Article
Reference
Trigonal Boracites - A New Type of Ferroelectric and Ferromagnetoelectric that Allows no 180° Electric Polarization
Reversal
SCHMID, Hans
Abstract
The space group of the trigonal phase of the Fe-Cl, Fe-Br, Fe-I, Co-Cl, and Zn-Cl boracites is established as C63v. Ferroelectricity is evidenced by domain switching. High coercive fields at room temp. (up to 8000 kV/cm) are found. Polarization-microscopic studies show that the polarization vector is not reversible by 180°, but can jump only from, e.g., [111] to [111], [111], or [111], etc., in accord with crystal-structure and group-theoretical symmetry considerations.
Two twinning "laws" are observed: (a) head-head (tail-tail), domains with {110}cub as compn.
plane and (b) head-tail domains with {100}cub as compn. plane. The domain structure and the relevant twinning operations are discussed. The onset of ferromagnetism at low temp. in Fe-Cl, Fe-Br, Fe-I, and Co-Cl boracites leads to ferromagnetoelectricity. In the case of Co-Cl boracite, the ferromagnetoelec. point group is m.
SCHMID, Hans. Trigonal Boracites - A New Type of Ferroelectric and Ferromagnetoelectric that Allows no 180° Electric Polarization Reversal. Physica Status Solidi. B , 1970, vol. 37, no. 1, p.
209-223
DOI : 10.1002/pssb.19700370125
Available at:
http://archive-ouverte.unige.ch/unige:32931
Disclaimer: layout of this document may differ from the published version.
1 / 1
H. Scmrm: A New 'l'ypc of Ferroelectric-and Ferrornagnetoelect.ric 209 pbys. stat. sol. 37, 209 (1970)
,'ubject classification: 14.4.2; 1.2; 3; 4; 18.2 Battelle Instit~tte, Genet•a Resecwch Gent1·e, Geneva
' fri gonal Boracites - A New Type of Ferroelectric and Ferro- ma.gnetoel ectric tha.t Allows no 180 ° Electric Polarization
Reversal
1)By H. I CHMID
I"'""' The spate group of the tl'igomd phase of the Fe~CJ. Fe-J3r. I~e-I. Co-01. and Zn-01 bora-
cites is established
as cgv·
Ferroelectricity is evidenced by domain switching. High coercive fields at room temperatuJ·e (up to 800 .kV Jcm) are found. Polarization-microscopical stu-di.es show t.hat, t-he polarization vector is uot reversible by 180° but can jump only from.
e.g., [Ill] to Llllj, [Ill]. or [lll]. etc .. in accord with crystal structrn·eandgroup theoret- ical symmetry consideration::;. Two twinning "laws" at·e observed: a.) hea.d-head (tail-tail) domains with {ll O}~uh as composition plane and b) head-tail domains with {lOO}cnl> as composit.ion plane. TJ1o domnin structme and the relevant twinning operations are dis- cussed. The onset of fcn·omagnetism at low temperature ·in l!~e-01, Fe-Br. Fe-I. and Co-C'I boracites leads to ferromagnetocJectricity. In the case of Co-Ol boracite the ferro- ma.gnetoclectric point group is m.
Die Raumgruppe clcr trigonalen Phase der .Fe-CI-, .Fe-Br-, .li'e-I-, Co-Cl- und Zn-CI- Borazite W<ll'de w. CZv bestimmt. Ferroelektrizita.t wird durch Bereichnmklappung nach- gcw.iesen. Die Koerzitivfelder bei Zimmertempemttu· sind sehr hoch (bis zu 800 .kVJcm).
