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Optical birefringence and successive phase transitions of hexagonal ABX3 type antiferromagnets with spin frustration K. Iio, M. Sano, H. Tanaka, and K. Nagata Citation: Journal of Applied Physics 64, 5959 (1988); doi: 10.1063/1.342516 View online: http://dx.doi.org/10.1063/1.342516 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/64/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Phase transition of Potts model on a frustrated 3D lattice J. Appl. Phys. 87, 5905 (2000); 10.1063/1.372562 Magnetic phase diagrams of spinfrustrated stacked triangular antiferromagnets: Application to ABX 3 compounds (invited) J. Appl. Phys. 70, 5961 (1991); 10.1063/1.350090 The antiferromagnetic spin glass with frustrations (abstract) J. Appl. Phys. 63, 4002 (1988); 10.1063/1.340579 Elementary excitations and phase transition in uniformly frustrated Heisenberg spin systems J. Appl. Phys. 61, 4422 (1987); 10.1063/1.338396 Anisotropy, magnetic field, and stress influences on the phase transitions of spinfloptype antiferromagnets J. Appl. Phys. 56, 3490 (1984); 10.1063/1.333901 [This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 147.143.2.5 On: Sat, 20 Dec 2014 18:09:52

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Page 1: Optical birefringence and successive phase transitions of hexagonal ABX3 -type antiferromagnets with spin frustration

Optical birefringence and successive phase transitions of hexagonal ABX3 typeantiferromagnets with spin frustrationK. Iio, M. Sano, H. Tanaka, and K. Nagata Citation: Journal of Applied Physics 64, 5959 (1988); doi: 10.1063/1.342516 View online: http://dx.doi.org/10.1063/1.342516 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/64/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Phase transition of Potts model on a frustrated 3D lattice J. Appl. Phys. 87, 5905 (2000); 10.1063/1.372562 Magnetic phase diagrams of spinfrustrated stacked triangular antiferromagnets: Application to ABX 3compounds (invited) J. Appl. Phys. 70, 5961 (1991); 10.1063/1.350090 The antiferromagnetic spin glass with frustrations (abstract) J. Appl. Phys. 63, 4002 (1988); 10.1063/1.340579 Elementary excitations and phase transition in uniformly frustrated Heisenberg spin systems J. Appl. Phys. 61, 4422 (1987); 10.1063/1.338396 Anisotropy, magnetic field, and stress influences on the phase transitions of spinfloptype antiferromagnets J. Appl. Phys. 56, 3490 (1984); 10.1063/1.333901

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Page 2: Optical birefringence and successive phase transitions of hexagonal ABX3 -type antiferromagnets with spin frustration

Optical birefringence and successive phase transitions of hexagonal ABXa ... type antiferromagnets with spin frustration

K. lio, M. Sano,a) H. Tanaka, and K. Nagata Department of Physics, Faculty of Science, Tokyo Institute of Technology. Oh-okayama. Meguro-ku. Tokyo 152, Japan

To investigate the successive ordering processes of the triangular lattice antiferromagnet CsNiC!3' a Heisenberg system with an easy-axis anisotropy, optical birefringence has been studied on various hexagonal ABX3 systems involving other types of anisotropy. The birefringence for light propagating along the c axis dearly shows that the basal plane component of spins in CsNiCl3 is ordered below the lower Ned point T N2' A cusplike anomaly in the temperature dependence of the birefringence for Ught propagating perpendicular to the c axis is observed at the upper Ned point TN I of the Heisenberg system with an easy~axis anisotropy. A plausible expianation for this anomaly is presented in connection with a spin frustration effect.

INTRODUCTION

Through mea..<;urements made on various transparent magnetic materials, optical birefringence has been recog­nized as a useful means for measuring the temperature de­pendence of the magnetic energy of uniaxial or biaxial sys­tems. l In this paper, we report that the birefringence has another capability to obtain information on the change of magnetic symmetry accompanying the onset of long-range order. 2 The substance with which we are here concerned is CsNiCl, , regarded as a representative of hexagonal ABX3 -

type antiferromagnets. 3 The compounds with this generic chemical formula have chains of octahedrally coordinated B ions along the c axis, In the basal plane, the B ions are located on the triangular lattice sites. A notable feature of these com­pounds is that the intrachain exchange interactions ofB ions are much stronger than the interchain exchange interac­tions, The one-dimensional magnetic behavior exhibited in them has been the subject of a number of previous studies. The spin frustration inherent in the triangular lattice antifer­romagnet makes ordering behavior complicated so as to give rise to successive phase transitions.4 The ordering process in the antiferromagnetic ABX3 system is a current topic in magnetism.5

