- Email: [email protected]
Study of domains in reentrants Fe—Zr by Lorentz transmission electron microscopy and neutron depolarisation measurements
136
Journal of Magnetism and Magnetic Materials 93 (1991) 136-142 North-Holland
Study of domains in reentrants F e - Z r by Lorentz transmission electron microscopy and neutron depolarisation measurements S. Hadjoudj, S. Senoussi Laboratoire de Physique des Solides, Bat..510, 91405 Orsay cedex, France
and
I. M i r e b e a u Laboratoire L~on Brillouin (CEA-CNRS), CEN-Saclay, 91191 Gif-sur-Ycette, France
Neutron depolarisation studies and Lorentz transmission electron microscopy (LTEM) observations of domains structure of R-S.G. Fe,:Zrm0 x with 89 _
I. Introduction According to theoretical predictions [1] reentrant spin glasses would be characterized by the freezing of the transverse magnetization at some temperature Tx.y and the freezing of the longitudinal magnetization at very low temperature below Tf. Now, it is well established that real ferrospin-glasses exhibit a macroscopic domain structure which is generally the same in the reentrant and in the ferromagnetic phases (i.e. either sides of the irreversibility line in the T - H plane). Moreover, there are evidences that such a macroscopic structure is formed in the ferromagnetic region just below Tc and is essentially imposed by the interplay between several classical energy terms including: the exchange, the magnetocrystalline, the magnetoelastic and the magnetostatic (or dipolar) energies (the latter three terms are not accounted for in the theoretical treatment). As a consequence, in macroscopic experiments the measured signal is almost exclusively imposed
by the intradomain magnetization with little contribution from the frozen transverse spins (this is at least for concentrations much lower than the critical concentration, x~, separating the reentrant and pure spin-glass states). Nevertheless, spin-glass effects are readily present below Tx, y and manifest themselves in different ways, in particular through the onset of a regime of strong irreversibilities, time dependent effects and short range fluctuations within the domains. Having in mind the theoretical predictions, it is natural to identify the intradomain magnetization with the longitudinal component and to associate the intradomain fluctuations with the transverse components. As we have already noted, transverse spins does not contribute significantly to the measured magnetization. However, transverse freezing gives rise to anisotropy fields and to coercivity effects which appear below Tf. It turns out that one important mechanism directly related to such freezing is the Dzialoshinsky-Moriya ( D - M ) exchange energy [2]
0304-8853/91/$03.50 © 1991 - E l s e v i e r Science Publishers B.V. (North-Holland)
137
S. Hadjoudj et al. / Domains in reentrant F e - Z r
(EDM not taken into account either in the theories referred to above) which can be written as follows [3]:
posed into an average unidirectional anisotropy field H~, (parallel to the intradomain magnetization) and a random (i.e. spatially fluctuating) term
Ahi: (1)
EDM=CEDij[SiXSj]. l ,J
hdj =
Here, Dij is a vector in the real space and C is a constant depending on the spin-orbit coupling of the alloy. To understand the role of D - M anisotropy and see how it takes place during cooling through the reentrant phase, it is interesting to decompose (at least formally) the spin system into longitudinal spins (SI) and transverse spins (S t) and rewrite eq. (1) as below:
EDM=CEDij[S]×S)] I ,J
(2)
Since S~ is approximately constant (inside a given domain) and proportional to the intradomain magnetization ( M d) of such a domain we can again transform the D - M energy and get: E'DM = OldomainsEMd[~jDij
=-
E
MdEhdj,
domains
j
H,, + Ah/.
(4)
Both terms are expected to contribute to M vs. T and M vs. H relationships as well as to coercivity phenomena. It is also expected that far above the critical concentration, x c, the spontaneous anisotropy field H a would vanish whereas it should dominate the random one well below x c. It is also possible that for very large EDM (as in AuFe systems) and close to xc the random term Ah i could reduce and eventually suppress the spontaneous (or the intradomain) magnetization of the reentrant phase according to the arguments developed by Imry and Ma [4] for random anisotropy magnets. In order to clarify further the magnetic structure of the reentrant spin glass phase, we have carried out L T E M and neutron depolarisation measurements on F e Z r amorphous ribbons.
