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


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Submitted on 1 Jan 1959

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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�






Clarendon Laboratory, Oxford.



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.



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.


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


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


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



(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



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.


[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.


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

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


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



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