Possibility of soft-matter effects in solids
Shape variation under the action of small external fields is a peculiar feature of soft matter. In the present paper we demonstrate a possibility of the analogous shape variation in the solids that combine the properties of antiferro- and ferromagnetic materials and show strong magnetoelastic coupli...
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| Zitieren: | Possibility of soft-matter effects in solids / H.V. Gomonay, I.G. Kornienko, V.M. Loktev // Condensed Matter Physics. — 2010. — Т. 13, № 2. — С. 23701: 1-9. — Бібліогр.: 8 назв. — англ. |
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| citation_txt | Possibility of soft-matter effects in solids / H.V. Gomonay, I.G. Kornienko, V.M. Loktev // Condensed Matter Physics. — 2010. — Т. 13, № 2. — С. 23701: 1-9. — Бібліогр.: 8 назв. — англ. |
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| description | Shape variation under the action of small external fields is a peculiar feature of soft matter. In the present paper we demonstrate a possibility of the analogous shape variation in the solids that combine the properties of antiferro- and ferromagnetic materials and show strong magnetoelastic coupling. The antiferromagnetic subsystem provides a macroscopic deformation of a sample in the external magnetic field while the ferromagnetic component ensures high susceptibility of the domain structure.
Зазначено, що характерною рисою м'якої матерії є її властивість змінювати форму під впливом слабких зовнішніх полів. Показано можливість аналогічної зміни форми в твердих тілах, які поєднують властивості антиферо- та феромагнітних матеріалів і мають сильний магнітопружний зв'язок. Макроскопічні деформації зразка в зовнішньому магнітному полі виникають за рахунок антиферомагнітної складової, а феромагнітна компонента обумовлює високу сприйнятливість доменної структури.
|
| first_indexed | 2025-12-07T18:32:13Z |
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Condensed Matter Physics 2010, Vol. 13, No 2, 23701: 1–9
http://www.icmp.lviv.ua/journal
Possibility of soft-matter effects in solids
H.V. Gomonay∗1,2, I.G. Kornienko2, V.M. Loktev1
1 Bogolyubov Institute for Theoretical Physics NAS of Ukraine, Metrologichna Str. 14-b, 03680, Kyiv, Ukraine
2 National Technical University of Ukraine “KPI”, Peremogy Avenue, 37, 03056, Kyiv, Ukraine
Received February 22, 2010
Shape variation under the action of small external fields is a peculiar feature of soft matter. In the present pa-
per we demonstrate a possibility of the analogous shape variation in the solids that combine the properties of
antiferro- and ferromagnetic materials and show strong magnetoelastic coupling. The antiferromagnetic sub-
system provides a macroscopic deformation of a sample in the external magnetic field while the ferromagnetic
component ensures high susceptibility of the domain structure.
PACS: 75.60.Ch, 46.25.Hf, 75.50.Ee
Key words: domain walls and domain structure, shape effects, thermoelasticity and electromagnetic
elasticity, antiferromagnets
1. Introduction
It is of common knowledge that the solids, in contrast to soft matter materials, have a fixed,
invariable shape. Variation of physical properties (including deformation) induced by external
fields is described locally, in the thermodynamic limit, which excludes the sample boundaries from
consideration. Soft matter (such as liquids, gels, etc.), as usual, has got fixed local properties
(invariable in the presence of external fields) but can easily change the shape under the effect of
thermal stresses or thermal fluctuations. However, the divide between the soft and “hard” matter
is rather conditional because some solids can also change their shape without variation of the
sample volume and local characteristics (like magnetization, polarization, etc). Good example of
such shape-flexible systems is given by the nano-sized particles of antiferromagnetic (AFM) or
martensitic materials.
The materials of these types show noticeable spontaneous deformations coupled with the pri-
mary order parameter (related to spin or charge distribution). Moreover, equilibrium states are
usually realized in a set of different but equivalent configurations (domains) with the different
strain tensors. The shape of the sample then depends on the domain structure (DS) and in many
cases can be easily changed by small external fields.