Pola.risationsmikroskopische Studien zeigen. daB der Polarisationsvektor n.icht um 180°
umklappb<lr ist, sondern our von z . .B. [Ill] nach [11 I], [lll] oder [Ill] usw. springen .kann. Dies steht in trbereinstimmung mit der Krjstallstruktur und Synunetriebotrachtun- gcn. Zwei Zwillings.,gesetzc" treten auf: a) Kopf-Kopf (Schwnnz-S<:hwanz) -Bereiche mit {llO}cul> und b) Kopf-Scbwa.nz-Bereicbe mit {JOO}cul> als Verwachsungsebene. D.ie .Be- reichstruktur uncl die entsprechenden Zwillingsoperationen werden besprochen. Das Auf- trcten von Fcrromagnetismus bei tiefcm Temperaturen fiihrt bei Fe-CI-. Fe-Br-, Fe-I- nncl Co-01-Bora.ziten :r.n Ferromugnetoelekt:rizitlit. Co-01-Borazit hat die ferromagneto- elektrischc Pulll,tgruppe m.
1. Introduction
The structure family of boracites :Me3B7013X (.'Me bivalent metal ion, X = Cl, Br. or I) has eecently become of interest because one of its representatives - Ni-I boracite - has been found to be ferromagnetoelcctric (i.e. simultaueous1y ferromagnetic and ferroelectric) with strong coupling between spontaneous polarization and magnetization [1, 2]. Fe-CI, Fe-Br, Fe-1, Co-C1, and Zn-CL boracites were reported to display polymorphic transitions from cubic over orthorhombic to trigonal symmetry by decreasing t.he temperature [3). This paper is intended to prove the ferroelectric character of the trigonal phases, to interpret by means of their crystal structure the pecu"liar switching behaviour of the domains, and to show that some of these phases - reported as ferro- magnets [4) - necessa.r.ily must become fen-omagnetoelectrics be.low t-heir Curie temperatures.
l) ·work supported by the Ba.ttclle Tnstitute, Geneva Research Centre (Physics De- partment).
H physlca 37/1
210 H. 'clG\rro
2. Stru.ctttral ASJ)Octs
2.1 ~'lm·]>llotogy and smnple 1>l'epm·ation
The investigated crystals were obtained by gas-phase transport [51. They bad natural (100), (UO), and (lll) facets as described for the Ni-I bot·acite [2).
Only small crystals ( 1 to 4 rom diameter) were crack-free and a.clequat.e for meas- urements. After X-ray or morphologic orientation, the crystals ·were cut by a diamond saw, ground on SiC paper. and polished with cliamond paste (down to 0.25 fJ.Ul diamond grain size).
2.2 Space gl'OitJI a 11ct tm it celt
Weissenberg CuKa photographs were .made on a single domain (0.4 .mm3 ) that was cut of an as-growu Fe-01 boracite crysta.L The extinction laws were compatible only with space groups D~ and
cg".
The former is ruled out. by multiple reasons (ferroelectric switching. etc.), hencecg"
(R.3c) is the-correctspace group. This result agrees with the gwup theoretical precliction based on Ascher's selection rules of maximal polar subgroups [6, 7): the o.nJy trigonal equi-translation subgroup of Ta (F4 3c) being mac.Ximal and polar. and which should hence designate the fen oelectr:i.c symmetry. is C~v· Furthermore, the extinction Jaws show that the sm<tllest trigonal cell conesponds to the primitive trigonal cell of the face-centi·ed cubic phase (Fig. 1). Therefore, in boracitcs,
qv
is really an equi-ti·au.<>lation subgeoup of T~, thus fully satisfying Ascher's ruJe. RiJti [8] ha: confirmed the space groupqv
for the Fe-01 bomeite byprecession photographs (lV[o radiation) and has found the Fc-Br. Co-01, and Zn-01 boracites to be isotypio. There :is evidence from M:ossba,uer effect data [3] that Fe-I boracite is also isotypic.
