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ISSN 1063-7761, Journal of Experimental and Theoretical Physics, 2017, Vol. 125, No. 3, pp. 480–494. © Pleiades Publishing, Inc., 2017.
Original Russian Text © V.D. Zhaketov, Yu.V. Nikitenko, A.V. Petrenko, A. Csik, V.L. Aksenov, F. Radu, 2017, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki,
2017, Vol. 152, No. 3, pp. 565–580.
ELECTRONIC PROPERTIES
OF SOLID
Relaxation of the Magnetic State
of a Ferromagnetic–Superconducting Layered Structure
V. D. Zhaketova, Yu. V. Nikitenkoa*, A. V. Petrenkoa,
A. Csikb, V. L. Aksenova,c, and F. Radud
a Joint
Institute for Nuclear Research, Dubna, Moscow oblast, 141980 Russia
MTA Atomki, Institute for Nuclear Research, Debrecen, H-4001 Hungary
c
Konstantinov St. Petersburg Institute for Nuclear Physics, National Research Center,
“Kurchatov Institute,” Gatchina, Leningradskaya oblast, 188300 Russia
d
Helmoltz-Zentrum Berlin für Materialen und Energie, Berlin, 12489 Germany
*e-mail: nikiten@nf.jinr.ru
b
Received February 1, 2017
Abstract—We have proposed a real-time method of neutron reflectometry. The magnetic state of the
Ta/V/FM/Nb/Si ferromagnetic–superconducting system has been analyzed. Relaxation of the inhomogeneous magnetic state with a characteristic time of several hours, which depends on the magnetic field magnitude and temperature, has been observed. The relaxation of the domain structure has changed upon a transition of the V and Nb layers to the superconducting state. It has been concluded that real-time reflectometry
data for polarized neutrons are important for determining the origin of magnetism in ferromagnetic–superconducting layered structures.
DOI: 10.1134/S1063776117080210
1. INTRODUCTION
Complex systems are characterized by relaxation
behavior of physical quantities. This is typical, for
example, of superconductors [1–3] and systems of
magnetic nanoparticles [4, 5]. It was noted in [6] that
close analogy exists in the behaviors of ferromagnetic
ensembles of particles and superconductors. The logarithmic dependence of the temporal relaxation typical of such systems was also observed in thin magnetic films [7]. Magnetism in superconductor/ferromagnet/superconductor
(S/FM/S)
layered
structures was analyzed in [8, 9]. It was found that
the mean value of the magnetic induction, as well as
the mean value of the local magnetic induction in
domains, clusters, and superconducting vortices,
varies with time.
In this study, we propose a method of real-time
reflectometry of polarized neutrons and report on the
data concerning the effect of superconductivity on the
magnetic state of Ta/V/FM/Nb/Si ferromagnetic–
superconducting layered structure, which were
obtained using this method.
2. Ta/V/FM/Nb/Si LAYERED STRUCTURE
The structure under investigation was prepared by
sequential magnetron sputtering of elements on the
Si(0.5 mm) substrate in the MAGSSY chamber at the
Helmholtz center (Berlin, Germany). The residual
pressure in the chamber was below 5 × 10–9 mbar.
The deposition was carried out in ultrapure gaseous
argon with a partial pressure of 1.5 × 10–3 mbar. The
deposition rate was calibrated using a microbalance
of a quartz crystal. The substrate was the Si(100)
crystal with the surface cleaned in a ultrasonic bath.
During the deposition, the substrate was not heated,
but was maintained at room temperature to exclude
additional thermal diffusion and to ensure a smooth
profile of the surface. The deposition of layers onto
the substrate was carried out in the following
sequence: Nb, Fe0.7V0.3, V, Fe0.7V0.3, V, and Ta. We
assumed that the magnetic moments of two Fe0.7V0.3
layers were antiferromagnetically ordered, due to
indirect exchange interaction via the intermediate V
layer. We also assumed that due to suppression of the
exchange interaction between iron atoms due to dilution with vanadium, as well as due to antiferromagnetic ordering of the magnetic moments of iron
atoms relative to the magnetic moments of vanadium
atoms induced by them [10, 11], the magnetization of
Fe0.7V0.3 iron atoms is much lower than for pure Fe.
These measurements were used to facilitate the realization of the superconducting state in Fe0.7V0.3.
480
RELAXATION OF THE MAGNETIC STATE
481
Fig. 1. Spatial profile of the elements of the Ta/V/FM/Nb/Si
layered structure.
which is close to the value of the magnetic moment of
the saturated state. The negative value of the magnetic
moment can apparently be explained by the interaction of clusters with magnetic domains. Indeed, the
system of clusters has two energy minima [14] corresponding to the directions of the moments along the
magnetic field (positive moment) and against it (negative moment). Since the minimum for the magnetic
moments directed along the field is deeper, the probability of detecting the system of clusters in this state is
higher. However, the energy minimum for the cluster
and domain systems corresponds to a negative value of
the total moment. Since the magnetic moment of
clusters is larger than the magnetic moment of
domains, the negative value of the total moment is
apparently associated with the interaction between the
two magnetic systems. It should be noted that the existence of such interaction will be confirmed below in
dynamic experiments (see Section 3.4).
Figure 1 shows the profile of the Ta/V/FM/Nb/Si
structure, which was measured by neutral atomic mass
spectrometry with a spatial resolution of 1 nm [12]. It
can be seen from the curves that two magnetic Fe0.7V0.3
layers are not resolved and form in fact a single layer.
The boundaries of the niobium and vanadium layers are extended towards the depth and have a thickness close to the width of the magnetic layer. The
depth at which the boundaries are located increases
with increasing distance from the silicon substrate.
For example, for the Nb boundary closer to the substrate, its extension defined as the distance at which
the concentration of the element varies in the range
50–100% amounts to 10 nm, while the extension of
the distant boundary is 20 nm. The magnetic layer
together with the vanadium interlayer has a thickness
of 20 nm, which is 6.3 times larger than the thickness
determined proceeding from the amount of deposited
elements. As a result of mutual penetration of elements, the layer of iron atoms is additionally diluted by
14 times with Nb and V atoms so that the concentration of iron atoms is about 7% (over the width of spatial distribution).
Figures 2a and 2b show the temperature dependences of the magnetic moment of the structure for
zero-field cooling (ZFC regime, curve 1) and cooling
in a magnetic field (FC regime, curve 2). The curves in
Fig. 2a diverge at blocking temperature T = 140 K. The
blocking temperature is the temperature above which
the orientations of the magnetic moments of clusters
change due to thermal fluctuations of the medium.
