Ni-I boracite: latent antiferromagnetism and improper ferroelectricity-ferroelasticity

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Reference

Ni-I boracite: latent antiferromagnetism and improper ferroelectricity-ferroelasticity

TOLEDANO, Pierre, et al.

Abstract

A theor. model of the 61.5 K transition in Ni-I boracite is presented. Based on a 6-dimensional irreducible corepresentation of the F̅43cl' paramagnetic group, it shows, within the framework of the Landau theory, that the simultaneous onset of the magnetic ferroelec. and ferroelastic properties can be foreseen from the symmetry of the transition order-parameter.

The primary order-parameter is identified as a latent antiferromagnetic ordering. The weak magnetization, polarization and strain components originate in an improper coupling of these quantities with the antiferromagnetic sublattice magnetization. The corresponding magnetic, dielec., elastic and magnetoelec. anomalies are briefly discussed.

TOLEDANO, Pierre, et al . Ni-I boracite: latent antiferromagnetism and improper

ferroelectricity-ferroelasticity. Japanese Journal of Applied Physics , 1985, vol. 24, Suppl.

24-2, p. 179-181

DOI : 10.7567/jjaps.24s2.179

Available at:

http://archive-ouverte.unige.ch/unige:32138

Disclaimer: layout of this document may differ from the published version.

1 / 1

Proceedings of the Sixth International Meeting on Ferroelectricity, Kobe 1985 Japanese Journal of Applied Physics, VoL 24 (1985) Supplement 24-2, pp. 179-181

Ni-l Boracite: Latent Antiferromagnetism and Improper Ferroelectricity-Ferroelasticity

P. Tou'.DANO, *H. ScHMID,t M. CuNt and J. P. RIVERA!

-Dipartement de Chimie mimlrale, analytique at appliquee Universite de Geneve, CH-1211, Genive 4, Suisse

*Group de Physique theorique, Faculte des Sciences 33, rue Saint-Leu, 80039 A miens Codex, France

A theoretical model of the 61.5 K transition in Nickel-iodine boracite is presented. Based on a six-dimensional irreduci- ble corepresentation of the F43cl' paramagnetic group, it shows, within the framework of the Landau theory, that the simultaenous onset of the magnetic ferroelectric and ferroelastic properties can be foreseen from the symmetry of the transition order-parameter. The primary order-parameter is identified as a latent antiferromagnetic ordering. The weak magnetization, polarization and strain components originate in an improper coupling of these quantities with the antifer- romagnetic sublattice magnetization. The corresponding magnetic, dielectric, elastic and magnetoelectric anomalies, are briefly discussed.

§1. Introduction

Nickel-iodine bo.racite (Ni-l) is the unique example of ,..., boracite in which a magnetic and structural transition oc-

curs directly from the paramagnetic F43cl' phase to a monoclinic phase of magnetic class m'. The consistency of the preceding symmetries and the simultaneity of the onset of weak ferromagnetism and ferroelectricity have been demonstrated by magnetic, ¹' dielectric, ¹'

magnetoelectric,^2' piezoelectric" and birefringence^1' measurements. It is noteworthy that the smooth anomalies of various physical properties found around 120 K^2,'-'' or below the 61.5 K transition'·" have been shown recently to be associated with relaxation mechanism due to defects'·'' and not with a structural transtion, as was claimed by some authors.'·" Besides, the domain pattern observed below T,=6!.5 K, shows the existence of twelve ferroelectric domains and twenty- four ferromagnetic domains. The number and orienta- tions of both types of domains^10' are consistent respec-

~ively with the structural 43ml' ~ml', and magnetic 43ml' ~m' symmetry modifications.

In this paper, we present a theoretical analysis of the magnetostructural transition in Ni-l. Within the frame- /'"' work of the Landau theory, ¹¹' the symmetry of the order- _rarameter associated with the transition is identified ( §2).

- It shows that the simultaneity of the magnetic and struc- tural modifications is not accidental, but can be pre- dicted on a phenomenological basis. Using the specific Landau-Dzialoshinskii approach to magnetic systems, ¹²•13

' the nature of the magnetic ordering arizing below T" is precised (§3). Finally the critical behaviour of Ni-l is briefly discussed (§4).