Xst] (3)
where hdj is a local anisotropy field. In the ferromagnetic phase the transverse spins are expected to precess very rapidly (compared to usual experimental time scales) so that the time average of any transverse spin is zero and the same is true for hdj and thus for EDM (from eq. (3)). However, as the temperature is lowered below Tx,y the transverse spins are gradually frozen in and locked to the longitudinal ones via D - M interactions. Now, because of D - M anisotropy, the frozen spins are not randomly distributed in space. In other words, this means that D - M anisotropy is no longer zero and that the field hdj in formula (3) can be interpreted and decom-
2. Lorentz
Transmission
Electron
Microscopy
(LTEM) To facilitate the interpretation of the observed domain structure, it is useful to recall briefly the basic concepts of the Lorentz transmission electron microscopy (LTEM) (for experimental details see ref. [5]). In the classical approximation, the only force acting on the travelling electron is the Lorentz force induced by the local flux density B(r) = Heft(r) + 4-rrM(r) at a point r of the magnetic substance. That is (Gaussian units), g
F(r) = - -v C e
-
-
AB(r)
-Cv A [Heff(r ) + 4"rrM(r)]
(5)
138
s. Hadjoudj et al. /Domains in reentrant Fe Zr
with
(6)
Hdf( r ) = H o - NMto t and
Mtot= l f M ( r ) d 3 r .
(7)
Here H 0 is the sum of all possible external fields including eventually the field of the objective lens of the microscope itself, N the demagnetizing factor of the film in the direction of H 0 and Mto t is the total magnetization (in e m u / c m 3) of the same film. It is to be emphasized that M ( r ) refers to the spontaneous magnetization moment at point r and is related to Mto t by eq. (7). As usual e refers to the electron charge whereas c is the velocity of light. For the present experimental conditions we have H 0 = _+ 10 G (the residual field of the objective lens in the "off" position), N = 4"rr (since H 0 is generally perpendicular to the surface of the film) and M = 1 0 0 0 e m u / c m 3. In addition, we know from direct magnetic measurements that the present reentrant alloys are very soft (in the ferromagnetic phase) with therefore Hcff = 0, then
Electron
from eq. (6), we get Mtot -~ Ho/4"rr = + 1 e m u / cm 3 to be compared with M , = 1 0 0 0 e m u / c m 3. To complete this discussion, we add that we know also from magnetic measurements as a function of temperature that the field cooled magnetization is essentially independent of temperature and equal to H c / N in the reentrant phase, where H c is the applied field. This means that the effective cooling field could be considered as zero even though the external cooling fields could be as high as 1 kG. Therefore, for the present experimental conditions we can consider that the effective cooling field H~ff seen both by the magnetic sample and by the incident electrons is zero and rewrite eq. (5) in the simple form below: F= -4~rev X M(r),
(8)
equating this force with the centrifugal force acting on the electron on tranversing the film, leads to an angular total deflection in the plane of the film: e
4,(x,:,,{m(x,y) }~d ? 2 m V *
"
Here (M(x,y)}+: is the component of the mag-
Beam
;d r
"~" c
the domains D w Q ~ c h)
(9)
C-on..~r'gmtwall(Bright )
(~agmetizin 9 field r~tected )
Fig. 1. Top view of a schematic thin film and trajectories of the incident electrons through the film.
S. Hadjoudj et al. / Domains in reentrant F e - Z r
netization perpendicular to the axis of the microscope, averaged over the trajectory of the electron in the sample, m is the electron mass whereas V* [ = U(1 + eU/2mc2)] is an accelerating potential taking into account the relativistic corrections and U the accelerating potential of the incident electrons. Fig. 1 shows a top view of a schematic thin film and the trajectories of the incident electrons through its thickness. We see that these trajectories, which enter the sample perpendicular to its surface, are deviated (after traversing the sample) in opposite direction, either sides of a given domain wall. It is to be noted that two consecutive walls bordering the same domain behave as a divergent and a convergent wall, respectively. Their images will then appear as dark and bright line, respectively. If we now suppose that the magnetization is not uniform in the domains themselves, it will appear on the image plane secondary walls (in comparison with the true walls) depending on the local deflection. These lines are labelled magnetic ripples. We note that the longitudinal magnetization is perpendicular to these ripples as is revealed by fig. 1. Fig. 2 shows the magnetic structure of domains of FesgZrll at two different temperatures, 18 and 130 K. At first, we observe that the bright lines of one of the micrographs correspond to dark lines of the other one and vice versa. This illustrates the fact that the same domain can be either convergent or divergent depending on whether the corresponding image is over or under-focused. We note that, apart from this trivial difference, the two images are very much the same. In other words, we see no detectable changes in the magnetic structure as the lines Tf and T,, v [5] are crossed. Moreover, we have been able to follow the evolution of the domain structure upon warming the sample through the expected ferromagnetic transition temperature ( f c = 260 K). We found that as the Tc is approached the magnetic contrast drops continuously but no change is seen in the domain and in the domain wall network. The domains become invisible to the eyes at approximately Tc (within _+5 K). However, it is to
139
Fig. 2. Domain structure of Fes,~Zr~ amorphous ribbons (a) T = 18K and (b) T = 130K. We note the presence of a lot of defects introduced by the thinning technique. In the insert of fig. 2b intradomain fine magnetic structure at 14K in a film of the same F e - Z r concentration.