While the physical mechanism of the DS formation is related with the sample boundary, recon-
struction and restructurization of the domains under external fields depend upon the properties
of the domain walls. If the potential barrier for the domain wall formation is high, the behaviour
of the sample is solid-like, the switching between different macroscopic states is sharp, and field
dependence of macroscopic properties shows a hysteresis. In an opposite case of low potential
barrier, reconstruction of the DS takes place through nucleation and growth of new domains and
shows the features of liquid-like behaviour: nonhysteretic transitions between different macroscopic
states, shape deformation, etc. The most interesting case on which we concentrate our attention in
the present paper, lies in-between: i.e., in multiferroics with the domains of different nature some
types of domains can easily nucleate and show soft-like behaviour while the others could have high
nucleation barrier and reveal themselves as solids. In particular, we consider a multiferroic (like
Sr2Cu3O4Cl2 or Ba2Cu3O4Cl2) that simultaneously shows ferromagnetic (FM) and AFM ordering
on different systems of copper ions [1].
∗E-mail: malyshen@ukrpack.net
c© H.V. Gomonay, I.G. Kornienko, V.M. Loktev 23701-1
http://www.icmp.lviv.ua/journal
H.V. Gomonay, I.G. Kornienko, V.M. Loktev
The DS in such a material is characterized by two independent (FM and AFM) order parame-
ters. Though macroscopic state of both FM and AFM could be controlled by the same, magnetic,
field, the responses of the FM and AFM domain structures are different, as illustrated in figure 1.
The domain structure of FMs reconfigures in the magnetic field which is parallel to magnetiza-
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Figure 1. Behaviour of the FM (a) and AFM (b) DS in the external magnetic field H. In the
absence of field both types of domains (shown by arrows) are equally represented. (a) FM do-
mains have opposite direction of magnetization vector. The magnetic field which is parallel to
an easy axis (upper panel) removes degeneracy of the domains. As a result, the fraction of favor-
able domain increases. If H is perpendicular to easy axis, both types of domains are equivalent,
the domain fraction does not change, the magnetic field induces tilt of magnetizations (lower
panel). (b) AFM domains have different (perpendicular) orientation of AFM vectors. Degener-
acy of domains is removed for any of two mutually perpendicular orientations of magnetic field.
tion and does not change if the magnetic field H is perpendicular to magnetization. In any case,
switching between different domain states or smooth variation of the DS has an effect on macro-
scopic magnetization of the sample that grows linearly with the field value. The shape of the sample
remains invariant. In contrast, the DS in antiferromagnets reconfigures for both (mutually perpen-
dicular) orientations of the magnetic field and gives rise to variation of macroscopic deformation
(and, hence, the shape) of the sample proportional to H2. So, a material that at the same time
bears the features of FM and AFM can show some new type of behaviour governed by competition
between the domains of different nature in the external magnetic field.
In the present paper we analyze the physical mechanisms of soft-like behaviour in a multiferroic
that combines shape softness of AFMs and magnetic softness of FMs.
We dedicate this paper to the 50-th anniversary of a well-known Ukrainian physicist
Prof. I.M. Mryglod who greatly contributed into the field of soft-matter and, in particular, into the
theory of magnetic liquids and whose results have deepened our understanding of corresponding
systems.
2. Shape softness induced by magnetoelastic interactions
In FM and in ferroelectrics, the shape of the sample governs an equilibrium DS but is almost
unchanged under the field effect because i) the domains with opposite magnetization/polarization
have the same strain tensor; ii) magnetoelastic coupling in these materials is usually much weaker
compared to AFMs and martensites. On the contrary, in ferroelastic materials (such as martensites
and AFMs with the pronounced magnetoelastic coupling) the shape of the sample is, in a certain
23701-2
Possibility of soft-matter effects in solids
sense, a free thermodynamic variable that can be adjusted by application of external fields. In this
Section we present a general approach to a consideration of shape-related effects in AFMs.
Let us consider a tetragonal easy plane AFM in which AFM ordering is accompanied by the
appearance of magnetoelastic strains. Equilibrium orientation of AFM vector L and deformations
described by the strain tensor û could be found by minimization of the free energy Φ of the sample.
