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Submitted on 1 Jan 1971
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MAGNETIC SUSCEPTIBILITY AND ANOMALOUS BEHAVIOUR OF KNIGHT SHIFT IN SmPt2 AND
SmSn3
S. Malik, R. Vijayaraghavan
To cite this version:
S. Malik, R. Vijayaraghavan. MAGNETIC SUSCEPTIBILITY AND ANOMALOUS BEHAVIOUR
OF KNIGHT SHIFT IN SmPt2 AND SmSn3. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-
1028-C1-1030. �10.1051/jphyscol:19711368�. �jpa-00214405�
JOURNAL DE PHYSIQUE Colloque C I, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 1028
MAGNETIC SUSCEPTIBILITY
AND ANOMALOUS BEHAVIOUR OF KNIGHT SHIFT IN SmPt, AND SmSn,
S. K. MALIK and R. VIJAYARAGHAVAN Tata Institute of Fundamental Research, Bombay, 5, India
R6sum6. - La variation avec la tempQature du dkplacement de Knight dans SmSn3 ne suit pas les pre5visions de White et Van Vleck. Ce comportement anormal est attribue au melange de l'ktat excite5 J
=712 avec l'ktat fondamental du fait de I'existence de forts champs cristallins. On montre l'influence de forts champs cristallins sur < S, > et x,.
Abstract. - The temperature dependence of Knight shift of Sn119 in SmSn3 does not follow the prediction of White and Van Vleck. This anomalous behaviour
1sexplained as due to the mixing of excited (J
=712) state into ground state of Sm3+ion by strong crystalline fields. The effect of strong crystalline fields on
iS, > and x, is shown.
There have been several studies of the Knight shift and susceptibility of the rare-earth intermetallic compounds [I]. Such measurements give information about the magnetic properties of the rare-earth ions and the nature of conduction electron polarisation. It is currently believed that, apart from a temperature independent part KO, the Knight shift at the non- magnetic site of the rare-earth intermetallic compounds arises due to the polarisation of the conduction electron spin s by the rare-earth spin S through an exchange interaction of the form [2]
X = - 2 J(0) S.S (1)
In the simplified RKKY model, where the conduction electron polarisation is oscillatory, the expression for the Knight shift has been calculated by De Gennes [3]
to be
where F(x) stands for (x cos x - sin x)/x4 and KO is the Knight shift in the absence of any 4 f - s exchange interaction and is usually taken as the Knight shift in the corresponding non-magnetic isostructural com- pound. For the rare-earths where only the ground state is mainly populated, < S, >,dB is proportional t o the 4 f susceptibility xf so that K is linearly related to xf. Such a linear relation was demonstrated earlier for the cubic rare-earth platinum intermetallic compounds of the type RPt, [R = La, Ce, Pr, Nd]
from which the magnitude and sign of the phenome- nological exchange constant J(0) has been evaluated
PI. The case of Sm3+ is different in the sense that the separation between the two lowest J states is not very large so that < S, >,JH is no longer proportional to xF. Further, White and Van Vleck [5] have shown that in Sm3+ there is appreciable temperature inde- pendent negative contribution, associated with the second order Zeeman effect, to the spin average
< S, >,,, which would cancel the spin average from
the ground state at about 300OK. From eq. (1) we notice that (K - KO), which is the Knight shift due to 4f electrons, is proportional t o the spin average of Sm3". Therefore (K - KO) is expected to reverse
sign at about 300 OK (henceforth called the cross over temperature). This has been experimentally verified in the case of SmAl, by DeWijn et al. [6] and in SmX(X = As, Sb, P, Bi) by Jones [I]. We have studied the temperature dependence of the lg5Pt Knight shift in SmPt, [7] which is isostructural to the other RPt, compounds reported earlier. The crossover of the lg5Pt Knight shift has been observed in SmPt, also at 250 OK in good agreement with the theory.
The '19Sn Knight shift and susceptibility in RSn, [R = La, Ce, Pr, Nd] compounds have also been studied earlier 181. We have measured the '19Sn Knight shift in SmSn, (isostructural to RSn,) in the tempe- rature range of 77O to 400 OK. It is found that the crossover of (K - KO) as predicted by White and Van Vleck does not occur in this compound. Similar absence of crossover has been reported [9] for SmAl, also (though Jaccarino [lo] reported a crossover at 150 OK). Both in SmSn, and SmA1, the behaviour of the Knight shift is different compared to that in other samarium intermetallics where the crossover has been observed. This is shown in figure 1, (K - KO) for SmSn, is negative throughout the temperature range studied and becomes more negative at lower tempe- ratures. For comparison the Knight shift in SmPt, is also shown in the same figure.
