Electric Control of Spin Helicity in a Magnetic Ferroelectric

0.64 MB·English

by  Y. Yamasaki

Electric Control of Spin Helicity in a Magnetic Ferroelectric
Y. Yamasaki1, H. Sagayama2, T. Goto1, M. Matsuura3, K. Hirota3, T. Arima2,4 and Y. Tokura1,4,5
1Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan
2Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577, Japan
3The Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
4Spin Superstructure Project, ERATO, Japan Science and Technology Agency, Tsukuba 305-8562, Japan and
5Correlated Electron Research Center (CERC), National Institute of Advanced
7
Industrial Science and Technology (AIST), Tsukuba 305-8562, Japan
0
(Dated: February 6, 2008)
0
2 Magnetic ferroelectrics or multiferroics, which are currently extensively explored, may provide a
n good arena to realize a novel magnetoelectric function. Here we demonstrate the genuine electric
a control of the spiral magnetic structure in one of such magnetic ferroelectrics, TbMnO3. A spin-
J polarized neutron scattering experiment clearly shows that the spin helicity, clockwise or counter-
8 clockwise, is controlled by the direction of spontaneous polarization and hence by the polarity of
1 thesmall cooling electric field.

]
l Electric control of magnetic spins or their ordering ing Tb, Dy, and their solid solution, have recently been
e
- structurehaslongbeenabigchallengeincondensedmat- demonstratedtoundergoaferroelectrictransitionatthe
r
t ter physics. Furthermore, manipulating the magnetiza- Curie temperature TC of 20 − 30 K (see the example
s
tionbyelectricfieldmayprovidealowenergy-consuming shown in Fig. 1(c)) [13, 14]. Below T ∼ 40 K, the
. N
t
a wayinspin-electronicsandahigherdatadensityininfor- compounds undergo a long-range spin ordering with the
m mation storages[1, 2]. There are a number of magneto- modulationvectorQ =(0,±q,1)withq =1/2−1/4(in
s
- electric materials whose magnetization can be changed, Pbnm orthorhombic setting)[9, 15]. This has been as-
d
though minutely, with an externalelectric field, yet only cribedtothe spinfrustrationeffectcausedbythe combi-
n
o averyfewareknownwhosemagneticstructureitselfcan nation of GdFeO3-type distortion and staggered orbital
be controlled by an electric field[1, 3, 4, 5]. The use of order (so-called C-type orbital order) [9, 16]. The fer-
c
[ ferroelectricity is perhaps indispensable to enhance the roelectricity in this antiferromagnet is derived from the

electric field action on the magnetic spins.[2] transverse-spiral or cycloidal spin ordering[17, 18] (Fig.
1
v One of the robust mechanisms to produce the fer- 1(a) and (b)) in accord with the KNB model[6], being
0 distinct from the collinear spin configuration at higher
roelectricicty of magnetic origin has been recently pro-
3 temperatures, T < T < T . In a single crystal of
posed by Katsura, Nagaosa, and Balatsky (KNB) [6]. C N
4
1 The overlap of the electronic wave function between the TbMnO3 (orthorhombic with the space group Pbnm at
roomtemperature)investigatedhere,asinusoidalincom-
0 two atomic sites (i and i + 1) with mutually canted
7 spins (Si and Si+1) can generate electric polarization, mensurate antiferromagnetic ordering of the Mn3+ mo-
0 pi = Aei,i+1 × (Si × Si+1), where ei,i+1 denotes the ments takes place at TN = 42 K with a magnetic wave
/ vector q ∼ 0.27[9, 15]. The ferroelectric polarization
t unit vector connecting the two sites and A is a con-
a along the c-axis (P ) emerges upon the magnetic phase
stant determined by the spin exchange interaction and c
m
transitionfrom the collinear(kb) to the transversespiral
the spin-orbit interaction. (Note that the similar the-
- spin structure at T =27 K (Fig. 1(c)).