In the finite-size sample the potential Φ includes the bulk- (b) and the surface- (S) dependent terms
and, in the simplest case, (in neglection of a spin-dependent surface tension) it could be written
as follows:
Φ =
∫
V
[
f (mag)(L) − û : λ̂ : L ⊗ L +
1
2
û : ĉ : û
]
dV +
1
2
∮
S
{
K(S)
[
(L · τ1)2 + (L · τ2)2
]
}
dS. (1)
Here f (mag)(L) is the density of magnetic anisotropy energy within the bulk of the sample, the
4-th order tensors λ̂ and ĉ are magnetoelastic and elastic constants, respectively, V is the sample
volume. The last term in equation (1) is the surface energy that originates from the difference
in the atomic environment in the bulk and at the surface. Vectors τ1,2 are space-dependent unit
vectors tangential to the sample surface S.
Spatial distribution of L(r) and a displacement vector u(r) are then calculated from the set of
differential equations
δf (mag)
δL
= L · λ̂ : ∇⊗ u, ∇ · ĉ : ∇⊗ u = ∇ · λ̂ : L ⊗ L, (2)
with the (nontrivial) boundary conditions
K(S)
[
τ1(L
(S) · τ1) + τ2(L
(S) · τ2)
]
= 0, n · ˆ̂c : ∇⊗ u |S = n · ˆ̂
λ : L(S) ⊗ L
(S), (3)
where n is a surface S normal at a given point rS .
Analysis of equations (2) and (3) shows that for an arbitrary orientation of sample faces (i.e.,
vectors τ1,2) equilibrium orientations of AFM vector within the bulk (L(b)) and at the surface
(L(S)) are different, L
(b) 6= L
(S). This means that an AFM vector L and, as a result, a strain
tensor û are space dependent functions. Due to the long-range character of the elastic forces this
gives rise to the formation of equilibrium DS consistent with the shape of the sample.
To elucidate this point let us suppose that space dependence of L(r) is known. In this case the
second of equations (2) for the displacement vector u together with the boundary conditions (3) is
treated as a Neuman problem. Once Green function Ĝ(r, r′) of an operator ∇ · ĉ · ∇ is known, an
equilibrium tensor of magnetoelastic strains can be presented as a symmetrized (sym) combination
of the distortion, namely,
û(r) = λ̂ : (L(b) ⊗ L
(b)) + sym
∮
S
[
L
(S) ⊗ L
(S) − L
(b) ⊗ L
(b)
]
: λ̂ · ∇ · Ĝ(r, r′)dS′. (4)
The first term in (4) is a standard magnetostriction that usually arises in the thermodynamic
limit (when the surface effects are ignored). It can have different values if L
(b) is degenerated
(magnetic anisotropy allows the states with different, noncollinear orientations of AFM vector).
The second term, which is generally nonzero, depends upon the shape of the sample. It represents
an additional strain induced by the surface “magnetoelastic charges”. If the surface curvature is
not too large (characteristic scale of τ1,2 and L
(S) variation is much larger than the magnetic
inhomogeneuity length), then, equilibrium magnetic structure of the sample consists of domains
that in average compensate the field of magnetoelastic “charges”. Equilibrium shape of the sample
can be characterized by an average deformation which in this particular case is equal to
〈û〉 = λ̂ : 〈L(b) ⊗ L
(b)〉 ≡
∑
j
λ̂ : L
(b)
j ⊗ L
(b)
j ξj , (5)
23701-3
H.V. Gomonay, I.G. Kornienko, V.M. Loktev
where ξj is the volume fraction of the domain of j type.
Figure 2 illustrates some possible shape effects induced by the surface energy. In the magneti-
cally homogeneous sample (figure 2 (a)), the preferable orientation of AFM vector at the surface,
L
(S), differs from L
(b) at the “top” and “bottom” faces and sets conditions for the formation of
“magnetoelastic charges” at these faces (see the second term in (4)). Corresponding stress field can
be relaxed in two ways: i) by homogeneous deformation (and corresponding shape variation) if the
sample size is of the order of magnetic inhomogeneity, figure 2 (b); ii) by forming a fine DS that
compensates the stress field in average, figure 2 (c). Restructurization of the DS in the external
magnetic field is related with the shape variation, as shown in figure 2 (d).