2.8 Lattice pantmete1·s
In Table 1, we give the lattice parameters of omc trigonal boracites as determined by HiJti [8] by means of Jagodzinski a-nd de Wolff diagrams. The spontaneous strains relative to the cubic phase are very small. ..While the Zn-Cl boracite is elongated along 1\, the Fc-01 and Fe-Br boracites are com- pressed along that direction (Fig. 2). A magnetostrict~ve contribution of the paramagnetic ions to the spontaneous strain may a.ccount for the opposite behaviour. The trigonal splitting of the Co-Ol bo:r:acite was not resohed.
Jfig. 1. 'f.rigoualunH cPII in l.h~ f.r:noework of lllo cubic tligh-t.cmpcro ..
turo tuJit .:ell (trigonal ce.ll = -primitive cell of cubic f.c. phase)
!;::
Table L
Lattice pan~rneters (refined by the least-squares method) of tlwee rb.ombobedn\1 boracites (2-5 °0. CuK,. radiation [SJ)
Borac'itc
Fe-Cl Fe-.13r Zn-01
Smallest hesagoual <:ell
an (A)
8.6240
±
0.0002 8.6339±
0.00048.5367
±
0.0002eli (A)
21.04,89
±
0.0007 21.1004±
0.00]420.9722
±
0.0007Smallellt rhombohed.ral cell
a , ,
(A)8.6036
±
0.0002 8.6208±
0.00048.5535
±
0.0002C<
60°09'1'\6"
60c06'02"
59°52'12''
Pseudo-cubic rhombohedral cell
I
a.ll, (A) I 0.12.1817
±
0.000:3 90°08'12"12.2009
±
0.0005I
90°05' L4"12.0846
±
0.0003 89°53'16"cjq'
Rl
c
"'
"'
cC 0
..,
"'
..,
i
I
~
~ ~
~ H
(P
c
...,
b:j
"'
~!2..
0 (>
....
..., 5'
~ p..
~ ~
6
s
OS ... ~
g.
0 g..
"'
"'
~(>
l-.:l
...
...
212 /)
'~'-
H. CIJ}f[D
1•"1!!- 2. l'scudo-cuiJiC trigontd ccU. a) <'onrprc~scd t~long J•.; b) elnngRtcll along J>,
2.-1- Pen ·oe/Pdric su;itl:lli11g
2.4.1 Pa.rticulca·ities of the transition from Tj to C~"
b
Bccau ·e the (Ill] directions of TS, the "motl1er" phase of
cg"'
arc already polar (owing to the boron-oxygen net). it becomes clear that 180° domain reversal .·bould be impossible in the tr-igonal borar..i.tes. However, domain"j um ping" cou lei be e:>..-pected between the four preferential clirection.' -
l
I II],[ll I], [Ill]. and flll] - of P8 (Fig. 3). For t-he general case. Ascher [9] bas shown by group t.heory how to determine those ferroelectrics for which P8 has different directions but cannot be reversed: it is necessary to determine a) the number of C conjugates in the paraelectric (high-temperature) symmetry group H of a given subgrotlp G1, and b) the index I of G1 in H. Then, either 1
=
C or I = 2 0. ln the former case. there exist 0 different orientations of P8 tbat cannot be reversed: in the latter one the number of P~-orientations is the same but their vector can be teversed. Aizu [ 10] has classified all possible pairs of high-temperature/low-temperature symmetry that lead to fcrroelectrics with an "irreversible but di.vertible" polarization vector.2.4.2 Sample ptepara.tion
Platelets (20 to 100 !J-Dl thick) of tbe Fe-Cl, Fe-BJ-. Co-Cl. and Zn-Cl bora- cites were cut parallel ( 111 lcuh· For domain swjtcbi.ng, these sa.mples were mount- ed on a sample holder. wl1jch is schematically shown in :Fig. 4: the crystal (e) was mounted by means of a resin (d) above tbe cone-Like llole (0.3 to 2 mm diam- eter) of a Resocell plate (f). The electrodes (a) were painted with silver paste close to the crystal on the Resocell. Droplets of salt water solution (LiF) (b)
