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Ultrasonic paramagnetic resonance of Pr3+:CaF2
Volume
30A.
number 1
PHYSICS
8 September
LETTERS
The exponential increase of the linewidth with temperature suggests that the relaxation occurs mainly by an Orbach-process making use of an energy level which G ohmann et al. [4] have shown to be located 47 cm- r above the ground state in the absence of a magnetic field, and consequently 460K at resonance. The temperature independent linewidth of 30 G below 5’K cannot nearly be accounted for by the inhomogeneity of the magnetic field across the sample. The contribution of direct relaxation between the Zeeman levels to the observed linewidth seems to be also negligible: This relaxation rate measured at low magnetic fields [5] and extrapolated to hi h fields according to the relationI - T leads at H = 40 kG and at 4OK ship [6] Ti’ CCH to a linewidth of only AH = 2 mG. Likewise a twostepphonon emission using an intermediate energy level, located 18 cm-’ above the ground state at resonance [4], appears much too slow (AH e 0.1 G) to account for the observed linewidth [?I. In order to measure the intrinsic spin-lattice relaxation at low temperatures in the presence of a possible inhomogeneous line broadening saturation techniques would be necessary. In order to
1969
provide the high power needed for such measurements Q-switch experiments with the same laser are in progress. The authors are much indebted to Dr. K. F. Renk for helpful discussions and aslo wish to thank Professor W. P. Wolf and Drs. F. Pobell and J. J. Wooldridge for many stimulations, Professor S. Htifner for providing the samples and to acknowledge the financial support of the Deutsche Forschungsgemeinschaft and Fraunhofer-Gesellschaft.
References K. Dranfeld and K. F. Renk. Phps. Let1. J. Boettcher. ters 26A (1968) 146. Appl. Opt. 7 (1968) 2422. 2. J. P.Kotthaus. 3. J. M. Baker and B. Bleaney. Proc. Roy. Sot. (London) A245 (1958) 156. 4. I. Grohmann. K. H. Hellwege and H. G. Kahle, Z. Phpsik 164 (1961) 243. Z. Physik 181 (1964) 13. 5. H.Kalbfleisch. 6. C. B. P. Finn, R. Orbach and W. P. Wolf, Proc. Phys. Sot. (London) 77 (1961) 261. Proc. Roy. Sot. (London) A264 (1961) 458. 7. R.Orbach,
*****
ULTRASONIC
PARAMAGNETIC
RESONANCE
OF
Pr3+:
CaF2
t
G. C. WETSEL Jr., C. G. ROBERTS *, E. L. KITTS Jr. $* and P. O’HAGAN * Southern Methodist University, DalEas, Texas, USA Received
29 July 1969
Ultrasonic-parsmagnetic-resonance investigations of the ground-state energy levels of praseodymium ions in CaF2 are reported. A new resonance, not observed by previous EPR investigations. was observed at 9.0 GHz and 4.2oK and is attributed to Pr3+ in sites of tetragonal symmetry.
The ground-state energy levels of praseodymium ions in crystals of calcium fluoride have been previously investigated using the techniques of electron paramagnetic resonance (EPR) [I -31. Weber and Bierig [l] reported a negative result, Merritt et al. [2] examined Pr2+, and McLaughlan t Work supported in part by NASA Grant 44-007-006 and ARPA Grant DAHC15-67-G2. * Honors Co-operative Graduate Students, Texas Instruments, Inc. $ Present address: Univ. of North Carilina, Chapel Hill, N.C., USA.
