The determination of the hyperfine coupling in ferromagnetic metals by nuclear orientation and low temperature specific heats

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The determination of the hyperfine coupling in ferromagnetic metals by nuclear orientation and low

temperature specific heats

N. Kurti

To cite this version:

N. Kurti. The determination of the hyperfine coupling in ferromagnetic metals by nuclear ori- entation and low temperature specific heats. J. Phys. Radium, 1959, 20 (2-3), pp.141-144.

�10.1051/jphysrad:01959002002-3014100�. �jpa-00236004�

141

THE DETERMINATION OF THE HYPERFINE COUPLING IN FERROMAGNETIC METALS BY NUCLEAR ORIENTATION

AND LOW TEMPERATURE SPECIFIC HEATS

By ^N. KURTI,

Clarendon Laboratory, ^Oxford.

Résumé.

On a déterminé le couplage hyperfin dans le cobalt métallique ^{et dans des} alliages ^de

cobalt. On compare les résultats, ^obtenus par orientation nucléaire et à partir ^des chaleursspéci- fiques, ^{avec les} prévisions théoriques ^de Marshall. Les mesures de la chaleur spécifique ^{du Terbium} métallique mettent ^{en évidence un} couplage hyperfin dont la valeur est 6 % inférieure à celle

qu’on trouve pour l’ion Tb+ ^{+ +} dans un sel paramagnétique.

Abstract.

The hyperfine coupling in metallic cobalt and in cobalt alloys has been determined both by nuclear orientation and by ^low temperature specific heats. The results are discussed in the light of Marshall’s theoretical predictions. Specific ^heat measurements in Terbium metal indicate a hyperfine coupling which is about 6 % smaller than that found for the Tb+ ^{+ +} ion in

a paramagnetic ^salt.

PHYSIQUE 20, ^FÉVRIER 1959,

1. Introduction.

The knowledge ^{of the} hyper-

fine coupling ⁱⁿ ferromagnetic substances, espe-

cially ⁱⁿ metals, ^could give, ⁱⁿ principle, ^valuable

information about the states of the electrons ^res-

ponsible ^for ferromagnetism. ^{The idea} is very

simple. ^At temperatures ^{that are low} compared

with the Curie point, ^all electronic moments are

oriented parallel ^to each other within a domain.

Each nucleus will find itself therefore ^{in an} effec- tive magnetic field, Hegg, ^{which is the same for all.}

If the nucleus has a magnetic moment (1., and, ^if the’temperature ^{is low} enough for the condition u Heff ^kT (usually ^{T or « 1} OK) ^{to be} satisfied,

the nuclear moments will take _up the energetically

most favourable orientation with respect ^to Heff·

This ordering ^{of the nuclear} spins may be observed in one of the two following ways.

(a) If the domains throughout ^the specimen ^are

oriented parallel ^to each other and if some of the atoms are replaced by ^a radioactive isotope ^emit- ting ^y-rays, then these y-rays will show ^an aniso-

tropic intensity distribution depending ^{on the} degree ^of orientation of the nuclei.

(b) ^{There will be an} additional, ^anomalous spe- cifie heat on account of the redistribution _among the nuclear magnetic sub-states of différent ener-

gies. ^Because of the low temperatures ^involved

this anomalous specific ^{heat can be} easily sepa- rated from the smaller lattice, electronic and

magnetic contributions.

Once Heff ^is determined by either of these

methods, ^one may compare its absolute value with that found in a paramagnetic ^{salt ôf the same} ion,

or one may study its variation with alloying ^or

with change ⁱⁿ crystal structure. The _analysis ^of

such results has been discussed in detail recently by

Marshall [1] ^and only the essential features need be

mentioned here. Heff (for ^{ions of the iron} group)

may be regarded ^as resulting ^{from the action of}

d-electrons and s-electrons. The contribution from an s-electron is appreciably stronger ^than

that from a d-electron, ^{since the} s-electron has a

finite expectation ^{value at the} nucleus ; moreover, it is insensitive to a change ^of crystalline symmetry.