d oretical results have been obtained independently also C
n in refs. [7, 8]). In case the transverse-spiral (cycloidal)
The helicity of such a transverse-spiral magnetic
o spin order is realized (Fig. 1(b)), the uniform sponta-
structure can be ascertained by the polarized-neutron-
c
neous polarization is expected to emerge as the sum of
: diffractionintensityofmagneticsatellitereflection[19,20,
v the local polarization p in the direction perpendicular
i 21,22,23]. Thespinhelicityisdeterminedbymeasuring
i
X to the spiralpropagationvector and the vector chirality, intensities of two magnetic satellites with the polarized
r C ≡ iSi × Si+1 (ref. [6]). This spin-driven ferro- neutron spin Sn parallel and anti-parallel to the vector
a electricPity has recently been found in several transverse- chiralityC. The firstsuccessfulcontrolofthe spinhelic-
spiralmagnetssuchasTbMnO3 (ref. [9]), Ni3V2O8 (ref. ity as demonstrated by a polarized neutron diffraction
[10]), MnWO4 (ref. [11]), and also in a transverse cone- study was on a spinel crystal of ZnCr2Se4 which was
spiral magnet CoCr2O4 (ref. [12]). We report here the cooledthroughthe helical spintransitionpoint in simul-
quantitativeelucidationofsuchmagneticallyinducedfer-
taneously applied magnetic and electric fields[23]. This
roelectricity in terms of the spin ellipticity as the order
materialexhibits a proper screw spin structure below 20
parameter and show the successful electric control be-
K, which can host no ferroelectric polarization of mag-
tweentheclockwise(CW)andcounter-clockwise(CCW)
netic origin because of the spin helicity C being parallel
spin helixes.
to the modulation vector Q . As a result, a magne-
m
Afamilyofperovskitemanganites,RMnO3 withRbe- toelectric cooling procedure with relatively strong field
2
40min. AHeuslermonochromatorwasutilizedtoobtain
(cid:0)(cid:0)(cid:0)
thespin-polarizedneutronbeamwithakineticenergyof
(cid:4)(cid:4)(cid:4)(cid:5)(cid:5)(cid:5)(cid:6)(cid:6)(cid:6)
36.0meV.Thespinoftheneutronbeamcouldbeflipped
(cid:1)(cid:1)(cid:1)(cid:1)(cid:1) by a spin-flipper, so as to be parallel (when the flipper
(cid:7)(cid:7)(cid:7)
(cid:2)(cid:2)(cid:2)(cid:2)(cid:2) was off) or anti-parallel(on) to the scattering vector Qs
with a guide-fieldofabout 1 mT applied by a Helmholtz
(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)
(cid:8)(cid:8)(cid:8) coil, as depicted in Fig. 2(b). The spin flipping ratio of
the incident neutron beam was 11.6(4). All the neutron
(cid:9)(cid:9)(cid:9)(cid:9)
diffraction measurements were performed without appli-
(cid:4)(cid:4)(cid:4)(cid:5)(cid:5)(cid:5)(cid:6)(cid:6)(cid:6)
cationofelectricfieldaftercoolingthesamplefrom50K
in a poling field (160 kV/m). Peak profiles of magnetic
(cid:7)(cid:7)(cid:7) satellite reflections(4,+q,1)and(4,−q,1)with q ∼0.27
wereobtainedbyrotatingthesamplearoundthevertical
(cid:10)(cid:10)(cid:10)
axis, which approximately corresponded to the L scan
in the reciprocal space (see Fig. 2(a)). For the mea-
...),/),/),/+++---*** (cid:16)(cid:16)(cid:16)(cid:11)(cid:11)(cid:11)(cid:11)(cid:11)(cid:11) 8888889;9;9;:::::: (cid:16)(cid:16)(cid:16) ###///!!!(((555 wsuarsemmeenatsuorfeedlewctitrhicapnolealreicztartoimonetPer,(pKyeriotehlleecytr6ic51c7uArr)enint
((( 777 a warming run without the application of electric field
%%%
###!!!&&& 444555666 after cooling the sample in a poling field (80 kV/m).
