Nuclear magnetic resonance in alloys

HAL Id: jpa-00236657

https://hal.archives-ouvertes.fr/jpa-00236657

Submitted on 1 Jan 1962

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Nuclear magnetic resonance in alloys

N. Bloembergen

To cite this version:

N. Bloembergen. Nuclear magnetic resonance in alloys. J. Phys. Radium, 1962, 23 (10), pp.658-664.

�10.1051/jphysrad:019620023010065801�. �jpa-00236657�

lattice would result in an exponential dissipation ^Discussion

of the partial waves with increasing ^{distance, and} B. CAROL!. - Dans un travail effectué ^{en 1961 (1)}

consequently an exponential ^{term in the} decay ^of _{on a étudié les effets des} interactions entre impu-

the resistivity contributions. ^{Finally, it may be} commented that while ^{thé the} retés dans un gaz d’électrons thode de perturbation poussée ^{au libres} second ordre. Le ^{par une mé-}

coherent and multiple scattering contributions to potentiel d’impureté est schématisé par un poten- the electron density distribution in the

lattice are tiel de Yukawa. On établit les formules donnant les

oseillatory in nature, and may not contribute variations de densité électronique ^{et de} dépla- greatly to the predicted Knight shift in dilute cement de Knight dues aux interactions. ^{On obtient}

alloys, the oscillatory character will nevertheless

des formules analogues à celles de M. Flynn, et des

result in a contribution to the mean square value of

résultats comparables. La résistivité résiduelle due

the density at nudear sites of électrons at the ^aux interactions entre impuretés est évaluée et Fermi surface, ^{and thus to the width} of nuclear

dans le cas particulier des bilacunes les résultats resonance lines. These effects are therefore of inte- suivants sontobtenus : des bilacunes les resultats rest as a possible explanation ^{of the anomalous} _{- Pour courant} d’électrons parallèle à ^l’axe

width obtained experimentally [6] ^{for the} ma- de la bilacune, ^{courant d} électrons parallèle a 1 ^sur

gnetic ^résonance lines of solvent nuclei in dilute

l’autre est telle que la résistivité totale est à peu

alloys. près la moitié de ce qu’elle ^{serait sans} interférence.

- Par contre, lorsque le courant électronique Acknowledgement. - ^{It is a} pleasure ^{to thank est} perpendiculaire ^à l’axe de la bilacune, ^{les deux}

Professor D. Lazarus for his encouragement ^and lacunes diffusent _{à peu} près indépendamment.

Mr. R. Odel for his assistance in the computations ₍₁₎ B. CAROLI, ^{Thèse de 3e} cycle, Faculté des Sciences

1nvolved in this work. d’Orsay, ^1961.

REFERENCES

[1] ^ZIMAN (J. M.), Electrons and Phonons, Oxford, 1960.

[2] ^FLYNN (C. P.), Phys. Rev., 1962,126.

[3] ^FLYNN (C. P.), Phys. Rev., 1962, 125, 881.

[4] ^BLATT (F. J.), Phys. Rev., 1959, 108.

[5] ^BROSS (H.) and SEEGER (A.), ^J. Phys. ^Chem. Solids, 1959, 11, ^115.

[6] ^ROWLAND (T. J.), Phys. Rev., 1962, 126.

NUCLEAR MAGNETIC RESONANCE IN ALLOYS

By ^N. BLOEMBERGEN,

Harvard University.

Résumé. 2014 On étudie d’abord l’effet d’une impureté

^non

magnétique

^sur

la résonance nucléaire dans

une

matrice métallique. ^Au voisinage ^de l’impureté, la densité d’électrons est modifiée et cette perturbation ^{s’étend à d’assez} longues distance. Il

en

résulte : 1) ^{Un effet}

^sur

la resonance

quadrupolaire des noyaux de spin ^I > 1/2 qui ^est

^en

général beaucoup plus fort que l’effet des distorsions du réseau. 2) Une modification du déplacement ^de Knight moyen, accompagnée (en

phase solide) ^d’un élargissement de la raie. On rappelle ensuite les propriétés ^anormales (signe ^et

variation thermique) ^du déplacement ^de Knight ^dans certains matériaux purs ^avec des bandes d

ou

f incomplètes, et enfin les résultats récents relatifs

aux

alliages ferromagnétiques.