The d-electron contribution ^on the other hand has the character of a magnetic dipole ^{field and will} depend ^{both on the} symmetry ^{of the} crystal ^field

and on the dégree ^of quenching ^{of the orbital}

moments.

2. Nuclear orientation in cobalt.

The first nuclear orientation experiments ^{on a} ferromagnetic

were done about simultaneously ^{in Oxford} [2] ^and

in Moscow [3]. ^{The Oxford} experiments ^were

carried out on a single crystal ^of hexagonal cobalt,

in which all the domains are aligned parallël ^{to the} hexagonal ^{axis. 6°Ca was used as} radioactive com-

ponent ^{and the} anisotropy e ^=1- W(O) /W(7r /2)

of the y-ray intensity ( W(0) ^and W(7r/2) ^{are the}

intensities emitted respectively parallel ^and per-

pendicularly ^{to the axis of} alignment), ^measured

down to .04 OK was found to be

From this, using ^{the best value} [4] of the nuclear moment of 6°Co we find for the effective field

TheMoscowexperimentswerepresumablycarried

out on a polycrystalline specimen magnetised by

an external field, ^{and the} only results quoted (1) This is smaller than the value quoted ⁱⁿ (2b).

The différence is due to the omission in that publication ^{of a}

correction to the temperature measurement.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-3014100

142

(10-15 % anisotropy ^{in the} temperature range 0.05 °K-0 . 08 OK) ^are considerably larger ^{than the} Oxford ^ones.

3. Low température spécifie ^{heat in cobalt and}

in cobalt alloys.

^Once these nuclear orientation

experiments have shown the existence of an appre- ciable hyperfine coupling ⁱⁿ ferromagnetic ^{cobalt it}

was clear that spécifie ^heat measurements would

provide ^{a more} convenient alternative for these determinations [5]. ^Such measurements ^on Co metal were carried out by ^{Heer and Erickson} [6]

and by Arp, ^{Kurti and Peterson [7]. Below 1 °K}

both lattice and the spin ^wave contribution are

negligible, ^{and the} spécifie ^{heat C/R down}

to 0.3 OK ^can be represented ^{as a sum of an elec-}

tronic term T and a hyperfine coupling ^term a1T2.

Heer and Erickson find a ⁼ CT21R ^{= 4. 0 X 10-4}

while the experiments ^of Arp ^{et al.} give CT2 jR ^{= 4.7 X 10- 4 . The values of Heil calcu-}

lated ^from these results ^are 183 k0 and 200 k0

respectively, ^as compared with 193 k0 found in the nuclear orientation experiments. ^A quanti-

tative comparison ^{of these} results with those obtained in Go+ + salts is difficult since in the salts the hyperfine coupling ^{cannot be} strictly repre- sented by ^{an effective} magnetic ^{field. A} quali-

tative comparison ^{with the} specific ^{heats which in} magnetically ^diluted salts range from

CT2JR ^{= 10 x 10-4 to 25 X 10-4} [8]

indicates that in the metal there can be no appre- ciable conduction electron polarization ^{since that}

would tend to increase the effective field and hence the specific ^{heat as} compared ^{with the salt.}

More recently, ^further specific ^{heat measu-}

rements have been carried out in Berkeley by Arp

and Peterson [9] ^{on a 60} % ^{Co - 40} % ^{Ni and}

an 18 % ^Co

⁸² % ^Fe alloy. ^The expected

behaviour of these alloys ^{has been discussed} by

Marshall [1] ^and [10] who has shown that although

both these alloys ^are cubic, they ^will have different values of Heff. In the Co-Ni alloy ^{the electronic}

structure of the Co remains fundamentally unchanged ^as compared with pure cobalt. But,

because of the cubic symmetry, ^the dipolar coupling

between electron spin and nuclear spin ^vanishes

and the Heff ^is expected ^to be reduced from the 200 kOe in pure ^{Co to} about 100 k0 in the Co-Ni

alloy. Arp and Peterson [9] ^find Hefr ^{= 160} k0,

that is the right ^{trend but no} quantitative agree- ment.