We wish to point out here that the anomalous behaviour of the Knight shift in SmSn, and SmAI, may arise because of the strong crystalline fields. Just like the second order Zeeman effect becomes important because of the narrow multiplet width, the mixing of the excited J states into the ground state of the rare- earth ion by strong crystalline fields also becomes important because of the same reason. Earlier calcu- lations have either completely neglected the crystal fields or taken them up to the first order in perturba- tion by considering the splitting of the ground state ( J = 512) of Sm3', which in the case of cubic sym- metry (e. g. Sm3+ in SmSn, and SmA1,) splits up into quartet and doublet energy levels. Such a splitting reduces the x, and < S, >,,/H from the free ion value by the factor [I 11
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711368
MAGNETIC SUSCEPTIBILITY AND ANOMALOUS BEHAVIOUR O F KNIGHT SHIFT C 1 - 1029
FIG. 1. - Temperature dependence of the 4 f susceptibility in SmSn3 (the peak in
~pat low temperatures is not shown).
The lower two curves show the temperature dependence of 119Sn Knight shift (119K-Ko) in SmSn3 and 195Pt Knight shift in
SmPt2.
where x = 360 B:/RT and 360 B: is the separation between the quartet and the doublet energy levels. The expression for < S, >,,/H is given to be [6]
where for J = 512 state, a / T in the numerator and the
FIG. 4. - Plot of crossover temperature as a function B!.
Dotted curve is obtained when mixing due to crystal fields is not included and Jff
=0.0.
FIG. 2. - Computed < Sz
> a v / N- Temperature curves for different values of the crystal field parameter BI(.
FIG. 3. - Computed x,-Temperature curves for different
values of the crystal field parameter BI(.
C 1 - 1030 S. K. MALIK AND R. VIJAYARAGHAVAN denominator is to be replaced by af(l')/T. In all the
calculations we have taken (E,,, - E,,,)/k = 1400 OK and all the values of B: are in degree Kelvin. Dotted line in figure 4 gives the dependence of the crossover temperature (Tco) on the crystal field strength para- meter B: using eq. (4) and (3). It is seen that the crossover temperature is more or less independent of the crystal field strength. However when the crystal fields are large one cannot neglect the mixing of the excited J states into the ground state of Sm3 * due to them. We have recalculated < S, >,,,/H, X, and Tco as a function of B: after taking into account the mixing of J = 712 state into J = 512 state.
Very interesting results are to be noticed as the crystal field strength is increased. Figure 2 shows the variation of < S, >,,/H with temperature for various JONES (E. D.), Phys. Rev., 1969,180,455 and references
therein.
JACCARINO (V.), MATTHIAS (B.), PETER (M.), SUHL (H.) and WERNICK (J. H.), Phys. Rev. Letters, 1960, 5 , 251 and JACCARINO (V.), J. Appl. Phys.
Suppl. 1961, 32, 102.
DE GENNES (P. G.), J. Phys. Radium, 1962, 23, 510.
VIJAYARAGHAVAN (R.), MALIK (S. K.) and RAO (V. U.
S.), Phys. Rev. Letters, 1968, 20, 106.
WHITE (J. A.) and VAN VLECK (J. H.), Phys. Rev.
Letters, 1961, 6 , 412.
values of B:. As B: increases, the crossover tempera- ture reduces, then two crossover temperatures occur and for still larger values of B: the crossover is comple- tely suppressed. Moreover for large values of B: the spin average becomes more negative at low tempera- tures as has been observed experimentally in SmSn, and SmAI,. One can now get at least the correct sign of J(0) consistent with that obtained from other compounds of the same series. Figure 3 shows the variation of X, as a function of temperature for various values of B:. The dependence of the crossover tempe- rature on B: is shown in figure 4 (solid curve). Now the crossover can occur only if B: lies in the proper range. We have neglected the sixth degree terms in the crystal potential which may also somewhat affect the crossover temperatures.
DE WIJN (H. W.), VAN DIEPEN (A. M.) and Bus-
CHOW
