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Paramagnetic linewidth analysis of ESR in spin glasses
132
Journal
PARAMAGNETIC P. MONOD,
LINEWIDTH
A. LAND1
*, C. BLANCHARD
Physique des Solides, UniversitC Paris&d, Received
9 October
ANALYSIS
of Magnetism
and Magnetic
Materials 59 (1986) 132-134 North-Holland, Amsterdam
OF ESR IN SPIN GLASSES *, A. DEVILLE
* and H. HURDEQUINT
91405 Orsay, France
1985
ESR investigation of the system Eu,Sr, _XS is presented for 0.01 i x -C1 as a function of temperature and, at room temperature, for 4.5, 9.3 and 35 GHz. For x > 0.2 the resulting T + cc ESR linewidth varies like a + b& with a and b decreasing as the frequency increases. This behaviour is compatible with exchange narrowed dipolar width, as proposed by Levy and Raghavan, with the frequency dependence due to the “10/3” effect.
1. Introduction The motivation of this study is to understand the physical origin of the high temperature’ linewidth of the electron spin resonance (in the paramagnetic limit) of spin glass compounds. Indeed a remarkably different behaviour is observed for metallic alloys such as -CuMn or -AgMn [l] on one hand and insulators or semiconductors on the other hand like (Al,O,),(MnO),(SiO,), [2] Eu,Sr,_,S [3] or Cd,_,Mn,Te [4]. The metallic spin glasses display at high temperature (T > 2T’,) essentially the paramagnetic linewidth of isolated ions, that is, a linear increase with temperature whose slope is independent of Mn concentration (up to at least 20 at’%) but strongly depends on spin-orbit scattering. This regime is the well known bottleneck limit: the Mn-Mn exchange or dipole-dipole interactions play no role since they are much weaker than the prevailing s-d interaction of individual ions with the conduction electron sea. In contrast the insulating or semiconducting spin glasses display, at high temperature (T > 20 T,), a constant temperature independent linewidth which markedly increases with concentration. In both cases it is essential to obtain a good physical * Dept.
d’Electronique,
Universite
de
Provence,
Marseille,
France.
0304~8853/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
description of the high temperature linewidth in order to be able to substract this contribution from the total linewidth as T + Tg [l]. Furthermore, the high temperature linewidth is a simple natural limit which can be used to check the validity of current models for the spin glass resonance properties [5] as a function of concentration, temperature and frequency.
900
700
500
Fig. 1. Temperature dependence of the peak to peak linewidth of the derivative of ESR absorption signal at 9.3 GHz for Eu,Sr, _XS with x = 0.1, 0.2, 0.4 and 0.44. The ESR lineshape is Lorentzian and isotropic.
B.V.
P. Monad et al. / Paramagnetic
2. Temperature
linewidth analysis of ESR in spin glasses
dependence
p Hpp(lOOG)
The temperature dependence of the ESR linewidth has been investigated in the Eu,Sr,_,S system for x = 0.44 [3], x = 0.56 and 0.70 [6] and for x = 1: EuS [7]. We present in fig. 1 the results for x = 0.1, 0.2, 0.4 and 0.44 from 3.8 K to room temperature at 9.3 GHz. Besides the high temperature plateau to be discussed next the low temperature increase of linewidth below 30 K for x = 0.1 and 0.2 is remarkable in view of the fact that the corresponding spin glass temperature is 0.1 and 0.6 K, respectively. This behaviour is not found for x = 0.0085 whose linewidth is temperature independent in the range of investigation.
For 0.85 X lop2 < x < 1, the samples were single crystals (fee structure), except EuS (crystalline powder). The ESR spectra were recorded at three frequencies: 4.5, 9.3 and 35 GHz, at room temperature. For 9.3 and 35 GHz, we used the E 112 Varian spectrometer; the 4.5 GHz measurements were made with a heterodyne 2-5.5 GHz spectrometer. For each europium concentration, the measurements at the three frequencies were all made on the same sample; as the sensitivity is less at 4.5 than at 35 GHz, we first had to carefully choose the size of each sample in order to get a lOOO-
’ -
I
’
’
’
I ’ ’ ’ i ’
q&l) vl”’
500,’
,-,’
I,I
/
* Eq&(S
,,L t!l 0
I
x)1
I
I
.l
I
.2
I
I
,
VT ,
,
.3 II .5.6.7.8.9
,
1
Fig. 2. Concentration dependence of the high temperature limit of the linewidth of Eu,Sr, _,S at 9.3 GHz for 0.01 < x < 1 as a function of 6. (0): this work; (W): ref. [6]. Note the anisotropy between [lOOI and [llO] axes for x < 0.07 (non-Lorentzian lineshape) represented by two points.
