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Low field ESR spectrum of trivalent gadolinium in single crystal throrium oxide
PHYSICS
Volume 28A, number 4
2 December 1968
LETTERS
and amplitude modulation can be seen with a periodicity of about 20 kHz. Now, we can understand such a behavior if we excite the wave only during few periods and extract the signal from the noise with a PAR Waveform Eductor. Fig. 2 represents the collected signal in the upper trace and the applied signal in the lower trace. The frequencies are 55 kHz (fig. 2a) corresponding to the second minimum and 65 kHz (fig. 2b) corresponding to the next maximum (fig. 1). After a delay of about 15 ps, we can observe
the ionic plasma frequency. Such a pseudowave has been previously observed [3 - 41 corresponding to ion bursts [3] or plasma bursts [4] accel-
a Pseudowave. The ion acoustic wave. delaved of adout 60 ps appears clearly at the enh of t
References
wave continuously, a mixing of the two different components gives destructive (2a) or constructive (2b) result. This mixing effect is very similar to non linear collisionless damping. The faster signal, now being studied, seems to appear only at frequencies higher than a critical frequency close to
erated by the grids. But the nature of the fast component observed here is different because the measured velocity is indipendent of the excitation amplitude.
J. H. Malmberg and C. B. Wharton, Phys. Rev. Letters 19 (1967) 775. W. Sato, H. Ikesi, Y. Yamashita, N. Takahashi and T. Obiki, Phys. Letters 26A (1968) 333. H. J.Doucet and D.Gresillon, Phys. Letters 25A (1967) 697. K. Lonnnren. D. Montgomery. I. Alexeff and W. D. Jones, Whys’. Letters‘iSA (ii67) 629. 4. Y. Tamashita, H. Ikezi, N. Sato and N. Takahashi Phys. Letters 27A (1968) 79.
*****
LOW
FIELD ESR SPECTRUM OF TRIVALENT GADOLINIUM IN SINGLE CRYSTAL THORIUM OXIDE* S. A. MARSHALL and G. A. JOHNSON Argonne
National Laboratory,
Argonne,
Illinois
Received 17 October 1968
The low field ESR spectrum of trivalent gadolinium in single crystal thorium oxide has been reinvestigated at 3 cm wavelength. Zeeman field strengths for all permitted transitions are found to be in substantial agreement with predictions as are relative intensity ratios.
The first published study of the electron spin resonance (ESR) absorption spectrum of trivalent gadolinium in single crystal thorium oxide (ThO2) was that of Low and Shaltiel [l]. Recently other studies of this crystal-ion system have appeared in which were provided improved spectral parameters as well as the temperature dependence of b4, one of the coefficients to the crystalline electric field potential [2,3]. In addition to the principal seven-line spectrum, which occurs between
2000 Oe and 5000 Oe for 3 cm wavelength radiation, Low and Shaltiel observed a supplementary, low intensity spectrum of six lines between 600 Oe and 1000 Oe. This latter spectrum was identified as arising from transitions between terms which are characterized by mixed spin vectors which span the S = { manifold. This mixing is brought about through the action of off-diagonal operators in the crystalline electric field potential whose form is given by
* Based on work performed under the auspices of the
Vcf = b4&5(Yi+
U.S. Atomic Energy Commission.
256
Y,4)] + b6[Y;+21(Y;+
Yi4)] (1 )
Volume 28A, number 4
PHYSICS
where the YE are electron spin polynominal operators which transform upon rotation as the spherical harmonics of like indices. At 4.2OK, the two parameters to the potential are !14 = - 60.900 Oe and b6 = - 0.438 Oe [31 and the spectroscopic splitting factor is reevaluated to be g = 1.9913. Under the action of a crystalline electric field exhibiting cubic symmetry, the 8s ground term of trivalent gadolinium will have its eight-fold spin degeneracy lifted into two terms each of twofold degeneracy and one term of four-fold degeneracy [4]. Upon the application of a Zeeman field, all proper degeneracy will be lifted. The energy spectrum then consists of eight curvilinear functions of the Zeeman field each of which is a mixture of spin vectors corresponding to the projection numbers M and M f 4 with the mixing ratios being prescribed functions of the Zeeman field strength as well as of the spectral parameteres bq andibe. The eight state functions are labeled by $@I), where @(M(M) + 1 M > as B -+ m. With the Zeeman field vector directed along a cube edge, it may be demonstrated that in principle there can occur twenty transitions between these eight terms. Seven of these are the normally allowed transitions whose intensities, to within first order approximation, are independent of the degree of mixing of spin vectors. Of the remaining thirteen transitions, twelve have intensities proportional to (b I2 while one has intensity proportional to (bq) 4. IThe influence of b6 upon intensities has been ignored). Using the eigenvalue expressions given by eqs. (2) in ref. 3 along with the aforementioned values of g, b4, and bei absorption field strengths for each of the twenty transitions were obtained by machine calculations. The thirteen low field transitions, usually referred to as forbidden are given in table 1 along with polarization and intensity dependence upon b4. All relative intensity measurements were refexenced to the normally allowed ition’and were found to be $(- 6) -+ J/(i) tr within 25% of pr ctions. It is conclude,F that a complete ESR spectrum corresponding to the selection rules AM = 0, f 1 has been observ ed for this crystal-ion system when the Zeeman field vector is oriented along
LETTERS
2 December
1968
Table 1. List of low field transitions for Gd3+ in single crystal thorium oxide. Zeeman field strengths are given in oersted. Except for the eighth transition, all field strengths in the observed column are estimated to be uncertain by l 0.1 Oe. 2, = 9611.64 MHz. Transition 4wf) -twf’)
Polarization
Order in b4
Field Calc. Obs.