###&"&"&"’’’ (cid:11)(cid:11)(cid:11) (cid:11)(cid:11)(cid:11) )))&"&"&" Figure2(c)showstheL-scanprofilesofmagneticsatel-
(cid:30)(cid:30)(cid:30)%%% 333
(cid:30)#(cid:30)#(cid:30)#(cid:29)$(cid:29)$(cid:29)$!!!(cid:31) " (cid:31) " (cid:31) " (cid:17)(cid:17)(cid:17)(cid:16)(cid:16)(cid:16)(cid:11)(cid:11)(cid:11)(cid:11)(cid:11)(cid:11) <<<=== <<<>>> (cid:17)(cid:17)(cid:17)(cid:16)(cid:16)(cid:16) 000000111222 wElithe=ischa±tw1Qe6rs0e=mkVe(a4/s,mu±rqea,ds1)ashfftooewrrntchoieonlfienFrgirgoi.enle2ac(ntbr)eic.lescIttnarticethfiaeetlcd9asoKef
of P > 0, the intensity of the satellite (4,+q,1) is ap-
(cid:11)(cid:11)(cid:11) (cid:12)(cid:12)(cid:12)(cid:11)(cid:11)(cid:11) (cid:13)(cid:13)(cid:13)(cid:11)(cid:11)(cid:11) (cid:14)(cid:14)(cid:14)(cid:11)(cid:11)(cid:11) (cid:15)(cid:15)(cid:15)(cid:11)(cid:11)(cid:11) (cid:16)(cid:16)(cid:16)(cid:11)(cid:11)(cid:11) c
proximately9timesashighwithneutronspin(S )anti-
(cid:18)(cid:18)(cid:18)(cid:19)(cid:19)(cid:19)(cid:20)(cid:20)(cid:20)(cid:21)(cid:21)(cid:21)(cid:19)(cid:19)(cid:19)(cid:22)(cid:22)(cid:22)(cid:23)(cid:23)(cid:23)(cid:24)(cid:24)(cid:24)(cid:25)(cid:25)(cid:25)(cid:22)(cid:22)(cid:22)(cid:19)(cid:19)(cid:19)(cid:26)(cid:26)(cid:26)(cid:27)(cid:27)(cid:27)(cid:28)(cid:28)(cid:28) n
parallel(I )tothescatteringvectorQ asthatwithpar-
↓ s
allelS (I ). Asforthesatellite(4,−q,1),conversely,I
n ↑ ↑
is much stronger than I . These behaviors are typical of
↓
FIG.1: (ColorOnline)(a)Aschematictransverse-spiral(cy-
a spiral magnet with a single helicity, where the spiral
cloidal)magneticstructureofTbMnO3 (a×4b×c/2inPbnm
plane is almost perpendicular to the scattering vector.
orthorhombiccell)intheferroelectricphasebelowTC =27K.
(b) A schematic magnetic structure projected onto bc-plane Here, it is to be noted that the spiral plane of TbMnO3
(including the both a =0 and a=1/2 planes). The electric is perpendicularto thea axis. Whenthe directionofthe
polarization P emerges along the c-axis, that is the direc- cooling electric field is reversed,the intensity I of satel-
↑
tion perpendicular to the spiral propagation vector and the lite (4,+q,1) becomes much stronger than I , demon-
↓
spin vector chirality. (c) Temperature dependence of electric
stratingthatthe opposite helicitydomainbecomes dom-
polarization alongthec-axisandthedifferenceoftheintensi-
inant. ThereversaloftheratioofI toI inducedbythe
tiesofmagneticsatellites(4,+q,1)whenspinsoftheneutron ↓ ↑
beamsisanti-parallelandparalleltoscatteringvector,I↓−I↑, reversalof the poling electric field suggests that the spin
with cooling electric field E >0 and E <0. helicitycanbesuccessfullycontrolledbyapolingelectric
field.