[3] reported the observation of two trigonal spectra which he attributed to Pr3+, Dobrov [4], using the method of ultrasonic paramagnetic resonance (UPR), also reported a negative result. We have observed [5] intense UPR absorption at 4.2OK from 9.0 GHz longitudinal elastic waves propagated along a [loo] direction of calcium fluoride containing 0.1% praseodymium (material obtained from the Harshaw Chemical Co., Cleveland, Ohio). After the source of the absorption was established by UPR to be due to Pr3+ in tetragonal sites, a weak EPR spectrum was also detected. As in the case [6] of Cr2+: MgO, our 35
Volume
30A, number 1
PHYSICS
observation marks a (formerly) rare case where a paramagnetic impurity was detected by the ultrasonic technique before its detection by EPR. We have subsequently detected other resonances in CaF2 apparently not yet observed by EPR. Trivalent praseodymium has two 4f electrons, which are responsible for its paramagnetism. The 3H4 free-ion ground state is split by a cubic crystalline field to leave a triplet lowest in energy [l]. In a field of tetragonal symmetry such as might be produced by a charge-compensating interstitial F- ion, the triplet splits into a singlet and a lower-lying doublet. This split triplet can be treated by a spin-Hamiltonian of the form [7]
-D[S;-dS(S+l)]+A,,.‘?&
+A&Z~+syzy),
where the nuclear spin is i , the effective electronic spin is 1, and D is the zero-field splitting between doublet and singlet. Zero-field splitting of the doublet is neglected. Since the charge compensation can occur along any one of the [loo]type directions, there are three types of magnetic ion with the tetragonal symmetry axis of each ion parallel to a major cubic axis of CaF2. Resonant absorption of energy from the elastic wave occurs when the paramagnetic-resonance condition is satisfied. Taking note of the experimentally determined small value of g, and A,, the resonance condition to second order is (Bz f 0) hf = 2g,, /JBBz + (2g,, &‘,/D2)
[6(&B’
9
wheref is the frequency of the elastic wave and MI is the nuclear magnetic quantum number. Eq. (1) is valid for the AM, = 2 transitions predicted by a spin-lattice Hamiltonian quadratic in spin Intense absorption from longitudinal waves propagated along the [OOl] direction by ions with symmetry axes perpendicular to [OOl] was observed. No absorption by ions with symmetry axes parallel to [OOl] was observed, as expected [7]. The spectrum consisted of 6 hyperfine lines with each line having the shape characteristic of a non-Kramers ion. The angular variation of the magnetic field required for resonance showed that the ions were in sites of tetragonal symmetry with their magnetic axes directed along a major cubic direction. Within the accuracy of the data reported here, the angular dependence 36
8 September
1969
of the magnetic field required for resonance was proportional to (cos 0)-l. Thus, in this case the resonance condition is well described by the first and last terms of eq. (2). The measured parameters are [8] g,,= 1.94 + 0.5%, g, = 0,A ,, = 2.77 GHz f 0.5%, A, = 0. Using the values ofA ,, and g,,, the nuclear magnetic moment of Pr was calculated to be 4.2 I-(Nusing the value of (r-3) given by Freeman and Watson [9]. This compares favorably with the value given by Baker and Bleaney [lo]. Using the second term of eq. (2) the zerofield splitting was estimated to be greater than 20 cm-l. The optical absorption spectrum at 3000K showed a peak at about 2184 A which corresponds to a 4f -5d transition identified by Loh [ 1 l] as due to Pr3+. Also, infrared absorption at about 2300 cm-l for our material agreed with the well-known 3H4 - 3H5 transition. The observed resonance can unambiguously be attributed to Pr3+ in sites of tetragonal symmetry in view of the above evidence. The results of this investigation and others [8,6] clearly establish the value of ultrasonic paramagnetic resonance in microwave spectroscopy, particularly for the case of non-Kramers ions. We gratefully acknowledge the aid of Professor Truman Black for supplementing our EPR measurements and Dr. Kent Watts for the use of an absorption spectrophotometer.
)2 +
+2A,,Mz
PI*
LETTERS
References 1. 2.
3. 4. 5.
6. 7. 8.
9. 10. 11.
M. J. Weber and R. W. Bierig, Phys. Rev. 134 (1964) 1492. F. R. Merrit. H. Guggenheim and C. G. B. Garrett, Phvs. Rev. 145 (1966) 145. S. b. McLaughlan, Phys. Rev. 150 (1966) 118. W. I. Dobrov. Phys. Rev. 146 (1966) 268. Preliminary results were reported by C. G. Roberts, E. L. Kitts Jr. and G. C. Wetsel Jr. Bull. Am. Phys. Sot. 12 (1967) 199. J.R. Fletcher, F. G. Marshall, V. W. Rampton, P.M. Rowe11 and K. W. H. Stevens. Proc. Phys. Sot. (London) 88 (1966) 127. G. C. Wetsel Jr. and P. L. Donoho. Phys. Rev. 139 (1965) A334. G. C. Wetsel Jr., Bull. Am. Phys. Sot. 14 (1969) 314: (The values reported are for an effective spin of 3.) A. J. Freeman and R. E. Watson, Phys. Rev. 127 (1962) 2058. J. M. Baker and B. Bleaney, Proc. Phys. Sot. (London) 68A (1955) 936. E. Loh, Phys. Rev. 147 (1966) 332.