Using the value of T = 140 K and anisotropy constant
Keff = 103–107 erg/cm3 [13], we find that the diameter
of magnetic clusters lies in the range of d ≈ 1–20 nm.
At T = 8 K, the magnetic moment is negative and is
equal to –6.6 × 10–6 CGSM units in the ZFC regime,
The insets to Fig. 2 show the temperature dependences of the magnetic moment in the temperature
interval near temperatures of the superconducting
transitions. The ZFC (1) and FC (2) curves for a magnetic field of 20 Oe (see Fig. 2a) demonstrate a complex temperature behavior. For example, in the ZFC
regime, which is realized by cooling in zero field followed by the application of the field and the increase
in temperature from 3 K, a diamagnetic moment of
‒2 × 10–6 CGSM units appears in the temperature
interval from 4 to 5 K, which corresponds to a change
in the magnetic induction in the Nb layer (it was found
from magnetic measurements that TC = 4 K for the V
layer and TC = 6.8 K for the Nb layer) equal to –7 G
(35% of the magnetic field value). The existence of an
extended interval in which the diamagnetic moment
appears (T = 4–5 K) apparently indicates the existence of a surface potential barrier. The diamagnetic
moment vanishes at T = 7 K. In the FC regime in
which cooling from T = 300 K to T = 2.5 K occurs
after the application of the field, a paramagnetic
moment of 4 × 10–6 CGSM units appears in the temperature interval from 7 to 4.7 K, while in the interval
from 4.7 to 3.8 K, a paramagnetic moment of 1.6 ×
10‒6 CGSM units also appears. It is well known [15]
that the emergence of a paramagnetic moment is
explained by the nonuniformity of the superconducting properties of the layers. Both curves (ZFC and
FC) have an inflection associated with a change in the
magnetic moment in the mixed state of the V layer at
T = 3.5 K. In the ZFC regime for a field of 1 kOe (see
inset to Fig. 2b), the diamagnetic moment existing at
T = 2 K decreases upon a change in temperature from
2 to 7 K. Consequently, the superconducting layers are
in the mixed state for these values of the magnetic field
Concentration, %
100
Ta
10
V
O
C
H
Nb
Fe
Si
1
0.1
0
50
100
150
200
250
300
350
400
z, nm
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482
ZHAKETOV et al.
y
M × 106, CGSM units
0
Lx
M × 106, CGSM units
−2.0
2
−4.0
−1.0
−2.0
−6.0
−3.0
−8.0
2
6
(a)
Ly
θi
10
n
−4.0
−5.0
ki Q z
θf
αf
θi
km
xz
1
−6.0
kf
x
Qy
Qx
z
2
−7.0
20
60
100 140
M × 106, CGSM units
9.0
2
(b)
1
8.0
180
220
0
300
T, K
2
−8.0
7.0
260
M × 104, CGSM units
4.0
−4.0
−12.0
2
1
4
6
8
6.0
5.0
4.0
θi
dy
8
xz
αf
αi
1
4
xy
dx
20
60
100
140
180
220
260
300
T, K
Fig. 2. Temperature dependence of the magnetic moment
for the Ta/V/FM/Nb/Si structure upon zero field cooling
(1) and cooling a magnetic field (2) at H = 20 Oe (a) and
H = 1 kOe (b). The insets show the temperature dependences of the magnetic moment in the vicinity of the
superconducting transition temperature TC = 6.9 K in the
niobium layer.
in this temperature range. In this case, almost the
entire diamagnetic moment is due to superconductivity of the Nb layer.
Further, it follows from Fig. 2b that at H = 1 kOe,
the magnetic moment increases by 2.2 times to a value
of 9 × 10–6 CGSM units upon the decrease in temperature from 300 to 11 K, which gives a value of 4πJ =
235 G for the magnetization of a magnetic layer of
thickness 20 nm, while the magnetic moment per iron
atom is μFeV = 0.33μΒ, which constitutes 0.15 of the
magnetic moment of an atom in an iron crystal.
Such a small value of μFeV is apparently associated
with the anticollinear mutual directions of the mag-
Fig. 3. (Color online) Geometry of reflection and scattering at grazing angles of radiation incidence.
netic moments of iron and vanadium atoms [10, 11].
Extrapolating the curve in Fig. 2b to zero value of the
magnetization, we obtain TC = 450 K for the Curie
temperature. Therefore, we can state that the magnetic
layers of the structure contain two phases of the substance. The first phase in the form of clusters contains
70% of iron atoms and 30% of vanadium atoms and
has a Curie temperature of 450 K, while the second
phase (medium surrounding the clusters) contains 7%
of iron atoms and has a Curie temperature of about
150 K.
3. NEUTRON STUDIES
We used reflectometry of polarized neutrons [16],
which makes it possible to measure the profiles of
magnetization and nuclear scattering length for neutrons in the bulk of the structure and to determine the
structure of the inhomogeneous state in the plane of
the layers.
3.1. Reflectometry of Polarized Neutrons
A polarized neutron beam (denoted by n in Fig. 3)
is incident at grazing angle θi on the sample. Neutrons
reflected and scattered from the sample are detected
by a 2D position-sensitive detector. Neutrons
reflected specularly at angle θf = θi, having wavevector
km, and transmitted through the structure provide
information on the nuclear (Un(z)) and magnetic
(Um(z)) complex potentials of interaction of a neutron
with the structure, which are averaged over the plane
of the sample [17]:
U n(z) = V n(z ) − iW n(z ),
(1)
U m(z) = μ(B(z) − i Δ B(z)),
where Vn(z) and Wn(z) are the real and imaginary parts
of the nuclear interaction potential, μ is the magnetic
moment of neutron, B(z) and ΔB(z) are the vectors of
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RELAXATION OF THE MAGNETIC STATE
UR, neV
125
1
100
3
75
50
25
2
0
−25
0
50
100
150
200
250
300
350
400
z, nm
Fig. 4. (Color online) Coordinate dependence UR(z) from
the data in Fig. 1 for the Ta/V/FM/Nb/Si structure (1)
and for iron atoms (2) and from the fitting of the results of
calculations to experimental data on neutron reflection
from the Ta/V/FM/Nb/Si structure (3).
