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ISING CHAIN WITH SPIN IMPURITY 311given in Sec. 2, it follows from inspection that a ± 2 +b ± 2 =a + 2 +aJ= b + 2 +bJ= 1, and a + a-+b + b^.= a + b + +a-b-.=0.With the above information one obtainsBy using the fact that in the bulk limit (coV^-f)^""^2"""^ for positive temperatures and t=2, 3, • •, 2V/2-1, one findsFrom (Al) and (A2) ar 1 i(^)/d^| t , t=1 = w+^( a + 2 -~6 + 2 ), dri2(t?)/dt;| v=a i=co + Z"^(a + a_--& + 5_),rn(l) = w + , ri 2 (l) = r 21 (l) = 0, and (d/dv) (rn (») T21 (») + T12 (t>) T 2 2 (») ) | v**l = 2a) + oo-J[h (a + a^-b+bJ).After referring back to (1), (30, and the derivation of (2) one arrives at (9) by differentiating with respect to X in (A3) and substituting Z=(2S+l)ai+x-2 D,Two new electron-spin-resonance spectra, one having trigonal and the other having orthorhombic symmetry, have been observed in CaF 2 doped with small amounts of Ce0 2 . The x and y axes of the orthorhombic spectrum lie in the (110) plane and are tilted by an angle 5= 13.8±0.2° from the [110] and the [001] axes, respectively, and the z axis lies along the [110] axis. The components of the g tensor for the two spectra are: orthorhombic, fo-0.844dz0.001, & = 0.22=1=0.05, g*=3.286±0.001; trigonal, g u =3.673±0.002, £i<0.3,

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Paramagnetic resonance from rare-earth ions in sites having rhombic symmetry have been observed from calcium fluoride crystals doped with rare-earth and sodium fluorides. The ions investigated were Ce 3+ , Nd 3+ , Dy 3+ , and Yb 3+ , and for each the axes of the g tensor were found to lie along the [110], [110], and [001] directions. In the case of the ytterbium-doped crystals, replacing the sodium fluoride by lithium or potassium fluoride generated new, but similar, rhombic spectra. It is proposed that all these spectra arise from trivalent-rare-earth-monovalent-alkaline-earth ion pairs, the ions occupying adjacent Ca 2+ ion sites. New tetragonal spectra have also been observed from Ce 3+ and Nd 3+ ions in crystals heavily doped with NaF, and it is suggested that these might arise from the association of the rare-earth ions with sodium ions on the next nearest Ca 2+ ion sites, though this is not firmly established.