-f-
I
u
4
474.5
474.5
-6
9
u
2
521.9
521.9
-83 -5
-f
r
2
873.7
873.7
u
2
1188.8
1188.7 645.4
-I
$
0
2
645.4
-3
3
lr
2
973.8
973.8
-3
t
0
2
1573.0
1573.1
-#
+
-34 -!
%
-4) -4
4
$f
u
2
788.6
790a
*
2
666.2
666.4
o
2
1106.3
1106.6
r
2
814.2
814.2
u
2
659.6
659.6
lJ
2
1110.4
1110.4
a) This entry uncertain by l 3 Oe due to obscuring effects arising from components of unrelated spectra.
(100) direction. From a comparison of observed and calculated resonance absorption field strengths, it is further concluded that the fine structure energy operator may reasonably well be approximated by a first order Zeeman term and a crystalline electric field potential of the form given in eq. (1). a crystal
R.
The authors express their appreciation to H. Land for providfng machine calculations.
References
1. W.Low and D.ShaItiel, J. Phys. Chem. Solids 6 (1958) 315. 2. M.M.Abraham, E.J.LeeandR.A.Weeks, J.Phys. Chem. Solids 26 (1965) 1249. 3. S.A.Marshall, Phys. Rev. 159 (1967) 191. 4. H.A.Bethe, AM. Phys.3 (1929) 333.
259
Volume 28A, number 4
2 December 1968
LETTERS
and amplitude modulation can be seen with a periodicity of about 20 kHz. Now, we can understand such a behavior if we excite the wave only during few periods and extract the signal from the noise with a PAR Waveform Eductor. Fig. 2 represents the collected signal in the upper trace and the applied signal in the lower trace. The frequencies are 55 kHz (fig. 2a) corresponding to the second minimum and 65 kHz (fig. 2b) corresponding to the next maximum (fig. 1). After a delay of about 15 ps, we can observe
the ionic plasma frequency. Such a pseudowave has been previously observed [3 - 41 corresponding to ion bursts [3] or plasma bursts [4] accel-
a Pseudowave. The ion acoustic wave. delaved of adout 60 ps appears clearly at the enh of t
References
wave continuously, a mixing of the two different components gives destructive (2a) or constructive (2b) result. This mixing effect is very similar to non linear collisionless damping. The faster signal, now being studied, seems to appear only at frequencies higher than a critical frequency close to
erated by the grids. But the nature of the fast component observed here is different because the measured velocity is indipendent of the excitation amplitude.
J. H. Malmberg and C. B. Wharton, Phys. Rev. Letters 19 (1967) 775. W. Sato, H. Ikesi, Y. Yamashita, N. Takahashi and T. Obiki, Phys. Letters 26A (1968) 333. H. J.Doucet and D.Gresillon, Phys. Letters 25A (1967) 697. K. Lonnnren. D. Montgomery. I. Alexeff and W. D. Jones, Whys’. Letters‘iSA (ii67) 629. 4. Y. Tamashita, H. Ikezi, N. Sato and N. Takahashi Phys. Letters 27A (1968) 79.
*****
LOW
FIELD ESR SPECTRUM OF TRIVALENT GADOLINIUM IN SINGLE CRYSTAL THORIUM OXIDE* S. A. MARSHALL and G. A. JOHNSON Argonne
National Laboratory,
Argonne,
Illinois
Received 17 October 1968
The low field ESR spectrum of trivalent gadolinium in single crystal thorium oxide has been reinvestigated at 3 cm wavelength. Zeeman field strengths for all permitted transitions are found to be in substantial agreement with predictions as are relative intensity ratios.