483
The neutron beam scattered in the zx plane at angle
θf (nonspecular scattering of neutrons) and associated
with the transfer of wavevector Qx provides information on the roughness of the interfaces and inhomogeneities with a correlation length in the direction of the
x axis ranging from 1 to 100 μm. The neutron beam
scattered in the xy plane with grazing angle αf (grazing-incidence small-angle scattering (GISAS) or diffraction scattering (GIND)) associated with the transfer of wavevector Qy provides information on inhomogeneities with a correlation length in the direction of
the y axis in the range 1–100 nm.
Magnetic elastic scattering of neutrons in the case
with energy transfer considerably exceeding the interaction potential is determined by vector M = Δm –
e(eΔm) [18], where Δm is the difference in the amplitudes of magnetic scattering of neutrons for the scattering region of the medium and e is the unit vector in
the direction of the transferred neutron wavevector.
The value of M is maximal for Δm perpendicular to e
and is zero when these vectors are parallel. The neutron scattering cross section can be written in terms of
the components of M:
σ(±) ~ [(M || ± Δ bnuc )2 + M ⊥2 ],
magnetic induction and induction increment in the xy
plane.
The transmission of neutrons through the structure
is described by the coefficients of neutron reflection
(R+, R–), transmission (Tr+, Tr–), scattering (S+, S–),
and absorption (M+, M–), which depend on the spin
states of the neutron (“+” for neutrons with spin projection along the magnetic field and “—” with the spin
projection against the field). The coherent propagation of neutrons is described by the reflection and
transmission coefficients, while the incoherent process is described by scattering coefficients. The coefficients of neutron scattering and absorption are
responsible to the leakage of neutrons from the coherent propagation channel and are therefore determined
by the imaginary parts of the potential of interaction of
neutrons with the structure.
Neutron scattering coefficients S+(–)(Qz) can be
determined from the data characterizing the neutron
coherent propagation channel using the relations
S +(−) = 1 − (R + Tr + M ) +(−).
(2)
The coefficient M of neutron absorption by the elements of the structure does not exceed 10–3; the coefficient of scattering by hydrogen impurity atoms is also
smaller than 10–3; therefore, relation (2) was used for
determining the value of S(Qz) from experimentally
determined neutron reflection and transmission coefficients R(Qz) and Tr(Qz) to within 10–3.
(3)
where M|| and M⊥ are the components of M along and
across the quantization axis (the axis on which the
polarization of neutrons is fixed) and Δbnuc is the difference of the nuclear scattering lengths for the scattering region and the medium.
For a nuclear-homogeneous medium, Δbnuc = 0 as
well as the polarization of scattered neutrons (e.g., in
the case of magnetic domains). The polarization of
scattered neutrons in a heterogeneous medium is
equal to zero in the case of the demagnetized magnetic
state, for which the distribution of magnetic moments
is isotropic. Nevertheless, neutron scattering exists
due to the gradient of the local magnetic induction.
The data represented in Fig. 1 were used for constructing the spatial dependences of the potential of
nuclear interaction of neutrons (Fig. 4) with the structure under investigation (curve 1) and with a layer of
iron atoms (curve 2). Figure 4 also shows the neutron
interaction potential profile obtained by fitting to neutron experimental data on the intensity of neutrons
reflected from the structure (curve 3). It can be seen
that curves 1 and 3 do not coincide in the interval 125–
300 nm. The interval 175–300 nm corresponds to the
niobium layer. Here, the potential calculated from the
neutron data is lower that calculated from the concentration of individual elements. This can be due to the
fact that niobium is packed with a nearly 90% density
relative to its density in a crystal. Conversely, in the
interval 125–175 nm, the potential obtained from neutron reflection data is higher than that calculated from
the concentrations of the elements. This can be associated, for example, with the presence of vanadium in
the form of compounds with a density higher than the
JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS
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ZHAKETOV et al.
density of the mixture of vanadium, hydrogen, and
oxygen. The resultant potential of interaction of neutrons with the structure is such that the vanadium
layer forms a potential well for neutrons, while the
tantalum and niobium layers form potential barriers.
For the given spatial dependence of the potential
(see Fig. 4), two regimes of the neutron wave field are
realized. For the energy of neutrons in the direction
perpendicular to the interfaces and exceeding the
potential of interaction with the Nb layer, the regime
of a propagating neutron wave is realized. For the
energy of neutrons lower than the potential of interaction with the Nb layer, the regime of a standing neutron wave takes place. As a result, we used in our measurements the potentialities of measuring the real and
imaginary parts of the neutron–medium interaction
potential, which are typical of these regimes. It is
known that the imaginary part of the potential
describes the absorption of neutrons by nuclei of the
medium and the scattering of neutrons by nuclei,
atoms, and the medium [19]. Scattering of neutrons by
the magnetic layer located at the interface between the
V and Nb layers is maximal for the transverse neutron
wavevector component equal to the critical value of
the neutron wavevector (0.007 Å–1).
3.1.1. Results of static measurements. Figure 5
shows the dependences of neutron scattering coefficient S integrated over the neutron wavelength (we
assume that scattering at H = 0 is zero) out of solid
angle Ω = 1.6 × 10–4 srad, which were obtained at T =
300 K. It can be seen that with increasing magnetic
field, the scattering intensity increases, while the difference of the intensities for the “plus” and “minus”
polarizations decreases. The intensification of scattering can be explained as follows. First, this means that
the medium is magnetically heterogeneous and consists of atomic (nuclear) magnetic clusters (Fig. 5b) for
which the density distribution of nuclear amplitude of
neutron scattering coincides with the distribution of
the magnetic scattering amplitude density. If the
medium contained magnetic domains and were
nuclear-homogeneous, an increase in the magnetic
field would result in the disappearance of magnetic
domains and, as a consequence, to a decrease in the
neutron scattering intensity. With increasing magnetic
field, the moments of clusters are aligned in the direction of magnetic field H. Therefore, we must consider
two factors. First, magnetic channels are formed (see
Fig. 5b), which intensifies scattering; however, scattering in this case becomes less dependent on the
polarization of neutrons, which is precisely observed
in experiments. Second, with increasing magnetic
field, the “degree of orthogonality” of the magnetic
moments of clusters to the transferred magnetic
moment of scattered neutrons increases (e ⋅ Δm → 0),
which also intensifies neutron scattering.