For the Co-Fe alloy ^the position ^is différent since in these alloys accordingto ^{Lomer and Marshall} [11]

the electronic configuration ^{of the Co is} changed ^as compared with the pure metal. Marshall [10]

predicts that because ^of the less effective _quen-

ching of the orbital ^moment the Heff will actually

be higher than in pure hexagonal ^{cobalt. The} figure ^he gives ^{is 670 kØ while} Arp ^{and Peterson} [9]

find 300 k0. Here again the trend is as expected

but there is no quantitative agreement.

4. The speeihc heat of Gd and Tb.

The study

of rare earth metals seemed promising, ^{since in} them, ^{thanks to} good shielding, ^the 4 f ^shell may be e’xpected ^{to be} sensibly ^the same in the metal and in the salts. Thus _any contribution irom con- duction electron polarization ^could be detected

more easily. Moreover, ^{because of the low Curie} points the relative importance ^{of the} spin ^wave

term is bigger ^{than in the} iron group, and specific

heat measurements at low temperatures might permit ^its separation ^from the electronic term.

FIG. 1.

Anisotropy ^{of s°Co} y-radiation ^{from a} single crystal ^of cobalt-metal.

It was with these two objects ^{in view that the} spécifie ^{heats of Gd and Tb} (1) ^{have been measured}

in collaboration with Dr. R. S. Safrata (on ^{a visit}

from the Institute of Nuclear Physics, ^Czechos-

lovak Academy ^of Sciences, Prague) [12].

The complete specimen consists of the rare earth metal (about ²⁰ g) ^a heater, ^{a carbon resistanc} thermometer, ^{and a} paramagnetic crystal (Cerium- Magnesium-Nitrate) ^which permitted ^{to cool the}

whole specimen ^{down to about 0.2 OK} by ^adia-

batic demagnetization ( 2).

(1) ^{We are} very grateful ^{to Mr. A. R.} Powell, F. R. S. of Johnson, Matthey ^{and Co. for the} loan of these samples.

(2) ^A disturbing effect observed first in the Co experi-

ments of Arp ^{et al.} [8] ^{and later more} markedly ^{in the} experiments ^{on Gd and Tb} might be mentioned. Hyste-

resis heating, ^{which at} ordinary temperatures ^is very diffi- cult to measure calorimetrically ^can become troublesome when a ferromagnetic specimen is cooled below 1 0 K by

adiabatic demagnetization ^{of a} paramagnetic ^salt. Thus, in the experiment ^with Gd, demagnetization ^{of the} speci-

men from 25 k’0 to 1 k0 resulted in a temperature ^of

about 0.15 0 K. Further reduction of the field produced warming, ^and by the time the field was reduced to zero the

specimen reached 0. 6 °K. In the case of Tb the heating ^was

In the case of Gd one would ^not expect any

hyperfine coupling contribution at these tempe- ratures, ^{not even} from conduction electrons, ^and

our main purpose ^{was to} check by measurements below 4,DK the analysis ^of Hofmann, Paskin, ^Tauer

and Weiss (13), ^{based on the} results of Griffel,

FIG. 2.

The specific ^{heat of} gadolinium.

FIG. 3.

The specific heat of terbium.

Skochdopole ^and Spedding [14], ^{obtained at} higher temperatures. ^{As may be seen from} Figure ^{2 the} specific heat of Gd shows ^ân anomaly ^{below 4 OK} (the ^{curve is based on} the data of Hofmann ^et al. [13]). ^The origin ^{of the} anomaly is uncertain.

even more pronounced ; in fact the experimental ^arran- gement ^had finally ^{to be altered, so as not to} expose the Tb

specimen ^to magnetic ^fields during ^the magnetic cooling

process. It is obvious from these results that low tempe-

rature calorimetry ^{could be a} very useful tool for deter-

mining the small réversible and irreversible energy changes occurring ^{in the} " technical ^" magnetization ^curve.

Its entropy ^contrent S/R ^{= .} .036 is about 2 % ^of

the total spin entropy ^{of In} 8, and it is possible

that the anomaly ^{is of} magnetic origin. ^Alterna- tively, it could be due to an austenitic transfor- mation which might ^also explain ^the abnormally high ^{scatter of the} points ^{between 4,DK and 6 IDK.}

Figure ^{3 shows the} spécifie ^{heat of Tb. The}

curve represents ^{the sum of} lattice, ^conduction electron, spin ^wave and nuclear contributions.

