N. M. R. STUDY OF HYPERFINE AND QUADRUPOLE INTERACTIONS IN FERROMAGNETIC GdAl2

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N. M. R. STUDY OF HYPERFINE AND QUADRUPOLE INTERACTIONS IN

FERROMAGNETIC GdAl2

N. Shamir, N. Kaplan, J. Wernick

To cite this version:

N. Shamir, N. Kaplan, J. Wernick. N. M. R. STUDY OF HYPERFINE AND QUADRUPOLE

INTERACTIONS IN FERROMAGNETIC GdAl2. Journal de Physique Colloques, 1971, 32 (C1),

pp.C1-902-C1-904. �10.1051/jphyscol:19711320�. �jpa-00214353�

JOURNAL DE PHYSIQUE

Colloque C I, slrpplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 902

N. M. R. STUDY OF HYPERFINE AND QUADRUPOLE INTERACTIONS IN FERROMAGNETIC GdAI, (*)

N. SHAMIR and N. KAPLAN

Physics Department, Hebrew University, Jerusalem, Israel and

J. H. WERNlCK

Bell Telephone Laboratories, Murray Hill, N. J., U. S.

R h r n e . - Un nouveau spectre de

de A127 dans GdA12 ferromagnetique

ete dkcouvert. Les rais de

presentent des oscillations d'amplitude d'echos de spin par rapport au temps de separation

entreles impulsions

Un modkle phenomenologique tenant compte des donnees experimentales est propod. On conclut que

L'ani- sotropie maximale probable de l'tkhange effective

est de

%.

Un assez grand gradient de champselectriquedepen- dant de I'aimantation existe dans les deux sites de Al27.

Abstract.

A new A127 n. m. r. spectrum is reported in ferromagnetic GdA12. The n. m. r. lines exhibit spin echo amplitude oscillation vs. the time separation

between the exciting r.

pulses. A phenomenological model is suggested to account for the observed data and it is concluded that

The.possible anisotropy in the effective exchange

is less than

%.

A sizable magnetization-dependent electric field gradlent exist at the A127 sites.

11.

Experimental Procedure and Results.

Several GdAI, powder samples

40

particle size) were prepared and X-ray analized in different laboratories.

The r. f. absorption profile was measured using conven- tional spin echo techniques in the (1.40 - 900)K range with external fields up to 15 kg. Power and field dependence of the spin echo amplitude indicate the observed absorbtion to be from nuclei in domains.

Results for all samples were identical. A new absorb- tion line

centered around v(a)

60.5 MHz (line a) has been observed, as well as the previously reported line [I], centered around v(b)

49.5 MHz (line b) (see Fig. 1). The normalized intensity ratio, Z(a)/l(b), is approximately 113. The temperature dependence, and therefore the magnetization dependence, of v I. Introduction.

It is generally believed that

FIG. I. -

Un-normalized

absorption profile.

magnetic order in RB, intermetallic compound of the Laves Phases group (R is Rare earth and B is nonmagnetic) is caused by some RKKY type indirect 5 exchange interaction. Therefore, it is of some interest .=

to study the exchange interaction between the 4 f electrons at the R site and the conduction electrons

indicate that both lines are centered around magnetic transitions, and external field dependence of

verifies that both lines are caused by AI2' nuclei. Two addi- tional lines (not shown) associated with GdM5.

were also observed. P I

The echo amplitude for both lines was measured as function of the time separation

between the two r. f. pulses, both for the primary echo E(1) at t

2

and for the secondary echo E(2) at t

3

As shown in figure 2, both lines exhibit marked echo amplitude oscillations, with fundamental frequencies

f (a)

520 + ^{50 kHz}

in this structure. With Gd forming a truly S state, GdAI, is perhaps the most amenable for such study, .s

and thus we shall describe an experimental n. m. r. ?

study of A12' in ferromagnetic GdAI, and outline a phenomenological model which provides infor- { mation with regard to the conduction band and the S(4 f)-S(conduction) interaction. In particular it .&

will be demonstrated that the effective exchange J,, is isotropic even in the markedly nonspherical conduction band in GdAI, and that the electric field gradient, e. f. g., at the nonmagnetic site has a large magnetization dependent contribution.