Low-temperature measurements were carried out
over 3.5 years. The first measurements were taken
S
0.10
0.09
(a)
0.08
0.07
0.06
0.05
0.04
0.03
0.02
1
0.01
2
2000
1000
0
3000
4000
5000
H, Oe
m
m
(b)
Q
H
m
m
m
1
2
Fig. 5. (Color online) (a) S(H) dependence at T = 300 K
for P0 = +1 (1) and –1 (2). (b) Magnetized (1) and demagnetized (2) systems of clusters with magnetic moments m
and scattered field fluxes connecting them in magnetic
field H; Q is the transferred wavevector of neutrons.
3 months after the preparation of the sample. The
results of first measurements are shown in Fig. 6a
illustrating the temperature dependence of the scattering coefficient
S (T ) = 1 − (R(T ) + Tr (T ))/(R(150 K) + Tr (150 K))
of polarized neutrons with wavelength λ = 1.28 ±
0.015 Å (scattering at T = 150 K is zero).
At T = 8 K, neutron scattering intensity is maximal
and amounts to 55–59%; the polarization of scattered
neutrons is negative and equal to –0.035. It should be
noted in this connection that a nonzero value of the
polarization of scattered neutrons is determined by the
system of clusters, while the neutron scattering intensity in a weak magnetic field is mainly determined by
domains. On the other hand, the magnetization in a
weak field is determined predominantly by clusters.
Therefore, the negative value of polarization at T =
8 K indicates that the magnetic moments of clusters
are oriented against the magnetic field, which is in
conformity with the negative value of the magnetization (see Fig. 2a). Therefore, the neutron scattering
intensity at H = 17 Oe at T = 8 K (see Fig. 6a) is 7 times
JOURNAL OF EXPERIMENTAL AND THEORETICAL PHYSICS
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RELAXATION OF THE MAGNETIC STATE
S
0.7
(a)
0.6
S
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
P0 = −1
+1
0.5 H = 17 Oe
0.4
0.3
H = 17 Oe,
P0 = +1
2 4 6 8 10 12
T, K
9.5 kOe
0.2
0.1
+1
0
1
S
0.24
10
3
1000
T, K
100
1000
T, K
(b)
0.20
0.16
100
2
0.12
0.08
1
0.04
0
1
αΔS
0.05
10
(c)
0.04
5
6
0.03
0.02
3
4
0.01
0
1
2
−0.01
1
2
3
4
5
6
7
8
9
10 11 12
T, K
Fig. 6. S(T) dependence for the structure Ta/V/FM/Nb/Si:
(a) 3 months after the preparation of the structure;
(b) 1.5 years later for H = 17 Oe (1), H = 17 Oe after preliminary magnetization in a field of 2 kOe (2) and H =
1 kOe (3); (c) 3.5 years later for H = 28 Oe: λ = 2 ± 0.2 Å,
P0 = +1 (1); λ = 2 ± 0.2 Å, P0 = –1 (2); λ = 4.6 ± 0.46 Å,
P0 = +1 (3); λ = 4.6 ± 0.46 Å, P0 = –1 (4); λ = 7.2 ±
0.72 Å, P0 = +1 (5); λ = 7.2 ± 0.72 Å, P0 = –1 (6).
485
higher than the intensity at H = 5 kOe and T = 300 K
(Fig. 5a), while the magnetization has increased by
only 1.5 times (see Figs. 2a and 2b). This means that at
H = 17 Oe and T = 8 K, about 70% of the neutron
scattering intensity are determined by the domain
structure and 30% are due to clusters.
Figure 7 shows the pattern of scattering of neutrons
with λ = 3.8 ± 0.2 Å on the cluster lattice at T = 10 K
and H = 1 kOe. The first (Ny = 135 and Nz = 135),
third (Ny = 90 and Nz = 90), and fifth (Ny = 25 and
Nz = 40) scattering (reflection) orders corresponding
to an interplanar spacing of the cluster array of 6.5 nm
can be seen. The reflection planes of the lattice are
inclined at an angle of about 45° to the y axis in the yz
plane (Fig. 8). Near the spots of the first and third
reflection orders, the satellite spots corresponding to
spatial periods of 20 and 60 nm along the y axis are
observed [9]. These periods can be attributed to longperiodic magnetic structures formed by clusters. However, in all probability, these values correspond to the
domain wall thickness and the magnetic period of the
domain structure (the domain size is 40 nm) in the
medium containing clusters.
It follows from Fig. 6a that at T = 3 K, the polarization has increased to 0.11 and has become positive.
The increase in the neutron polarization is associated
with an increase in the fraction of neutrons scattered
by clusters. At T = 1.6 K, the scattering intensity is
even lower and amounts to 0.1. The scattering intensity
has decreased by approximately 5.7 times as compared
to the intensity at T = 8 K. The decrease in the neutron
scattering intensity by 70% due to the domain structure can be explained by an increase in the domain size
and disordering of the directions of magnetic
moments of clusters (demagnetization of the cluster
system). The increase in the domain size is favorable
for the superconducting state if the magnetic moments
of domains are oriented perpendicularly to the planes
of the structure [19]. In this case, upon an increase in
the domain size, the magnetic induction in a domain
decreases due to the demagnetization factor, which
facilitates the passage of superconducting pairs
through domains. Figures 9a and 9b show the magnetic state of the structure in a weak magnetic field of
17 Oe at 8 K and 1.6 K. The circles and rectangles indicate the clusters and domains, respectively; arrows
show the directions of the magnetic moments of clusters and domains. In the nonsuperconducting state
(at T = 8 K) in a weak magnetic field (H = 17 Oe), the
magnetic moments of domains are disordered and
directed at right angles to the magnetic layer, while the
moments of clusters are ordered and directed against
the field. In the superconducting state (T = 1.6 K, H =
17 Oe), the domains grow, and the magnetic moments
of clusters become disordered in direction.
Figure 6a also shows the data for a strong magnetic
field of 9.5 kOe, which demonstrate scattering by the
third magnetic system (namely, superconducting vor-
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ZHAKETOV et al.
Ny
180
160
y
×10−6
5.0
(a)
2d
4.5
n
4.0
140
3.5
120
3.0
100
2.5
80
2.0
2d
1.5
60
1.0
40
0.5
40
60
80 100 120 140 160 180
Nz
Ny
180
160
z
Detector
1 2
x
×10−6
4.5
3
(b)
4.0
140
3.5
120
3.0
2.5
100
2.0
80
Fig. 8. Schematic diagram of the experiment on detection
of neutron scattering from the cluster lattice in the magnetic layer (reflection plane is shown by the gray rectangle)
in the case of grazing incidence of neutrons on the
Ta/V/FM/Nb/Si layered structure: (1) transmitted beam;
(2) reflected beam; (3) neutron beam diffracted on the
cluster lattice. The interplanar distance for the reflection
being detected is 21/2d = 6.5 nm.
