some recent neu-}

tron experiments ^on ferromagnetic alloys ^at

Harwell are worth reporting. Form factor measu- rements of the localised perturbation ^{of magnetic}

moment density in nickel based alloys ^{have been}

made using the elastic scattering ^of long ^wave- length ^neutrons. The first result to notice is that for Fe dissolved in Ni the form factor is nearly constant, ^{over the} observable angular range, ^as

expected ^{for the} d-f unction of a single ^atom (fig. 9a). This is in sharp ^{contrast to the second}

result. When V is added to Ni, ⁵ I£B ^are removed from the saturation magnetisation per added atom,

FIG. 9.

Observed from factors due to magnetic ^disorder scattering ^{in FeNi} (a), ^{and NiV} (b).

and the form factor demonstrates that the dema-

gnetisation spreads ^{on to at} least third order neigh-

bours (fig. 9b). The third result is that in more

concentrated alloys ^{in the} composition ^{range near}

25 % Fe, ^{with différent} degrees ^of order, the angu- lar distribution of scattering ^from magnetic

moment follows closely ^the angular distribution of

scattering ^{from iron nuclei} (this ^{latter can be made}

dominant by using ^the separated isotope ^6°Ni

which has small nuclear cross-section) (fige 10).

FIG. 10.

Form factor due to local ordering ^of spin ^den- sity ^{in FeNi} compared with that due to nuclear scattering from FeNi.

This = demonstrates ^{that the moment} addedlby ^the

iron atoms is well localised round the atoms even

in the concentrated alloys.

Similar experiments ^{lead to} the measurements of

the individual moment localised around the cobalt

and iron atoms. This shows that the high ^{rate o}

dependence ^of saturation moment on iron concen

720

tration is in fact satisfactorily explained by saying

the iron atoms carry ^{a moment} of 2.8 _(LB (fig. 11).

FIG. 11. - Atomic moments on iron and cobalt atoms

in the alloys.

A last result to quote here is the dependence ^of ferromagnetic spin ^wave energy ^on composition ^of alloys in iron-nickel alloys. ^The spin ^wave energy becomes _very low as the composition approaches

30 % ^Ni 70Fe. ^The parameter plotted ⁱⁿ figure ¹²

is ,T

hwl S > k2.

Conclusion.

The behaviour of transition metals and their alloys ^is complex. ^{At the} «present time, ^{there seems} great hope that the Fermi sur-

faces of the pure metals may be studied with as

much success as the simpler metals. The dilute

alloys ^{are sometimes} paramagnetic following ^Curie-

Weiss behaviour, ^{and the evidence} is that this

occurs only in solvents with a low density ^{of states.}

The high density solvents show a kind of behaviour

FiG. 12.

Spin ^wave energy ^{as a} function of composition

in Fe-Ni. The parameter plotted ^is w/ S > k2 where S > is the mean spin ^value.

consistent with perturbed ^band theory. ^{The ener-} getics ^{of these two} situations are presumably ^{to be}

described along ^the And erson-Clogston -Wolff ^lines.

The distribution of magnetic ^{moment in ferro-} magnetic alloys ^{is also} probably consistent with a

perturbed ^band theory, ^{but at the moment there}

seems to be no description of the range of the moment distributions in alloys ^{of this kind.}

Thus, ⁱⁿ all, ^{it seems as} though ^{the next few}

years will ^see the theory ^of transition metals and their alloys ^{become as well} developed, ⁱⁿ principle,

as that of the simpler ^metals.

Acknowledgements.

^{I am} _very grateful ^to

Dr. W. E. Gardner for supplying ^{the Table and} figure 7, ^{and to Drs.} Lowde, Low, Collins and Mallet for results quoted ⁱⁿ figures 9,10,11 ^and 12,

before publication, ^{and to all} my colleagues ^for

many discussions ^on this general subject.

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[2] ^SHOENBERG (D.), Private communication.

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