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Zero field electron spin resonance of Cu Mn in the spin glass state
Z E R O F I E L D E L E C T R O N S P I N R E S O N A N C E OF C u M n IN T H E S P I N G L A S S S T A T E P. M O N O D * and Y.. B E R T H I E R Laboratoire de Spectrometrie Physique, Universite Scientifique et M~dicale de Grenoble, 38000 St-Martin d'Heres, France The low frequen,:y, low field and zero field investigation of CuMn of 1.35% and 4.7% Mn reveals that the electron spin resonance frequency in the field cooled spin-glass state is best described by a linear relation 60 = 3,H0 + ~0a where ~0a is a measure of the macroscopic anisotropy field present.
Owen et al. [1] have discovered in their pioneer work on CuMn most of what is now considered as the typical characteristic of the spin-glass state i.e. susceptibility maximum, irreversibility, remanent magnetization with slow time dependence, and approximate scaling of these properties with concentration. Their major effort was devoted to the spin resonance in the paramagnetic region and to what happens to it in the now so-called spin-glass regime. Their conclusion was that the large resonance shift observed is describable with a "special kind of antiferromagnetic resonance" and offered an admittedly oversimplified two-sublattice analysis of this situation which has since been invariably invoked by other workers [2] except Malozemoff and Jamet [3]. In this model the resonance frequency is related to the external field H 0 by:
o~2= 3"2(Hg + HE),
(I)
where H c is a measure of the antiferromagnetic gap. In view of the difficulty of defining and measuring an order parameter in the spin-glass state [3] such a relation as (I) is paradoxical as it provides, if true, an experimentally precise and non=ambiguous determination of it. However relation (I) has only been tested in high field i.e. H 0 > H c where it merely states that the resonance shift (0/3, - H 0 decreases approximately as the inverse of the field H 0 [2]. The purpose of our work is to study the frequency-field relationship of the resonance of C u M n in the spin-glass state for low and zero field. Fr---om this we show that relation (1) is not valid and, instead, a linear relation is found. The alloys were identical to those used for the magnetization and hysteresis study [4] with concentration of 1.35% and 4.7% Mn. They were prepared as de*Physique des Solides, Universit~ de Paris Sud, 91405 Orsay, France.
scribed in [4] and carefully annealed after rolling into sheets 40 /tm thick. About 20 sheets were stacked between kapton films for each sample. The spectrometer used [5] was essentially the CW version of an existing variable frequency pulsed N M R rig in the range 500-3500 Mc, the heart of which is a ~1 wave re-entrant coaxial cavity continuously matched and tunnable in that range. The sensitivity was limited by the lack of A F C facility but was quite convenient in our case. The temperature could be set down to 1.25 K. The magnetic field, 25 k G at maximum, was produced by a superconducting coil. In order to understand our results it is essential to refer to the magnetization properties of the spin-glass state [6]. Previous results of ESR in this regime [1-3] were such that the field applied (typically ~ 3 kG) induced a reversible magnetization larger than the irreversible (remanent) magnetization acquired in this field by the isothermal remanent magnetization (IRM) process. However as shown in [1] the resonance shift properties depend critically of the magnetization process chosen, even though the magnetization amplitude is dominated by the reversible part of it. That is why Owen et al. [1] were very careful to always start from the zero-field condition. We have checked that no resonance in the range up to 3 G H z could be detected in our samples at zero or low field (500 G) when cooled in zero field. This fact was later related to the lack of a net magnetization present. We have systematically adopted the opposite condition i.e. cool the s p i n glass in such way as to produce the m a x i m u m value of the remanent magnetization. Our results then depict the frequency-field resonance relation of essentially the remanent magnetization alone whereas previous resonance work [1, 2] refers to a superposition to the reversible magnetization of a partial remanent magnetization induced by an I R M process. Fig. 1 shows the variation of the resonant field for different
Journal of Magnetism and Magnetic Materials 15-18 (1980) 149-150 ©North Holland
149
150
P. Monad, Y. Berthier/ Zero fieM ESR of Cu Mn in the spin glass state