1.5
60
1.0
40
0.5
40
60
80 100 120 140 160 180
Nz
0
Fig. 7. (Color online) Neutron scattering intensity on the
[Ny, Nz] plane for (a) P0 = +1 and (b) –1 for λ = 3.8 Å,
where Ny and Nz are the numbers of channels of the neutron detector along the y and z axes, respectively.
tices). Measurements in a magnetic field of 9.5 kOe
were taken using the following procedure. A magnetic
field of 9.5 kOe was set at a temperature of 3 K. Then
the temperature was reduced to the minimal value
(1.6 K), and measurements were taken again. After
this, the temperature was raised to the next closest
higher value, and measurements were carried out, and
so on up to the maximal value of T = 10 K. It can be
seen that in the range of 3–7 K, scattering of neutrons
is observed, which is attributed to scattering by vortices
in the mixed state of the superconducting vanadium
and niobium layers. At T < 3 K, the Meissner vortexfree state is realized, while at T > 7 K, superconductivity disappears. In both cases, neutron scattering inten-
sity decreases to the level determined by scattering
from magnetic clusters.
The second series of measurements was carried out
1.5 years after the sample preparation (Fig. 6b). This
figure shows the S(T) dependence for a magnetic field
of 17 Oe (curve 1), in the same field after preliminary
magnetization of the structure in a magnetic field of
2 kOe (2) and in a magnetic field of 1 kOe (3). Curve 1
is generally analogous to the dependence in Fig. 6a. It
can be seen, however, that scattering intensity
increases in a narrow interval of 5–6 K, which probably indicates the formation of a domain structure of
the cryptoferromagnetic phase [20–25]. The intensification of scattering on curves 2 and 3 is more pronounced. Since these dependences correspond to a
higher magnetization, we can propose that the magnetizations of domains now lie in the plane. Therefore, a
decrease in the domain size upon cooling now
becomes favorable for the superconducting state [26–
28]. Figures 9c and 9d show the magnetic structure in
a moderate magnetic field of 1 kOe at T = 2 K (see
curve 3 in Fig. 6b) and 10 K, respectively. With
increasing magnetic field in the superconducting state
(2 K, 1 kOe), the magnetic moments of domains
become oriented along the field, and their size
decreases. In the nonsuperconducting state in a magnetic field of a moderate magnitude (10 K, 1 kOe), the
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487
8 K, 17 Oe
1.6 K, 17 Oe
2 K, 1 kOe
10 K, 1 kOe
(a)
(b)
(c)
(d)
H
Fig. 9. (Color online) Magnetic state of the structure in the ranges of T = 1.6–10 K and H = 17 Oe–1 kOe according to the neutron scattering data: (a) magnetic moments of clusters are oriented against the field; magnetic moments of domains are oriented
perpendicularly to the magnetic field; (b) magnetic moments of clusters are disordered, the domain size has increased as compared to state (1); (c) clusters are magnetized in the direction of the field, the magnetic moments of domains are oriented along
the magnetic field, but their density has increased due to a decrease in the domain size; (d) magnetic moments of clusters are
oriented along the magnetic field; the density of domains has decreases.
density of domains decreases, and the magnetic
moments of clusters are oriented along the field.
The third neutron measurement was taken
3.5 years after the preparation of the structure. The
results of these measurements are represented in
Fig. 6c. The results of these measurements at H =
28 Oe are shown in Fig. 6c. It can be seen that the neutron scattering intensity in the range from 10 to
1.5 K changes by just 1.5–3%. The small value of scattering intensity indicates that the nuclear and magnetic contrasts have decreased. This can be primarily
due to diffusion of iron atoms from the magnetic layer.
This follows from the results of analogous repeated
measurements (see Fig. 1) of the spatial profiles, indicating the decrease in the spatial distribution width for
iron atoms by 11.4% from 22.8 to 20.2 nm over
3.5 years.
3.2. Real-Time Reflectometry of Neutrons
The real-time experiments with neutrons, in which
specularly reflected and scattered neutrons are
detected during time t in the n = t/Δt time interval of
duration Δt, make it possible to measure nonstationary
processes with period of variation T exceeding Δt (T >
Δt). In this case, Δt obviously determines the time resolution of measurements. The minimal value of Δt is
determined by neutron intensity J and change ΔJ of
the neutron intensity due to the temporal process
under investigation. Let us suppose that the change in
the intensity of neutron count by the detector over the
entire measurement time t is ΔJ = βJ, where β < 1. Let
the minimal change during time interval Δt be determined by parameter μ and amount to δJ = μΔJ, where
μ < 1. Obviously, the statistical error of neutron count
measurement Nst = (JΔt)1/2 over time interval Δt must
be smaller than count increment ΔN = βμJΔt. We can
write the relation connecting these quantities in the
form Nst = αΔN, where α < 1. For time measurement
interval Δt, we can write from this relation
(4)
Δ t = 1/(α 2β 2μ 2 J ).
It follows from this relation that to reduce Δt, we
must increase neutron count intensity J, which corresponds to an increase in the neutron spectrometer
luminosity. High-transmission methods of measurements include, for example, diffraction and depolarization measurements. In [29–31], neutron-diffraction and spin-precession (variant of depolarization)
real-time measurements were reported. In [29, 32],
various possibilities of diffraction studies were also
indicated. It was noted that for different experimental
setups, irreversible transition processes can be measured with a resolution from 1 min to 1 ms, while the
resolution for reversible processes can be down to 1 μs.
In [31], the magnetic field relaxation averaged over the
volume exposed to the neutron beam was measured in
a superconducting ceramic with the minimal value of
Δt = 1000 s, which made it possible to observe magnetic field inductions with frequencies lower than
0.1 mHz to a high statistical degree of accuracy.
Because of the small viewing solid angle of the neutron source (~10–5 srad) and the small neutron beam
cross section on the experimental sample (~0.1 cm2),
neutron reflectometry is not a high-transmission
method of measurements. Let us estimate the value of
Δt for the realization of the method on the REMUR
spectrometer of the IBR-2 pulsed reactor [33]. The
neutron flux recorded by a position-sensitive detector
at a reactor power of 2 MW in the operation conditions
(e.g., fan polarization analyzer) amounts to 1.6 ×
105 (s cm2)–1, which gives the count intensity J0 =
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ZHAKETOV et al.