be emphasized that the cross-over line T~ can be detected by investigating the viscosity of the domain walls as their motion is found to be considerably reduced in the F-S.G. phase. The insert of fig. 2b shows that the magnetization (perpendicu-
140
S. Hadjoudj et al. / Domains in reentrant F e - Z r
lar to the ripples) is not uniform in the domain itself. 3. Neutron depolarisation measurements
In an unsaturated ferromagnet, the magnetic domains depolarize the neutrons passing through the samples due to the Larmor precession of the neutron spins in the magnetic field of the domains [6, 7]. By contrast no depolarisation is expected in a disordered system like a paramagnetic or a true spin glass since the neutron spin cannot follow the temporal or spatial changes of the magnetic induction which occur on very short scales. In this respect, the depolarisation measurement provide a useful tool to study the long range correlations in frustrated ferromagnets or R-S.G. [8]. The depolarisation measurements were performed using an incident beam of wavelength A = 5,~. The samples were set up in a magnetic field of 5(3 aligned in the vertical z direction with the plane surface x z perpendicular to the neutron beam. The temperature was varied in the range 15-300K. The beam was polarized along the z direction using a supermirror and analyzed in the z direction as well. Thus, the z z component of the depolarisation matrix [9] was determined. The intensity 1 + and 1- corresponding to an incident neutron spin, respectively parallel and antiparallel to the magnetic field were determined using a flipper. The polarisation P was deduced from the flipping ratio I + / I through the usual expression P = ( R - 1)/ (R + 1). In fig. 3 the flipping ratio R and the polarisation P are plotted versus temperature for three FexZri00 ~ samples of concentration x = 90, 91 and 92. For x = 90, P decreases strongly below the Curie temperature and then remains constant down to the lowest temperature. For x = 92, we observe a very small but noticeable depolarisation. As a striking result, unlike the susceptibility and magnetization data, the depolarisation does not reveal any transition at low temperature even in the sample very close to the critical concentra-
tion-. This result strongly suggests that the domain size does not vary with temperature and that the strong depolarisation observed below Tc simply arises from the thermal increase of the mean induction within a domain. A semi quantitative evaluation of the domain size can be given by assuming that the polarisation behaves as P = exp( - a a 2)
with ce = I).25~:2BZd3.
(lO) o
In this formula, A is the neutron wavelength (A), B the magnetic induction within a domain (G), d and 6 are, respectively, the sample thickness and the mean domain size (cm). The constant K is equal to 4.63 × 10-= within these units. The coefficient 0.25 corresponds to a random orientation of the domains within the sample plane. The wavelength dependence of eq. (10) corresponds to the case of small domains in which the neutron spins perform only a part of their Larmor precession ( K B 6 A < < 2 v ) . In order to measure the wavelength dependence of the polarisation, the use of a pulsed neutron source would be necessary.
10 0
. . . . . . . . . . .
0
50 I
p 4.o0
- - -
I
150
20Q
l
I
1
250 T ( K ) I
x =92
.
/+
+l+.i__"
X =91 0.95 -
/ + +-+ +--+--+--
000
I
100
i 50
+.....+i~, ~
e_e_o~
i 100
.
.
.
X =90
--
0.5
/ ,.-"
1.0
,I
FexZ~_x
•
E 150
l 200
t 250
0
T(K) Fig. 3. (a) Flipping ratio R polarisation P measured as a function of temperature in the Fe,Zru~ 0 , amorphous ribbons. In the sample x = 92, the very small depolarisation effect (note the change of scale) could only be evidenced with a high value of the incident flipping ratio.
S. Hadjoudj et al. / Domains in reentrant Fe-Zr
In the x = 90 and 91 alloys we obtain a mean domain size of about 6 and 4 ixm, respectively. The value of the mean domain induction was deduced by extrapolating the applied field, to zero the magnetization measured in high fields above the technical saturation plateau. For x = 92, the very low depolarisation observed, together with the slope of the M ( H ) curve suggest that there are no well defined domains in this case. The residual depolarisation likely arises from the onset of long range correlations whose size would be rather comparable to a typical Bloch wall thickness (-- 2000 A).
