Spin-lattice coefficients for substitutionaL Gd3+ in CaF2

J. Phys. Chem. Solids

Pergamon Press 1969. Vol. 30, pp. 1661-1664.

Printed in Great Britain.

SPIN-LATTICE COEFFICIENTS FOR SUBSTITUTIONAL Gd3+ IN CaF, C. M. BOWDENtS Physics Department, Clemson University Clemson, S. C. 2963 1, U.S.A. and J. E. MILLER Florida Institute of Technology Melbourne, Florida, U.S.A. (Received

5 July 1968; in revisedform

3 1 January

1969)

Abstract-For the purpose of evaluating the spin-lattice coefficients Cl1 and C,,, for CaF,: Gd3+ in cubic sites, uniaxial stress studies were conducted at room temperature on a single crystal of CaF, doped with 0.02 at. % Gd3+. From the measured shifts of the magnetic field positions of certain of the fine structure components, corresponding to known increments in applied stress, the spinlattice coefficients were evaluated in magnitude and sign. Taking compressive stress as negative, the experimentally determined values are C,, = - 2.4kO.8 X 10-13cm/dyn and Ca4 = -5.5 -t 1.1 x lo-l3 cm/dyn. INTRODUCTION THE purpose of determining the effect of applied stress on the crystal field interaction of Gd3+ in CaF,, unixial stress studies were conducted using an Optovac CaF, single crystal with approximately O-02 at. % Gd3+ impurity substituted in cubic sites. The measurements were performed at room temperature with a Varian 4500 EPR spectrometer at 9.8 GHz. The stress was applied in increments to the crystal in the microwave cavity. The results of these studies[l] were reported previously and, though they are revised here, they constitute the first report on the effect of uniaxial stress on the EPR spectrum of an S-state rare earth ion in a cubic field environment. The signs of the previously reported values for CI1 and C,, correspond to the arbitrary choice of taking compressive stress as positive. Feher [2] reported results of uniaxial stress studies for FOR

tf’resent address: Solid State Physics Branch, Physical Sciences Laboratory, Redstone Arsenal, Alabama, U.S.A. SWork performed as part of a Ph.D. dissertation under NASA Fellowship.

the S-state ions of the iron group Mn2+ and Fe3+ in the cubic electrostatic field environment of MgO; these measurements were performed at x-band at 77°K. Recently, Calvo and Sroubek[3,4] reported results of similar studies on two rare earth S-state ions, Gd3+ and Eu*+ in CaF,; the measurements for these two ions were done at 9 GHz and 77”K, and 35 GHz and 300°K respectively. Our results are compared with the results given by these authors. THEORY

The effect, on the EPR fine structure components, of the application of uniaxial stress, is described by the term added to the spin Hamiltonian, S.SD.S

(1)

which describes the perturbation to lower than cubic symmetry induced by the applied stress. The elements of the tensor 6D can be written as a linear combination of the applied stress components, xkl, where

(2)

1662

C. M. BOWDEN

For an initially cubic symmetry, there are two independent coupling, or spin-lattice coefficients [S] which must be experimentally determined. In terms of the contracted Voight notation, these are C1, and C,,. The development given by Feher[2] gives for the shift in resonance magnetic field position of a fine structure component corresponding to a first order shift in the energy levels due to applied uniaxial stress, 6I-j

=-

(2Ms-‘) g(@ g@

4

x..)

’ ’ 13

BCOS*

n

(3)

where the component corresponds to the transition M, + M, - 1; 0 and $I are the polar angles of the applied magnetic field H, relative to the crystal axes, and the x0 are the components of applied stress. The function LB in terms of the spin-lattice coefficients is 9(fI, 4, &j) = S(C,,[xll(j$sin”

and J. E. MILLER

4-f)

Tef Ion rod

Puma

Fig. 1. Uniaxial stress apparatus. The quartz tube containing the crystal fits through the stacks of the Varian room temperature microwave cavity which operates in the TE 102 mode.

+ xz2(3 sin* 8 sin* d, - B) + x33($ co9 B- 4) ] + 2C4Jx12 sin2 8 sin 4 cos #3 + xz3 sin 8 cos 0 sin cf, +X,,sinBcosBcos+]}.

(4)

EXPERIMENTAL

The uniaxial stress apparatus used in this experiment is shown in Fig. 1. A General Electric Quartz tube of about _rbin. thick and gin. in dia. and flared at the upper end, fits through the cavity and contains the crystal to be stressed, and the means for transmitting a force. The flared end rests on O-rings which are held in place in slots in the brass head. The micrometer barrel is mounted on a bearing which is rigidly imbedded in the brass cap, and the screw is slotted vertically, with the set screw, which screws in from the side of brass cap, riding in the slot. Hence, by turning the brass micrometer barrel, the micrometer screw is advanced without rotating. This is important due to the anisotropy of the ESR spectrum 161.

The brass screw compresses a calibrated phosphore-bronze spring, and a force is transmitted to the sample by a teflon piston which is machined at the top so as to accommodate the spring. The sample rests between two quartz spacers each approximately $X&X &in., which distribute the load on the end of the teflon rod. The base pedestal is also teflon and the lower end of the quartz tube is packed with pumice so that the load is uniformly distributed over the hemispheri~a1 surface. The teflon gives onty a very weak EPR signal and corresponds to a single very broad resonance with a g-value slightly less than the free electron value. Teflon does not bind with the quartz walls; however, as an added precaution, the piston was well greased with Dow Corning High Vacuum silicone grease, which shows no EPR signal. Referring to the cubic crystalline axes and taking the applied stress, P, in the [I IO] and the applied magnetic field, H,,, parallel to the [OOl] direction, the magnetic field shift of the

SPIN

LATTICE

1663

COEFFICIENTS

component co~esponding to the transition M, -+ M, - 1 under applied stress P is

where g = 1~992[7]. If now, H, is taken parallel to the [lil] direction, the magnetic field shift for each fine structure component becomes

AP KG/CM2 Fig. 3. Magnitude of the magnetic field shift, /&HI, of the indicated fine structure components vs. increase in uniaxial stress AP for Ho parallel to [ 1001 direction and P parallel to [I 1O] direction, with H, perpendicular to P.