-8

The presently known magnetic structures established on the hexagonal lattice are classified into about seven types,9 Three typical spin configurations are illustrated in Fig. 1, where theIsing-type system (e.g., CsCoC13 ), the Hei­senberg type one with an easy-axis anisotropy (e.g., CsNiCI3 ), and the Heisenberg type with an easy-plane an­isotropy (e.g., CsMnBr3) take the collinear (P6; /m'cm'), the ac-plane triangular (em' e2i ), and the c-plane triangular structures (P 62'm'), respectively. The former two have two ordered phases and the latter has a single ordered phase. There are controversies over what kind of spin structure is stabilized in the intermediate phases of CsNiC13 and CsCoC13 •

To investigate a probable sequence of successive order­ing, we have undertaken accurate measurements of the tem-

.J Department of Applied Electronics, Graduate School of Nagatsuta, To­kyo Institute of Technology, 4259 Nagatsuta-cho, Midori-ku, Yokohama 227, Japan.

perature dependence of the birefringence. The present study involves both the observation of the well~established mag­netic part dominated by the nearest-neighbor spin correla­tion function, and a novel part associated with the breaking of magnetic symmetry. By referring to a previous study made on CsCoC13 and CsMnBr 3' lO the ordering process of the ac-plane triangUlar structure in CsNiC13 will be dis­cussed.

DESCRIPTION OF BIREFRINGENCE

The axes both perpendicular and parallel to [I 120] (normal to a cleavage face) and the c axis are taken as the x, y, and z axes, respectively. The magnetic part of llnzx

( = nZ - nX) for light propagating perpendicular to the c axis is expressed in terms of the spin-dependent polariz­abilityll as

D.nZX = IAij(SiS) + 2.Bij(2<S~Sj) - (SfSj) ij ij

- (S{S}» + "LCij( (SfSj~) - <S~SJ», (1) ij

where A,i' Bij' and Cij are the linear combinations of appro­priate photomagnetic coefficients effective between near­neighbor spin pairs i andj. As the temperature is decreased, and the short-range order evolves, the first term of the iso­tropic spin correlation function grows, and governs the gen­eral feature of Anzx (T). Its critical behavior is the same as that of the magnetic energy. For uniaxial crystals the second

FIG. 1. Schematic illustrations of typic a! spin structure established in hex­agonal ABX, antiferrumagnets. Arrows indicate the ordered directions of spin moments. The coordinate system (x,y,z) taken in the text is shown for the ac-plane triangular structure.

5959 J. Appl. Phys. 64 (10).15 November 1988 0021 ~8979/88/225959-03$02.40 @ 1988 American Institute of Physics 5959

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Page 3: Optical birefringence and successive phase transitions of hexagonal ABX3 -type antiferromagnets with spin frustration

term, reflecting an enhancement of uniaxial anisotropy, is not truly singular at TN' Provided that the basal plane spin component is set in a long-range ordered state, an additional contribution to ~nZX (1') is expected below TN from the third term of Eq. (I). Because the crystal may transform from the group of hexagonal point symmetry to that of the orthorhombic one at TN through magnetoelastic coupling, the vanishing of the axial symmetry around the c axis per­mits (S fS~) =1= <S rS f). In this case, ~nZX (T) may display a

J J

sharp bend at TN' On the other hand, the basal plane birefringence Anxy

( = n~ - nY ) for light propagating along the c axis is given by

(2)

This birefringence, which can be designated as "the symme­try breaking birefringence," provides us with direct informa­tion on the lowering of the basal plane magnetic symmetry.

EXPERIMENTAL PROCEDURE AND RESULTS

The experiment was performed at the 632,8-nm emis­sion line of a He-N e laser by making use of an automatic data processing system equipped with a rotating analyzer. 12

,!3

For the measurement of Anzx, the light beam was incident on

a (1120) cleft slab of about 0.5 mm thickness. A c-plate specimen carefully cut parallel to the basal plane to about 1 mm thickness was used for the measurement of t:mxy

Figure 2 shows a general feature of the temperature de­pendenceof anzxin CsNiC13 , where Anzx (T) is approximat­ed as a linear combination of a magnetic part and a lattice part. The temperature dependence of the lattice part can be

",30 'S'

9.0 ~

~ fig "

~2.5 ;:c C

'" 2. I

4 5 6 TEMPERATURE

. / "f/ ''''''" '''' 1 z T

o 100 200 300 TEMPERATURE (K }

FIG. 2. Temperature dependence of An2x in CsNiCl,. A heavy curve shows the gross temperature variation of an"X and a fine curve the lattice part of CsNiCl, estimated from tin" of CsMgCl, .