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Figure 2. Destressing effects in an AFM of rectangular shape. (a) Single domain sample. Equi-
librium orientation of the bulk, L
(b), and the surface, L
(S), AFM vectors are different at some
faces. Shaded area shows surface regions. (b) Misfit between L
(b) and L
(S) induces elongation of
“favourable” (shown with arrows) and contraction of “unfavourable” faces. Orientation of AFM
vector at the surface (not shown) is the same as in (a). (c) DS eliminates the misfit between
L
(b) and L
(S) in average. The shape of the sample is not changed. (d) External magnetic field
gives rise to restructurization of the DS and, as a consequence, to shape variation.
An effective formalism for the description of the DS in this case is based on consideration of
the destressing energy [2]
Φdest =
V
2
〈L ⊗ L〉 : λ̂ : ℵ̂ : λ̂ : 〈L ⊗ L〉, (6)
where the brackets 〈· · · 〉 mean averaging over the sample volume, as in equation (5). The compo-
nents of the destressing tensor ℵ̂
ℵ̂ ≡ ∇ ⊗∇
∫
V
Ĝ(r − r
′)dV ′ (7)
depend upon the shape of the sample and anisotropy of the elastic forces.
In a particular case of tetragonal crystal cutted in a form of an ellipsoid (semiaxes a > b� c)
whose principal axes X , Y are parallel to an AFM easy plane (see figure 4), the destressing energy
(6) takes a form :
Φdest=
V
2
{
Ndes
2 〈L2
X − L2
Y 〉 +Ndes
is
[
〈L2
Y − L2
X〉2 + 4〈LXLY 〉2
]
−Ndes
4an[〈L2
X − L2
Y 〉2 − 4〈LXLY 〉2]
}
.
(8)
23701-4
Possibility of soft-matter effects in solids
An explicit form of the effective shape-induced anisotropy constants N des depends upon the elastic
and magnetoelastic properties of the crystal which we assume to be isotropic (that means, in
particular, the following relation between the elastic modula: c11 − c12 = 2c44). Then [2],
Ndes
is =
λ2(3 − 4ν)
8c44(1 − ν)
, Ndes
2 =
c
b
· [λ2(2 − 3ν) + λvλ]J2(k)
4c44(1 − ν)
, Ndes
4an =
c
b
· 2λ2J4(k)
3c44(1 − ν)
, (9)
where λ, λv are magnetoelastic constants, c44 is the shear modulus, ν = c12/(c11 + c12) is the
Poisson ratio and we have introduced the dimensionless shape-factors J2,4(k) as follows
J2(k) =
π/2
∫
0
(sin2 φ+ cos 2φ/k2)dφ
√
1 − k2 sin2 φ
, J4(k) =
π/2
∫
0
(1 − 8 cos 2φ− k2 sin2 φ+ 8 cos 2φ/k2)dφ
√
1 − k2 sin2 φ
.
(10)
Here the parameter k2 = 1 − b2/a2 depends upon the aspect ratio b/a of the sample.
In the next section we will show how to change an average deformation (5) and, correspondingly,
the shape of multiferroic by application of small external field.
3. Field-induced variation of the sample shape
We consider the model FM+AFM multiferroic [3–5] whose magnetic structure consists of two
weakly coupled subsystems, AFM, and FM, localized on different types of magnetic ions CI and
CII, as shown in figure 3. A FM subsystem is unambiguously described by a magnetization vector
MF and an AFM subsystem is described by two vectors: an AFM vector L = (S1−S2 +S3−S4)/4
and a FM vector M =
∑
j Sj/4.
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Figure 3. Magnetic structure of a square lattice in two domain configurations. Magnetic field is
parallel to 〈110〉. Two types of magnetic ions are represented with the filled and hollow circles.
The FM ordered moments of CII could be (a) parallel (domain A) or (b) perpendicular (domain
B) to the applied magnetic field. Small canting of the CI spins induced by the external magnetic
field is not shown.
