SPIN RELAXATION SPECTRA OF Γ8 QUARTET

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SPIN RELAXATION SPECTRA OF Γ8 QUARTET

G. Shenoy, B. Dunlap, S. Dattagupta, L. Asch

To cite this version:

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SPIN RELAXATION SPECTRA OF r

8

QUARTET (*)

G. K. SHENOY and B. D. DUNLAP

Argonne National Laboratory, Argonne, 111. U. S. A. S. DATTAGUPTA

Reactor Research Center, Kalpakkahm 603102, India L. ASCH

Physics Department, Technical University of Munich, Garching, Germany and

Laboratoire de Chimie Nucleaire, 67037 Strasbourg, France

Résumé. — On a calculé et mesuré des spectres de relaxation de i66jEr dans le cas où le niveau électronique fondamental est un quartet A . Pour le composé cubique Cs2NaErCl6 (où le processus dominant est le couplage spin) et pour PEr dilué dans Cs2NaYCl6 (où les processus spin-phonons dominent) on peut rendre compte des résultats expérimentaux ; cependant, les temps de relaxation sont tels qu'une discussion détaillée ne s'avère pas utile. Pour l'Er dilué dans le Pd, où la relaxation est due aux électrons de conduction, on observe des spectres résolus. Afin de les décrire, il est nécessaire de considérer de faibles distorsions par rapport à la symétrie cubique et d'inclure des phénomènes de relaxation.

Abstract. — Calculated and experimental relaxation spectra are presented for the case of i««Er

in compounds where the electronic ground state is a A quartet. For the cubic compound Cs2NaErCl6 (dominated by spin-spin coupling) and for Er dilute in Cs2NaYCl« (dominated by spin-phonon processes), the experimental results can be described although the relaxation times are such that detailed discussion is not useful. For Er dilute in Pd, with relaxation processes driven by conduction electron coupling, resolved spectra are seen. In order to describe the data, it is found necessary to include small distortions from cubic symmetry as well as relaxation phenomena.

1. Introduction. — In considering paramagnetic

rela-xation phenomena in Mossbauer spectroscopy, lan-thanide systems have proven to be very instructive. This is so because the hyperfine interactions are generally large, making the time regime probed more likely to match available electron spin relaxation times, and because the electronic state is generally more easily defined than for d-electron systems. In particular, there have recently been a number of investigations of lanthanide ions in cubic systems, both insulating and conducting [1]. If the rare-earth ion has an odd number of electrons (the most common case for Mossbauer isotopes), a cubic crystalline elec-tric field will split the free-ion electronic ground state into a number of levels which are either Kramers doublets (labelled f6 or T7) or quartets ( r8) [2].

Considerable attention has been devoted to parama-gnetic relaxation spectra for the frequent case of 0 -» 2 Mossbauer transitions when the electronic ground state is either T6 or F7 doublet. In this paper we will

consider some aspects of the electronic spin relaxation

(*) Work at Argonne performed under the auspices of the U. S. Energy Research and Development Administration.

problem for the 0 -* 2 Mossbauer transitions when a r8 level is the ground state.

In the case of r6 or r7 Kramers states, calculation

of the hyperfine spectrum is greatly simplified due to the fact that a simple spin Hamiltonian may be used with an effective spin S = 1/2 describing the properties of the electronic state. Thus one sees that the state is truly isotropic and the hyperfine interaction is simply 360 = A0I.S, where A0 is the effective magnetic

hyperfine coupling constant. Furthermore, since only two levels are involved, a single frequency correspond-ing to the transition probability between the conjugate states of the Kramers doublet is sufficient to describe the effects of relaxation.

When we are dealing with a f8 state, the above

aspects are complicated though the anisotropic nature of the electronic wave functions [3]. Although the state is fourfold degenerate, it can not be described as a single S = 3/2 level. Because of the anisotropic charac-ter of r8 levels, quadrupole interactions will be

present even in cubic systems. In describing the spin relaxation processes between the four levels of a f8

state, in principle six transitions are possible, their frequency and probability being governed by the

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C6-86 G. K. SHENOY, B. D. DUNLAP, S. DATTAGUPTA AND L. ASCH

nature of the bath to which T , is coupled. Sivardiere and Blume [4] have recently addressed this question invoking the random phase approximation (RPA) which means in essence that all the six electronic transition probabilities are equal. Here we shall consider some more aspects of this problem and make comparison with experimental results obtained on the following systems : 100 ppm of Er impurity in Pd ;

10,000 ppm of Er impurity in cubic compound Cs,NaYCl, ; and Cs,NaErCl,.