1
1
\ ‘-_ 2
f(G H )
I I I llllll 1
3. Frequency and concentration dependence
133
I I I~~~~~1 ‘I I IIll 10
100
Fig. 3. Frequency dependence of the high temperature limit of the linewidth from figs. 1 and 2. The dashed line is the “10/3” effect for EuS as calculated by Levy and Rhagavan [5] adjusted at low frequency (see ref. [8]).
sufficient S/N ratio at 4.5 GHz, we then had to move the sample away from the center of the cylindrical cavity in order to get an undistorted ESR signal. The anisotropy of the ESR line was studied by varying the direction of the driving field in a [OOl] plane. The results are presented in figs. 2 and 3. We found an isotropic line for x > 0.1. At 34 GHz the line was isotropic within experimental error for x = 0.07 while for 4.5 and 9.3 GHz it was anisotropic; at lower concentrations, the anisotropy was detected at all frequencies; for x = 0.85 X 10e2, the ratio between the extreme values of the linewidth was 1.45 f 0.14. When x > 0.1 the width between the extrema of the derivative of the absorption line, AHr,, can be fit with the following expression: A Hpp = a + b&, with a = (100 k 50) G, b = (900 + 200) G at 4.5 GHz; a = (130 + 100) G, b = (900 f 200) G at 9.3 GHz; a = (60 f 50) G, b = (780 + 100) G at 35 GHz (the 35 GHz values being valid for x > 0.2 only). For x -C 0.07, the variation of A Hpp with the orientation is shown in fig. 2, for the driving field along the [loo] and [llO] axes. For x < 0.03, the line has a complex shape, while for x > 0.1 it has a nearly Lorentzian shape. For x > 0.1, at a given concentration the line has nearly the same width at 4.5 and 9.3 GHz,
134
P. Monad et al. / Paramagnetic linewidth analysis of ESR in spin glasses
while it is narrower at 35 GHz (fig. 3); However, for x < 0.07, it has the same width within experimental error at all frequencies. These results can be interpreted qualitatively considering that the line has a dipolar origin, and is exchange-narrowed when x 2 0.1, leading to a Lorentzian shape [3]. A fi dependence is indeed expected on very general grounds [5], however the constant linewidth (if real) found by extrapolation at x = 0 must have a different physical origin. For x > 0.1, linewidth decreases when the resonance frequency increases, which indicates that the contribution of the non-adiabatic part of the dipolar Hamiltonian is less effective at higher frequencies; it is well known [S] that the contribution of this non-adiabatic term leads to the “lo/3 effect”, i.e. a broadening at low frequencies. It should be remarked at this point [9] that the high frequency limit of the “lo/3 effect” represented by a plateau of the dashed curve of fig. 3 (above 200 GHz) must be anisotropic since in that case only the truncated dipole-dipole Hamiltonian is considered (the 10/3 coefficient corresponds to the ratio of the low frequency limit to the powder average of this high frequency anisotropic linewidth). In contrast, the low frequency plateau (below 3 GHz) is isotropic [9] for cubic crystals. The fact that our lineshape are lorentzian and isotropic is thus a strong argument in favor of extreme narrowing of the full dipole dipole interaction in the low frequency regime [3,5].
Acknowledgements We thank Dr. F. Holtzberg for a critical reading of the manuscript and for lending us samples together with Dr. H. Maletta and Prof. S. Methfessel.
References VI J. Owen, M.E. Browne,
V. Arp and A.F. Kip, J. Phys. Chem. Solids 2 (1957) 85. P.R. Elliston, Phys. Stat Sol. (a) 3 (1970) 111. M.B. Salamon and R.M. Herman, Phys. Rev. Lett. 41 (1978) 506. G. Mozurkewich, J.H. Eliott, J.H. Hardiman and R. Orbach, Phys. Rev. B29 (1984) 278. 121J.P. Jamet, J.C. Dumais, J. Seiden, and K. Knorr, J. Magn. Magn. Mat. 15-18 (1980) 197. C. Blanchard, J.P. Jamet and 131 A. Deville, C. Arzoumanian, H. Maletta, J. de Phys. 42 (1981) 1641. [41 H.A. Sayad and S.M. Bhagat, Phys. Rev. 31 (1985) 591. [51 P.M. Levy and R. Raghavan, J. Magn. Magn. Mat. 54-57 (1986) 181; Phys. Rev. B30 (1984) 2358. R.L. Melcher, [61 F. Mehran, K.W.H. Stevens, F. Holtzberg, W.J. Fiztpatrick and T.R. McGuire, Solid State Commun. 52 (1984) 107. G.E. Everett and A.W. Lawson, J. Appl. [71 M.C. Franzblau, Phys. 38 (1967) 4462. S.C. Kondal and MS. Seehra, J. Phys. C 15 (1982) 2471. and R.N. Rogers, Phys. Rev. 152 (1966) PI A.J. Henderson 218. [91 B.R. Cooper and F. Keffer, 125 (1962) 896.