c b d e a
~, ~~ ~~ ~~ ~'''
a c b
r
+(-) Fig. 3. Til<' fottr possilolc dlrcctlous or I he
spontane<,us J•ol:uizatitJn lu thr c,, ... bo· }'ig. 4. ~nmJllf' holde.r (schcuudic) for switc·hiug experiments with racitc pltasu lhtulcl elcctrorlcs nnd aulcro~cope ol.,;cn·ation~
'I'rigonal Borncites - A Kew Type of Fcr.r:oelectric and Ferromagnetoelectric 213
b
l'ig. 5. a) Lamcllllr tlomtlin ~tTuotou:c of the lln-01 borncltc. Q,. phase, 25 •c, (lll) en!.: cxplanntion on Fig. l3 QfR. o) The same crystal in the c,. phase, 350 •o
214 H. SCIIli'UD
.Wig.~-l)ornain "witching in tl1e Co-OL born<·ilc, (111) cut, pohlrlzlll"\5 crossed. a) P0 perpenillcu·lnr to plntelet; I)) llomnlns of tho tl.ree othcrprcfri'Olltinl directions of 1',, all dom11.ins in non-extinctiOn position
A
rrrigon::tl Bor11oites - A New Type of Ferroeleot-rio and Ferromagnet.oelectric 215
Fig. 6 c. J>~plnnntlCJII to l'ig. (.IIJ
Fig. 7. Scl1r.runtlc n;;ymmetric hysteresis loop :ls CX])cCteo for a ••
borncitcs
A z z'
y'
y 73
)( b
li'ig . . 1'hc :lie•• :mol hAlogen !li~plllCcwEm~ in l·llc C,v tJhase {If the Nl.g-01 hornl'ite rclati\'C to the cell of the Tu·phns<:. J~oron-oxygen sl<eiHon not sh0\\"11
216 H .• OIDrTD
proviclecl the electrical contact between leads a.nd crystal. To aJJow for good optical image quality, the droplets were stretched out by means of a cover glass adhering by capillary effect. The whole assembly was mounted on the gliding stage of a polarizing microscope. The <tclbering problem of the resin was crucial.
particularJy for t.b.e extremely b.igh Yoltages a.pplied. After trial of several products, a bee wax-colophony mixtm·e (about l: 1) waR found to meet be:t the requirements both of isolation and of a certa:in pla.sticity.
2.4.3 Results of sw-itching e.>.:periments
The (111) platelets of the J!e-Cl, .l!'e-Br, Co-Cl. and Zn-Cl bora cites cou lei be switched at room temperatme. The electric field strengths at which part of the domains began to move lay between. 5 to l 0 kV fern. whereas those for satura- tion were found between 400 and 800 kVfcm. In Table 2. we give some typical values of the coercive fields. For .most Co-Ol bo1'acite cryr;tals, the remanence was equa.J to saturation after saturation at 500 kV /em, whereas for· the other com- positions, the remanence lay app.reciably below satLU·ation.
T~tble 2
Switching field st.rength of some trigonal bomcites (25 °0, (U J) cut)
Beginning
I
Saturation ThicknessBora.cite of pla,telet
(kVfcm) (f.tln)
Fe-CI 320 800 25
Fe-Br 50 75 107
Co-Ol 240 GOO 50
Zn-CJ 280 35
Closely related to the b:igh coercive fields are the long switchjng times . .For example, at 50 Hz a.nd 800 kVfcru only a.bout l to 5% of the domains of the Co-Ol boracit.e were optically observed to be .in a state o.f switching (twinkling: of colo·uts between crossed polarizers); t.heremain.dcr of the crystal wa.s completeJy blocked. Therefore, very low frequency measurements are now being prepared to mea.sme the spontaneous polarization and study the switching heb<wiour.