1 L\:

L 5 50 55 60

3 - ^{H e x t} = 0

-

(*)

Supported by thc Israeli

K.

and f (b)

240 + 20 kHz for E(l) and twice these

(*) a hi^ line base been reported in an

unpublished

frequencies for E(2). No oscillation could be detected by R. Gegenwarth. in the lines associated with Gd155,

Preliminary

- -

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711320

N.

M.

FIG. 2. - ,4127 spin echo amplitude modulations induced by quadrupole interaction. Insert at lower right-A1 tetrahedron in GdA12 showing the two different site symmetries in magne-

tized crystal.

measurement, performed as yet with line (a) only, indicate that f (a) increases slightly with increasing temperature.

111. Data Analysis. - A two step model calcula- tion can account phenomenologically for all of the results reported above. We first treat the positions, v(a) and v(b), and the intensities of lines a, b. In a magnetic domain of GdAl, with M I[ [I,

11, there are two magnetically inequivalent Al sites [2] labelled a and b (see insert, lower right of fig. 2) with number ratio of 1 to 3 respectively. At site (a), M points along the local axial symmetry direction whereas at (b) sites M forms an zfigle of 70° 32' with the local sym- metry axis. We shall partition the total magnetic field, He,,, at each site into two parts

a hyperfine field H,, arising from the Jsr interaction and taken to be antiparalles to M and a dipolar field H d i p caused by the localized magnetic dipoles at Gd sites with components

Gd

where rk is the distance vector from the siteconsidered to the kth G'd site and <S> is the time average of the Gd spin. Using a(GdA1,)

7.900 A [3], gPS

7

and carrying out the summations for

T

0 OK we obtain : H z Y ( a )

(4.05 + 0.1) k g ,

HdiP(a)

(7.1 + O . l ) k g ,

H i p I f a

H:;; (b)

0

While (3) is correct only for a particular b site, all (b) sites are obtainable from (3) by permuting x, y,

leaving Hdip (b) and its angle with H,, (b) unchanged.

Provided the variation of Hbf from site (a) to site (b) is not too large, we may conclude that Hef,(a) > Heff(b).

This conclusion, as well as a comparison between the experimental and the predicted intensity ratio, indicate clearly that line (a) should be associated with All7 in site (a), and line (b) with site (b). Substi- tuting the calculated values Hdip and the measured values for H,,,, and using

1.1

lo3 (gauss s)-', we find from (2) and (3)

~ ; , ( b ) + 2 Hdip(b) cos 125' 16'

From (2) (3) and (5) we also obtain that Heff(a) is along the local symmetry axis while H,,,(b) forms an angle 0,

660 20' +_ 6' with the local symmetry direction.

With the above results we can now take the second step and treat the oscillations. Abe et al. [4] have shown that oscillations identical in character to those presented in figure 2 are caused in a ferromagnet by quadrupole interaction. As applied to the present case the oscillation frequency for E(l) at site (i) is given by

where Q is the AlZ7 nuclear quadrupole moment, qi is the e. f. g. at site (i) (assumed axialy symmetric) and Oi the angle between He,, and the symmetry direction. Assuming first that q depends only on the nonmagnetic point symmetry a t each site, and there- fore is identical for both sites, we may readily calculate from (6) the expected ratio f (a)/f(b). Substituting in (6) 0,

00, 0,

66020' 5 6' we find

a ratio which is clearly inconsistent with the observed ratio, 2.16 + 0.3. Clearly, a single q parameter is insufficient t o fit the theory and we shall try a model in which the e. f. g. at each site will consist of two parts, a nonmagnetic term qO along the local symmetry direction and a magnetically induced term q' assumed axialy symmetric along M. We now have two inde- pendent relations

f (a)

