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Submitted on 1 Jan 1979

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**A nuclear orientation study of hyperfine interactions in** **terbium**

### J. Grimm, W. Brewer, G. Wilson

**To cite this version:**

J. Grimm, W. Brewer, G. Wilson. A nuclear orientation study of hyperfine interactions in terbium.

Journal de Physique Colloques, 1979, 40 (C5), pp.C5-58-C5-60. �10.1051/jphyscol:1979523�. �jpa- 00218940�

**JOURNAL DE PHYSIQUE ** **Colloque C5, supplkment au no 5, Tome 40, Mai 1979, page C5-58 **

**A nuclear orientation study of hyperfine interactions in terbium **

J. Grimm, W. D. Brewer and G. V. H. Wilson

Fachbereich Physik der Freien Universitat Berlin, F.R.G.

**RBsumB. **^{- }Nous decrivons une mCthode pour Ctudier I'interaction hyperfine et la distribution de I'aimantation
locale dans les terres rares lourdes utilisant l'orientation nucleaire. Dans le cas d u MnTb dilue, le champ hyperfin -

sur le noyau de Mn est de **18,5 **f **1,5 **T.

**Abstract. **- It is shown that the hyperfine interactions of impurity nuclei and the magnetization distribution in
magnetically hard rare earths may be studied by means of low temperature nuclear orientation. For dilute MnTb -

the hyperfine field a t the Mn nuclei is 18.5 f 1.5 **T. **

The magnetic hyperfine interactions of impurity nuclei in a wide variety of transition metals (and to a lesser extent gadolinium) ferromagnetic host lattices have been studied using nuclear orientation, which is in fact the only widely applicable technique for transition and sp-impurities in rare earth hosts because of limited solubilities. Because of the difficulty of magnetizing the magnetically harder rare earths, almost no nuclear orientation studies have been reported in these hosts. One means of overcoming this difficulty is to use single crystal samples ; however, apart from the radioactivity which may be produced by in situ neutron irradiation, the production of single crystals incorporating radioactive nuclei in trace quantities can prove difficult. We show that it is possible to apply nuclear orientation to incompletely magnetized polycrystalline samples and that, in addition to the hyperfine interactions, some results concerning the magnetization directions are obtai- nable. Terbium has a large uniaxial anisotropy constant and, even in applied fields up to 15 T along the c-axis, is far from being fully magnetized 11, 21.

In the basal plane, fields of ca. 0.3 T are sufficient for
magnetic saturation [3]. In previous nuclear orien-
tation studies of 160Tb nuclei in Tb Leblanc and
Sommer [4] used a single crystal, but, possibly because
of poor tliermal contact, did not observe y-radiation
* anisotropy. Parfenova et al. [5] used a polycrystalline *
sample and incorrectly analyzed the data from
incompletely magnetized samples, obtaining a value
for the hyperfine interaction which was a factor of
4 too small.

In the present studies, two samples were employed :
a polycrystalline alloy into which 54Mn and 51Cr
dilute impurities had been melted, and an oriented
single crystal. Both samples were neutron-irradiated
to obtain 160Tb activity also. Each was cooled to
ca. * 6 mK in a standard CMN demagnetization *
cryostat which included a solenoid permitting fields

of up to 7.5 T to be applied to the cooled sample.

Temperatures on both sides of the sample were determined using 60Co- and "CoFe thermometers and were found to agree, thus r u z g out thermal gradients in the samples. The "Cr results, a more detailed account of the theoreticalanalysis, and further data from the single-crystal experiments will be published elsewhere.

The normalized distribution of y-radiation from
nuclei oriented at low temperatures in a uniform
magnetic field H is **[6] **

w(6) = **A, Bk Pk(cos ****0) **

**even ****k **

(1)
where the A, depend on the nuclear decay scheme
**and the B, are known orientation functions of **

= * pH/Ik, *T. For the 298-keV y-radiation from
160Tb only A, is non-zero, while for 54Mn,

*contribute to the sum. In our experiments, y-radiation emitted parallel and perpendicular to the applied field Ho was detected and the anisotropies W(0) and W(7t/2) were obtained as ratios of the*

**A , and A,***cold to the*

*warm (isotropic) counting rates. For the*

**ldOTb**we may assume that the hyperfine field

*is*

**H i**### >>

*that*

**H , so**where * K: * = P,(cos a) is the average value of

*taken over all angles*

**P,***a*of the local magnetization relative to the applied field. At the low temperatures used here the 1 6 0 ~ b nuclei are fully oriented along the local magnetization direction so that the saturated

*value A,*

**B,**^{= }0.5 may be assumed and

*easily obtained from the measured W(0). The limiting low temperature value of the orientation constant will not be affected by the presence of an electric quadrupole hyperfine interaction. In moderately strong applied fields an appropriate model assuming*

**K,O**Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979523

**A NUCLEAR ORIENTATION STUDY ****OF HYPERFINE INTERACTIONS IN TERBIUM ** (25-59

easy magnetization in the basal plane and none
along the c-axis yields K; = 0.5 for a polycrystalline
sample. Figure 1 shows the observed dependence of
* K t upon N o for the polycrystalline sample and *
indicates the accuracy with which the magnetization
distribution may be studied. It shows that basal

*2 T and that, as expected, the remanence is associated mainly with a redistribution of spins in the basal plane.*

**plane magnetization is complete for H ,**zPreliminary results with the single crystal indicate
that the spins are almost evenly distributed in the
basal plane prior to magnetization (K: * x *0.25) and
are fully polarized in the basal plane in higher fields.