Abstract.

²⁰¹⁴

The effect of

a

non magnetic impurity ^on the nuclear resonance of the host metal is considered first. The impurity ^is responsible ^for

^a

change in the electron density, ^{which has a} long range in space. ^This gives : 1)

^a

strong ^effect

^on

^the quadrupole ^{resonance of} nuclei with

spin ^I > 1/2 (the effect of lattice distortions being usually ^much scaller) ; 2)

^a

change ^{in the} Knight shift, ^and (in ^{the solid} state)

^a

corresponding ^line broadening. ^In

^a

^second part the anomalous behaviour (sign ^and

tem erature variation) ^{of the} Knight shift in pure metallic systems ^with incomplete d

^or

f ^shells (e.g. V3Ga, Pt, etc...), ^{is recalled and} finally tho recent results

on

ferro-

magnetic alloys

^are

^reviewed.

LE

JOURNAL

DE

PHYSIQUE

ET LE RADIUM TOME

23,

^OCTOBRE

1962,

When the present author reviewed this same

topic eight ^{years ago} [1], only experimental ^results

of Rowland’s early ^{work were available} [2]. ^It

was already ^{clear at that time} that nuclear spins

are very suiialle Lü probe ^thé local distribution of internal magnetic fields and electric field gradients

in the vicinity ^{of a solute atom in} alloy systems.

At that time thé existence of électron coupled

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:019620023010065801

nuclear spin interactions of the éxchange ^and pseudo-dipolar type ^had already ^{been demons-}

trated experimentally in the thallium system, although ^{this was not} reported ^{on at the Bristol}

conférence. Ruderman and Kittel [3] gave ^a

theory for the scalar AI1.I2 coupling ⁱⁿ metals,

which was extended by ^{the author to} pseudo- dipolar coupling B[I1.12

^-

3rï23(I1° rl2) (12. ’12)],

and also to insulators [4]. ^The interesting ^result

of the theory in metals is the dependence ^{ot the}

constant A (and B) ^{on the} internuclear distance

This is a direct consequence of the abrupt drop

in the number of occupied states in momentum space ^at the Fermi surface. If the Fermi surface

was spread ^{out in the direction of r over an inter-}

val Ak, ^the interaction decays ^as exp (- Akr).

The nuclear spin I, ^{can be} considered as a local

(magnetic) imperfection, ^{which scatters the Bloch}

.

waves and changes the electronic spin density ^at

the position ^of I2, or ^{vice versa. The} concept ^of the spin ^{as a} point imperfection ^{takes on a more} tangible form, ^{if one} substitutes a magnetic impu- rity ^{in the} lattice, e.g. Mn in copper. A similar

coupling A1. S is obtained between the spin of ^the

copper nuclei and the magnetic electron of the Mn

impurity. ^{This case was studied} theoretically by

Yosida [5] ^and experimentally by Behringer [6].

The scattering ^{of Bloch waves} by the electro- static potential presented ^{by an} impurity ^atom,

first treated by Friedel, ^{should have a similar} spatial dependence. ^{It is a} curious fact that the relevance of this situation to the nuclear quadru- pole coupling ⁱⁿ alloys ^{was not} appreciated ^{in 1954.}

The Thomas-Fermi model used by ^{Mott for} impu- rity scattering ⁱⁿ alloys gives ^a short range expo- nential screening ^rather than the modulated inverse cube dependence of eq. (1). Since observed

quadrupole interactions extended so far as to include

more than a hundred neighboring ^{atoms, the effect}

of local strain which drops ^{off as} r-3 f romthe impuri- ty ^was considered more important. ^{The new expe-}

riments which led to a re-examination of the theory

of the charge density ^{around an} impurity ^{atom are}

reviewed in the ^next section. In the third section the new experimental ^{data in} alloys ^{with a} simple

band structure are compared ^{with the} theory. ^In

the fourth section recent work on more complicated

band structures is considered, while the nuclear

magnetic ^{resonance in} ferromagnetic alloys ^is

reviewed in the final section.