In the absence of the external field, the FM moments at CII sites are oriented along 〈110〉
crystal directions perpendicular to the staggered magnetizations of AFM subsystem, as shown in
figure 3. Due to tetragonal symmetry of the crystal, an equilibrium magnetic structure can be
realized in four types of equivalent domains (figures 3 and 4). Types A and B could be thought
of as AFM domains because they correspond to different orientations of L vector and thus are
sensitive to the orientation of magnetic field H with respect to crystal axes (see figure 1). Types
23701-5
H.V. Gomonay, I.G. Kornienko, V.M. Loktev
A1 and A2 (and, correspondingly, B1 and B2) are FM domains. They have opposite direction of
MF vector and could be removed from the sample by H‖MF.
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Figure 4. Four types of magnetic domains. Axes x and y are parallel to 〈100〉 crystal directions.
An external magnetic field H‖[110] (if any). Types A and B have different orientations of AFM
vector, types 1 and 2 correspond to opposite directions of FM vector MF. Ellipse (dash line)
images the shape of the sample and its orientation with respect to crystal axes.
Phenomenological description of the DS is based on the analysis of free energy potential Φ
that consists of three terms: the bulk magnetic energy Φmag, the destressing energy Φdest (see
equation (8)) that implicitly includes the surface contribution, and stray (demagnetizing) energy
Φstray,
Φ = Φmag + Φdest + Φstray . (11)
Following the papers [1, 4, 6] we take the magnetic energy in a form:
Φmag =
∫
V
dV
{
4
M2
0
[
2J0M
2 + JavM · MF + JpdMFσ̂zL
]
− 8
M4
0
K‖L
2
xL
2
y −H ·MF − 2H ·M
}
.
(12)
HereM0 is CI sublattice magnetization, orthogonal axes x and y are parallel to the crystal directions
[100] and [010], respectively. J0 is an exchange constant responsible for the AFM ordering, Jav and
Jpd describe, respectively, isotropic and anisotropic pseudodipolar interactions between the FM
and AFM subsystems, K‖ is in-plane anisotropy, σ̂z is a Pauli matrix.
For an elliptic-shaped sample, the stray energy can be written as follows:
Φstray =
V
2
[
Ndm
a 〈MFX + 2MX〉2 +Ndm
b 〈MFY + 2MY 〉2
]
. (13)
The components of demagnetization tensor Ndm
a,b are calculated in a standard way [7]
Ndm
a =
4πc
a
√
1 − k2
π/2
∫
0
sin2 φdφ
√
1 − k2 sin2 φ
, Ndm
b =
4πc
√
1 − k2
a
π/2
∫
0
cos2 φ dφ
√
1 − k2 sin2 φ
. (14)
Equations (12), (13), and (8) could be substantially simplified if we take into account that:
i) far below the Néel temperature the sublattice magnetizations M0 and MF are constant; as a
result, ii) L ⊥ M and L
2 +M
2 = M2
0 (normalization conditions); iii) if the magnetic field is much
23701-6
Possibility of soft-matter effects in solids
smaller than spin-flip field, H � J0/M0, the magnetization induced in AFM subsystem is small1,
M � M0, and vector M can be excluded from (12) as follows [8]:
M =
1
8J0
[
L ×
[(
H− 2
Jav
M2
0
MF
)]]
; (15)
iv) if an out-of-plane anisotropy is strong enough, all the magnetic vectors lie within xy (and,
equivalently, XY ) plane and could be described with the only angle variable, as shown in figure 4:
Lx = M0 cos θ, Ly = M0 sin θ; MFx = MF cosϕ, MFy = MF sinϕ. (16)
With account of the relations (15) and (16), the free energy (11) takes the following form
Φ = V
{
4MF
M0
Jpd〈cos(θ + ϕ)〉 +K‖〈cos 4θ〉− J2
avM
2
F
8J0M2
0
〈cos 2(θ−ϕ)〉 − Jav
8J0
HMF〈cos(2θ − ψ − ϕ)〉
− HMF
(
1− Jav
8J0
)
〈cos(ϕ− ψ)〉 +
H2M2
0
32J0
〈cos 2(θ − ψ)〉 − 1
2
Ndes
2 〈cos 2(θ − ψ)〉
+
1
2
M2
F
[
Ndm
a 〈cos(ϕ− ψ)〉2 +Ndm
b 〈sin(ϕ− ψ)〉2
]
+
1
2
(
Ndes
is +Ndes
4an
)
〈cos 2(θ − ψ)〉2 + 2
(
Ndes
is −Ndes
4an
)
〈sin 2(θ − ψ)〉2
}
. (17)
where ψ is an angle between magnetic field and x-axis, and we assume that the field is parallel to
one of the principal axes of the sample.