141
(5) Direct magnetic measurements are governed by domain and coercivity effects and by "macroscopic" anisotropy fields created during cooling through the reentrant phase and having the same directions as the intradomain magnetizations. Moreover, a complete interpretation of the M ( H , T ) curves requires proper account and treatment of the demagnetizing fields and other anisotropy sources as well. This interpretation is confirmed by direct L T E M observations which show the rearrangement of domains (and the movement of the domain walls) in response to small field variations.
4. Discussion and conclusion 4.2. x close to the critical concentration
The measurements reported in this p a p e r suggest the following description of reentrant spinglasses, the properties of which seem to be markedly different close and far from the critical concentration x c. 4.1. x f a r f r o m the critical concentration
(1) In this limit, both L T E M and neutron depolarisation experiments reveal the existence of a macroscopic domain-structure ( = 10 ~ m typically) which appears just below T,. and persists without any detectable change down to the lowest temperature explored here (T << T 0. (2) Nevertheless, the reentrant transition is detected directly by L T E M through the appearance of strong coercivity effects and strong slowing down of the dynamic of the domain walls: the response to a small pulsed field is almost instantaneous in the ferromagnetic phase, but exceeds 5 min in the reentrant one. (3) Small angle neutron scattering (SANS) [9, 10] reveal the existence of short range static fluctuations, on the scale of 10-100A. It is probable that these are related to transverse freezing. (4) In agreement with SANS data, L T E M studies show that the intradomain magnetization (fig. 2 and the insert) is not uniform but presents some degree of disorder and fluctuations extending from the dimension of the domains themselves down to ~- 500A. o
As we can expect, the magnetic behaviour is much more complicated close to the critical concentration. Moreover, this behaviour does not seem universal but depends on the material. At first, we have not been able to detect any domain structure by L T E M technique near x c. However, neutron depolarisation measurements on the same materials show the existence of domains about 2000,~ in size. This dimension is comparable to the domain wall thickness and can explain our failure to observe the domains by LTEM. Perhaps, more importantly, neutron depolarisation suggests that for x ~ x c some systems like A u - F e and F e - M n acquire a domain structure in the ferromagnetic region which disappears at lowest temperature. This effect seems to be correlated with a large drop of the FC-magnetization for the same materials. Both phenomena suggest the onset of long range ferromagnetic order below Tc which vanishes as T--* 0 (i.e. a real reentrant phenomenon). It is to be emphasized that such a reentrance is not predicted by theoretical models of Gabay and Toulouse type. Also, this reentrance p h e n o m e n o n is very pronounced in A u - F e where D - M anis0tropy is exceptionally large and is very unsignificant in NiMn and FeZr systems where D - M anisotropy is rather weak. For these reasons, we believe that this reentrance can be induced by D - M anisotropy following the
142
S. Hadjoudj et al. ~Domains in reentrant lab-Zr
mechanism discussed in the introduction. This is only a suggestion and more studies are needed to clarify this point. References [1] M. Gabay and G. Toulouse, Phys. Rev. Letl. 47 (1981) 2(/1. [2] S. Senoussi, Phys. Rev. Lett. 51 (1983) 2218: Phys. Rev. B 31 (1985) 6086. [3] A. Fert and P.M. Levy, Phys. Rev. B 23 (19811 4667. [4] Y. Imry and S.-K. Ma. Phys.Rev. Lett. 35 (1975) 1399.
[5] S. tladjoudj, S. Senoussi and D.II. Ryan, J. Appl, Phys. 67 (19901 5958. [6] O. Halpern and T. Holstein, Phys. Rev. 59 (1941) 960. [7] S. Mitsuda and Y, Endoh. J. Phys. Soc. Japan 54 (1985) 1570. [8] 1. Mirebeau, S. Itoh, S. Mitsuda, T. Watanabe, Y. Endoh, M. Hennion and R. Papoular, Phys. Rev. B 41 (19901 11405. I. Mirebeau, S. Itoh, S. Mitsuda, T. Watanabe, Y. Endoh, M, Hennion and P. Calamettes, J. Appl. Phys. 67 (1990) 5232. R.W. Erwin. J. Appl. Phys. 67 (19901 5229. [9] J.J. Rhyne, R.W. Erwin, J.A. Fernandez-Bara and G.E. Fish, J. Appl. Phys. 63 (1990) 4(180. [10] M. tlennion, 1, Mirebeau, B. Hennion, S. Lequien and F. Hippert, J, Appl. Phys, 63 (1988) 4071.