2. Static hyperfine interactions. - The hyperfine Hamiltonian for a I', state involves a magnetic and a quadrupolar part 15, 61 :

w w

+

3

I

.

J

-

3

I(1 -I- 1) (J) ( J

+

1)

)

(1)

where A is the free-ion magnetic coupling constant and

is the quadrupolar coupling constant. Various matrix elements of the above Hamiltonian operating on a specific

r,

wave functions can be conveniently calculated using the procedure described by Ayant, et al. [7]. It must be pointed out that the seven eigenvalues of Eq. (2) are determined not only by the values of A and B, but also by the details of the

r,

wave function, which in turn is determined by the fourth and sixth order crystal field potentials [2]. Using the notations of Ref. [2], in the case of Er3+ ion one will realize

rL3)

as the ground state for negative values of W and

-

1.0

<

x

<

0.84. I'(81) will be the ground state if Wis

positive and 0.58

<

x

<

1.0. It is interesting to point out that a complete understanding of T , hyperfine spectrum would permit one to obtain the crystal-field parameter, x and the sign of W.

3. Relaxation due to conduction electron coupling.

-

We shall assume the conduction electron bath to be isotropic so that the coupling of anisotropic

r,

can be described by the vector coupling X I = x % t ) where X(t) is a time dependent quantity determined by the details of the bath. Such a coupling would permit only four spin transitions between the

r,

levels, their relative probability being determined by the details of the

T,

wave functions. This should be contrasted with a RPA [4] calculation. In calculating the relaxation spectra, the eigenvalue procedure previously described [8] has been utilized to allow rapid compu- tation.

From the EPR measurements [9] on dilute impurity of Er in Pd host it has been found that the value of x = 0.47 and W =

-

0.15 K, which results in a

r(83)

ground state. Using this results to specify the

rL3)

wave .functions, and free-ion values of A(= 3.92 mm/s) and B(= 0.0065 mm/s), we have calculated the parama-

gnetic relaxation spectra for the 80.6 keV Mossbauer transition in '66Er. Some of these have been shown in figure 1.

1 l 1 1 1 1 1 / .

-60 -40 -20 0 20 40 60 80 VELOCITY (rnm/s)

FIG. 1.

-

Paramagnetic relaxation spectra for 166Er in a state ( x = 0.47). The ion-bath interaction is assumed to be an

isotropic vector coupling.

We have measured the spectrum of less than 100 ppm of Er in Pd at 4.2 K (shown in Fig. 2a). This spectrum is similar in many respects to the one reported earlier [6] excepting for a reduced central intensity in the present

FIG. 2.

-

(a) Experimental data for 166Er as a 100 ppm impurity in Pd metals at 4.2 K. (b) Calculated spectrum included a tetra- gonal distortion and relaxation, as discussed in text.

sample. The spectrum is far from a static hyperfine pattern ; however, it is considerably different from any of the relaxation lineshapes calculated earlier. For example, the overall asymmetry of the data is opposite to that of the calculation and the lines are spread over a smaller velocity range in the experimental data.

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system [lo]. Calculations show that varying B can change the overall asymmetry of the spectrum to correspond to the data, but the details of the lineshapes are far from satisfactory.

A second explanation for the discrepancy may be due to small distortions from pure cubicity of the host around the impurity due either to random strains or to a Jahn-Teller distortion [ l l , 121. If, for example, a distortion occurs along one of the three principal axes, viz., [loo] or [I101 or [Ill], then the fourfold degenerate

T 8

state is split into two doublets separated by some amount A described by the Hamiltonian

where P =

<

1

11

J,

11

1

>

and Q =

<

2

11

J,

11

2

>

defined by Ayant, et al., [7],

1

>

and

1

2

>

being the two Kramers states. If A x A, Eqs. (2) and (1) will have to be added to obtain the hyperfine eigenvalues and their intensities. Such dependences for various values of A are shown figure 3, for the case of

TETRAGONAL SPLITTING ( K )

I I I I I l l l i l l l I

0.04 0.08 0 12 0 16 0.20 TETRAGONAL SPLITTING (Kl

FIG. 3.

-

(a) Line positions and (b) intensities for spectra corresponding to

rA3)

state of Er in Pd, in the presence of a [I001

tetragonal distortion A. Values of A = 3.92 mm/s and B = 0.006 5 mmls

.