2.4 × 10 4 s–1 on the neutron detector for a neutron
beam cross section of 0.15 cm2.
Let us consider the channel of specularly reflected
neutrons with intensity JR = J0 of reflection from the
interface between the media (total reflection of neutrons). For realistic values of parameters α = 1/3 (statistical error is 30% of the effect), β = 0.1 (total change
in the count intensity amounts to 10% of the count
intensity), and μ = 0.03 (change in the count intensity
on interval Δt is 3% of the total change), we obtain
Δt = 9 × 106/(2.4 × 105) ≈ 40 s. This gives 5 min for the
minimal value of the period of temporal variation
Tmin ≈ 8Δt (maximal variation frequency is fmax =
3.3 mHz).
Let us now consider the neutron scattering channel. Let the intensity of scattered neutrons amount to
10% of the intensity of specularly reflected neutrons.
The change in the intensity of scattering of neutrons
with time is assumed to be 100% (β = 1). Then for
parameters α = 1/3 and μ = 0.03 (same as for specular
reflection), we obtain the same value of 5 min for the
minimal measured period Tmin.
3.3. Results of Dynamic Measurements
Let us now consider the results of measurements of
the dynamic behavior (namely, relaxation of the magnetic state of the layered structure). The main
dynamic measurements were taken in the second
series of neutron measurements. Figure 10 shows the
S(t) dependences for λ = 1.8 Å after the step variation
of the field and temperature. The structure was magnetized in a magnetic field of 2 kOe at a temperature of
10 K. Since the magnetic field lies in the plane of the
layer, the domains oriented perpendicularly to the
layer were oriented in the plane of the layer. Then the
field was reduced to 17 Oe; a temperature of 10, 6, 3,
or 2 K was set, and measurements were taken. It can be
seen that neutron scattering increases with time, and
the polarization changes its sign at T = 6, 3, and 2 K at
tch1 = 17000, 9000, and 7500 s, respectively. The intensification of scattering was associated with the increase
in the density of domain walls, while the change in
polarization was due to rotation of the magnetic
moments of clusters. The part of the intensity of neutrons independent of their polarization (averaged over
polarizations +1 and –1) for T = 6, 3, and 2 K consists
of two segments separated by instant tch2 = 17000,
15000, and 10000 s, respectively. The inflection on the
curve indicates the emergence of a new domain structure (namely, still smaller domains are formed). As a
result, the density of domain walls increases still further and, accordingly, the neutron scattering intensity
increases. It can be seen that tch1 and tch2 decrease upon
cooling, indicating that the processes of motion of
cluster magnetic moments and the formation small
domains are associated with superconductivity.
Thus, we can state that relaxation with the superconducting layers of the structure (T = 2, 3, and 6 K)
substantially differs from relaxation with nonsuperconducting layers (T = 10 K). It occurs in two stages in
the former case and in one stage in the latter case.
Superconductivity leads to the formation of domains
with a size smaller than usual. It cannot be ruled out
that this is connected with the cryptoferromagnetic
phase predicted and described in [20–25]. In the case
of superconducting layers, the directions of the magnetic moments of the clusters relative to the magnetic
field direction change simultaneously with the
changes in the domain structure. Both processes are
interrelated and are controlled by superconductivity.
The change in the scattering intensity during relaxation attains 100%. In the interval of measurements for
1 h (frequency range f < 3 × 10–4 Hz), the statistical
error of measurements is 3% of the change in the neutron scattering intensity.
Figures 11a–11c show the S(t) dependences
obtained in a magnetic field of 1 kOe in the temperature interval 2–10 K for neutron polarization P0 = +1
and neutron wavelengths of 1.8, 3, and 6 Å. The
sequence of measurements was as follows. The magnetic field of 1 kOe was stabilized at 10 K; then the
temperature was reduced to the value at which the
measurement was taken.
It can be seen that the scattering intensity maximum corresponds to a certain wavelength of 3 Å,
which indicates an admixture of neutron scattering
from the magnetic cluster lattice.
Figures 12a and 12b show the S(t) dependences for
P0 = +1, –1, and 0 in a magnetic field of 1 kOe at temperature (a) 10 K and (b) 2 K. It can be seen that
dependences for P0 = +1 and P0 = –1 oscillate and
intersect. This corresponds to the situation when the
magnetic moments of clusters are directed either along
the field (the curve for P0 = +1 is above the curve for
P0 = –1) or against it (curve with P0 = +1 is below the
curve with P0 = –1). The points of intersection of the
curves with P0 = +1 and P0 = –1 correspond to zero
mean magnetization of clusters, when all magnetic
moments are perpendicular to the magnetic field vector or when the directions of the moments are distributed symmetrically relative to the perpendicular to the
magnetic field vector. The dependences obtained at
T = 2 K indicate that the magnetization changes by
more than +40%. Let us estimate the value of the
magnetic induction at clusters. In the case where all
magnetic moments are oriented against the magnetic
field, the magnetic induction in their neighborhood is
in the range 1 kOe–235 Oe (2.2/0.33)/1.4 = –120 Oe ≈
0. For a nearly zero magnetic induction at a cluster, the
formation of the domain structure apparently
becomes favorable. In this case, the spatial distribution of the domains structure in the magnetic layer
must probably repeat the distribution of clusters oriented against the field. Figure 12c shows the S(t)
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RELAXATION OF THE MAGNETIC STATE
S
0.20
S
0.20
0.18
T = 10 K
(a)
0.16
−1
0.14
0.14
0.12
0.12
0.10
0.10
0.08
0.08
5000
10000
15000
20000
25000
t, s
T=3K
+1
0
5000
10000
15000
20000
25000
t, s
+1
0.12
0.10
0.10
0.08
0.08
5000
10000
−1
0.14
0.12
15000
20000
25000
t, s
(d)
P0 = +1
0.16
(c)
0.14
T=2K
0.18
P0 = −1
0.16
0
P0 = −1
S
0.20
S
0.20
0.18
(b)
T=6K
0.18
P0 = +1
0.16
0
489
0
5000
10000
15000
20000
25000
t, s
Fig. 10. S(t) dependence in a magnetic field of 17 Oe in the case of preliminarily magnetized sample in a magnetic field of 2 kOe
at different temperatures for λ = 1.8 Å.
dependences for P0 = 0 (mean magnetization of clusters is zero). It can be seen that at T = 2 K, scattering
coefficient S(t) increases with time. This means that
the magnetic domain structure that does not correlate
with the nuclear structure changes or is generated.