In the following, we consider the interrelation among
magnitudeswasnecessaryforthe controlofspinhelicity. the electric polarization, the spin helicity, and the cross
Bycontrast,thespontaneouspolarizationemergesinthe section of the elliptical spiral magnetic structure. In the
presenttransverse-spiralmagnetTbMnO3 withC ⊥Qm transverse-spiral magnetic phase below 27 K, the mag-
inwhichthespinhelicityisexpectedtobecontrolledonly netic moment M on the i-th Mn site is described as
i
withaweakcoolingelectric-fieldenablingtheproduction
of the single-domain ferroelectric state. M =m cos(2πQ ·R )+m sin(2πQ ·R ). (1)
i b m i c m i
A single crystal of TbMnO3 was grown by a floating-
zonemethodinaflowofArgas. Thecrystalwascutinto It was reported for TbMnO3 that mb ∼ (0,3.9,0)µB
athinplatewiththewidestfaceof(001)andathickness and m ∼ (0,0,2.8)µ at 15 K by a magnetic structure
c B
of 2.5 mm. Aluminum electrodes were deposited onto analysis[17,18]. Thismagneticmodulationproducestwo
thewidestfaces. Spinpolarizedneutrondiffractionmea- satellite peaks around each fundamental reflection. The
surementswereperformedwithatriple-axisspectrometer crosssectionsoftherespectivesatellites(4,±q,1)arecal-
PONTA at JRR-3, Japan. The sample was mounted on culated as
asapphireplate inaclosed-cycleheliumrefrigeratorand
±
irradiated with a spin-polarized neutron beam. The col- dσ
=I m2+m2∓2m m (Sˆ ·Cˆ) . (2)
limationofthe incident andscatteredneutronbeamwas (cid:18)dΩ(cid:19) on b c b c n o
3
UU VV DD __‘‘aabbbbFFIINNKK NNOOOO (plotted in Fig. 3(b)) were corrected with taking into
EEFFGGHHIIJJKK RR RRR account the imperfect spin polarization (about 92 %) of
SS SSS
the incident neutron beam prior to the calculation of el-
XXYYZZ]][[ZZ[[\\ XXYYZZ[[ZZ[[\\ ccTT PPQQLLL ccTT PPQQ lipticity. The magnetic satellite shows up below TN, but
XXYYZZ^^ZZ^^\\ WW PPTT MMMM PPTT ??@@AABB there is no difference between I↓ and I↑ because of the
ddeeffgghhii sinusoidally modulated collinear spin structure. The dif-
XXYYZZ]][[ZZ]][[\\ XXYYZZ[[ZZ]][[\\ ference betweenI↓ andI↑ emergesuponthe ferroelectric
phase transition at T due to the CCW spiral magnetic
C
CC (cid:157)(cid:157) structure. We showinFig. 3(a)the ellipticity ofthe spi-
(cid:139)(cid:139)(cid:140)(cid:140)(cid:141)(cid:141)(cid:142)(cid:142)(cid:143)(cid:143)(cid:144)(cid:144)(cid:145)(cid:145)(cid:146)(cid:146)(cid:147)(cid:147)(cid:148)(cid:148)
(cid:129)(cid:129)(cid:130)(cid:130)(cid:131)(cid:131)(cid:132)(cid:132)(cid:133)(cid:133)(cid:131)(cid:131)(cid:134)(cid:134)(cid:135)(cid:135) (cid:129)(cid:129)(cid:130)(cid:130)(cid:131)(cid:131)(cid:149)(cid:149)(cid:133)(cid:133)(cid:131)(cid:131)(cid:134)(cid:134)(cid:135)(cid:135) (cid:136)(cid:136)(cid:137)(cid:137) (cid:160)(cid:160)¡¡¢¢££⁄⁄¥¥ƒƒ§§¤¤''¡¡¤¤““««‹‹››¥¥fififlfl‹‹ƒƒ(cid:176)(cid:176)'' (cid:158)(cid:158)(cid:158) ralmagneticstructureofTbMnO3,definedastheratioof
mmjjjjjj ~~(cid:127)(cid:127)(cid:128)(cid:128)jj ~~(cid:127)(cid:127)(cid:128)(cid:128)jj (cid:136)(cid:136)(cid:138)(cid:138) (cid:159)(cid:159)(cid:159) amplitudeofthec-axisspincomponenttotheb-axisspin
}}rqvrqv|| lljjjjjj component in antiferromagnetic modulation, mc/mb, is
suysuynz{{nz{{ppppppoqorvworoqorvworxxtt lmlmkkjjjjjjjjjjjjjjjjjjjj (cid:129)(cid:129)~~(cid:130)(cid:130)(cid:127)(cid:127)(cid:131)(cid:131)(cid:156)(cid:156)(cid:132)(cid:132)(cid:133)(cid:133)jj(cid:131)(cid:131)(cid:134)(cid:134)(cid:135)(cid:135) (cid:129)(cid:129)~~(cid:130)(cid:130)(cid:127)(cid:127)(cid:131)(cid:131)(cid:149)(cid:149)(cid:156)(cid:156)(cid:133)(cid:133)jj(cid:131)(cid:131)(cid:134)(cid:134)(cid:135)(cid:135) (cid:160)(cid:160)''¡¡¤¤““««‹‹››¥¥fififlfl‹‹ƒƒ(cid:176)(cid:176)'' experimentally estimmmcbat=edptoII↓↓th−+epfirIIs↑↑t.approximation, (3)
p p
kkjjjjjj The small angle between the scattering vector and the