5960 J. Appl. Phys., Vol. 64, No. iO, 15 November 1988

estimated from the 6.nzx (T) of a nonmagnetic isomorph, CsMgC13 • The magnetic part extracted by subtracting the lattice part from the gross birefringence has been proven to be proportional to the short-range order of a Heisenberg lin­ear chain antiferromagnet wlth S = 1. 14 The inset of Fig. 2 shows AnZX( T) in the vicinity of the successive phase transi­tion points. After the fun growth of the one-dimensional short-range order, stepwise variations of !>.nZX (T) can be seen at the Nee! points TN 1 ( = 4.85 K) and T N2 ( = 4.27 K). The singularities of f:.n zx (T) exhibited at TN '8 seem to be much stronger than that of the magnetic energy usually observed in uniaxial systems by means of birefringence. A similar cusplike anomaly of AnZX is observed in other Ne +

compounds (CsNiBr), RbNiC13, and RbNiBr3 ) and in a Mn2-+- compound (CsMnI3 ). 15 An of the these take the ac­plane triangular structure at the lower ordered phase. How­ever, the fln zx (n of CsCoCl3 and CsMnBrJ reported pre­viously have no such anomalies below TN' so that the magnetic part of I1nv.: (T) is almost proportional to the short-range order of each linear chain system over the whole temperature range. 16 Since the one-dimensionality of the ABXJ systems is considerable, the ~nzx ( T) 's of CsCoC13

and CsMnBr3' where the inflexion point of I1nZX( T) indicat­ing a phase transition is hardly seen, are rather more nOimal than those of the Nil + members of the family.

The temperature dependence of llnxy in CsNiC13 is shown in Fig. 3, both in the absence and in the presence of a field H paranel to the y axis. For H = 0, llnxy (T) remains zero showing no anomalies at either TN I or T N2' although minor scattering of the data is seen at temperatures above TN I' A field of 4 kOe produces a Anxy of the order of 2 X 10- 7 in the paramagnetic phase. A noteworthy feature is that an additional birefringence grows with decreasing tem­perature below T N2' not below TN 1. Since I1nxy (H) at a fixed temperature above TN! is verified to be proportional to H 2, the threshold level of !>.nxy in a field can be attributed to the Cotton-Mouton effect, irrespective of the magnetic or­dering. Therefore, the additional contribution below T N2

... '0

x 2 -....

o

........... "

5 TEMPERATURE (K)

-3

10

FIG. 3. Temperature dependence of tlnxy in CsNiCl, for the absence and presence of the field perpendicular to the c axis. Under the applied field, an additional birefringence appears below the lower Neel point TN2 ( = 4.27 K). For zero external field no anomalies are seen for both the upper Neel point TNt (=4.85 K) and T"2'

lio etal. 5960

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Page 4: Optical birefringence and successive phase transitions of hexagonal ABX3 -type antiferromagnets with spin frustration

should be identified with the symmetry breaking birefrin­gence specified by Eq. (2). A quite similar behavior of anXY (1) is observed also in CsNiBr 3.

17 Those results indi­cate that the orthorhombic spin structure of the ac-plane triangular arrangement is established in a multidomain state under zero external field. The field perpendicular to the c axis can stabilize a single-domain structure of which basal plane moments align making an angle of 90' to the field. Figure 4 shows the field dependence of t:..nxy at 2.0 K for H lIx and H iiy, where the data are plotted by subtracting the Cot­ton-Mouton part from the gross birefringence. The saturat­ing behavior of Anxy for the field above about 3 kOe suggests the establishment of a single domain state.