30A.
number 1
PHYSICS
8 September
LETTERS
The exponential increase of the linewidth with temperature suggests that the relaxation occurs mainly by an Orbach-process making use of an energy level which G ohmann et al. [4] have shown to be located 47 cm- r above the ground state in the absence of a magnetic field, and consequently 460K at resonance. The temperature independent linewidth of 30 G below 5’K cannot nearly be accounted for by the inhomogeneity of the magnetic field across the sample. The contribution of direct relaxation between the Zeeman levels to the observed linewidth seems to be also negligible: This relaxation rate measured at low magnetic fields [5] and extrapolated to hi h fields according to the relationI - T leads at H = 40 kG and at 4OK ship [6] Ti’ CCH to a linewidth of only AH = 2 mG. Likewise a twostepphonon emission using an intermediate energy level, located 18 cm-’ above the ground state at resonance [4], appears much too slow (AH e 0.1 G) to account for the observed linewidth [?I. In order to measure the intrinsic spin-lattice relaxation at low temperatures in the presence of a possible inhomogeneous line broadening saturation techniques would be necessary. In order to
1969
provide the high power needed for such measurements Q-switch experiments with the same laser are in progress. The authors are much indebted to Dr. K. F. Renk for helpful discussions and aslo wish to thank Professor W. P. Wolf and Drs. F. Pobell and J. J. Wooldridge for many stimulations, Professor S. Htifner for providing the samples and to acknowledge the financial support of the Deutsche Forschungsgemeinschaft and Fraunhofer-Gesellschaft.
References K. Dranfeld and K. F. Renk. Phps. Let1. J. Boettcher. ters 26A (1968) 146. Appl. Opt. 7 (1968) 2422. 2. J. P.Kotthaus. 3. J. M. Baker and B. Bleaney. Proc. Roy. Sot. (London) A245 (1958) 156. 4. I. Grohmann. K. H. Hellwege and H. G. Kahle, Z. Phpsik 164 (1961) 243. Z. Physik 181 (1964) 13. 5. H.Kalbfleisch. 6. C. B. P. Finn, R. Orbach and W. P. Wolf, Proc. Phys. Sot. (London) 77 (1961) 261. Proc. Roy. Sot. (London) A264 (1961) 458. 7. R.Orbach,
*****
ULTRASONIC
PARAMAGNETIC
RESONANCE
OF
Pr3+:
CaF2
t
G. C. WETSEL Jr., C. G. ROBERTS *, E. L. KITTS Jr. $* and P. O’HAGAN * Southern Methodist University, DalEas, Texas, USA Received
29 July 1969
Ultrasonic-parsmagnetic-resonance investigations of the ground-state energy levels of praseodymium ions in CaF2 are reported. A new resonance, not observed by previous EPR investigations. was observed at 9.0 GHz and 4.2oK and is attributed to Pr3+ in sites of tetragonal symmetry.
The ground-state energy levels of praseodymium ions in crystals of calcium fluoride have been previously investigated using the techniques of electron paramagnetic resonance (EPR) [I -31. Weber and Bierig [l] reported a negative result, Merritt et al. [2] examined Pr2+, and McLaughlan t Work supported in part by NASA Grant 44-007-006 and ARPA Grant DAHC15-67-G2. * Honors Co-operative Graduate Students, Texas Instruments, Inc. $ Present address: Univ. of North Carilina, Chapel Hill, N.C., USA.