2. Quadrupole Interaction in Alloys.

^r-

^Row-

land [7] ^{has made a} systematic investigation ^{of the} apparent decrease in intensity ^{of the 63Cu reso-}

nuance- in copper alloys with -many différent solute atoms. The concentration dependence ^{can be des-}

TABLE 1

COMPARISON

OF THE EFFECTS OF VARIOUS

SOLUTES

OF EFFEC- TIVE CHARGE

Z’

IN

COPPER

ON

NUCLEAR

INTENSITY AT

4 Mc/sEc. ^{THE "}

^WIPE

^{OUT "}

NUMBER n IS A MEASURE FOR THE ELECTRIC FIELD

GRADIENT ; d(In a)/dc [REPRE-

SENTS

THE

RELATIVE

LATTICE MISFIT IN

(ATOMIC

^FRAC-

TION)-l.

FIG. 1. - The effect of fourth period ^solutes

^on

^{the 63Cu} absorption signal ^{at 4} Mc/s (after ^Rowland [7]).

^>

cribed by (1 - c)", where n is an effective " wipe- out " number, giving the number of neighbors

whose contribution to the intensity is made unob- servable. There is a strong correlation between this number n and the effective charge ^{of the} impurity, ^and little correlation with the strain due to misfit of atomic size. This is illustrated by

Rowland’s data reproduced ⁱⁿ Table I and figure ^1.

Quantitative measurements of the MNR inten-

sity ^{when strains are} induced in pure copper also

show that these high " wipe-out " ^{numbers cannot}

be explained by ^strain [8].

Redfield and Anderson [8] have detected zero

field quadrupole resonances, presumably arising

from first and second neighbors ^{near an} impurity

in Li and Al alloys ^{in the} audio-frequency ^range.

The experiment proceeds ^as follows. Observe the

intensity ^at high ^{field at low} températures ^where Ti

is long. Demagnetize adiabatically. ^{Raise the} spin temperature by ^{audio resonance observed.}

Observe the intensity ^at high field after adiabatic

magnetization.

Kohn and Vosko [10] and Daniel and Friedel [11]

have calculated the spatial ^{variation of the} charge

around an impurity ^{and the} resulting field gra- dient at nuclei in the vicinity ^{of the} impurity.

Their result for the gradient ^{at an distance r from}

the impurity ^is

where the constant C contains the antishielding

factor and the Friedel phase shifts for impurity scattering. ^The spatial dependence ^{is seen to be}

identifical with the Ruderman-KitteLYosida

expression (1), within the approximations ^made.

The theory ^{now accounts for the} main features of the observed wipe-out ^{numbers. The variation in} charge density increases with the effective charge

on the impurity. Usually only ^{the first two} phase

shifts in C are important. ^{These can be deter-}

mined from the Friedel sum rule and the observed value of the residual resistivity. ^{This determi-}

nation is least reliable for solute atoms pf ^{the same} valenoy ^{as the solvent. In this case strain effects}

and a polarization ^which depends ^{on details of the} scattering potential play ^a dominant role. The

theory ^{accounts for the} main features of the obser- vations.

3. Knight Shif t in Alloys ^with simple band struc- ture.

^-

Rowland [12] ^{has also made a} systematic investigation ^of the variation in the Knight ^shift

of the 107Ag ^and lo9Ag ^{resonance in silver} alloys

with many différent solute atoms. Drain [13]

studied the cadmium and silver resonances in the Cd Ag system.

The nuclei must have a spin ¹

⁼

1/2, ^{to avoid}

domination by quadrupole ^{effects. The} Ag ^reso-

nance lines are narrow because of the small dipolar

and exchange interactions. Yet the Knight ^shift

is rather large. ^{Silver can be} alloyed ^with many solute elements. It is a very good ^{choice to} study

the variation in Knight ^{shift near an} impurity.