Journal
PARAMAGNETIC P. MONOD,
LINEWIDTH
A. LAND1
*, C. BLANCHARD
Physique des Solides, UniversitC Paris&d, Received
9 October
ANALYSIS
of Magnetism
and Magnetic
Materials 59 (1986) 132-134 North-Holland, Amsterdam
OF ESR IN SPIN GLASSES *, A. DEVILLE
* and H. HURDEQUINT
91405 Orsay, France
1985
ESR investigation of the system Eu,Sr, _XS is presented for 0.01 i x -C1 as a function of temperature and, at room temperature, for 4.5, 9.3 and 35 GHz. For x > 0.2 the resulting T + cc ESR linewidth varies like a + b& with a and b decreasing as the frequency increases. This behaviour is compatible with exchange narrowed dipolar width, as proposed by Levy and Raghavan, with the frequency dependence due to the “10/3” effect.
1. Introduction The motivation of this study is to understand the physical origin of the high temperature’ linewidth of the electron spin resonance (in the paramagnetic limit) of spin glass compounds. Indeed a remarkably different behaviour is observed for metallic alloys such as -CuMn or -AgMn [l] on one hand and insulators or semiconductors on the other hand like (Al,O,),(MnO),(SiO,), [2] Eu,Sr,_,S [3] or Cd,_,Mn,Te [4]. The metallic spin glasses display at high temperature (T > 2T’,) essentially the paramagnetic linewidth of isolated ions, that is, a linear increase with temperature whose slope is independent of Mn concentration (up to at least 20 at’%) but strongly depends on spin-orbit scattering. This regime is the well known bottleneck limit: the Mn-Mn exchange or dipole-dipole interactions play no role since they are much weaker than the prevailing s-d interaction of individual ions with the conduction electron sea. In contrast the insulating or semiconducting spin glasses display, at high temperature (T > 20 T,), a constant temperature independent linewidth which markedly increases with concentration. In both cases it is essential to obtain a good physical * Dept.
d’Electronique,
Universite
de
Provence,
Marseille,
France.
0304~8853/86/$03.50 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
description of the high temperature linewidth in order to be able to substract this contribution from the total linewidth as T + Tg [l]. Furthermore, the high temperature linewidth is a simple natural limit which can be used to check the validity of current models for the spin glass resonance properties [5] as a function of concentration, temperature and frequency.
900
700
500
Fig. 1. Temperature dependence of the peak to peak linewidth of the derivative of ESR absorption signal at 9.3 GHz for Eu,Sr, _XS with x = 0.1, 0.2, 0.4 and 0.44. The ESR lineshape is Lorentzian and isotropic.
B.V.
P. Monad et al. / Paramagnetic
2. Temperature
linewidth analysis of ESR in spin glasses
dependence
p Hpp(lOOG)
The temperature dependence of the ESR linewidth has been investigated in the Eu,Sr,_,S system for x = 0.44 [3], x = 0.56 and 0.70 [6] and for x = 1: EuS [7]. We present in fig. 1 the results for x = 0.1, 0.2, 0.4 and 0.44 from 3.8 K to room temperature at 9.3 GHz. Besides the high temperature plateau to be discussed next the low temperature increase of linewidth below 30 K for x = 0.1 and 0.2 is remarkable in view of the fact that the corresponding spin glass temperature is 0.1 and 0.6 K, respectively. This behaviour is not found for x = 0.0085 whose linewidth is temperature independent in the range of investigation.
For 0.85 X lop2 < x < 1, the samples were single crystals (fee structure), except EuS (crystalline powder). The ESR spectra were recorded at three frequencies: 4.5, 9.3 and 35 GHz, at room temperature. For 9.3 and 35 GHz, we used the E 112 Varian spectrometer; the 4.5 GHz measurements were made with a heterodyne 2-5.5 GHz spectrometer. For each europium concentration, the measurements at the three frequencies were all made on the same sample; as the sensitivity is less at 4.5 than at 35 GHz, we first had to carefully choose the size of each sample in order to get a lOOO-
’ -
I
’
’
’
I ’ ’ ’ i ’
q&l) vl”’
500,’
,-,’
I,I
/
* Eq&(S
,,L t!l 0
I
x)1
I
I
.l
I
.2
I
I
,
VT ,
,
.3 II .5.6.7.8.9
,
1
Fig. 2. Concentration dependence of the high temperature limit of the linewidth of Eu,Sr, _,S at 9.3 GHz for 0.01 < x < 1 as a function of 6. (0): this work; (W): ref. [6]. Note the anisotropy between [lOOI and [llO] axes for x < 0.07 (non-Lorentzian lineshape) represented by two points.