Journal of Magnetism and Magnetic Materials 93 (1991) 136-142 North-Holland
Study of domains in reentrants F e - Z r by Lorentz transmission electron microscopy and neutron depolarisation measurements S. Hadjoudj, S. Senoussi Laboratoire de Physique des Solides, Bat..510, 91405 Orsay cedex, France
and
I. M i r e b e a u Laboratoire L~on Brillouin (CEA-CNRS), CEN-Saclay, 91191 Gif-sur-Ycette, France
Neutron depolarisation studies and Lorentz transmission electron microscopy (LTEM) observations of domains structure of R-S.G. Fe,:Zrm0 x with 89 _
I. Introduction According to theoretical predictions [1] reentrant spin glasses would be characterized by the freezing of the transverse magnetization at some temperature Tx.y and the freezing of the longitudinal magnetization at very low temperature below Tf. Now, it is well established that real ferrospin-glasses exhibit a macroscopic domain structure which is generally the same in the reentrant and in the ferromagnetic phases (i.e. either sides of the irreversibility line in the T - H plane). Moreover, there are evidences that such a macroscopic structure is formed in the ferromagnetic region just below Tc and is essentially imposed by the interplay between several classical energy terms including: the exchange, the magnetocrystalline, the magnetoelastic and the magnetostatic (or dipolar) energies (the latter three terms are not accounted for in the theoretical treatment). As a consequence, in macroscopic experiments the measured signal is almost exclusively imposed
by the intradomain magnetization with little contribution from the frozen transverse spins (this is at least for concentrations much lower than the critical concentration, x~, separating the reentrant and pure spin-glass states). Nevertheless, spin-glass effects are readily present below Tx, y and manifest themselves in different ways, in particular through the onset of a regime of strong irreversibilities, time dependent effects and short range fluctuations within the domains. Having in mind the theoretical predictions, it is natural to identify the intradomain magnetization with the longitudinal component and to associate the intradomain fluctuations with the transverse components. As we have already noted, transverse spins does not contribute significantly to the measured magnetization. However, transverse freezing gives rise to anisotropy fields and to coercivity effects which appear below Tf. It turns out that one important mechanism directly related to such freezing is the Dzialoshinsky-Moriya ( D - M ) exchange energy [2]
0304-8853/91/$03.50 © 1991 - E l s e v i e r Science Publishers B.V. (North-Holland)
137
S. Hadjoudj et al. / Domains in reentrant F e - Z r
(EDM not taken into account either in the theories referred to above) which can be written as follows [3]:
posed into an average unidirectional anisotropy field H~, (parallel to the intradomain magnetization) and a random (i.e. spatially fluctuating) term
Ahi: (1)
EDM=CEDij[SiXSj]. l ,J
hdj =
Here, Dij is a vector in the real space and C is a constant depending on the spin-orbit coupling of the alloy. To understand the role of D - M anisotropy and see how it takes place during cooling through the reentrant phase, it is interesting to decompose (at least formally) the spin system into longitudinal spins (SI) and transverse spins (S t) and rewrite eq. (1) as below:
EDM=CEDij[S]×S)] I ,J
(2)
Since S~ is approximately constant (inside a given domain) and proportional to the intradomain magnetization ( M d) of such a domain we can again transform the D - M energy and get: E'DM = OldomainsEMd[~jDij
=-
E
MdEhdj,
domains
j
H,, + Ah/.
(4)
Both terms are expected to contribute to M vs. T and M vs. H relationships as well as to coercivity phenomena. It is also expected that far above the critical concentration, x c, the spontaneous anisotropy field H a would vanish whereas it should dominate the random one well below x c. It is also possible that for very large EDM (as in AuFe systems) and close to xc the random term Ah i could reduce and eventually suppress the spontaneous (or the intradomain) magnetization of the reentrant phase according to the arguments developed by Imry and Ma [4] for random anisotropy magnets. In order to clarify further the magnetic structure of the reentrant spin glass phase, we have carried out L T E M and neutron depolarisation measurements on F e Z r amorphous ribbons.