For the first two of these we used the values given

by Jennings, ^{Stanton and} Spedding [15], ^{while the}

spin ^wave term was obtained from our results

144

between 4 °K and 7 "K. The hyperfine coupling

term which is predominant ^{below 10 OK is} given by CT2/R ⁼ (248 ± 12) ^X 10-4 ; ^this is only slightly

smaller ^than (282 ± 6) ^X 10-4, ^{the value one}

calculates from the paramagnetic resonance measu-

rements of Baker and Bleaney (14) ^{on Terbium-} Ethyl-Sulphate. The difference seems to be out- side the experimental ^{error and thus indicates a} slight change in the electronic configuration, ^pos- sibly ^{a small reduction of the mean value r-3 >}

of the 4/ ^{orbits in} going from the salt to the metal.

REFERENCES

[1] ^MARSHALL (W.), Phys. Rev., 1958, 110, 1280.

[2a] ^GRACE (M. A.), ^JOHNSON (C. E.), ^KURTI (N.), ^SCUR-

LOCK (R. G.) ^{and TAYLOR} (R. T.), Comm. Conf.

Basses Temperatures, Paris, 1955, p. 263.

[2b] ^{Bull. Amer.} Phys. Soc., 1957, 2, 136.

[3] ^See KHUTSISHVILI (G. R.), ^J. Exp. ^Theor. Phys.,

U.S.S. R., 1955, 29, 894.

[4] ^DOBROW (W.), ^JONES (R. V.) and JEFFRIES (C. D.), Phys. Rev., 1956, 101, 1001.

[5] ^HEER (C. V.) ^{and ERICKSON} (R. A.), Bull. Amer. Phys.

Soc., 1956, 1, ^217.

[6] ^HEER (C. V.) ^{and ERICKSON} (R. A.), Phys. Rev., 1957, 108, 896.

[7] ^ARP (V.), ^KURTI (N.) ^{and PETERSON} (R.), Bull. Amer.

Phys. Soc., 1957, 2, ^388.

[8] ^BLEANEY (B.) and INGRAM (D. ^J. E.), ^Proc. Roy. Soc., 1951, A 208,143.

[9] ^ARP (V.) and PETERSON (R.), Private communication.

[10] ^MARSHALL (W.), Private communication.

[11] ^LOMER (W. M.) and MARSHALL (W.), ^Phil. Mag., 1958, 3,185.

[12] ^KURTI (N.) and SAFRATA (R. S.), ^Phil. Mag., 1958, 3, 780.

[13] ^HOFMANN (J. A.), ^PASKIN (A.), ^TAUER (K. J.) ^and

WEISS (R. J.), ^J. Phys. ^Chem. Solids, 1956, 1, ^45.

[14] ^GRIFFEL (M.), SKOCHDOPOLE (R. E.) ^{and SPEDDING} (F. H.), Phys. Rev., 1954, 93, ^657.

[15] ^JENNINGS (L. D.), ^STANTON (R. M.) and SPEDDING

(F. H.), ^{J. Chem.} Phys., 1957, 27, 909.

[16] ^BAKER (J. M.) ^{and BLEANEY} (B.), ^Proc. Phys. Soc., 1955, ^A 68, ^267.

DISCUSSION

Mr. Wohlfarth.

^{Does this work then indicate a} change ^of the electronic structure in Fe-Co alloys ?

Mr. Kurti.

The increased Heff ⁱⁿ the Co-Fe

alloy ^as compared ^{with Co is in} qualitative agreement with what one predicts assuming ^a change ^{of the} electronic structure. If there was no

change ^one would have expected ^{a decrease in} Heff, just ^{as for the Co-Ni} alloy.

Mr. Kittel.

Marshall’s explanation ^{of the} large ^{effective field at} the nucleus in 82 Fe 18 Co

implies ^a large g value for this alloy. ^The g value

is being investigated experimentally by ^{Portis at}

Berkeley.