'Before a tr-igona.! as-grown and pobshed platelet is subjected to poling, it shows usually a very fine lameiiar structure (Fig. 5a, explanation Fig. 13 Q/R).
After repeated quasi-statio switching, large domains are fonncd. The htmel- Jar structure is reestablished only after heating above the transition tem- peratme t0 cubic and cooling in zel'o field.
The phot,ographs of Fig. 6 clearJy demonstrate the domain "jwnping" as seen in a (lll) Co-Gl-boracite platelet. In Fig. 6a, the electric field polarity pro- duced a. si11gle domain with the polaJization <:urecti.on and thereby the OJ)tical axis perpendjcular to the platelet. The entire domain appears black uetweeo crossed polal'izers. After reversal of the pol<trity of the field, the single domain splits up into the three .remaining possible domain orientations. the polariza,tion and optic axjs cli.rections of wbjch form an angle of arctg
1 /2/2
with the surfa.ce, their birefringences being correlated by a rotation of 120° (60°). Hence, at an adequate intermediate posit.ion of the crossed polarizers, there is contrast be-Tl'igorwl Boracites - A New Type of Ferroelectr·ic ttnd Fru:romagnet.oclcctric 217
ldL!. U. 'l'hf:' two kincl-:t uf ~Lc•+ environmE-nt in tile
\'." ln)r:wltc. (llO)tub cut, ion shifts in rlm plano
- ,,r th~ paper.
:o) )ft·' trre 1 (1/S or ~lc,. lousl:
IJ) llc'' ll'pc• 2 aud :l (~f;l or .lie'+ ions)
tween all three domain categories (Fig. !ib and c). One can expect
'%
that fOI' such crysta.l sections, the "'G-.;
hyslercsis loop will be asymmetric both in spont,ancotts polarization and in coercive fiel.cl (Fig. 7).
2.5 Stnwtrn·e mmlel and ubsulute conj'igtu·a t imt
'l'ho phase C~,. of Mg, Ni, etc., -bomcites is chara.ctcrized by the presence of three crystnllograh.i- cally inequivalent Me2+ sites, l, 2, and :l (reference [11] and Fig. 8).
o)m{070)o.r.
(111Jar.
a rrzfJar
1111lar.
O
)in {777)o.r.(.;at.egol'ics 2 and 3 have identical local environment (Fig. 9 b); that of kind 1 (mg. Oa) is quite tlifferent, leading to another electric field gradient at the metal site. Hence, there are two kinds of quadrupole splitting in the l\Iossbauer spectrum f3J. During tbe transition to the trigonal phase, only one kind of splitting survives. Because it evolve. out of the splitting due to sites 2 and 3 wit.h nearly no eli. continuity at tho phase tra.nsit.ion, one can conclude that only one typo (namely that of Fig. 9b) of local meta,[ environment occurs in tho t1·igon11 I pha~e. On the basis of this information a:nd the space group requirements for cgv, it turns out that only one kind of structure model is compatible with a polar axis along a cubic space diagonal [3, 12]. In Fig. 10 al'e repl'esentecl the shifts of the metal and halogen ions with. resp<>ct, to the ttnit cell of the cubic phase T~: all halogen ions move parallel to the d.i1·ection of spon- tancoui:> polal'iznt,ion [lll], whereas the metal ions move n,long [lOO]cub clirec-
Fig. 10. lie'' nnrl halogen ~hlf'ls iu the c.,. ph:~e re- lut"lvc to positions fu the 'l'd-phase
(/ff)Ho/=C/,Br,/
OMe•Fe,Co,Zn
218 H. Somun
t.io·ns as in the orthorhombic phase, their centre of gravity shifting oppositely to the cUsp.lacemcnt of the halogens. Recent structure work supports this model [ 13).