For the rest of the paper we assume that the magnetic field is parallel to one of the easy axes,
H‖[110], so, ψ = π/4. In an infinite sample (all Ndm, Ndes = 0) minimization of Φ with respect to
magnetic variables θ and ϕ gives rise to the four solutions labeled as domains A1,2 and B1,2 (see
figure 4). It should be stressed that in contrast to pure AFMs, the configurations with (MF,L)
and (MF,−L) are inequivalent, due to anisotropic pseudodipolar interactions (described by the
constant Jpd). Figure 5 illustrates the field-induced variation of equilibrium magnetic configurations
(represented by X-projections of MF and L vectors) obtained from the numerical minimization of
expression (17) with the data taken from [1, 4, 6].
One can distinguish three field intervals. At small fields, |H | 6 Hs−f1 ∝ Jpd, the DS of the
sample may include all four domain types. However, the energies Ej (j = A1, 2, B1, 2) of the states
are different: EA1 < EB < EA2 (domains B1 and B2 are equivalent if H‖[110]). In the interval
Hs−f1 < |H | < Hs−f2 ∝
√
J0K‖ the DS may consist of only FM domains, A1 and A2. At last, at
|H | > Hs−f2 the sample is a single domain (A1).
It can be seen from figure 5 (a) that the formation of AFM, B-type domain is energetically
preferable than the formation of FM domain A2. So, for certain conditions, the DS structure of a
sample may consist of the domains of only two types, A1 and B. This means that the field induces
the variation of average deformation
〈uXX − uY Y 〉 ∝ 〈cos 2(θ − ψ)〉 =
|H |M0
mF(Ndes
is +Ndes
4an)
, (18)
and, as a result, variation of the shape. It is interesting that in contrast to pure AFMs, 〈cos 2(θ −
ψ)〉 ∝ |H | (not to H2). This nontrivial behaviour is due to the presence of FM subsystem. Really,
relative fraction of A1 and B domains is proportional to the energy difference EB − EA1. The
main contribution into this difference arises from interaction of FM subsystem with the external
magnetic field (Zeeman term HMF in equation (12)). Magnetic susceptibility of shape/deformation
(= d〈u〉/dH) is inversely proportional to the destressing coefficient and can be much higher than
1 In FM+AFM multiferroic we have an additional (compared to pure AFM) limitation, JavMF � J0M0, which
means that the coupling between the FM and AFM subsystems should be weaker than the exchange interaction
between AFM coupled sites.
23701-7
H.V. Gomonay, I.G. Kornienko, V.M. Loktev
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Figure 5. Stability ranges of homogeneous configuration shown in figure 4 in the external mag-
netic field H‖[110]. (a) Energy of equilibrium homogeneous state vs H. (b), (c) Normalized
projections of FM and AFM moments on the field direction. Field induces rather noticeable
rotation of MF vector toward field direction (b) and slight tilt of L vector (c). Loss of stability
takes place at critical values H = Hs−f1,2, as shown with arrows.
in a pure AFM (where all the effects are enhanced due to the exchange coupling and N des should
be substituted for
√
NdesJ0).
Thus, in the FM+AFM multiferroic, the shape variation can be induced by small (compared
to pure AFMs) external magnetic field.
4. Conclusions
We have analyzed some possible shape effects in magnetoelastic materials and found a certain
duality that makes these solids similar to soft matter. In particular, not only the shape of the
sample affects its macroscopic parameters, such as magnetization, polarization, etc., but also the
field-induced variation of macroscopic parameters can define the sample shape. Change of the
shape may proceed by reconstruction of the DS. Susceptibility of the shape to the external fields
can be increased by the use of multiferroics instead of pure ferroelastic materials. In particular,
field dependence of the average deformation switches from quadratic (in pure AFMs) to linear (in
FM+AFM multiferroics).