Xst] (3)
where hdj is a local anisotropy field. In the ferromagnetic phase the transverse spins are expected to precess very rapidly (compared to usual experimental time scales) so that the time average of any transverse spin is zero and the same is true for hdj and thus for EDM (from eq. (3)). However, as the temperature is lowered below Tx,y the transverse spins are gradually frozen in and locked to the longitudinal ones via D - M interactions. Now, because of D - M anisotropy, the frozen spins are not randomly distributed in space. In other words, this means that D - M anisotropy is no longer zero and that the field hdj in formula (3) can be interpreted and decom-
2. Lorentz
Transmission
Electron
Microscopy
(LTEM) To facilitate the interpretation of the observed domain structure, it is useful to recall briefly the basic concepts of the Lorentz transmission electron microscopy (LTEM) (for experimental details see ref. [5]). In the classical approximation, the only force acting on the travelling electron is the Lorentz force induced by the local flux density B(r) = Heft(r) + 4-rrM(r) at a point r of the magnetic substance. That is (Gaussian units), g
F(r) = - -v C e
-
-
AB(r)
-Cv A [Heff(r ) + 4"rrM(r)]
(5)
138
s. Hadjoudj et al. /Domains in reentrant Fe Zr
with
(6)
Hdf( r ) = H o - NMto t and
Mtot= l f M ( r ) d 3 r .
(7)
Here H 0 is the sum of all possible external fields including eventually the field of the objective lens of the microscope itself, N the demagnetizing factor of the film in the direction of H 0 and Mto t is the total magnetization (in e m u / c m 3) of the same film. It is to be emphasized that M ( r ) refers to the spontaneous magnetization moment at point r and is related to Mto t by eq. (7). As usual e refers to the electron charge whereas c is the velocity of light. For the present experimental conditions we have H 0 = _+ 10 G (the residual field of the objective lens in the "off" position), N = 4"rr (since H 0 is generally perpendicular to the surface of the film) and M = 1 0 0 0 e m u / c m 3. In addition, we know from direct magnetic measurements that the present reentrant alloys are very soft (in the ferromagnetic phase) with therefore Hcff = 0, then
Electron
from eq. (6), we get Mtot -~ Ho/4"rr = + 1 e m u / cm 3 to be compared with M , = 1 0 0 0 e m u / c m 3. To complete this discussion, we add that we know also from magnetic measurements as a function of temperature that the field cooled magnetization is essentially independent of temperature and equal to H c / N in the reentrant phase, where H c is the applied field. This means that the effective cooling field could be considered as zero even though the external cooling fields could be as high as 1 kG. Therefore, for the present experimental conditions we can consider that the effective cooling field H~ff seen both by the magnetic sample and by the incident electrons is zero and rewrite eq. (5) in the simple form below: F= -4~rev X M(r),
(8)
equating this force with the centrifugal force acting on the electron on tranversing the film, leads to an angular total deflection in the plane of the film: e
4,(x,:,,{m(x,y) }~d ? 2 m V *
"
Here (M(x,y)}+: is the component of the mag-
Beam
;d r
"~" c
the domains D w Q ~ c h)
(9)
C-on..~r'gmtwall(Bright )
(~agmetizin 9 field r~tected )
Fig. 1. Top view of a schematic thin film and trajectories of the incident electrons through the film.
S. Hadjoudj et al. / Domains in reentrant F e - Z r
netization perpendicular to the axis of the microscope, averaged over the trajectory of the electron in the sample, m is the electron mass whereas V* [ = U(1 + eU/2mc2)] is an accelerating potential taking into account the relativistic corrections and U the accelerating potential of the incident electrons. Fig. 1 shows a top view of a schematic thin film and the trajectories of the incident electrons through its thickness. We see that these trajectories, which enter the sample perpendicular to its surface, are deviated (after traversing the sample) in opposite direction, either sides of a given domain wall. It is to be noted that two consecutive walls bordering the same domain behave as a divergent and a convergent wall, respectively. Their images will then appear as dark and bright line, respectively. If we now suppose that the magnetization is not uniform in the domains themselves, it will appear on the image plane secondary walls (in comparison with the true walls) depending on the local deflection. These lines are labelled magnetic ripples. We note that the longitudinal magnetization is perpendicular to these ripples as is revealed by fig. 1. Fig. 2 shows the magnetic structure of domains of FesgZrll at two different temperatures, 18 and 130 K. At first, we observe that the bright lines of one of the micrographs correspond to dark lines of the other one and vice versa. This illustrates the fact that the same domain can be either convergent or divergent depending on whether the corresponding image is over or under-focused. We note that, apart from this trivial difference, the two images are very much the same. In other words, we see no detectable changes in the magnetic structure as the lines Tf and T,, v [5] are crossed. Moreover, we have been able to follow the evolution of the domain structure upon warming the sample through the expected ferromagnetic transition temperature ( f c = 260 K). We found that as the Tc is approached the magnetic contrast drops continuously but no change is seen in the domain and in the domain wall network. The domains become invisible to the eyes at approximately Tc (within _+5 K). However, it is to
139
Fig. 2. Domain structure of Fes,~Zr~ amorphous ribbons (a) T = 18K and (b) T = 130K. We note the presence of a lot of defects introduced by the thinning technique. In the insert of fig. 2b intradomain fine magnetic structure at 14K in a film of the same F e - Z r concentration.