The shift is proportional ^to the average spin polarization ^{and the} charge density ^at the nucleus k

⁼

(dHgIHo) = (803C0/3) Xs Q 17(O)2 >F (3)

Here _xs is the volume spin susceptibility, ^{il the}

atomic volume. The relative variation in

is the same as the relative variation in the charge density ^{due to} scattering ^{of Bloch waves at the}

Fermi surface by ^the impurity.

The relative variation averaged ^{over all sites in}

an alloy with atomic concentration c 1 of impu-

rities which are considered as independent ^scat- terers, ^is given by,

The increase in the second moment, ^caused by

the distribution of Knight ^{shifts on different} sites,

is

KIf 0 ^{is the absolute} value of the shift in the pure solvent. The change ⁱⁿ charge density ^is again

calculated from scattering theory [14, 15].

Rowland found indeed ^a systematic ^{variation of}

the average Knight shift with the effective charge

on the impurity. ^A typical result for one column of the periodic system ^{is shown in} figure ^{2. The}

FIG. 2.

^-

The decrease in absolute Knight shift for the Ag

nuclear resonance at 10 040.7 Oe, ^as

^a

function of solute concentration of fourth period ^elements (after L Rowland [11]).

trends are similar to the quadrupolar effects of different solutes, ⁱⁿ agreement ^with scattering theory. ^An exponentially ^screened charge ^would

make predictions incompatible ^with experiment.

Rowland also found an asymmetric broadening

of the resonance. The nearest neighbor ^{sites have} generally ^{a smaller} Knight ^{shift in} agreement ^with

the theoretical spectrum ^of shifts ait different sites [15].

Rimai [16] ^{has made very detailed} measurements of the Knight ^shift in the Na K and Na Rb _sys- tems. In the liquid phase ^the motionally ^narro-

wed lines allow a very precise determination of the average shift given by eq. (4). Throughout ^the liquid composition ^{range both the 23Na and 87 Rb}

resonance frequency ^vary linearly ^{with the relai}

tive Rb concentration c. Figure 3 also shows the

sharp breaks that ^occur when a phase boundary ^is

reached. Both liquidus ^and solidus in the phase diagram ^{of the Na Rb} system ^{have been deter-}

mined by ^nuclear magnetic ^resonance.

The 23Na resonance can be observed in almost pure rubidium. This probes ^the charge density

inside the scattering ^center. Volume corrections

FIG. 3.

^-

The shift in the 87Rb resonance frequency

in Na-Rb alloys.

for dilatation of the Wigner-Seitz ^{cell can be made} experimentally, ^{because the} explicit ^volume depen-

dence is known from the _pressure dependence ^of

the Knight ^{shift in the} pure metal. The ^{shift of} 23Na resonance in almost pure Rb (c =1) ^with respect pure ^{Na is} according ^{to the} scattering theory

for free electrons,

The relative slopes ^K-1 (ôK jôc) ^{for Na and Rb}

can also be compared. They ^{should be the same}

on the basis of simple scattering theory. Experi-

mental relative slopes ^{are however} thirty percent

différent. At c

⁼

1 the value for Na is 0. 42, ^and

for Rb it is 0.27.

A square ^well potential ^of spherical ^volume

cannot account precisely ^{for all observed data.}

The theory ^{is very sensitive to} slight self-consistent variations in size and depth, especially ^{inside the} scattering ^{center. This may} partly ^{be due to the}

fact that solvent and solute have the same valency.

Again ^the theory gives good qualitative agreement, but does not predicts ^details quantitatively.

An important assumption that ^{has always been}

made is that of a spherical ^{Fermi surface. If the}

surface has however sharp spikes, ^even longer

range interactions may result from ^a slight ^excess

of scattering processes with ^a very small reduced

scattering ^vector. Some evidence for this has been obtained, from line width measurements in the Na-Rb system. ^The width ^{of both} the Na and Rb

resonance increases as a fifth power polynomial ⁱⁿ

the concentration c. It is proportional ^{to the Rb}

concentration and to the indirect exchange ^and pseudo-dipolar interaction _squares between 55Rb and 87Rb nuclei, ^or between Na and Rb. This

exchange interaction itself is proportional ^{to the} Knight ^{shift of} each nuclear species, ^{which in turn}

is a linear function of c. The very striking ^line

FIG. 4.