vectorchiralityoftheellipsoids(10.6degree)isneglected
jj
jj(cid:150)(cid:150)(cid:151)(cid:151)(cid:152)(cid:152) kk kk(cid:150)(cid:150)jj(cid:152)(cid:152)jj(cid:150)(cid:150)(cid:151)(cid:151)(cid:152)(cid:152) kk kk(cid:150)(cid:150)jj(cid:152)(cid:152)
(cid:134)(cid:134)(cid:129)(cid:129)(cid:153)(cid:153)(cid:150)(cid:150)(cid:154)(cid:154)(cid:150)(cid:150)(cid:155)(cid:155)(cid:150)(cid:150)(cid:135)(cid:135) (cid:134)(cid:134)(cid:129)(cid:129)(cid:153)(cid:153)(cid:150)(cid:150)(cid:154)(cid:154)(cid:150)(cid:150)(cid:155)(cid:155)(cid:150)(cid:150)(cid:135)(cid:135) in this estimate. The induced magnetic moments of Tb
ions were not taken into account because they are re-
ported to be aligned along the a-axis and insensitive to
FIG. 2: (Color Online) (a) L-scans of magnetic satellites theneutronscatteringwithQs approximatelyparallelto
(4,±q,1)withq∼0.27inthepresentexperimentasshownby the a-axis [17]. The ellipticity remains zero in the para-
red arrows in the reciprocal (K,L)-plane. (b) The schematic electric phase and develops below the ferroelectric phase
illustration of the apparatus. The spin of the neutron beam
transitiontemperatureinaccordancewiththeellipsoidal
(Sn) could be flipped by a spin-flipper so as to be parallel
spiralordering. The averageintensity , correspondingto
(when the flipper was off) or anti-parallel (on) to the scat-
the intensity of unpolarized neutron diffraction, almost
tering vector Qs. (c) Electric polarization dependence of in-
tensityofmagneticsatellites(4,±q,1)at9K.L-scanprofiles continuouslychangeseventhroughtheferroelectricphase
of magnetic satellites (4,±q,1) with Pc >0 and Pc <0. (d) transition, while the ellipticity mc/mb discontinuously
Therelation between thespin rotatory direction (orhelicity) changesfromzerotoafinitevalue. Theellipticityat15K
and the direction of electric polarization in TbMnO3. derivedfrom the present experiments, m /m ∼0.63(2),
c b
shows a good agreement with the value (m /m ∼0.72)
c b
determined by the magnetic structure analysis [17], con-
Here, I is the proportional constant determined by the sidering the assumption adopted in the calculation.
o
magnetic structural factor, m = |m |, m = |m |, and The temperature dependence of the polarized neutron
c c b b
the hat symbols indicate the unit vectors. This cross magneticscatteringintensitiesprovidesanotherclearevi-
section (2) is derived from the approximation that the dencethattheferroelectricpolarizationisinseparablyre-
scatteringvectorQ andtheneutronspinsS areparal- lated with the cycloidal spin structure. The KNB model
s n
lel or anti-parallel to the vector chirality C. In the case predictsthattheferroelectricpolarizationshouldbepro-
of CCW spiral magnetic structure (the a-component of portional to mbmc,
vector chirality; C > 0 ), the intensities of (4,+q,1)
a
P =∓Asin(2πqb)m m (4)
are calculated by using Eq. (2); I ∼ I (m −m ) and c b c
↓ o c b
I ∼ I (m +m ) for S being parallel and antiparal-
↓ o c b n where b is the lattice constant. We compare in Fig. 1(c)
lel to Q , respectively. Provided that m /m ∼ 0.7 and
s c b the temperature dependencies of the observed ferroelec-
alsotakingthe spinflippingratiooftheincidentneutron
tric polarizationand the differential intensity of satellite
beam into account, these intensities are in accordance
(4,+q,1), I −I =±4I m m . An excellent agreement
↓ ↑ o b c
withtheobservedrelativesatelliteintensitiesat(4,+q,1)
between the both temperature dependencies clearly con-
for the electric polarization P > 0. It is thus confirmed
c firmsthattheferroelectricpolarizationinthetransverse-
that the CCW spiral magnetic structure corresponds to
spiral magnetic TbMnO3 is proportional to mbmc, and
the electricpolarizationP >0andthe CWtoP <0in
c c hencecanbe explainedwiththe KNBorrelatedmodel.