An analogous treatment can be applied to multiferroics that combine electric polarization with
AFM ordering. Soft-like behaviour of these materials (if any) may open new ways to control the
shape of the sample with the electric field.
Acknowledgements
This work was partially supported by the Special Programme of Fundamental Research of the
Department of Physics and Astronomy of National Academy of Science, Ukraine.
23701-8
Possibility of soft-matter effects in solids
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Про можливiсть ефектiв м’якої матерiї в твердих тiлах
О.В. Гомонай1,2, Є.Г. Корнiєнко2, В.М. Локтєв1
1 IТФ НАН України iм. М.М. Боголюбова, вул. Метрологiчна 14-б, 03680, Київ, Україна
2 Нацiональний технiчний унiверситет України “Київський полiтехнiчний iнститут”,
пр. Перемоги, 37, 03056, Київ, Україна
Характерною рисою м’якої матерiї є її властивiсть змiнювати форму пiд впливом слабких зовнiшнiх
полiв. В роботi показана можливiсть аналогiчної змiни форми в твердих тiлах, якi поєднують вла-
стивостi антиферо- та феромагнiтних матерiалiв та мають сильний магнiтопружний зв’язок. Макро-
скопiчнi деформацiї зразка в зовнiшньому магнiтному полi виникають за рахунок антиферомагнiтної
складової, а феромагнiтна компонента обумовлює високу сприйнятливiсть доменної структури.
Ключовi слова: доменнi стiнки та доменна структура, ефекти форми, термопружнiсть та
електромагнiтна пружнiсть, антиферомагнетики
23701-9
Introduction
Shape softness induced by magnetoelastic interactions
Field-induced variation of the sample shape
Conclusions
|
| id | nasplib_isofts_kiev_ua-123456789-32098 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1607-324X |
| language | English |
| last_indexed | 2025-12-07T18:32:13Z |
| publishDate | 2010 |
| publisher | Інститут фізики конденсованих систем НАН України |
| record_format | dspace |
| spelling | Gomonay, H.V. Kornienko, I.G. Loktev, V.M. 2012-04-08T16:21:05Z 2012-04-08T16:21:05Z 2010 Possibility of soft-matter effects in solids / H.V. Gomonay, I.G. Kornienko, V.M. Loktev // Condensed Matter Physics. — 2010. — Т. 13, № 2. — С. 23701: 1-9. — Бібліогр.: 8 назв. — англ. 1607-324X PACS: 75.60.Ch, 46.25.Hf, 75.50.Ee https://nasplib.isofts.kiev.ua/handle/123456789/32098 Shape variation under the action of small external fields is a peculiar feature of soft matter. In the present paper we demonstrate a possibility of the analogous shape variation in the solids that combine the properties of antiferro- and ferromagnetic materials and show strong magnetoelastic coupling. The antiferromagnetic subsystem provides a macroscopic deformation of a sample in the external magnetic field while the ferromagnetic component ensures high susceptibility of the domain structure. Зазначено, що характерною рисою м'якої матерії є її властивість змінювати форму під впливом слабких зовнішніх полів. Показано можливість аналогічної зміни форми в твердих тілах, які поєднують властивості антиферо- та феромагнітних матеріалів і мають сильний магнітопружний зв'язок. Макроскопічні деформації зразка в зовнішньому магнітному полі виникають за рахунок антиферомагнітної складової, а феромагнітна компонента обумовлює високу сприйнятливість доменної структури. This work was partially supported by the Special Programme of Fundamental Research of the Department of Physics and Astronomy of National Academy of Science, Ukraine. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Possibility of soft-matter effects in solids Про можливість ефектів м'якої матерії в твердих тілах Article published earlier |
| spellingShingle | Possibility of soft-matter effects in solids Gomonay, H.V. Kornienko, I.G. Loktev, V.M. |
| title | Possibility of soft-matter effects in solids |
| title_alt | Про можливість ефектів м'якої матерії в твердих тілах |
| title_full | Possibility of soft-matter effects in solids |
| title_fullStr | Possibility of soft-matter effects in solids |
| title_full_unstemmed | Possibility of soft-matter effects in solids |
| title_short | Possibility of soft-matter effects in solids |
| title_sort | possibility of soft-matter effects in solids |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/32098 |
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