3 e2 Q(q0 + q') (3 cos2 O0 - 1) (4 1(2 I -

=

(520 5O)kHz

f

(b)

3 e2 Qq43 cos2 66020' - 1) (4 Z(2 I

I)-') $

+ 3 e2 Qq'(3 cos2 00 - 1) (4 1(2 I -

=

(240 f 2O)kHz

C 1 - 9 0 4 N. SHAMIR AND N . KAPLAN AND J. H. WERNICK

with Q q o and Qq' as unknowns. There is no way of

telling from the present measurements the sign relation between f (a) and f (b), although we may note that the nonmagnetic contribution to f does change sign from site (a) to site (b). Thus there are two formal solutions to q0 and q', apart from the absolute sign

e-qo

+ (4.1 + 0.3)MHz

e2 Qq'

+ ^(0.63 & 0.06)MHz

if sign f (a)

sign f (b) (9) e2 Qqo

+ ^(1.46 + ^0.15)MHz

e2 Qq'

+ ^(2.01 T 0.20)MHz

if sign f ( a ) # sign f (b) (10) Preliminary measurement of f(a) as function M exclude, however the solutions (10) and we are left with the experimental values (9) only. The feasibility for the choice of these values is further enhanced by noting that within the limit of experimental accuracy, out e"q0 agrees with the value of e2 Q q

4.27 reported by Jones et al. [I] for the high temperature parama- gnetic phase of GdAI,, as well as with e. f. g. values reported for other paramagnetic RAI, compounds

IV. Discussion and conclusions. - Within the framework of the model suggested above it is seen that although HCff(a)

HCff(b), the hyperfine field H,, is almost identical at both sites, with possible difference limited to about (1

I)%. The equality of the hyperfine fields is somewhat startling since it implies that the total magnetic interaction of Gd spins

with conduction electrons as well as with

inner core electrons is expressible by a single scalar para- meter J,, [6]. While for the validity of such a para- meter one should presuppose isotropic conduction band [6] and ignore interactions with non s electrons, there is no reason to believe that the conduction band in RB, compounds is indeed close to being spherical and therefore we are led to the conclusion that the assumption of an effective scalar exchange constant J,, is perhaps a good approximation even for nonsphe- rical conduction band.

The present results also indicate the existence of a sizeable e. f. g. induced by ordered Gd spins. While magnetically induced e. f. g. in magnetic sites was treated previously

this seems to be the first report of induced e. f. g. at the site of a nonmagnetic atom.

Two second-order mechanisms could, in principle, give rise to an induced e. f. g. 1) e. f. g. induced by variation of the density of states N(E,) of the conduc- tion electrons at the Fermi surface as function of magnetization 181 and 2) e. f. g. caused by partial

ct

unquenching

of A1 inner core electrons, such as 2 P electrons, via the combined effect of exchange and spin orbit coupling. However, crude estimates seem to rule out both of the above mechanisms as possible source for the sizeable q' value, and more experimental as well as theoretical effort is required to conclude the e. f. g. study.

V. Acknowledgements.

We are grateful to M.

Weger, S. Alexander and I. Nowik for helpful dis- cussions.

References

[I] JONES (E. D.) and BUDNICK

[51 JACCARINO

J . App. Phys., 1961,32, 102 S.

1966, 37, 1250. [6] YOSIDA (K.), Phys. Rev., 1957, 106, 893.

12]

w')

[7] GANIEL (U.) and SHTRIKMAN (S.), P h y ~ . Rev., 1968,

( J .

H.), Phys. Rev., 1964, 135, A 151.

;[3] WERNICK

H.) and GELLER (S.), Trans. Met.

167, 258.

AIM, 1960, 218, 958. [8] WATSON (R. E.), GOSSARD

C.) and YAFET

[4] ABE

YASUOKA (H.) and HIRAI (A.), J . Phys. Phys. Rev., 1965, 140, A 375.

SOC.

Japan, 1966, 21, 77.