The first published study of the electron spin resonance (ESR) absorption spectrum of trivalent gadolinium in single crystal thorium oxide (ThO2) was that of Low and Shaltiel [l]. Recently other studies of this crystal-ion system have appeared in which were provided improved spectral parameters as well as the temperature dependence of b4, one of the coefficients to the crystalline electric field potential [2,3]. In addition to the principal seven-line spectrum, which occurs between
2000 Oe and 5000 Oe for 3 cm wavelength radiation, Low and Shaltiel observed a supplementary, low intensity spectrum of six lines between 600 Oe and 1000 Oe. This latter spectrum was identified as arising from transitions between terms which are characterized by mixed spin vectors which span the S = { manifold. This mixing is brought about through the action of off-diagonal operators in the crystalline electric field potential whose form is given by
* Based on work performed under the auspices of the
Vcf = b4&5(Yi+
U.S. Atomic Energy Commission.
256
Y,4)] + b6[Y;+21(Y;+
Yi4)] (1 )
Volume 28A, number 4
PHYSICS
where the YE are electron spin polynominal operators which transform upon rotation as the spherical harmonics of like indices. At 4.2OK, the two parameters to the potential are !14 = - 60.900 Oe and b6 = - 0.438 Oe [31 and the spectroscopic splitting factor is reevaluated to be g = 1.9913. Under the action of a crystalline electric field exhibiting cubic symmetry, the 8s ground term of trivalent gadolinium will have its eight-fold spin degeneracy lifted into two terms each of twofold degeneracy and one term of four-fold degeneracy [4]. Upon the application of a Zeeman field, all proper degeneracy will be lifted. The energy spectrum then consists of eight curvilinear functions of the Zeeman field each of which is a mixture of spin vectors corresponding to the projection numbers M and M f 4 with the mixing ratios being prescribed functions of the Zeeman field strength as well as of the spectral parameteres bq andibe. The eight state functions are labeled by $@I), where @(M(M) + 1 M > as B -+ m. With the Zeeman field vector directed along a cube edge, it may be demonstrated that in principle there can occur twenty transitions between these eight terms. Seven of these are the normally allowed transitions whose intensities, to within first order approximation, are independent of the degree of mixing of spin vectors. Of the remaining thirteen transitions, twelve have intensities proportional to (b I2 while one has intensity proportional to (bq) 4. IThe influence of b6 upon intensities has been ignored). Using the eigenvalue expressions given by eqs. (2) in ref. 3 along with the aforementioned values of g, b4, and bei absorption field strengths for each of the twenty transitions were obtained by machine calculations. The thirteen low field transitions, usually referred to as forbidden are given in table 1 along with polarization and intensity dependence upon b4. All relative intensity measurements were refexenced to the normally allowed ition’and were found to be $(- 6) -+ J/(i) tr within 25% of pr ctions. It is conclude,F that a complete ESR spectrum corresponding to the selection rules AM = 0, f 1 has been observ ed for this crystal-ion system when the Zeeman field vector is oriented along
LETTERS
2 December
1968
Table 1. List of low field transitions for Gd3+ in single crystal thorium oxide. Zeeman field strengths are given in oersted. Except for the eighth transition, all field strengths in the observed column are estimated to be uncertain by l 0.1 Oe. 2, = 9611.64 MHz. Transition 4wf) -twf’)
Polarization
Order in b4
Field Calc. Obs.
-f-
I
u
4
474.5
474.5
-6
9
u
2
521.9
521.9
-83 -5
-f
r
2
873.7
873.7
u
2
1188.8
1188.7 645.4
-I
$
0
2
645.4
-3
3
lr
2
973.8
973.8
-3
t
0
2
1573.0
1573.1
-#
+
-34 -!
%
-4) -4
4
$f
u
2
788.6
790a
*
2
666.2
666.4
o
2
1106.3
1106.6
r
2
814.2
814.2
u
2
659.6
659.6
lJ
2
1110.4
1110.4
a) This entry uncertain by l 3 Oe due to obscuring effects arising from components of unrelated spectra.
(100) direction. From a comparison of observed and calculated resonance absorption field strengths, it is further concluded that the fine structure energy operator may reasonably well be approximated by a first order Zeeman term and a crystalline electric field potential of the form given in eq. (1). a crystal
R.
The authors express their appreciation to H. Land for providfng machine calculations.
References
1. W.Low and D.ShaItiel, J. Phys. Chem. Solids 6 (1958) 315. 2. M.M.Abraham, E.J.LeeandR.A.Weeks, J.Phys. Chem. Solids 26 (1965) 1249. 3. S.A.Marshall, Phys. Rev. 159 (1967) 191. 4. H.A.Bethe, AM. Phys.3 (1929) 333.
259