NOTES
1392 Acknowledgments. We wish to express our appreciation to Professor W. F. Forbes, University of Waterloo, for the generous use of esr facilities. P. D. S. wishes to thank the National Research Council of Canada for a studentship.
Small Tunneling Effect in the Electron Paramagnetic Resonance Spectrum of CuZ+-CaO at L2'K
by R. E. Coffman, D. L. Lyle, and D. R. Mattison Chemistry Department, Augsburg College, Minneapolis, Minnesota 66404 (Received October 6 , 1967)
Recently, several papers have reported detection of a tunneling effect in the lowtemperature epr spectrum of Cu2+ (3d)9 and Sc2+ (3d)', present as substitutional impurities in high-symmetry crystals.'B2 We wish to report our conclusions concerning the tunneling splitting in Cu2+-CaO at 1.2"K. Some information on the epr spectrum of Cu2+-CaO vs. temperature has been published earlier. We have repeated these measurements in order to see if there is any similarity in the angular dependence of the absorption lines at 1.2"K to. that found in Cu2+-MgO at 1.2'K.l We have studied the angular dependence of the Cu2+-CaO single-crystal resonancesin the (100) and (110) planes at 77 and 1.2'K. We found different types of spectra in each temperature range, as we expected, but the liquid helium temperature spectrum shows that the three tetragonal distorted-state functions interact weakly by way of an interference (tunneling) effect. Single crystals of copper-doped calcium oxide were obtained from Sernielements, Inc. and from W. N. C. Spicer, Ltd. Measurements in the (100) plane at 1.2"K showed a single absorption peak (A) and a set of four resolved hfs peaks (B) (Figure 1, top). The absorption peaks in the [110] direction indicate a considerably distorted and broadened line shape which becomes too broad to be detected for Hoparallel to a [loo] crystal direction. The [110]-direction line shape resembles the spectrum of Cu2+in a glass for which A corresponds to g1 and B corresponds to gl . 4 Line A is found to be nearly isotropic, but line B is definitely anisotropic. The (100)-plane angular dependence of the peaks of these lines is plotted in Figure 2. If we assume a frozen out Jahn-Teller distortion, as was previously done8 for a compressed octahedron having 911 = 2 and gL = 2 6u (u= /Xj/A = 0.0552 cm-', where h is the spin-orbit coupling parameter and A is the crystal field splitting), then the (100)-plane resonances would consist of three lines at the g values
+
The Journal of Physical Chemistry
91 = gl.
gz = gll cos2 I9
g3 = 911 sin2 I9
+ gL sin20 + g1 cos2 I9
(la> Ob) (IC)
where I9 is the angle between HOand a [loo] axis. The experimental points in Figure 2 are curiously similar to eq 1, but the crossover predicted by eq l b and I C was definitely not found, a point which was carefully checked. Moreover, we proved that line A is a Cu2+ resonance by measuring the (110)-plane angular dependence, in which plane it could be resolved into four hfs lines (Figure 1, middle). Thus there are at least two strong resonances in the (100) plane (disregarding hfs), but the resonances, which are of the 1 ion/unit cell type do not obey eq 1. The tunneling effect, when large, transforms the behavior of the ground state of a Cu2+ ion so that the
I
I
20'
from [IIO]
3100 G Figure 1. Electron paramagnetic resonance absorption derivative spectra of single crystal Cu2-CaO a t 1.2OK. The bottom two traces were measured a t 9.606 GHB. The top trace, which was measured a t 9.272 GHe, has been shifted upfield by the factor 9.606/9.272. (1) R. E. Coffman, Phys. Letters, 19, 475 (1965); 21, 381 (1966). (2) U. T. Hochli and T. L. Estle, Phys. Rev. Letters, 18, 128 (1967). (3) W. Low and J. T. Suss, Phys. Letters, 7, 310 (1963). (4) W. B. Lewis, M. Alei, and L. 0. Morgan, J . Chewa. Phys., 44, 2409 (1966).
1393
NOTES
The method of calculation is as follows. A basis set of four spin-orbit functions may be used to describe the paramagnetic ground state of the Cu2+ ion in octahedral (sixfold coordinated) or slightly distorted (near octahedral) symmetry5z7
2.00
ai = r8“e,)
2.10
5I m
+ (3/2)”2Ur8i(t2p)
(3)
where i = a, b, c, and d. Using this basis set having fixed (z axis) quantization, we construct three sets of two functions each, representing the ground-state Kramers’ doublets for compressed octahedra having compression axes along the crystallographic x, y, or x axes
2.20
2.30
1 tI
0
30
60
90
6 (DEGREES) Figure 2. Experimental and calculated g values US. angle of Hofrom the [loo] direction in a (100) plane. Calculated g value are for frozen out compressed octahedra.
three transitions of eq 1 are replaced by an isotropic and two anisotropic transitions having g values‘~5 g1 = 2 g2,3
= 2
+ 4u *
+ 4u
(24
+ m2n2+ n2/2)]1’2(2b)
2~[1 3(Z2m2
where l-n are the direction cosines of HOwith respect to the crystalline [loo] axes. These equations represent transitions within a Kramers’ doublet and quartet separated by a tunneling splitting, the magnitude of which we denote by 3V. The symmetry of this spectrum is of the 1 ion/unit cell type. Spectra of this type have been observed for Cu2+-Mg0 and Sc2+-CaF2 in which cases the tunneling splitting is evidently quite large,’b2 since for both only the ground state Kramers’ quartet can be observed at 1.2”K1but the excited state doublets have been observed for Sc2+-CaF2 at higher temperatures.6 Now suppose that we could vary the magnitude of the tunneling effect. Then as 3V varies from 10 cm-’, for example, to 0 cm-’, we expect to find some type of transformation of the spectrum by which the g values of eq 2 transform into eq 1. So we asked the following question. If V were very small, would the resonances resemble eq 1 in some way while still exhibiting the 1 ion/unit cell property? I n order to answer this question, we programmed an eigenvalue, eigenvector, g value, and absorption-intensity calculation which numerically reproduced eq 1 and 2 for limits V = 0 and V > 1 cm-’, respectively, using3 u = 0.0552 cm-’.
where 4 = 0, ( 1 4 n / 3 ) for the distortion direction index Q = x , x, or y, The tunneling effect, which we represent by an operator p,arises when the vibrational functions xzn,xyn,xZn(vibrational quantum number n) are not orthogonal. p is then diagonal8 within these symmetrized linear combinations of eq 4 (in which we neglect certain small overlap terms necessary for proper normalizationg) q+1n
*fzn
=
1
+
#*zn
@*yn
+
1
= 76[2@*nn - @*zn
(54
@*znI
- a*tyn]
(5b)
We then solved this problem by matrix diagonalisation
+
+ 25)13