1
1
\ ‘-_ 2
f(G H )
I I I llllll 1
3. Frequency and concentration dependence
133
I I I~~~~~1 ‘I I IIll 10
100
Fig. 3. Frequency dependence of the high temperature limit of the linewidth from figs. 1 and 2. The dashed line is the “10/3” effect for EuS as calculated by Levy and Rhagavan [5] adjusted at low frequency (see ref. [8]).
sufficient S/N ratio at 4.5 GHz, we then had to move the sample away from the center of the cylindrical cavity in order to get an undistorted ESR signal. The anisotropy of the ESR line was studied by varying the direction of the driving field in a [OOl] plane. The results are presented in figs. 2 and 3. We found an isotropic line for x > 0.1. At 34 GHz the line was isotropic within experimental error for x = 0.07 while for 4.5 and 9.3 GHz it was anisotropic; at lower concentrations, the anisotropy was detected at all frequencies; for x = 0.85 X 10e2, the ratio between the extreme values of the linewidth was 1.45 f 0.14. When x > 0.1 the width between the extrema of the derivative of the absorption line, AHr,, can be fit with the following expression: A Hpp = a + b&, with a = (100 k 50) G, b = (900 + 200) G at 4.5 GHz; a = (130 + 100) G, b = (900 f 200) G at 9.3 GHz; a = (60 f 50) G, b = (780 + 100) G at 35 GHz (the 35 GHz values being valid for x > 0.2 only). For x -C 0.07, the variation of A Hpp with the orientation is shown in fig. 2, for the driving field along the [loo] and [llO] axes. For x < 0.03, the line has a complex shape, while for x > 0.1 it has a nearly Lorentzian shape. For x > 0.1, at a given concentration the line has nearly the same width at 4.5 and 9.3 GHz,
134
P. Monad et al. / Paramagnetic linewidth analysis of ESR in spin glasses
while it is narrower at 35 GHz (fig. 3); However, for x < 0.07, it has the same width within experimental error at all frequencies. These results can be interpreted qualitatively considering that the line has a dipolar origin, and is exchange-narrowed when x 2 0.1, leading to a Lorentzian shape [3]. A fi dependence is indeed expected on very general grounds [5], however the constant linewidth (if real) found by extrapolation at x = 0 must have a different physical origin. For x > 0.1, linewidth decreases when the resonance frequency increases, which indicates that the contribution of the non-adiabatic part of the dipolar Hamiltonian is less effective at higher frequencies; it is well known [S] that the contribution of this non-adiabatic term leads to the “lo/3 effect”, i.e. a broadening at low frequencies. It should be remarked at this point [9] that the high frequency limit of the “lo/3 effect” represented by a plateau of the dashed curve of fig. 3 (above 200 GHz) must be anisotropic since in that case only the truncated dipole-dipole Hamiltonian is considered (the 10/3 coefficient corresponds to the ratio of the low frequency limit to the powder average of this high frequency anisotropic linewidth). In contrast, the low frequency plateau (below 3 GHz) is isotropic [9] for cubic crystals. The fact that our lineshape are lorentzian and isotropic is thus a strong argument in favor of extreme narrowing of the full dipole dipole interaction in the low frequency regime [3,5].
Acknowledgements We thank Dr. F. Holtzberg for a critical reading of the manuscript and for lending us samples together with Dr. H. Maletta and Prof. S. Methfessel.
References VI J. Owen, M.E. Browne,
V. Arp and A.F. Kip, J. Phys. Chem. Solids 2 (1957) 85. P.R. Elliston, Phys. Stat Sol. (a) 3 (1970) 111. M.B. Salamon and R.M. Herman, Phys. Rev. Lett. 41 (1978) 506. G. Mozurkewich, J.H. Eliott, J.H. Hardiman and R. Orbach, Phys. Rev. B29 (1984) 278. 121J.P. Jamet, J.C. Dumais, J. Seiden, and K. Knorr, J. Magn. Magn. Mat. 15-18 (1980) 197. C. Blanchard, J.P. Jamet and 131 A. Deville, C. Arzoumanian, H. Maletta, J. de Phys. 42 (1981) 1641. [41 H.A. Sayad and S.M. Bhagat, Phys. Rev. 31 (1985) 591. [51 P.M. Levy and R. Raghavan, J. Magn. Magn. Mat. 54-57 (1986) 181; Phys. Rev. B30 (1984) 2358. R.L. Melcher, [61 F. Mehran, K.W.H. Stevens, F. Holtzberg, W.J. Fiztpatrick and T.R. McGuire, Solid State Commun. 52 (1984) 107. G.E. Everett and A.W. Lawson, J. Appl. [71 M.C. Franzblau, Phys. 38 (1967) 4462. S.C. Kondal and MS. Seehra, J. Phys. C 15 (1982) 2471. and R.N. Rogers, Phys. Rev. 152 (1966) PI A.J. Henderson 218. [91 B.R. Cooper and F. Keffer, 125 (1962) 896.