^-

The linewidth 1 JT2 of the 87Rb resonance in

Na-Rb alloys.

width dependence ^{on c is} reproduced ⁱⁿ figure ^4.

A detailed discussion has been given by ^{Rimai and} Bloembergen [16]. ^Further experiments ^on T,

and T2 ^{in other} liquid alloy systems, ^{and in the} Na Rb system ^with change ⁱⁿ isotopic ^consti- tution, ^{are needed to} clear up this point.

4. Knight ^{shift in} complex band structures.

^-

A negative Knight ^{shift was} first observed by

Rowland in the NaTI system [1]. ^A systematic investigation ^has recently ^{been made} by Clogston

and Jaccarino [17] ^{of the} V2X system (X

⁼

As, Au, Co, Ga, Ge, Si, Sb, ^{Sn and} Pt), ^where tempe-

rature dependent ^and negative Knight ^{shifts have}

been found. Metallic platinum ^{also bas a} nega.

tive shift [18]. ^A variation of K with temperature

is always accompanied by ^{a variation} of the suscep-

tibility Z ^with temperature. ^{There is a linear} relationship ^{between .K} and x, ^{but not a strict} proportionality.

Clogston ^has proposed ^{a two band model to} explain ^these observations, ^{shown in} figure ^{5 for}

FiG. 5.

^-

A schematic diagram ^{for the} density ^{of states vs.}

energy in V2 ^Ga (after Clogston [16]).

the case of V3Ga. ^The susceptibility xd of the very

narrow 3d band of vanadium is temperature dependent. ^The susceptibility ^{of the conduction}

band _xs, which consists of a mixture of 4s and 4p

wave functions, ^is temperature independent. ^It gives ^a temperature independent, positive ^contri-

bution to the Knight ^{shift at the V} nuclei, ^and through ^core polarization ^a temperature ^inde- pendent negative contribution at the Ga nuclei.

Although ^the magnetization ^{of the} 3d(V) ^band

cannot contribute directly ^{to the} Knight ^{shift of}

the Ga or V ^resonance because the 3p ^{and 3d wave}

functions vanish at the nucleus, ^{it can} polarize ^the

core functions 3s and 2s. This will produce ^a negative temperature dependent contribution at both nuclei.

One thus concludes that both Kv and KGa ^are linear functions of _Xs and _xa. Kv is positive ^and

decreases as the temperature ^is lowered, ^{KGa is} negative ^and increases in absolute magnitude ^as

thé temperature ^{is lowered. Kv and .KGa are} linearly ^{related to each other as the} temperature ^is varied. ^’These statements are in agreement ^with the experimental observations.

In metallic platinum and other intermetallic

compounds ^the conduction band _may have a predo-

minant p-character. ^{In this case the} negative

contribution ^{to the} Knight ^{shift from core} polari-

zation may be larger ^{than the} positive contribution from the small amount of s-character in the con-

duction band [18]. ^The Knight shift in Pt is

-

3.23 percent ^{at 290 OK and}

^-

^3.68 percent

at 20 OK. The spin susceptibility ^{has a tempe-}

rature dependent part. There may also be ^{a con-} tribution from diamagnetism ^{and second order} paramagnetism without any corresponding ^contri-

bution to the Knight.shift, x = Xa + Zd + xo.

The existence of the exchange interaction between s and d electrons is connected with ^a vio- lation of the Korringa ^{relation in} vanadium, plati-

num and niobium. The relaxation time Ti ^{is de-}

termined by ^the density ^{of states at the} Fermi level which may be obtained from the specific ^heat.

The Knight ^{shift is} proportional ^{to the} spin suscep-

tibility, which may be considerably larger ^--about

2. 5 in V and 2. 7 in Pt -than the simple expression

calculated from the density ^{of states without} exchange. Butterworth [19] ^{has shown that this}

observation can give ^a satisfactory ^{account of the}

fact that the Knight ^{shift is} larger ^{than calculated}

from the Korringa relation with the experimentally

observed value of Tl ^T.