[3] reported the observation of two trigonal spectra which he attributed to Pr3+, Dobrov [4], using the method of ultrasonic paramagnetic resonance (UPR), also reported a negative result. We have observed [5] intense UPR absorption at 4.2OK from 9.0 GHz longitudinal elastic waves propagated along a [loo] direction of calcium fluoride containing 0.1% praseodymium (material obtained from the Harshaw Chemical Co., Cleveland, Ohio). After the source of the absorption was established by UPR to be due to Pr3+ in tetragonal sites, a weak EPR spectrum was also detected. As in the case [6] of Cr2+: MgO, our 35
Volume
30A, number 1
PHYSICS
observation marks a (formerly) rare case where a paramagnetic impurity was detected by the ultrasonic technique before its detection by EPR. We have subsequently detected other resonances in CaF2 apparently not yet observed by EPR. Trivalent praseodymium has two 4f electrons, which are responsible for its paramagnetism. The 3H4 free-ion ground state is split by a cubic crystalline field to leave a triplet lowest in energy [l]. In a field of tetragonal symmetry such as might be produced by a charge-compensating interstitial F- ion, the triplet splits into a singlet and a lower-lying doublet. This split triplet can be treated by a spin-Hamiltonian of the form [7]
-D[S;-dS(S+l)]+A,,.‘?&
+A&Z~+syzy),
where the nuclear spin is i , the effective electronic spin is 1, and D is the zero-field splitting between doublet and singlet. Zero-field splitting of the doublet is neglected. Since the charge compensation can occur along any one of the [loo]type directions, there are three types of magnetic ion with the tetragonal symmetry axis of each ion parallel to a major cubic axis of CaF2. Resonant absorption of energy from the elastic wave occurs when the paramagnetic-resonance condition is satisfied. Taking note of the experimentally determined small value of g, and A,, the resonance condition to second order is (Bz f 0) hf = 2g,, /JBBz + (2g,, &‘,/D2)
[6(&B’
9
wheref is the frequency of the elastic wave and MI is the nuclear magnetic quantum number. Eq. (1) is valid for the AM, = 2 transitions predicted by a spin-lattice Hamiltonian quadratic in spin Intense absorption from longitudinal waves propagated along the [OOl] direction by ions with symmetry axes perpendicular to [OOl] was observed. No absorption by ions with symmetry axes parallel to [OOl] was observed, as expected [7]. The spectrum consisted of 6 hyperfine lines with each line having the shape characteristic of a non-Kramers ion. The angular variation of the magnetic field required for resonance showed that the ions were in sites of tetragonal symmetry with their magnetic axes directed along a major cubic direction. Within the accuracy of the data reported here, the angular dependence 36
8 September
1969
of the magnetic field required for resonance was proportional to (cos 0)-l. Thus, in this case the resonance condition is well described by the first and last terms of eq. (2). The measured parameters are [8] g,,= 1.94 + 0.5%, g, = 0,A ,, = 2.77 GHz f 0.5%, A, = 0. Using the values ofA ,, and g,,, the nuclear magnetic moment of Pr was calculated to be 4.2 I-(Nusing the value of (r-3) given by Freeman and Watson [9]. This compares favorably with the value given by Baker and Bleaney [lo]. Using the second term of eq. (2) the zerofield splitting was estimated to be greater than 20 cm-l. The optical absorption spectrum at 3000K showed a peak at about 2184 A which corresponds to a 4f -5d transition identified by Loh [ 1 l] as due to Pr3+. Also, infrared absorption at about 2300 cm-l for our material agreed with the well-known 3H4 - 3H5 transition. The observed resonance can unambiguously be attributed to Pr3+ in sites of tetragonal symmetry in view of the above evidence. The results of this investigation and others [8,6] clearly establish the value of ultrasonic paramagnetic resonance in microwave spectroscopy, particularly for the case of non-Kramers ions. We gratefully acknowledge the aid of Professor Truman Black for supplementing our EPR measurements and Dr. Kent Watts for the use of an absorption spectrophotometer.
)2 +
+2A,,Mz
PI*
LETTERS
References 1. 2.
3. 4. 5.
6. 7. 8.
9. 10. 11.
M. J. Weber and R. W. Bierig, Phys. Rev. 134 (1964) 1492. F. R. Merrit. H. Guggenheim and C. G. B. Garrett, Phvs. Rev. 145 (1966) 145. S. b. McLaughlan, Phys. Rev. 150 (1966) 118. W. I. Dobrov. Phys. Rev. 146 (1966) 268. Preliminary results were reported by C. G. Roberts, E. L. Kitts Jr. and G. C. Wetsel Jr. Bull. Am. Phys. Sot. 12 (1967) 199. J.R. Fletcher, F. G. Marshall, V. W. Rampton, P.M. Rowe11 and K. W. H. Stevens. Proc. Phys. Sot. (London) 88 (1966) 127. G. C. Wetsel Jr. and P. L. Donoho. Phys. Rev. 139 (1965) A334. G. C. Wetsel Jr., Bull. Am. Phys. Sot. 14 (1969) 314: (The values reported are for an effective spin of 3.) A. J. Freeman and R. E. Watson, Phys. Rev. 127 (1962) 2058. J. M. Baker and B. Bleaney, Proc. Phys. Sot. (London) 68A (1955) 936. E. Loh, Phys. Rev. 147 (1966) 332.