TbMnO3. In summary, we have investigated the spin helicity of
We show in Fig. 3(b) the temperature dependence spiral magnetic structure in the magnetic ferroelectric
of the Q-integrated polarized-neutron-diffraction inten- TbMnO3bypolarizedneutrondiffractionmeasurements.
sity of the magnetic satellite (4,+q,1) in the P > 0 The intensities of satellite (4,±q,1) with the neutron
c
state. Note that the experimentally obtained intensities spin parallel (I ) and antiparallel (I ) to the scattering
↑ ↓
4
††
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(cid:190)(cid:190)(cid:190)(cid:190)»»»»Æ(cid:226)Æ(cid:226) ––(cid:222)(cid:222)¶¶ (cid:29)(cid:29)(cid:30)(cid:30) aonmtehcehannoinsm-coollfingeeanrermataignngeetliecctorridceprionlgarsizuagtgioesntsasfubrathseedr
(cid:224)(cid:224)(cid:190)(cid:224)(cid:224)(cid:190)(cid:223)(cid:223) (cid:29)(cid:29)(cid:31)(cid:31) possibilities of electrically controllable magnetism.
––
‚‚––––––
The neutron scattering experiments were carried out
(cid:221)(cid:221) (cid:210)(cid:210)(cid:211)(cid:211) (cid:242)(cid:242)(cid:243)(cid:243)(cid:244)(cid:244)–– ˇˇ(cid:181)(cid:181)ıı(cid:246)(cid:246)(cid:247)(cid:247)ıı††(cid:209)(cid:209) ææ (cid:19)(cid:19)(cid:16)(cid:16)(cid:20)(cid:20)(cid:21)(cid:21)(cid:22)(cid:22)(cid:20)(cid:20)(cid:23)(cid:23)(cid:24)(cid:24) under the ISSP joint-research program. The authors
••–––––– (cid:12)(cid:12)(cid:1)(cid:1)(cid:8)(cid:10)(cid:3)(cid:8)(cid:10)(cid:3)(cid:11)(cid:11) (cid:240)(cid:240) (cid:16)(cid:16)(cid:25)(cid:25)(cid:14)(cid:14) (cid:26)(cid:26)(cid:26)(cid:26)(cid:27)(cid:28)(cid:27)(cid:28) are grateful to H. Katsura and N. Nagaosa for en-
(cid:1)(cid:1) lightening discussions. This work was supported in
(cid:190)˘(cid:190)˘»»”‰”‰ (cid:9)(cid:9)(cid:0)(cid:0)(cid:7)(cid:7)(cid:6)(cid:8)(cid:6)(cid:8) (cid:239)(cid:239) (cid:17)(cid:17)(cid:18)(cid:18)(cid:14)(cid:14) part by Grants-In-Aid for Scientific Research (Grant
¯¯ (cid:216)(cid:216)(cid:210)(cid:210)(cid:211)(cid:211)(cid:217)(cid:217)(cid:210)(cid:210)(cid:215)(cid:215)(cid:218)(cid:218)(cid:219)(cid:219)(cid:220)(cid:220) (cid:4)(cid:5)(cid:4)(cid:5) No.15104006, 16076207, 16076205 and 17340104) from
ˆˆ`´`´˜˜ (cid:181)(cid:181)–––––– (cid:2)(cid:2)(cid:1)(cid:1)(cid:3)(cid:3) (cid:238)(cid:238) (cid:15)(cid:15)(cid:16)(cid:16)(cid:14)(cid:14) the MEXT of Japan.
(cid:192)(cid:192) (cid:255)(cid:255)(cid:0)(cid:0)
¿¿ (cid:254)(cid:254)
(cid:190)(cid:190)»»”‰”‰ ØØ (cid:13)(cid:13)(cid:14)(cid:14)
…… ØØŒŒºº(cid:236)(cid:236) (cid:237)(cid:237) (cid:237)(cid:237)ŒŒØØ(cid:236)(cid:236)
„„»»”” ‡‡–––––– łłøøœœŒŒßߌŒ(cid:252)(cid:252)ŒŒ(cid:253)(cid:253)
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