^,

Pronounced maxima and other variations occur

in the density ^of states at the Fermi level, ^{as a} band ^is gradually ^filled by changing ^the alloy ^com- position. ^{This was} already ^discussed by ^Mott

and Jones and gives ^an interpretation ^{for the} Hume-Rothery ^{rules. The} Knight shift does ^not reflect these changes ^{in the} density ^{of states di-} rectly. ^A striking example ^{of this occurs in the}

Cr-V system [20, 21]. ^{One reason is that the} sharp

variations in the density ^occur mostly ^{for states}

which have a dominant p-character. ^{In other} words, ^a pronounced ^{variation in the} density ^of

states is usually accompanied by ^a pronounced

variation the relative s-character of the band wave

functions. Furthermore the effects of spin exchange may vary with alloy composition. ^It

would be of interest to measure Tl ^{in the Cr V} sys- tem in this connection.

In the rare earth intermetallic compound XA’2 ^a negative ^{shift occurs when the} 4f-shell is less than half filled, ^{but the shift is} positive for the other half. This is related to the relative orientation of S and J. The magnetization ^is determined by

the total angular ^momentum J, ^the Knight ^shift through exchange polarization of s-orbitals by ^the spin 8 ^{of the} f -electrons [22]. ^{This indirect} exchange interaction _{may have} a negative sign ^at

the position ^{of Al} according ^{to Yosida’s} theory.

This situation is discussed fully by ^Jaccarino [23].

A similar situation exists in the hexaborides.

If atoms with partially ^{filled d or} f ^{shells are}

added in low concentration as solute atoms, ^charac- teristic broadening by inhomogeneous magnetic polarization ^{of the} conduction band around the

impurity by ^its average magnetization ^{will occur,}

These effects were studied by Behringer [6].

Chapman ^and Seymour [24], Weinberg [25] ^and

others.

5. Ferromagnetie alloys.

^-

The nuclear reso- nance in the internal field of ferromagnetic ^metals

was discovered by Portis and Gossard [26]. ^The intensity is enhanced by ^{a motion of} magnetism ⁱⁿ

domain walls. One may say that the spontaneous magnetization ^{creates a} spontaneous (isotropic

and anisotropic) Knight ^shift. In pure metals

one has a polarization of the conduction band by exchange overlap ^and perhaps ^an 4s-type ^orbital

admixture to the 3d-band. These eff ects would

give ^a positive ^{internal field at the nucleus.} Expe- rimentally ^the sign ^{can be} determined by adding

an external field. This is difficult inside domain

walls, ^{but can} conveniently ^{be done on the} hyper-

fine interaction of the Môssbauer effect. The ^reso-

nance frequency ^{goes down in} Co, indicating ^a negative fnternal field. It appears, therefore, ^that

core polarization ^{of the 3s} and 2s electrons is the dominant mechanism.

Ferromagnetic alloys ^were investigated by

Kushida [27] ^{and other} [28, 29]. They ^observe

the ^resonance of the solute atoms as well as the

resonance of the solvent in the neighborhood ^{of the.}

impurity. ^The temperature and pressure depen-

dence of these " spontaneous Knight shifts " can

be determined as well. They ^are proportional ^to

the variation of the spontaneous magnetization

and ^{to the} intrinsic variation of [W(0)[2. ^Some

data ^are listed in Table II..

^,

..

Since the non-magnetic ^solute (Cu ⁱⁿ Fe) ^{has tbe}

TABLE II

same order of magnitude ^of internal field as a

magnetic ^solute (Co ⁱⁿ Fe), ^{it seems that the most} important ^{mechanism to} produce ^{a field at the}

solute nuclei is the polarization of 4s electrons in the conduction band by ^{the’ 3d} electrons of the

magnetic ^{host lattice. There are} perhaps ^some

smaller contributions from transfer of 3d-electrons

on alloying ^{and core} s-polarization ^{at the solute}

atoms.