Inspection of the Mrailable space around the halogen (point symmetry T-23) in the cubic structure T~ shows that there is ample space fo1· the haloaens to move in tbe [111) directions only tow1.trds the B-faces2) (Fig. lJ ). There is much less space i1~ the direction towards the A-facets. In other words, there exists a saddle-uke potential distribution, the (110) sect.ions of wlllch we ha,-re schematically represented in Fig. 12. Tbe absolute configtu·ation of the ortho- rhombic ph a e
Cg.,.
and the cubic phasc T~ of the Ni-Cl boracite had been deter- mined by a procedure combining pyroelectric, polarization-optical, X-my- Weisscn berg (without using anomalous dispersion!), and etclllng data (2].(Independently thereof Abrahams et al. [14] used tho pyroelectric effect in a similar manner for the determination of the absolute configuration ofLiNb03 .) Tho pr:oblem of t.bc absol11te configuration of the trigonal phase of boracites, based. on the abo,rc-mentioued model. can be solved jo a much simpler way than for the orth01·hornblc phase: The contribution to the spontaneous dipole moment 1·esulting from the very small deformation of the boron-oxygen skele- ton \\rill be negligible relative to that caused by the shlfts of the halogen and meta.! ions wlllch arc of the order of 0.1 A [11). It is clear f1·om spatial considera- tion that the internal dipole moment (owin.g to the halogen and metal ion shifts) must point from the B-to the A-corner, if we define its direction conventionally by - -+
+·
In order to determine now the A, B (111) facets of a real ct·ystaJ, we can do this by poling a thin (111) platelet (see above, Section 2.4). Then the polarity of tlte electrodes, wl1ich produces a single domain (or the tripleJo'ig. 11. lt<•prc~oll!.atiOD Of the pOs.<ible llll] di·
rcrt ions of mu,·cmrnt or 1 he hnlogcn ions
/ / /
Fig. 12. Sc.hemnUc rupresentnlion of the (!'10) section through the Sllddic·like clcctrost:lli~ potential or the bnlo·
gen en,•ironmunt
~) We have defi11ecl the A-comers as those corners where u boron tetrahedron 'dth an oxygcu in its centre points wit.h one of its corners into the unit cell. The A-corner is iden·
tical with t.lle origin of lto's unit cell setting [11].
Trigonal Bora,cites - A New Type of Ferroelectric and Ferromagnetoelectric 219
domain configuration), indicates the A-B facets (cf. Fig. 10). We have made these experiments for the Oo-01 and Zn-Cl boracites and correlated the results with the orientation of the etch pits on the (100) facets. We can formulate the outcomeln the rul.e: "The long asis of the etch pit rhomb of a boracite (100) facet always po111ts to adjacent (111) B-facets." This result is in accol"d with the in- depenclent"Jy determined absolute couiiguration of cubic boracite via the ortho- rhombic phase (2]. In the case of tbe Co-Ol bol'acite, the (Ul) B-facets are nearly always larger than the A-facets. However, t,he situation is often reversed, or there is no cJjfference in size at a,JI (e.g., for the Fe boracites. etc.). Therefore, poling or etching gives the most re"Jiable determiation of the absolute configur·a- tion of a bora.cite crystal. The form of the strain field of a growth centre, re- ported for the Ni-l boracite (100) growth sectm·s [2], is very reliable too; how-
.
.-f. ever. it has been found useful so fa1· only foT diagnostic purposes in that compo-
sition.
a.
~'winning Laws.'l.1_ GeiiCJ'ltl wspeets
J3y group theoretical and stuctnral considerat.ions it was shown (Sections 2.4.1 and 2.5) that there are fom possible domain orientations with only fo1u·
polarization directions ill the Oav phase of boracite (Jl'ig. 3). These different domains are related by twinning operations that are given by the lost symmetry elements of the 0:3v phase relative to the high-temperature "mother" phase T<L
[9]. These are: 3 trlads [111], 3lnversion tetrads [lOOl, and 3 symmetry planes (110).
We have observed two kinds of composition plane, (100) and (110), between the rb.om bohedral domains. The fust kind leads to head-tail and the second to head-head (tail-tail) configurations.