§2. Identification of the order-parameter symmetry in Ni-l.

The F43cl' Shunbnikov group possesses ten active¹' ' ir- reducible corepresentations (IC's): five at the Brillouin- zone center

r,

and five at the X point¹' ' of the face- centered Brillouin-zone surface (k10=(0, 0, rr/a) in the Kovalev notation^16'). The results of the Landau sym- metry analysis^14' of these IC's are summarized in Table I.

T~ey reveal that the paramagnetic to feromagnetic F43cl' ~m' symmetry change observed in Ni-l can be unequivocally related to a six-dimensional IC, labelled

Tt. at the X point of the reciprocal lattice. Actually, as it can be seen in Table I, the other IC 's lead either to an- tiferromagnetic groups, or to ferromagnetic groups of symmetry distinct from m'.

The change in magnetic structure induced by r1 has the

remarkable property of being necessarily connected with a structural transition, a feature which is verified in Ni-l.

This property deserves justification. In this respect, one must keep in mind that the magnetic symmetry of a para- magnetic crystal (the grey Shubnikov group) embodies its structural symmetry (the Fedorov group) in such a man- ner that the IC's of the paramagnetic group depict not only the degrees of freedom of the spin distribution, but also an eventual motion of the atoms in the crystal. This latter situation has been shown to be realized only for a small minority of zone-boundary IC 's, the larger number of IC 's inducing a purely magnetic modification.^17' Let us stress that in Ni-l the structural change gives rise to spontaneous polar tensors (i.e. polarization and strain components). It thus differs in an essential manner from the mere magnetostriction in which only non-symmetry breaking polar tensors (transforming as the identity representation) are induced by the magnetic transition.

The Shubnikov group of the low-temperature phase in Ni-l can be identified as Cc', On Fig. I we have represented schematically the magnetostructural lattice change corresponding to the F43cl' ~cc' transition. It in-

Table I. Results of the Landau symmetry analysis for active IC's <;of the paramagnetic group F43c1', (b) High symmetry points of the paramagnetic Brillouin zone (c) Ferromagnetic (F) and antifer- romagnetic (AF) low symmetry group (d) Primitive translations and antitranslations of the low-temperature phase primitive ce11s, with reference to the paramagnetic primitive translations.

(a) (b)

Ilk,)

X(kw)

179

(c)

AF F43c (r_1), F4'3c' (r,)

AF (14c2, lll4'c'2) (r,)

AF (I I4' c2'. ll R3c) (r,)

F (ll4c'2', U R3c') (r,)

AF I Pr4c2(r_2, r_5), P₁4b2 (r3 , r4)

AF 11 P43n {r_2, r_5}, P43n' (r_{3 ,} r4)

AF IP1c21a, IICA2221

AF III P421c, IV P2,3, VR3c F VI R3c' VIII Cc'

Vlll Cc

(d)

180 P. TOU3DANO, H. SCHMID, M. CLIN and J.P. RIVERA

t'

₃

Fig. 1. Lattice modification at the F43cl' -Cc' transition in Ni-L The monoclinic cell has the primitive translations:

t;=tl -t2+t~, t~=t1--+-t2-t~,

t;=

-11 +-t2-+ t,

volves a euadrupling of both the paramagnetic and crystallographic unit-cell. One can note that the Cc' fer- romagnetic group displays, on a theoretical ground, another remarkable characteristics, namely to be a non- maximal subgroup of the F43cl' group. Such a property, which can be immediately verified from Table I (as Cc' is included in the R3c' maximal subgroup), should make of Ni-l the first experimental counter-example of the max- imal subgroup rule¹' ' conjectured for phase transitions associated with a single irreducible degree of freedom of the high-temperature phase. A theoretical counter-exam- ple has been already pointed out in Ref. 19.

§3. Latent Antiferromagnetism in Ni-l.

In Ni-l, a number of experimental facts strongly sug- gest that the primary order-parameter is an antifer- romagnetic ordering of the magnetic moments. These facts are: !) neutron-diffraction evidences of antifer- romagnetic sublattices below T,;²⁰·20 2) the typical negative asymptotic Curie-Weiss temperature deduced from the magnetic susceptibility'" 3) the weak value of the measured magnetization compared to the hypothetical values corresponding to the sum of the effec- tive magnetic moments. ²³' In this respect it must be pointed out that one cannot assume the spontaneous polarization P (or strain components e,J) to be the primary order-parameter (as suggested in ref. 24), the spontaneous magnetization M arising as a secondary order-parameter, as the two quantities would be neces- sarily connected by a coupling term of the form P"M (or

e~ M) with n > 1. "' Such a coupling is forbidden by the time-reversal operation which belongs to the paramag- netic phase.