Er in Pd by assuming the distortion to be along the [loo] direction. The 20 transitions at A = 0 reduces to only 10 when A % A, B ; these 10 transitions being overlap of two effective field 5-line patterns, each of them due to a Kramers doublet. Following standard procedures we have added relaxation effects to such a situation to obtain the lineshapes for various values of A and rate W. In figure 2b, a spectrum simulated with free-ion hyperfine coupling constants, A = 0.24 K(= 77 mm/s) and W = 6.5 MHz is shown. Although the detailed comparison with the data is not good, the general features of the experimental spectra are now reproduced. It must be pointed out that if the distortion is due to random strain, one should consider various distortion axes to describe the

r8

wave functions and carry out a powder average. Details of these calculations will be presented elsewhere.

4. Relaxation due to spin-spin coupling. - The vector coupling relaxation calculations described above are correct to first order in describing the spin-spin coupling in a material, with

T 8

ground state ions. Data obtained on the insulating compound Cs2NaErC16 at 4.2 K using the 166Er resonance is shown in figure 4a. In this cubic compound with ideal cryolite structure, the electronic ground state of Er3+ ions is

r(81)

[13]. TWO Er3+ ions are separated by about 10

A,

and hence the relaxation process at 4.2 K is dominated by the spin-spin coupling. The solid line in figure 4a represents the calculated spectra for this compound. Due to lack of structure in the spectrum it is difficult to make any detailed discussion.

VELOCITY (mmls)

FIG. 4. - ( a ) Points show experimental data for Er in Cs2NaErC16 at 4.2 K. Solid line is calculated with a relaxation frequency W = 195 MHz. (b) Points show data for Er diluted

in Cs2NaYC16. Solid line is calculated with a relaxation frequency

W = 123 MHz.

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C6-88 G. K. SHENOY, B. D. DUNLAP, S. DATTAGUPTA AND L. ASCH

Er3" ion in this compound again has a cubic envi- ronment and the ground state is a

ril'

[13]. In this system, unlike in the concentrated salt, spin-spin coupling is not important and relaxation is primarily driven by the phonon process. This could be single phonon process of the van Vleck type ; in which the interaction between the ion and bath is a tensor. In formulating the relaxation matrix, we have followed the prescription of Scott and Jeffries [14]. The evolu- tion of relaxation spectra with increasing W differ in detail from those due to a vector coupling (Fig. I), although the qualitative features are the same. The solid line in figure 4b is a simulation which closely reproduces the experimental data. The value of

x = 0.625, deduced from the analysis of the suscepti- bility data [13], is used to obtain the

r(81)

wave functions in this case.

6. Conclusions. - We have presented experimental Mossbauer spectra for Er3+ ions in conducting and insulating systems in which the electronic ground state is a

T,.

The procedures for calculating the relaxation spectra in the presence of conduction electron, spin, and phonon baths have been described. The influence of very small crystalline distortions (compara- ble to the hyperfine interaction) on the hypedine structure of

T,

state has been discussed. Further details of the present work will be reported elsewhere.

References

[I] GONZALEZ-JIMENEZ, F. and IMBERT, P., Solid State Commun. [6] SHENOY, G. K., STOHR, J. and KALVIUS, G. M., in Proc.

11 (1972) 861 ; Rare Earth Conference, Carefree, Arizona, 1973.

SHENOY, G. K., ~ C H , L., MEDT, J. M. and DUNLAP, B. D., 171 AYANT, Y., BELORIZKY, E. and ROSSET, J., J. Physique 23

J. Physique Colloq. 35 (1974) C 6-425 and references _{11962) 201.}

therein.

LEA, K. R., LEASK, M. J. M. and WOLP, W. P., J. Phys. Chem. Solids 23 (1972) 1381.

For a detailed discussion of the properties of

rs

states, see

RAG AM, A. and BLEANEY, B., Electron Paramagnetic

Resonance of Transition Ions (CIarendon Press, Oxford) 1970, p. 721 ff.

SIVARDI~RB, J. and BLUME, M., Hyperfine Interactions 1

(1975) 283.

BLEANEY, B., in Hyperhe Interactions, edited b y Free- man, A. J. and Frankel, R. B. (Academic Press, New York) 1967, p. 1.

, ,

SHENOY, G. K. and DUNLAP, B. D., Phys. Rev. B 13 (1976) 1353.

ZING, W., BILL, H., BULLET, J. and PETER, M., Phys. Rev.

Lett. 32 (1974) 1221. PEZL, J., Z. Phys. 251 (1972) 13.

See ref. [3], p. 279.

HAM, F. S., in Electron Paramagnetic Resonance, Edited

by Geschwind, S. (Plenum Press, New York) 1972, p. 1. DUNLAP, B. D. and SHENOY, G. K., Phys. Rev. B 12 (1975)

2716.