frequencies between 900 Mc and 2500 Mc for C u M n 1.35% and 4.7% (annealed) after cooling in a 13 k G field down to 1.25 K. In the upper branch of points the signals have the shape characteristic of fixed magnetic impurities with A/B lobes ~ 2.5 + 0.2 and peak to peak width less than 100 G, allowing a precise determination of the shift. As is evident a linear law of the form, 0~ = ~0 + ~ , is followed in both cases with ~0,(1.35%) = 1250 Mc and t0~(4.7%) = 1440 Mc corresponding to an anisotropy field of 445 G and 515 G respectively for a ferrimagnetic-like collective mode. It is most remarkable that at zero and negative fields the resonance signal shape is that due to an internal positive field in the direction of the cooling field. At about - 2 0 0 G a sudden reversal of the remanent magnetization takes place [4] and a new signal (upside down) can be observed along the other branch of the points of fig. 1 . The width of the inverted signal is 0.7 time narrower than the positive field signal and the corresponding zero field frequency is about 900 Mc in both cases. At about - 100 G the magnetization reverses back and the former signal is recovered identically. We have studied in detail the parameters involved in determining the value of ~,, as will be reported elsewhere. Our conclusions are: at fixed temperature ~0~ varies like the inverse of the total magnetization. This fact explains why relation (1) appears to hold in the high field. At fixed remanent magnetization to~ increases as the temperature decreases (as does the displacement field of the hysteresis [4]). For variable temperature: ¢0~ is governed by the value of the remanent magnetization compatible with the temperature and thus increases exponentially with T until the resonance signal is lost, as its width also increases with T. Finally by studying the same 1.35% alloy in a powdered form (unannealed) it is observed in the same conditions that to~(powder)= 2.0 G H z this stresses the fact that the origin of the anisotropy cannot be dipolar
t
I
I
/
~
I
I
l
I
I
t
~ ,
°
i
" jJ
S/
<
- ooo
J
- 2 O00
_300 '
'0 Magnetic
100 ' 20 fletd
30° ' -
' <®
H0 (.gaus~
Fig. 1. Resonance frequency around zero field for CuMn 1.35% and 4.7% alloys field cooled down to 1.35 K. For the-4.7% alloy, relation (1) predicts a zero field frequency ~ 3 GHz from the X-band data [1].
in accordance with the more complete work of Okuda and Date [2]. In conclusion the resonance in low and zero field of C u M n in the spin-glass state show a ferrimagnetic behaviour and allows us to define a macroscopic anisotropy field in agreement with other methods [7]. References [1] J. Owens, M. E. Browne, V. Arp and A. F. Kip, J. Phys. Chem. Solids 2 (1957) 85. [2] D. Griffiths, Proc. Phys. Roy. Sac. 90 (1967) 707; K. Okuda and M. Date, J. Phys. Sac. Jap. 27 (1969) 839; F. W. Kleinhans, J. P. Long and P. E. Wigen, Phys. Rev. B I 1 (1975) 2638. [3] S. Edwards and P. W. Anderson, J. Phys. F5 (1975) 965. [4] P. Monad, J. J. Pr6jean and B. Tissier, M M M Intermag AlP Conf. (1979) to be published. [5] Y. Berthier, to be pub_lished. [6] J. L. Tholence and R. Toumier, J. Phys. C6 (1978) 910. [7] H. Alloul, Phys. Rev. Lett. 42 (1979) 603; H. Alloul and P. Monad to be published.
Owen et al. [1] have discovered in their pioneer work on CuMn most of what is now considered as the typical characteristic of the spin-glass state i.e. susceptibility maximum, irreversibility, remanent magnetization with slow time dependence, and approximate scaling of these properties with concentration. Their major effort was devoted to the spin resonance in the paramagnetic region and to what happens to it in the now so-called spin-glass regime. Their conclusion was that the large resonance shift observed is describable with a "special kind of antiferromagnetic resonance" and offered an admittedly oversimplified two-sublattice analysis of this situation which has since been invariably invoked by other workers [2] except Malozemoff and Jamet [3]. In this model the resonance frequency is related to the external field H 0 by:
o~2= 3"2(Hg + HE),
(I)
where H c is a measure of the antiferromagnetic gap. In view of the difficulty of defining and measuring an order parameter in the spin-glass state [3] such a relation as (I) is paradoxical as it provides, if true, an experimentally precise and non=ambiguous determination of it. However relation (I) has only been tested in high field i.e. H 0 > H c where it merely states that the resonance shift (0/3, - H 0 decreases approximately as the inverse of the field H 0 [2]. The purpose of our work is to study the frequency-field relationship of the resonance of C u M n in the spin-glass state for low and zero field. Fr---om this we show that relation (1) is not valid and, instead, a linear relation is found. The alloys were identical to those used for the magnetization and hysteresis study [4] with concentration of 1.35% and 4.7% Mn. They were prepared as de*Physique des Solides, Universit~ de Paris Sud, 91405 Orsay, France.