DISCUSSION

The symmetry-breaking birefringence in CsNiC13 below T N2 reveals that the spin reorientation structure where the basal plane component of moments oriented in the zy plane below TN 2 is rotated by 90· around the c axis 18 is not appro­priate for the structure of the intermediate phase, although the present authors once supported this model for explaining the anomaly of !l.nzx

( T). [6 The most probable structure may be a configuration where only the longitudinal component of moments is in an ordered state, as shown by a recent neutron diffraction study. 19

The single-domain state below T N2 is stabilized above 3 kOe for the field normal to the c axis. Such a domain realign­ment effect in CsNiC13 has already been found in the a forced magnetostriction experiment by Rayne, Coilins, and White,20 although they did not determine the temperature below which this effect occurs. As seen in Fig. 4, the absolute value of Anxy saturated for H Ilx is nearly equal to that for H !ly and their signs are opposite. These results clearly dem­onstrate that the spin plane of this triangular array rotates freely around the c axis, holding its relative arrangement unchanged in response to a switch of the field direction from x to y; the hexagonal anisotropy in the basal plane is there­fore quite weak.

Since Anxy appears only under the applied field, the anomaly of AnZ-\ which is observable even at H = 0, cannot be attributed to the symmetry breaking term of Eq. (1). When the spin moments of CsNiC13 are ordered in the ac­plane triangular configuration, there exists a competition be­tween the uniaxial anisotropy and the exchange energy. That is, no spin moment can align along the preferred c axis with­out competing with the exchange interactions, since, as is wen known, to minimize the exchange energy, the spins on the triangular lattice tend to make an angle of 1200 with each other in the ac plane. As a result, the apparent uniaxial an­isotropy is diminished, and the crossover from Heisenberg to Ising critical behavior is suppressed in the paramagnetic re­gion even close to TN I . As an elastic degree of freedom in­fluences the appearance of Anzx ,15 a macroscopic strain gen­erated by the ordering of the longitudinal moments may be responsible for a sharp anomaly of AnZX via the second term

5961 J. App!. Phys., Vol. 64, No. 10, 15 November 1988

Hi'l(

a 234 5

MAGNE;/C F1ELD(kOe)

FIG. 4. Field dependence of Anxy at 2.0 K for H Ilx and H lIy. It call be seen that a single-domain structure whose basal plane component of spins aligns perpendicular to each field is stabilized above 3 kOe.

of Eq. ( 1), which is usually not truly critical at 'F.v. There is no such competition in the ordering process for the Ising­type CsCoC13 and the xy-Hke CsMnBr3' because the former and the latter spins are restricted to the c axis and the basal plane, respectively. The behavior of t:..nZX( n may be attrib­uted to the presence or absence of competition in spin frus­trated systems.

"J. Ferre and G. A. Gehring, Rep. Prog. Phys. 47, 513 (1984). 2G. A. Gehring, J. Appl. Phys. 53, 8152 (1982). 'N. Achiwa, J. Phys. Soc. Ipn. 27, 561 (1969). 4M. Mekata, J. Phys. Soc. lpn. 42, 76 (1977). SF. Matsubara, J. Phys. Soc. Jpn. 51, 2424 (1982). oS. Miyashita and H. Kawamura, J. Phys. Soc. Ipn. 54, 3385 (1985). 7X. Zhu and M. B. Walker, Phys. Rev. B 36,3830 (1987). "M. L. Plumer, K< Hood, and A. Caille, Phys. Rev. Lett. 60, 45 (1988). "M. Melamund. H. Pinto, J. Makovsky, and H. Shaked, Phys. Status Solidi B 63,699 (1974)<

WK. lio, M. Sano, and K. Nagata, J. Magn. Soc. lpn. 11, SuppL 51, 59 (1987).

liT. Moriya, J. Phys. Soc. Jpn. 23,490 (1967). 120. E. Aspnes and A. A. Studna, Appl. Opt. 14,220 (1975). uT. Nishino, K. lio. and K. Nagata,J. 5pectroc. Soc. Jpn. 29, 263 (1980). 14K. lio, H. Hyodo, and K. Nagata, 1. Phys. Soc. lpn. 49, 1336 (1980). 15K. lio, H. Hotta, M. Sana, H. Masuda, H. Tanaka, and K. Nagata, J.

Phys. Soc. Jpn. 57, 50 ( 1988). If'K. lio and K. Nagata, J. Magn. Magn. Mater. 54-57, i393 (1986). 17M. Sano, K. lio, and K. Nagata (unpublished). ,gW. B. Yelon and D. E. Cox, Phys. Rev. B 7,2024 (l973). !9H, Kadowaki, K. Ubukoshi, and K. Hirakawa, J. Phys. Soc. Jpn. 56,751

( 1987). o(JJ. A. Rayne, J. G. Collins, and G. K. White, J. Appl. Phys. 55. 2404

(1984 ).

lio et al. 5961

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