The monoclinic Cc' cell has the same volume (4V) as the conventional cubic cell of symmetry F43cl', Assum- ing, without loss of generality, that the lowering of sym- metry is entirely connected with the displacement of the nickel ions, the twenty-four metallic ions will thus be distributed among twelve independent monoclinic sub lat- tices. The position of the ions forming each sublattice are given in Fig. 2, in projection on the pseudo-cubic plane (001). Having regard to their structural environment, the twelve independent nickel ions form three groups, denoted (1, 2, 3, 4), (5, 6, 7, 8) and (9, 10, 11, 12) on Fig.

2.

Let us symbolize the spins of the ions by Sto S,, . . . ,

S12 , and denote by Sn, S1,, • • • ,

S,,

the spins of the ions

respectively obtained by reflexion in the monoclinic plane uw We introduce the auxiliary vectors M" and LJ (j, a= I, 2, 3) defined by the equations:

t

( t;)

• Zc 6 B • • yC

Oj.

_{5 • 7}

( t;)

17 13

2~.

^{16 17}

18

• .

_{22 3 18}

10 12'-.

• 9 11

1~.

¹⁵ 2 14 19

.

_{• 20 4}

_•

• 24 2

.

₂₀

6 " ·

.

8

5 7

X c x'm

( t ~)

Fig. 2. Position of the 24 nickel ions in the monoclinic phase of ~Ii-I. ~

Projection on the xy cubic plane. Numbers below or above the metals indicate whether they are located at: i) z= 1 I 4 or z= 3/4 for metals 5- 12 and 17-24; ii) z=O or z=l/2 for metals 1-4 and 13-16.

L[ =St + Sn+ S,+ St,- S,- St,- S,- St,

a=~+~,-~-S,,+~+~,-~-Sto

Ll=S1 +Sn -S,-St,-S,-Sts+S,+Sto (3.1) L}=L}(S,_,), L]=L)(S~+s)()= 1,2,3),

(i= 1-4, and 12-16)

M¹ =St

+

Sll+ S,+St,+ S,

+

S"+ S, + St,

M²=M¹(S~+,), M³=M¹(S;+8) (i= 1-4, and 12-16)

It can easely be shown¹⁰> that the IC Tt inducing the transition describes the transformation properties of the components (L~y, Lfz, L'ix, L~z, L1x. Ljy). The exchange part of the Landau free-energy, which expresses ex- changes interactions, can be written (omitting the

superscript a): ,...

Fcx=

~ ~

^(L/f

⁺ ~~ ~

^[(LJl']'

⁺ ~ ~

^(Lj)4

+

B,

L;

(L₁LJ²

+

C M'

4 ^1¢-j 2

+ D[(MLt)L,L, + (ML,)LtL, + (ML,)L tLz] (3 .2)

+ ~~

^(M)'[

~

^(Lj}'J

⁺ ~

²

~

^(ML)'

where the B1, D, D, E1 are constant coefficients, and a - (T- T,). One of the absolute minima ofF,., correspon- ding to:

Lf=±L~=±L~ (3.3) is associated with the non-zero magnetization.

M"=-

~ [Lf(L~Ln+LHL~Ln+L1(L7LnJ

(3.4) As the Li vary as L)' -(T,-T)¹¹², M" is proportional to (T,-T)³'2• Besides, introducing (3.3) in (3.1) leads to:

S,+S,+t2=4 (M"±3L\'), I

Ni~l Boracile: Latent Antiferromagnelism and Improper Ferroelectricity-Ferroelasticity 181

and S1+S1+"=4 ^I (M"±LY)(j*i) ^(3.5) where the number i in (3 .5) is determined by the signs in eq. (3.3) (e.g. for LT=L~=L~. i=l,j=2, 3, 4),

From Eq. (3.5) it can be seen that the average spins of the ions can be divided into two groups, the absolute magnitude of the spins differing from one group to the other. Such a property is usual for ferrimagnets.