* Experiments using applied fields along the a-, b-, *
and c-axes are now in progress.

**Fig. 1. - ****Dependence of the magnetization distribution parameter **
**K i *** upon applied field Ho for polycrystalline Tb *;

**0**=

**Ho increasing,***=*

**x**

**Ho****decreasing.**

For the more general case of dilute impurity, such
* as 54Mn, where H , may not be neglected in comparison *
with

*it can be shown that*

**Hi***W(0) **2~ * 1

## + *1 *

A&BkKk
**even *** k * (3)

where K, = **P,(cos y) and the B, are functions of **

= * yHr/Zk, T with Hr *=

**Hi**### +

*Here y is*

^{a , }^{H,. }**the angle between the local resultant of H, with Hi**and

**H,,**the

*a,*are constants and the approximation

*,< 0.3 as we have shown by computer simulation. The calculations also indicate*

**is quite accurate for Ho/Hi***tropy measurements using K t instead of K, in*

**that, if eflective values of H, are deduced from y-aniso-****(3),**we have H,(eff) =

**Hi**### +

*where*

**aH,,***is a constant.*

**a****For **a polycrystalline sample with the axes of easy
* magnetization in the basal plane, a z *1.8. The
same result applies for a negative hyperfine field with

*> 1 is asso-*

**a change in the sign of a. The value of a**ciated with the vector sum of the two fields **H, *** and Hi *
at the nucleus and with the difference between the
angles

*cc*and y.

To carry out the analysis for 54Mn it is necessary
to eliminate the parameter K4. This is done by deducing
* values of H, from W(0) at each temperature using *
K,O from the 160Tb measurements for several assumed
values of

*As B4 tends to zero much more rapidly*

**K,.*** Fig. 2a. *-

**Dependence of the deduced value of**

**H,**

**upon l / T for***=*

**Ho****1 and 7.35 T and for several values of**

**K,.****Fig. *** 2b. *-

**Dependence of H, upon Ho showing determination****of the hyperfine field at Mn nuclei in Tb.**

**C5-60 ** **J. ****GRIMM, W. D. BREWER ****AND ****G . V. ****H. WILSON **
than does **B, ****as the temperature is increased, H, tends **

to the common correct value at higher temperatures.

In figure * 2a *the deduced values of

*are shown as*

**Hr***It can be*

**functions of 1/T for several values of**K,.*seen that it is possible to obtain correct values of H,*because of the characteristic variation towards a single value at high temperatures. In figure 2b the dependence of

*the predicted linear relationship with slope a -, 1.8.*

**Hr**upon H , is shown and obeys wellThe hyperfine field is plainly positive, and we deduce,

neglecting the influence of a quadrupole interaction which in any case would be very small for 54Mn, a value for

**Hi **

= **Hi**

### +

^{18.5 }

## +

1.5 T. Since the main contribution to the hypefine field of Mn comes from the (negative) core polarization due to the local d-spin moment (expected - 35 to - 40 T), the observed positive field indicates that the local moment is aligned antiparallel to the host magnetiza- tion. A similar situation has been observed in dilute**MnGd [7].**

## -

**References **

**[I] ****RHYNE, ****J. J. ****and CLARK, ****A. E., ****J. ****Appl. Phys. ****38 ****(1967) 1379. **

**[2] ****LEVITIN, ****R. 2. ****and PONOMAREV, ****B. K., ****Soviet Phys. JETP ****26 ****(1968) 1121. **

**[3] ****HEGLAND, ****D. E., LEGVOLD, ****S. and SPWDING, ****F. H., ****Phys. Rev. **

**131 ****(1963) 158. **

**[4] ****LEBLANC, ****M. ****A. ****R. and S O ~ E R , ****W. ****T., Proc. VIII, Intl. Low **
**Temp. Conf. London, ****1962, p. 432. **

**[5] ****PARFENOVA, ****V. P., ANISHCHENKO, ****V. ****N. ****and SHPINEL, ****V. S., **
**Soviet Phvs. JETP ****19 ****(1964) 333. **

**[6] ****BUN-STOYLE, ****R. ****J. and **

**GRACE, **

^{M. }

**A., Handb. Phys.****42**

**(1957)**

**555.**

**[7] ****CAMPBELL, ****I. ****A., BREWER, ****W. D., FLOUQUET, ****J., BENOIT, ****A,, **
**MARSDEN, ****B. W. and STONE, ****N. ****J., ****Solid State ****Commun. **

**15 ****(1974) 711 ; **

**BREWER, ****W. D. and WEHMEIER, ****E., ****Phys. Rev. B ****12 ****(1975) 4608. **