be emphasized that the cross-over line T~ can be detected by investigating the viscosity of the domain walls as their motion is found to be considerably reduced in the F-S.G. phase. The insert of fig. 2b shows that the magnetization (perpendicu-
140
S. Hadjoudj et al. / Domains in reentrant F e - Z r
lar to the ripples) is not uniform in the domain itself. 3. Neutron depolarisation measurements
In an unsaturated ferromagnet, the magnetic domains depolarize the neutrons passing through the samples due to the Larmor precession of the neutron spins in the magnetic field of the domains [6, 7]. By contrast no depolarisation is expected in a disordered system like a paramagnetic or a true spin glass since the neutron spin cannot follow the temporal or spatial changes of the magnetic induction which occur on very short scales. In this respect, the depolarisation measurement provide a useful tool to study the long range correlations in frustrated ferromagnets or R-S.G. [8]. The depolarisation measurements were performed using an incident beam of wavelength A = 5,~. The samples were set up in a magnetic field of 5(3 aligned in the vertical z direction with the plane surface x z perpendicular to the neutron beam. The temperature was varied in the range 15-300K. The beam was polarized along the z direction using a supermirror and analyzed in the z direction as well. Thus, the z z component of the depolarisation matrix [9] was determined. The intensity 1 + and 1- corresponding to an incident neutron spin, respectively parallel and antiparallel to the magnetic field were determined using a flipper. The polarisation P was deduced from the flipping ratio I + / I through the usual expression P = ( R - 1)/ (R + 1). In fig. 3 the flipping ratio R and the polarisation P are plotted versus temperature for three FexZri00 ~ samples of concentration x = 90, 91 and 92. For x = 90, P decreases strongly below the Curie temperature and then remains constant down to the lowest temperature. For x = 92, we observe a very small but noticeable depolarisation. As a striking result, unlike the susceptibility and magnetization data, the depolarisation does not reveal any transition at low temperature even in the sample very close to the critical concentra-
tion-. This result strongly suggests that the domain size does not vary with temperature and that the strong depolarisation observed below Tc simply arises from the thermal increase of the mean induction within a domain. A semi quantitative evaluation of the domain size can be given by assuming that the polarisation behaves as P = exp( - a a 2)
with ce = I).25~:2BZd3.
(lO) o
In this formula, A is the neutron wavelength (A), B the magnetic induction within a domain (G), d and 6 are, respectively, the sample thickness and the mean domain size (cm). The constant K is equal to 4.63 × 10-= within these units. The coefficient 0.25 corresponds to a random orientation of the domains within the sample plane. The wavelength dependence of eq. (10) corresponds to the case of small domains in which the neutron spins perform only a part of their Larmor precession ( K B 6 A < < 2 v ) . In order to measure the wavelength dependence of the polarisation, the use of a pulsed neutron source would be necessary.
10 0
. . . . . . . . . . .
0
50 I
p 4.o0
- - -
I
150
20Q
l
I
1
250 T ( K ) I
x =92
.
/+
+l+.i__"
X =91 0.95 -
/ + +-+ +--+--+--
000
I
100
i 50
+.....+i~, ~
e_e_o~
i 100
.
.
.
X =90
--
0.5
/ ,.-"
1.0
,I
FexZ~_x
•
E 150
l 200
t 250
0
T(K) Fig. 3. (a) Flipping ratio R polarisation P measured as a function of temperature in the Fe,Zru~ 0 , amorphous ribbons. In the sample x = 92, the very small depolarisation effect (note the change of scale) could only be evidenced with a high value of the incident flipping ratio.
S. Hadjoudj et al. / Domains in reentrant Fe-Zr
In the x = 90 and 91 alloys we obtain a mean domain size of about 6 and 4 ixm, respectively. The value of the mean domain induction was deduced by extrapolating the applied field, to zero the magnetization measured in high fields above the technical saturation plateau. For x = 92, the very low depolarisation observed, together with the slope of the M ( H ) curve suggest that there are no well defined domains in this case. The residual depolarisation likely arises from the onset of long range correlations whose size would be rather comparable to a typical Bloch wall thickness (-- 2000 A).