Both Ja.ws a.re ofteu fouud in one and the same crystal.
8.2 l lemt-tait t.lonwcins
Tbe most frequent domain pattern consists of lamellas (thickness ~ l fLm) of bead-tail configurations wjtJt (100) as composition plane (Fig. 5. 13 R, and 14). Smail crysta.ls and tllin platelets often show only one of these three mutually perpendicular _possible orientations of layer piles (one of the three sets of pile is shown in Fig.13 0/R a, 14 and two in Fig. 16), beca.use such an anangement can be free of constraints. The head-tail layers are favourable because they minimize the electrostatic energy by preventing "spa.ce charges" on the inter- faces. 1<his explains tbeil" appearance in higJJ!y isolating crystals as separation walls between the three equivalent domains of a (lll)cub platelet (Fig. 6 b, c); however, freque.nt.ly strong angular deviations from (lOO)cub were observed.
3.3 llea(l-lleCtd (ta"il-ta.il) don·wins
Much less feequently than head-tail domains, the head-head (tail-tail) junc- tions are observed (Fig, 13 S). This configuration creates "space charges" on the composition planes, since cliv P 1s not zero. It is obvious that this kind of twinning will occur more easily in conduct.ing than in IIighly insuJating crystals.
In Fig. 15 a ra.t·e example of a large head-bead boundary is shown.
220 H. Scmu.u
Head -tail domains
{100} R
A
Head-head (/ail-tail J domains
{770}
s
:riJ:
AFig. 13. chcmutic representation of hearl-hend 111111 hr:ut-lail <lomnlns tts •ecn on (IOO)cub, (llO)eub, nnd {lll)rub cuts
'J'rigonal Boracites - A New Type of Fer:roelect.rio ami FerTOlll<tgnetoeleotrio 221
J.'lg. l 4. l:lcad-tnil dornains on n (llO)cub cut (thickness 28 1uo) of the Fc-0! boraclt.o
}"lg. J 5. Lnr{te lteild-hcatl dorll!lin~ of the lfe-CI boracite, (lll)cub cu,L (cxp'lannti<ln on Fig. l3 Q/S)
222 H. 'cHMID
A
-+- cp
'_," /<;:/· a '
/'
·" / /cp -+-
A' ',,,r\a
.... .... '-+- cp
.... '/ ',<? +
' '
'
....;:.-;;7 ""
/ /-+- cp "'"' a //"'Cp
_L__ I-+- cp ',r><r
/qJ -+-
-+- 9
_,/ ....//;<r
(f." cp-+-
',~,\a
'-+- ~ /
.... .... .... ....q=> -+-
b B B
Fig. 16. J,lloking of 1 wu sets of hea<l-tnil lnmellno by henri-head domailc•, (110) r:ut, of f•'tt--01 horacitc. n) I<cnl;
ll) i!thomntic
If all fou:r polarization directions are present .in one and the sam.e crystal.
usually two or three ID\ltually perpendicular sets of bead-tail lamellas appear.
The rufferent sets are then joined by head-head (tail-tail) composition planes.
1l.l.is is shown in Fig. l6a for a (11 0) cut ofthe ]'e-Cl botacite and is schemn.t.i- cally explained in Fig. L6 b. The juxtaposition of these two lands of twiml.ing must create mechanical constraints, but since the deviations f_rom cubic sym- metry aTe extremely small (see reference [15] and Table 1), the aiTangement. becomes C()mprehensible.
Trigonal Boracites - A New •rype of J!~en·oelectl'i~ and Fenomagnetoeleot.ric 223
4. Romarks on Ferromaguotoolectrici.ty
Magnetic measurements have shown [4J that the trigonal phases of t.he Fe-Cl.