It is to be noted that in (5) and (6) a positive increment SH corresponds to a shift to higher magnetic field. For Ho parallel to the [lil] direction, the observed shift in magnetic field position under the applied stress is shown in Fig. 2 for the magnetic dipole transitions MS= g-+ MF=$ and &f,=-#+ MS=--+. Zero

Fig. 2. Magnitude the indicated fine uniaxial stress AP P parallel to [ IlO]

of the magnetic field shift, ISH/, of structure components vs. increase in for & paraliel to [ 11 I] direction and direction, with Ho perpendicular to P.

initial stresses indicated on the graph actually corresponds to 20 kg/cm* to 30 kg/cm*, so the stress values given are referred to the initial stress. With the magnetic field Ho in the [OOl] direction, the observed shifts under applied stress for the components corresponding to the transitions M, = --$ --+ M, = 4 and M, = $ -+ M, = 2 are represented in Fig. 3. At the beginning of the final measurement for the M, = $ * M, = 3 transition, the

sample powdered. For the four transitions observed under applied stress, the magnetic field shift 6H was to higher field for positive values of M, and to lower field for negative values. RESULTS AND DISCUSSION

From the magnitudes of the slopes of the lines drawn through the data points in Figs. 2 and 3 together with the sign of the slopes, the spin-lattice coupling coefficients were evaluated. These values are given in the Table along with the corresponding values quoted by Feher for Mn*+ and Fe3+ in MgO and the values given by Calve et al. for Gd3+ and Eu*+ in CaF,. No detectable change in the g tensor under applied stress was observed in our measurements. The major source of the uncertainty in our measurements stems from an observed dependency of the stress characteristics of the crystal on its previous stress history. This is manifest as an observed departure of the magnetic field positions of the components from the initial values when the stress is reduced to the initial value. Another source of uncertainty is due to observed broadening of the resonance absorption as stress is applied. This broadening was about 3 per cent at maximum applied stress for the data shown in Fig. 2; however, it was as large as 15 per cent for that shown in Fig. 3. The larger scatter of the data shown in Fig. 3 is evidently

1664

C. M. BOWDEN

and J. E. MILLER

Table 1. Experimentally determined spin-lattice coeficients units of 1O-l3 cm/dyn

MgO MgO CaF, CaF, CaF,

: Mn*+ : Fe3+ : Gd3+ : Gd3+ : Eu2+

+7.1-+0.2 +26&O+? -2.4kO.8 -1.8kO.2 -1.7kO.2

associated with this broadening which may be due largely to non-uniform distribution of the applied force caused by difficulty in polishing the ends of the crystal flat and parallel. Comparing the values for the spin-lattice coefficients presented in Table 1, it is seen that they are well within the same order of magnitude for the four different cases. This is surprising, since it would be expected that the interaction would be less strong for the rare earth ions where the magnetic 4f electrons are inside filled 5s and 5p shells, than for the iron group ions, where the electrons of the half-filled 3d shell are exposed directly to the neighboring ligands. It seems that considerable admixture of higher energy states into the ground state is necessary in order to account qualitatively for the large values for the spin-lattice coefficients of the rare earth ions. A theory using the point charge model and treating the relaxation process of an S-state ion in terms of spin-orbit interaction due to admixture of higher energy states into the ground state has been presented by Blume and Orbach@] for the S-state ion of the iron

-2.1 kO.1 -5.5kO.3 -.5.5+- 1.1 -3.OkO.3 -10.9-tO.l

in

Feher[2] Feher [2] Bowden and Miller Calve and Sroubek[3] Calvo and Sroubek[3]

group Mn’+ in a cubic environment. This theory predicts the correct order of magnitude for the coefficients, C,, and Cd4, but fails to predict the correct signs as obtained from experiment [2]. Another theory presented by Leushin[9], which uses the spin-spin interaction between electrons as the relaxation mechanism, predicts the correct sign but does not give the correct ratio of the coefficients. A similar calculation for a rare earth ion in the S-state does not seem to exist in the literature. AcX-lrowledgements-Gratitude is expressed to R. A. Shatas of the Physical Sciences Laboratory for some helpful suggestions in the preparation of the manuscript. REFERENCES 1. BOWDEN C. M. and MILLER J. E., Bull. Am. phys. Sot. 13,245 ( 1968). 2. FEHER E. R., Phys. Rev. 136, 145 (1964). 3. CALVO R. and SROUBEK Z., Bull. Am. phys. Sot. 13.901 (1968). 4. CALVO R., ISAACSON R. A. and SROUBEK Z.. Phys. Rev. Lett. 21, A2 (1968).

5. FUMl F. G. Acfa crystallogr. $44 (1952). 6. KITTEL C. and LUTTINGER J. M.. Phys. Rev. 73. 162(1948).

7. RYTER C., Helv. Phys. Acta 30,353 (1957). 8. BLUME M. and ORBACH R., Phys. Rev. 127, 1587 (1962).

9. LEUSHIN

A. M., Soviet Phys. so/idSf.

5,440

(I 963).