141
(5) Direct magnetic measurements are governed by domain and coercivity effects and by "macroscopic" anisotropy fields created during cooling through the reentrant phase and having the same directions as the intradomain magnetizations. Moreover, a complete interpretation of the M ( H , T ) curves requires proper account and treatment of the demagnetizing fields and other anisotropy sources as well. This interpretation is confirmed by direct L T E M observations which show the rearrangement of domains (and the movement of the domain walls) in response to small field variations.
4. Discussion and conclusion 4.2. x close to the critical concentration
The measurements reported in this p a p e r suggest the following description of reentrant spinglasses, the properties of which seem to be markedly different close and far from the critical concentration x c. 4.1. x f a r f r o m the critical concentration
(1) In this limit, both L T E M and neutron depolarisation experiments reveal the existence of a macroscopic domain-structure ( = 10 ~ m typically) which appears just below T,. and persists without any detectable change down to the lowest temperature explored here (T << T 0. (2) Nevertheless, the reentrant transition is detected directly by L T E M through the appearance of strong coercivity effects and strong slowing down of the dynamic of the domain walls: the response to a small pulsed field is almost instantaneous in the ferromagnetic phase, but exceeds 5 min in the reentrant one. (3) Small angle neutron scattering (SANS) [9, 10] reveal the existence of short range static fluctuations, on the scale of 10-100A. It is probable that these are related to transverse freezing. (4) In agreement with SANS data, L T E M studies show that the intradomain magnetization (fig. 2 and the insert) is not uniform but presents some degree of disorder and fluctuations extending from the dimension of the domains themselves down to ~- 500A. o
As we can expect, the magnetic behaviour is much more complicated close to the critical concentration. Moreover, this behaviour does not seem universal but depends on the material. At first, we have not been able to detect any domain structure by L T E M technique near x c. However, neutron depolarisation measurements on the same materials show the existence of domains about 2000,~ in size. This dimension is comparable to the domain wall thickness and can explain our failure to observe the domains by LTEM. Perhaps, more importantly, neutron depolarisation suggests that for x ~ x c some systems like A u - F e and F e - M n acquire a domain structure in the ferromagnetic region which disappears at lowest temperature. This effect seems to be correlated with a large drop of the FC-magnetization for the same materials. Both phenomena suggest the onset of long range ferromagnetic order below Tc which vanishes as T--* 0 (i.e. a real reentrant phenomenon). It is to be emphasized that such a reentrance is not predicted by theoretical models of Gabay and Toulouse type. Also, this reentrance p h e n o m e n o n is very pronounced in A u - F e where D - M anis0tropy is exceptionally large and is very unsignificant in NiMn and FeZr systems where D - M anisotropy is rather weak. For these reasons, we believe that this reentrance can be induced by D - M anisotropy following the
142
S. Hadjoudj et al. ~Domains in reentrant lab-Zr
mechanism discussed in the introduction. This is only a suggestion and more studies are needed to clarify this point. References [1] M. Gabay and G. Toulouse, Phys. Rev. Letl. 47 (1981) 2(/1. [2] S. Senoussi, Phys. Rev. Lett. 51 (1983) 2218: Phys. Rev. B 31 (1985) 6086. [3] A. Fert and P.M. Levy, Phys. Rev. B 23 (19811 4667. [4] Y. Imry and S.-K. Ma. Phys.Rev. Lett. 35 (1975) 1399.
[5] S. tladjoudj, S. Senoussi and D.II. Ryan, J. Appl, Phys. 67 (19901 5958. [6] O. Halpern and T. Holstein, Phys. Rev. 59 (1941) 960. [7] S. Mitsuda and Y, Endoh. J. Phys. Soc. Japan 54 (1985) 1570. [8] 1. Mirebeau, S. Itoh, S. Mitsuda, T. Watanabe, Y. Endoh, M. Hennion and R. Papoular, Phys. Rev. B 41 (19901 11405. I. Mirebeau, S. Itoh, S. Mitsuda, T. Watanabe, Y. Endoh, M, Hennion and P. Calamettes, J. Appl. Phys. 67 (1990) 5232. R.W. Erwin. J. Appl. Phys. 67 (19901 5229. [9] J.J. Rhyne, R.W. Erwin, J.A. Fernandez-Bara and G.E. Fish, J. Appl. Phys. 63 (1990) 4(180. [10] M. tlennion, 1, Mirebeau, B. Hennion, S. Lequien and F. Hippert, J, Appl. Phys, 63 (1988) 4071.