Fe-B1·. F.e-1. and Co-Cl boracites becorne ferromagnetic below 11.5. 15, 30, and 15 °K, respecth~ely. In the case of Co-OL bora.ci.te
it
could be shown by observation of the Faraday effect. that the spontaneous magnetization lies per- pendicular to the spontaneous polarization of the 3m 1' paramagnetic phase.Combining tbjs result with magnetoelect.ric measurements [17]. we find tbe Shubnikov point group m, wbich is compatible with the coexistence of ferroelec- tl'icity and feTromagnetism. Tltis symmetry allows tho linear and high-order maguetoelectric effects (ail E,f11, o.,1" f-1; E1 Ek, {J;p; El H1 Hk (16]). Strong ferro- magnetic-ferroelectric coupling is expected as occurring in Ni3B703T. The linear maguetoelectric effect should lead to a. "butt01:fly" loop a.s in Ni3B7013 I [2].
A.c/,·nmclcdgentellts
Jt is a pleasure to thank Dr. E. Ascher for helpful discussion:s, Dr. E. Hilti for providing lu.ttice parameter data, H. Baier for taking the Wcissenberg- photographs, and H. Tippmann fo1· the ca.reful preparation of single crystals.
References
(ll E. .AsCUER. H. RLEDER, H. Smmm, 11nd H. STOESSJ·:L, J. a.ppl. Phys. 37, 1404 (1966).
[2] H. ScmuD, Acta cry st. 21, (• 'uppl.) A263 (1966) (abstract); Rost Kristallov 7, 32 (1967) (full text.).
[3] H. ScHMID and J. kL TRoosTEn.. Solid Stat.e Commun. 5, 31 (1967).
(4] 0. QuEzEL and H. ScHM:tD. Solid State Commun. G. 447 (1968).
L5] H. Scmm:o. J. Phys. Chem. Solids 26, 973 (1965).
[6] E. Ascrow, Phys. Letters (Netherlands) 20. 352 (1966).
[7] E. AsmmR, Lattices of Equi-Transla.tion Subgroups of the Spa.ce Groups, Battelle Institute, .A.S.C .. Geneva 1968 (ava.ilable on request).
[8] E. HJLTI, private corrnnuuication (ETH Zi:il'i<:h; to be published).
[9] E. ASCHER, private con:rmun.ications (to be p11.blisbed). - .Material concerning the rehttions between pha,se transi.tions and symmetry is contained .in the .following docLt- m.ents by E. Ason.En. which mn.y be obtained on request: "A propos de ferromugneto- cleotricite" (Conf. Neuchfitel, .J11ne 1966); "Symetrie et changements de phase con- t.inus" (Conf. Geneva, lVJ.ay 1967). "Group-Theoretical Considerat.ions on Ferro-Elec- tric Phase Transitions u.nd Pol&rization Rel'(:n·s&ls" (Conf. Prague, May 1968), "Rela- tions entre structlll'e et. propriet6s - exe1nple des boracites" (Conf. Strasbom:g, 'ep- tember 1968).
[JO] K. ~lZU'. J. Phys. Soc. Japan 23, 794 (1967).
[11] T. Joro, N. MORil\101'0, and R. '_-\DA .. '<AG;I. Aot11 cryst. 4-, 310 (1951).
[12] J. 1\L TnooSTl!.'R, Thesis, Nijmogen 1967; pbys. sta.t.. sol. 32, 179 (1969).
[13] H. ,'CllACflN0R aud H. Scrorru, to be published.
(14] S. L. ABRA'HA?>ts, J. i\1. REDDY, and J. L. BERNSTEIN, J. Phys. Chern. Solids 27, 997 (1966).
(15] J. KoBAYASHT, N. YA~UUA. and T. Azmm, .Bev. sci. Instrnm. 30, 1647 (1968).
(16] E. Ascm:n, PhH. Mag.li, 199 (1968).
[17] H. ScmiiD, t.o be published.
( BeceiJJe(l August 20, 1969)