However, here the spins are associated with one identical type of magnetic ions, which is found in equivalent crystallographic positions in the paramagnetic phase.

This is in contrast with the situation found in standard ferrimagnets such as ferrites or garnets. ²⁶l Dzialoshinskii and Man'ko^13' suggested to denominate this new type of uncompensated antiferromagnetism, latent antifer- romagnetism. As noted by the these authors, no confu- sion should be made with ferrimagnetism because of the peculiar temperature dependence of the magnetization M. Another distinctive feature that was partly overlooked by the authors of Ref. 13, is that, despite its exchange origin, the magnetization must be expected to assume very weak values at any temperature below T,. This is

~ connected with the improper character of the transition, i.e. to the fact that Mresults from a coupling to the third power of the antiferromagnetic sublattices. In Ni-l, the magnetization at 4.2 K is found to be about 0.9 Gauss"' which represents I% of the nominal value. Furthermore, as for the case of Ni-l, it can be shown"' that latent antiferromagnetic transitions should always be accom- panied by marked structural modifications, possibly in- volving spontaneous polar tensors.

§4. Magnetostructual Anomalies

The existence of a coupling between the magnetization components Mx, Mn M, and the antiferromagnetic sublat- tices L't, with a v=3 faintness index,²⁸> allows to exp- lain'0l the remarkable magnetic anomalies which have been observed at the transition in Ni-l, namely I) a magnetic susceptibility which shows a sharp decrease on cooling to about 30 K, where it starts increasing again down to 4 K;²' 2) an asymmetric hysteresis loop"' 3) for a magnetic field H//[III], the curve M(H) decreases above 3 kOe and changes sign above 20 kOe. ²⁷¹ On the other hand, the

~ dielectric and elastic anomalies clearly denote the im-

r

proper character of the ferroelectric-ferroelastic transi- tion. In particular the value of the spontaneous polariza- tion Pat 4.5 K (P-0.078!1 C/cm²)'1 is about two orders of magnitude smaller than the corresponding value for GMO. Besides, near below T" a linear variation P- (T,- T) is observed'l in agreement with the theoretical prediction of a faintness index v=2.''' Here below we will restrain ourselves to discuss the spontaneous magnetoe- lectric properties of Ni-l, which are among the most dis- tinctive features of this material.

Magnetoelectric effects were evidenced experimentally by the switching of electric and magnetic domains under conjugated fields. In our model such effects are ac- counted by the coupling term:

F,"E-Pxfl1yM,+ PyMxM,+ P,MxMy (4.1) From the minimization of the Landau free-energy¹⁰l in- cluding (4.1), one gets the equation of state:

p

:-E,- (M:)' sin 6 cos 6

Xo (4.2)

where the spontaneous magnetization M," is located in the x, y plane,

8

being the angle between

MC:

and the x axis (Fig. 3(a)). Eq (4.2) shows that a change of sign of P,

z z

E

ct ^Ps' _M"' ^{Hs "}

^P."

~

^s

^Ms

^"

'

_, s

-Ef -~

e,

^y

Hs

e• "'

^y

-~'t

M~ ' M ' " s

X X

-P.

_s

tal tbJ

Fig. 3. (a) Rotation of the spontaneous magnetization component lying in the xy plane (Msj_) when the polarization parallel to z changes sign under suitably applied electric field E. (b) Reversal of the polarization P./ when M. is turned in the xy plane under applied magnetic field H,.

under application of a field-£, should result in a 90°

rotation of M," in the xy plane (6-+0+rr/2). This effect was obtained by Ascher eta/. ²¹ by application of -5 kV

I

em field at 56 K. The inverse effect, i.e. the reversal of P, when an external magnetic field is applied perpendicular to the magnetization, evidenced by the same authors near Ti), is expressed by the equation:

[(xil')-'M,"- Hy] sin 6- M," P, cos 6 (4.3) One can see (Fig. 3(b)) that when turning the magnetiza- tion by 90° from the initial position O=H/4, under ap- plication of the corresponding magnetic field (8-+B+n/

2) one has the reverse sign of P, for eq. (4.3) to remain unchanged.

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