Obviously, the system of clusters oscillates near the
equilibrium state right to t = 460 min, while the
domain structure has not yet attained saturation. Consequently, the evolution of the domain structure with
time at T = 2 K is accompanied with an increase in the
amplitude of oscillations of the magnetic moments of
clusters.
Therefore, in a moderate magnetic field of strength
1 kOe, the behaviors of the two magnetic systems are
rigidly coupled and depend on time, and the angular
range of oscillations of the magnetic moments is determined by the domain structure. At T = 2 K, the angular range increases together with the density of domain
walls due to the formation of the structure of small
domains at tch2 = 10000 s, while at T = 10 K, both
parameters become saturated with time. It is important to know whether small domains are formed inside
large domains or large domains first disappear and
then small domains are formed. There is no answer to
this question as yet. For example, the curve in Fig. 12c
for T = 2 K appears as monotonically increasing,
which speaks in favor of the first version. However, the
curve in the same figure for T = 3 K has a weakly pronounced minimum, which indicates the second version. Furthermore, since the magnetic field scattered
from the domain structure decreases upon an increase
in the domain wall density, the magnetic action of the
domain structure on the system of clusters also
becomes weaker. In this case, the system of clusters is
in an unstable oscillatory state, passing from one state
in the magnetic field to the other and back. Obviously,
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S
0.12
S
0.28
(a)
(a)
0.24
0.08
0.20
0.04
T=2K
0.16 6 K
3K
0.12
10 K
0.08
0
0 2
λ = 1.8 Å
5000
S
0.32
10000 15000 20000 25000 30000
t, s
T = 10 K
−0.04 3
−0.08
1
0
S
0.24
5000 10000 15000 20000 25000 30000
t, s
(b)
0.28
0.20
0.24
0.16
T=2K
6K
0.20
(b)
2
3
0.12
1
0.16
0.12
0.08
3K
λ=3Å
5000
S
0.20
10000 15000 20000 25000 30000
t, s
(c)
0.16
0.08
0.04 1
T=3K
λ=6Å
−0.04
0
5000
(c)
0.12
0.04
0
5000 10000 15000 20000 25000 30000
t, s
0.16
10 K
6K
0.08
0
S
0.24
0.20
2K
0.12
−0.08
T=2K
0.04
10 K
0
0.08
10000 15000 20000 25000 30000
t, s
0 2
3
−0.04 4
−0.08
5000 10000 15000 20000 25000 30000
t, s
Fig. 11. S(t) dependence in a magnetic field of 1 kOe at different temperatures for P0 = +1.
Fig. 12. S(t) dependence for H = 1 kOe: (a, b) P0 = –1 (2),
0 (3), +1 (1); (c) P0 = 0, T = 10 (4), 6 (3), 3 (2), and
2 K (1).
the oscillatory motion of the magnetic moments of
clusters with increasing amplitude in the presence of
two magnetic systems is a manifestation of the domain
phase consisting of small domains.
Figure 13 shows the S(t) dependences at T = 3 K in
the range H = 17 Oe–8 kOe of magnetic field variation. The value of the magnetic field was stabilized at
T = 12 K, after which the temperature was decreased
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S
0.26
T=3K
λ = 1.8 Å
0.24
0.22
6
7
0.20
4
5
0.18
8
0.16
3
2
1
0.14
0.12
0
5000
10000
15000
20000
25000
t, s
Fig. 13. S(t) dependence for P0 = +1 and H = 17 Oe (1),
1 (2), 2 (3), 4 (4), 6 (6), 7 (7), and 8 kOe (8); P0 = –1,
H = 4 kOe (5).
to 3 K, and measurements were taken. Curves 4–8 at
H = 4–8 kOe are characterized by a decrease in the
neutron scattering intensity on the initial time interval, which can be explained by a decrease in the density of the pinning centers in the superconducting layers. This is confirmed by the fact that the polarization
of neutrons scattered by the superconducting current
loops around the pinning centers is negative right to
t = 1.5 × 10 4 (curves 4 and 5). The latter mechanism is
also confirmed by the observed form of the neutron
scattering law, which corresponds to the theory of
magnetization relaxation in low-temperature superconductors [1, 2] and explains the relaxation by the
separation of vortices from the pinning centers. The
curve for H = 4 kOe in the interval 3000–10000 s is
described by the logarithmic law S = 0.25 – 0.0725 ×
ln(t(min)/60). Beginning from instant t = 15000 s,
curves 4 and 5 demonstrate the reciprocal nature with
a rather sharp increase in the neutron scattering intensity. We can assume that the end of the straightening of
the vortex lattice somehow increases the rate of formation of the domain structure.
It is important to find out whether the value of
magnetization averaged in the plane of the layer
changes due to coherent reflection and transmission
of neutrons along with a local change in the magnetization determined by neutron scattering. It would also
be interesting to determine the position of the part of
magnetization varying with time over the depth. This
can be done using the time dependences of three coefficients R(t), Tr(t), and S(t) (Fig. 14). It can be seen
that there exist time intervals t ≈ 1000 s (a) and t ≈
12500 s (b) in which the behaviors of coefficients R(t)
491
R, Tr, S
1.0
T=2K
0.9
(a)
H = 1 kOe
0.8
0.7
0.6 Tr
0.5
0.4
0.3 R
0.2
0.1 S
0
−0.1
0
5000 10000 15000 20000 25000 30000
t, s
R, Tr, S
1.0
T=3K
0.9
(b)
H = 4 kOe
0.8
0.7 Tr
0.6
0.5
0.4
0.3
0.2 R
0.1
0 S
−0.1
0
5000
10000
15000
20000
t, s
R, Tr, S
1.0
(c)
0.9
Tr
0.8
0.7
0.6
T = 10 K
0.5
H = 4.5 kOe
0.4
0.3 R
0.2
0.1 S
0
−0.1
0
5000 10000 15000 20000 25000 30000
t, s
Fig. 14. S(t), R(t), and Tr(t) dependences for λ = 6 Å. Solid
and dotted curves correspond P0 = + 1 and –1, respectively.
and Tr(t) correlate. This means that apart from a
change in the local magnetization of the scattering
object, the value of magnetization averaged over the
plane also changes with time.