The solvent ^resonance shows a fine structure ^on alloying. ^{The 59Co resonance has been investi-} gated in fcc. ^Co-rich alloys ^of Co-Fe, Co-Ni, ^Co-Cu

Co-Al Co-Mn and Co-Cr as a function of impurity

concentration. Satellite resonances which _appear

on either side of the main Co-resonance at

213.5Mc/s ^{and are} displaced ^{from it} by ^1-5 Mc/s

are probably ^{due to} Co-nuclei with one adjacent

solute atom. This produces ^{a variation in the} isotropic ^{as well as the} anisotropic spontaneous Knight ^shift. Quadrupole ^{effects on the 59Co reso-}

nance probably produce ^{a fine structure of less}

than 1 Mc/s.

Although ^the many different mechanism ^{in tran-} sition metal elements make a detailed interpre-

tation difficult, ^it is nevertheless encouraging ^that

nuclear magnetic ^resonance provides many inte-

resting ^{data to aid in the} disentanglement ^{of the} complex ^{band structure} problem.

REFERENCES

[1] BLOEMBERGEN (N.), Bristol Conference

on

Defects in

Crystalline Solid, 1954 ; Physical Society ^of London, 1955,1.

[2] BLOEMBFRGEN ^(N.) and ROWLAND (T. J.), ^Acta Met., 1953,1, ^731.

[3] ^RUDERMAN (M. A.) and KITTEL (C.), Phys. Rev., 1954, 96, 99.

[4] BLOEMBERGEN (N.) and ROWLAND (T. J.), Phys. Rev., 1955, 97,1679.

[5] ^YOSIDA (K.), Phys. Rev., 1957, 106, ^893.

[6] ^BEHRINGER (R. F.), ^J. Phys. ^Chem. Solids, 1957, 2,

209.

[7] ^ROWLAND (T. J.), Phys. Rev., 1960, 119, ^900.

[8] ^AVERBUCH (P.),

^DE

^BERGEVIN (F.) and MULLER- WARMOUTH (W.), C. R. Acad. Sc., 1959, 249, ^2315.

[8a] ^FAULKNER (E. A.), Nature, 1959, 184, ^442.

[9] ^ANDERSON (A. G.), ^See remark at end of paper. Phys.

Rev., 1959, 115, ^863.

[10] ^KOHN (W.) ^{and VOSKO} (S. H.), Phys. ^Rev., 1960, 119,

912.

[11] ^BLANDIN (A.) ^{and FRIEDEL} (J.), ^J. Physique Rad., 1960, 21, ^689.

[12] ^ROWLAND (T. J.), Phys. Rev., 1962,125, ^459.

[13] ^DRAIN (L. E.), ^Phil. Mag., 1959, 4, 484.

[14] ^BLANDIN (A.), ^DANIEL (E.) and FRIEDEL (J.), ^Phil.

Mag., 1959, 4,180.

[15] ^DANIEL (E.), ^J. Physique Rad., 1959, ^{20, 769.}

[16] ^RIMAI (L.) and BLOEMBERGEN (N.), ^J. Phys. ^Chem.

Solids, 1960, 13, ^257.

[17] ^CLOGSTON (A. M.) and JACCARINO (V.), Phys. Rev., 1961,121,1357.

[18] BUTTERWORTH (J.), ^{Phys. Rev.} Letters,1962, 8, 423.

[19] BUTTERWORTH (J.), ^{Phys. Rev.} Letters, 1960, 5, 305.

[20] ^BARNES (R. G.) ^{and GRAHAM} (T. P.), Phys. ^Rev.

Letters, 1962, 8, ^248.

[21] ^DRAIN (L. E.), report ^{at this} conference, ^J. Physique Rad., 1962, 23,

[22] ^JACCARINO (V.), ^J. App. Phys., 1961, 32, 1025 ; also report ^{at this} conference, ^J. Physique Rad., 1962, 23,

000.

[23] ^GOSSARD (A. C.), ^JACCARINO (V.) and WERNICK (J. H.), Phys. ^Rev. (to ^be published).

[24] ^CHAPMAN (A. C.) and SEYMOUR (E. ^F. W.), ^Proc. Soc., London, 1958, 72, ^797.