scribed in [4] and carefully annealed after rolling into sheets 40 /tm thick. About 20 sheets were stacked between kapton films for each sample. The spectrometer used [5] was essentially the CW version of an existing variable frequency pulsed N M R rig in the range 500-3500 Mc, the heart of which is a ~1 wave re-entrant coaxial cavity continuously matched and tunnable in that range. The sensitivity was limited by the lack of A F C facility but was quite convenient in our case. The temperature could be set down to 1.25 K. The magnetic field, 25 k G at maximum, was produced by a superconducting coil. In order to understand our results it is essential to refer to the magnetization properties of the spin-glass state [6]. Previous results of ESR in this regime [1-3] were such that the field applied (typically ~ 3 kG) induced a reversible magnetization larger than the irreversible (remanent) magnetization acquired in this field by the isothermal remanent magnetization (IRM) process. However as shown in [1] the resonance shift properties depend critically of the magnetization process chosen, even though the magnetization amplitude is dominated by the reversible part of it. That is why Owen et al. [1] were very careful to always start from the zero-field condition. We have checked that no resonance in the range up to 3 G H z could be detected in our samples at zero or low field (500 G) when cooled in zero field. This fact was later related to the lack of a net magnetization present. We have systematically adopted the opposite condition i.e. cool the s p i n glass in such way as to produce the m a x i m u m value of the remanent magnetization. Our results then depict the frequency-field resonance relation of essentially the remanent magnetization alone whereas previous resonance work [1, 2] refers to a superposition to the reversible magnetization of a partial remanent magnetization induced by an I R M process. Fig. 1 shows the variation of the resonant field for different
Journal of Magnetism and Magnetic Materials 15-18 (1980) 149-150 ©North Holland
149
150
P. Monad, Y. Berthier/ Zero fieM ESR of Cu Mn in the spin glass state
frequencies between 900 Mc and 2500 Mc for C u M n 1.35% and 4.7% (annealed) after cooling in a 13 k G field down to 1.25 K. In the upper branch of points the signals have the shape characteristic of fixed magnetic impurities with A/B lobes ~ 2.5 + 0.2 and peak to peak width less than 100 G, allowing a precise determination of the shift. As is evident a linear law of the form, 0~ = ~0 + ~ , is followed in both cases with ~0,(1.35%) = 1250 Mc and t0~(4.7%) = 1440 Mc corresponding to an anisotropy field of 445 G and 515 G respectively for a ferrimagnetic-like collective mode. It is most remarkable that at zero and negative fields the resonance signal shape is that due to an internal positive field in the direction of the cooling field. At about - 2 0 0 G a sudden reversal of the remanent magnetization takes place [4] and a new signal (upside down) can be observed along the other branch of the points of fig. 1 . The width of the inverted signal is 0.7 time narrower than the positive field signal and the corresponding zero field frequency is about 900 Mc in both cases. At about - 100 G the magnetization reverses back and the former signal is recovered identically. We have studied in detail the parameters involved in determining the value of ~,, as will be reported elsewhere. Our conclusions are: at fixed temperature ~0~ varies like the inverse of the total magnetization. This fact explains why relation (1) appears to hold in the high field. At fixed remanent magnetization to~ increases as the temperature decreases (as does the displacement field of the hysteresis [4]). For variable temperature: ¢0~ is governed by the value of the remanent magnetization compatible with the temperature and thus increases exponentially with T until the resonance signal is lost, as its width also increases with T. Finally by studying the same 1.35% alloy in a powdered form (unannealed) it is observed in the same conditions that to~(powder)= 2.0 G H z this stresses the fact that the origin of the anisotropy cannot be dipolar
t
I
I
/
~
I
I
l
I
I
t
~ ,
°
i
" jJ
S/
<
- ooo
J
- 2 O00
_300 '
'0 Magnetic
100 ' 20 fletd
30° ' -
' <®
H0 (.gaus~
Fig. 1. Resonance frequency around zero field for CuMn 1.35% and 4.7% alloys field cooled down to 1.35 K. For the-4.7% alloy, relation (1) predicts a zero field frequency ~ 3 GHz from the X-band data [1].
in accordance with the more complete work of Okuda and Date [2]. In conclusion the resonance in low and zero field of C u M n in the spin-glass state show a ferrimagnetic behaviour and allows us to define a macroscopic anisotropy field in agreement with other methods [7]. References [1] J. Owens, M. E. Browne, V. Arp and A. F. Kip, J. Phys. Chem. Solids 2 (1957) 85. [2] D. Griffiths, Proc. Phys. Roy. Sac. 90 (1967) 707; K. Okuda and M. Date, J. Phys. Sac. Jap. 27 (1969) 839; F. W. Kleinhans, J. P. Long and P. E. Wigen, Phys. Rev. B I 1 (1975) 2638. [3] S. Edwards and P. W. Anderson, J. Phys. F5 (1975) 965. [4] P. Monad, J. J. Pr6jean and B. Tissier, M M M Intermag AlP Conf. (1979) to be published. [5] Y. Berthier, to be pub_lished. [6] J. L. Tholence and R. Toumier, J. Phys. C6 (1978) 910. [7] H. Alloul, Phys. Rev. Lett. 42 (1979) 603; H. Alloul and P. Monad to be published.