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αΔS
0.040
αΔS
0.030
0.025
8
7
H = 28 Oe
λ = 2 ± 0.2 Å
0.020
0.015
5
6
0.035
T = 1.68 K
λ = 2 ± 0.2 Å
0.030
5
6
3
4
0.025
0.010
0.005
1
2
0.020
0.015
0
3
4
−0.005
−0.010
7
8
0
10000
2
1
0.010
20000
30000
40000
50000
t, s
Fig. 15. Dependence αΔS(t): (1) T = 6 K, P0 = +1; (2) T =
6 K, P0 = –1; (3) T = 4 K, P0 = +1; (4) T = 4 K, P0 = –1;
(5) T = 3 K, P0 = +1; (6) T = 3 K, P0 = –1; (7) T = 1.68 K,
P0 = +1; (8) T = 1.68 K, P0 = –1.
It follows from the curves corresponding to H =
4.5 kOe and T = 10 K (Fig. 14c) that while S and Tr
mainly anticorrelate for t < 250 min, S and R anticorrelate predominantly for t > 250 min. This means that
the relaxation of the magnetic state shifts with time
from the deeper regions of the magnetic layer contacting with the Nb layer to the region located closer to the
surface and contacting with the V layer. For T = 3 K
and H = 4 kOe (Fig. 14b), prior to processes described
above (curves 4 and 5 from Fig. 13), an increase in the
average magnetization of the magnetic layer is first
observed. When T = 2 K and H = 1 kOe, the relaxation
in the surface regions of the structure is observed only
at the initial stage lasting to instant of 5000 s.
At the same time, for T = 3 K and H = 4 kOe (see
Fig. 12b), the transmission coefficient is determined
by neutron scattering more strongly as compared to
the reflection coefficient. This means that neutron
scattering mainly occurs at vortices in the niobium and
not the vanadium layer. Therefore, the curves in
Fig. 14 demonstrate that real-time neutron reflectometry makes it possible to simultaneously trace the temporal and spatial variation of the magnetic state in the
layered structure.
Some dynamic measurements were also performed
in the third series of experiments.
Figure 15 shows the αΔS(t) dependences in a magnetic field of 28 Oe, where α = 1/(1 – S(T = 10 K)),
which were obtained upon a gradual cooling in the
temperature range from 10 to 1.68 K. It can be seen
that after a short-term increase in the scattering intensity at T = 1.68 K and T = 3 K (reduction of the
domain size), its decrease is observed (increase in the
0.005
0
20000
40000
60000
80000
t, s
Fig. 16. Dependence αΔS(t): (1, 2) T = 1.68 K, H =
500 Oe, P0 = +1 (1) and –1 (2); (3, 4) T = 1.68 K, H =
1000 Oe, P0 = +1 (3) and –1 (4); (5, 6) T = 1.68 K, H = 28 Oe,
P0 = +1 (5) and –1 (6); (7, 8) T = 10 K, H = 1000 Oe, P0 =
+1 (7) and –1 (8).
domain size). Upon a decrease in temperature, the
range of neutron scattering intensity oscillations
increases. At T = 1.68 K, the curve resembles a transient process when the amplitude of oscillations relative to the equilibrium state decreases with time. Along
with the oscillations in the domain sizes, oscillations
of the magnetic moments of clusters are observed. No
such interrelation between the systems of domains and
clusters was observed in the first and second series of
experiments.
Figure 16 shows the S(t) dependences at T =
1.68 K, which were obtained for different values of the
magnetic field.
The change in the field magnitude leads to a
change in the domain structure; however, in contrast
to temperature variations, the long-term relaxation
occurs with a substantially smaller amplitude,
although it demonstrates a quasi-periodic nature
(change in the domain sizes). Ir can also be seen that
the effect of superconductivity leads to a decrease in
the domain size with time in a magnetic field of the
moderate value (H = 1 kOe).
4. CONCLUSIONS
Static and dynamic neutron studies have revealed
that the characteristics of the Ta/V/FM/Nb/Si magnetic structure have changed significantly during
3.5 years. For example, the distribution of elements in
the plane of the magnetic layer has become more uniform with time, which follows from an order-of-magnitude decrease in the neutron scattering intensity. We
have studied the relaxation of the magnetic state of the
hybrid layered structure consisting of ferromagnetic
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RELAXATION OF THE MAGNETIC STATE
and superconducting layers. The magnetic state relaxation was studied using polarized neutron reflectometry. Real-time dynamic neutron studies have confirmed their importance in determining the origin of
magnetism in ferromagnetic–superconducting layered structures.
It has been shown that the systems of magnetic
clusters and ferromagnetic domains interact, and their
behavior is determined by the superconducting layers
of the structure. The manifestations of the interaction
between the two systems change with time. For example, it has been established in experiments performed
during the first 1.5 years that the formation of ferromagnetic domains of the same size changes with time
under the effect of superconductivity to the formation
of domains of a smaller size. The rate of formation of
the new domain phase increases upon cooling to
below the critical point for the niobium layer. It has
been proposed that the structure with small domains is
probably the cryptoferromagnetic phase of the magnetic layer. It should be noted that the manifestation of
the cryptophase in the increase in the intensity of scattering of polarized neutrons is one of the first direct
indications of its formation in the layered structure.
Simultaneously with the formation of the smalldomain structure in a magnetic field of 1 kOe right to
an instant of 6 h, the amplitude of oscillations of the
magnetic moments in the cluster system from the
direction along the magnetic field to the opposite
direction increased. This was the result of suppression
of the magnetic interaction of clusters with the smalldomain structure and, as a consequence, the emergence of an unstable state of oscillation of the system
of clusters between two minima of its energy in the
magnetic field [14].
It was found in analysis of the structure 3.5 years
after its preparation that the interaction between the
two magnetic systems was manifested differently as
compared to that observed earlier, namely, in the
simultaneous change in the direction of the magnetic
moments of clusters and in the domain size. The
amplitude of oscillations of the domain sizes increased
upon cooling.
The intensity of the polarized neutron beam in the
REMUR spectrometer of the pulsed IBR-2 reactor
used in our experiment can in principle be increased,
which will make it possible to improve the time resolution in the investigation of irreversible processes to a
few minutes. It should be noted that some ideas concerning a further increase in the time resolution,
which can also be used in reflectometry of polarized
neutrons, were formulated in [29].
493
ACKNOWLEDGMENTS
The authors are grateful to Yu.N. Haidukov for
fruitful discussions of the results.
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