[25] ^WEINBERG (D. L.) ^and BLOEMBERGEN (N.), ^J. Phys.

Chem. Solids, 1960, 15, ^240.

[26] ^PORTIS (A. M.) and GOSSARD (A. C.), ^J. App. Phys., Supp.1960, 31, 205.

[27] ^KUSHIDA (T.), ^SILVER (A. H.), ^KOI (Y.) ^{and TSUJI-}

MARA

(A.), ^J. App. Phys., Supp.1962, 33,1079.

[28] ^LAFORCE (R. C.), ^RAVITZ (S. F.) ^{and DAY} (G. F.), Phys. ^Rev. Letters,1961, 6, 226 ; Kyoto Conference,

1961 ; J. Phys. ^Soc. Japan (in press).

[29] ^BUDNICK (J. I.), ^{LA FORCE} (R. C.) ^{and DAY} (G. F.)

Eindhoven Conference, 1962 (in press).

NUCLEAR MAGNETIC RESONANCE IN XAl2 ^COMPOUNDS

By ^V. JACCARINO,

Résumé.

²⁰¹⁴

La résonance magnétique ^nucléaire (R. ^M. N.) de27Al dans le composé métallique UAl2

a été étudiée pour les températures ^{de 4 à 300} °K. Considérant la variation du déplacement ^de Knight

K avec la température, ^{la faible} largeur de raie et le long temps de relaxation spin-réseau à ^basse température, ^on conclut que : 1° le système ^n’est pas ^{ordonné et, 2°} les electrons 5f ^{et 6d se dé-} placent, ^avec

^une

surface de Fermi qui coupe ^une pointe étroite de la courbe des densités d’états pour la bande de conduction. Les mesures de la susceptibilité ~ confirment ces conclusions. Pour

U Al2, K ^est fonction linéaire de ~: ^on peut ^{en déduire certaines} particularités ^{de la} structure de

bande, ^{en utilisant un modèle} analogue à ^celui proposé par Clogston [2] pour interpreter ^{les résul-}

tats de la R. M. N. dans les composés métalliques V3X. Ces résultats sont opposés à ^{ceux des}

métaux isomorphes des terres rares (par ^{ex. : Na Al2) ou} la localisation des électrons 4f ^{et les}

fortes interactions d’échange s-f conduisent à des comportements ^très différents pour les propriétés

de R. M. N. [3].

Abstract.

²⁰¹⁴

The nuclear magnetic ^resonance (NMR) of 27Al in the intermetallic compound UAl2

has been studied in the temperature range between 4 and 300 °K. From the temperature depen-

dence of the Knight shift ^{(K), the} relatively ^narrow line width and long spin-lattice ^relaxation

times at low temperatures it is concluded that 1) ^the system ^{does not order and} 2) ^the 5f ^{and 6d}

electrons are itinerant with the Fermi surface intersecting ^a relatively ^narrow peak ^{in the} density

of states curve for the conduction band. Susceptibility measurements [1] (~) support ^these

conclusions. From the linearity of the K vs. ~ ^curve for UAl2 certain details of the band structure may be deduced using ^{a mode’ similar to that} proposed by Clogston [2] ^for interpreting ^{the NMR}

results in the V3X intermetallic compounds. ^{The results are to be} contrasted with those obtained for the isomorphic ^{rare earth metals} (e.g. ^Nd Al2) where localization of the 4f electrons and large s-f exchange interactions lead to quite ^different behaviours for the NMR properties [3].

LE

JOURNAL

DE

PHYSIQUE

^{ET LE}

^{RADIUM TOME} 23,

^OCTOBRE

1962,

REFERENCES

[1] ^WILLIAMS (H. J.) and SHERWOOD (R. C.), private

communication.

[2] ^CLOGSTON (A. M.) and JACCARINO (V.), Phys. ^Rev., 1961, 121, 1357.

[3] JACCARINO, MATTHIAS, PETER, ^{SUHL and} WERNICK,

Phys. ^Rev. Letters, 1960, 5, 251.