Journal of Magnetism and Magnetic Materials 90 & 91 (1990) 251-254North-Holland

Invited paper

Phase transitions and spin dynamics In hexagonalABX 3 type antiferromagnets

Hidekazu TanakaDepartment 0/ Physics. College 0/ General Education, Nagoya University, Furo-cho, Chikusa-ku; Nagoya 464-01. Japan

251

We have measured ESR spectra of CsNiBr). RbNiBr] and CsMnI) in order to investigate the spin dynamics related to thesuccessive phase transitions. The resonance field of the "'I-mode, 'whose resonance condition at T= 0 K is given by "'/Y = l/for l/..L c, shifts toward the high-field side with increasing temperature and shows a tendency to diverge at the lower transitionpoint TN2 ' This fact seems to indicate that the local rotational fluctuations of the triangular spin structure around the c-axisare enhanced as temperature is increased and at TN 2 ,thc distribution of the directions of the local triangular structure becomesisotropic with respect to the c-axis.

A great number of compounds of the chemical for­mula ABX) where A is a monovalent ion, B a divalentmagnetic ion and X a halide ion crystallize in hexagonalstructures which are equivalent or closely related to theCsNiCI) structure [IJ. The features of the structure arelinear chains of face-sharing octahedra BX6 along thec-axis and their arrangement with the formation of atriangular lattice in the c-plane, The exchange couplingin the chain is very strong in comparison with thatbetween the chains . Consequently the magnetic phasetransition is considered to be the ordering of the chainsin which the short range spin correlation is sufficientlydeveloped. Recently there has been considerable inter­est in the magnetic phase transitions in the hexagonalABX) type compounds, because the interchain couplingis antiferromagnetic and the ordering process is in­Iluenced by the spin frustration effect which is char­acteristic of the anti ferromagnetic triangular lattice sys­tem. Many of the present compounds undergo succes­sive phase transitions [2-6]. The discovery of the phasetransitions has stimulated the theoretical and experi­mental study on the triangular lattice spin system [7-14].

This paper is concerned with the phase transitionsand spin dynamics of the compounds having the easy­axis anisotropy such as CsNiCl), CsNiBr), RbNiCI),RbNiBr), CsMnI). According to recent works [7-14J,

the successive phase transitions are described as follows.With decreasing temperature the ordering of the z-corn­ponent of the spins takes place at T NI' and then theordering of the xy-component occurs at TN2' so that thetriangular structure is constructed in a plane includingthe c-axis (ac-plane). Although some models for theintermediate phase have been proposed, e.g., the par­tialy disordered or ferrimagnetic structure, the micro­scopic spin structure of the phase has not been clarified.

Recently we have measured the ESR spectra onseveral of the present compounds with the easy-axisanisotropy i~ order to investigate the collective modesof spin motion and the microscopic process of the phasetransitions in the triangular lattic system. In a previouspaper, refered to as I hereafter [15J, the results atT= 1.5 K were reported and the ground state propertiesof the ESR modes were discussed. The obtainedfrequency-field diagrams which are not explainable bythe conventional two-sublattice model were well ex­plained by the six-sublauice model. A remarkable modeis the "'I-mode whose resonance condition is given by"'/'1 = Jl for Jl .1 c. In spite of the easy-axis anisotropy,the gap disappears due to the balance between theantiferromagnetic interchain exchange coupling and theeasy-axis anisotropy which are competing with eachother. In this paper we report the temperature depcn-

Table 1Magnetic parameters of CsNiBr], RbNiBr) and CsMnI), where Jo and J, denote the exchange constants in the chain and betweenthe chains

CsNiBr) Ref. RbNiBr) Ref. CsMnI) Ref.

IJol/k B 17K 13] 25 K [5] 9.1 K [4]

IJ.I/k B 7.5xlO- 2 K [15]

TN 1 14.25 K(3)

23.50 K[5]

11.42 K [4,6]TN 2 11.75 K 21.47 K 8.20 K

0304.8853/9O/S03.50 iD 1990 - Elsevier Science Publishers B.V. (North-Holland) and Yamada Science Foundation

252 J/. Tanaka / ESR in hexagonal ABXJ antiferromagnets

-r25

, I I I

5 10 15 20

TEMPERATURE (K)

a c t I Cs Ni atJI

I HieI,9.30GHz0 I,TN1= 14.25K,,TNz = 11.75Ko ,

0 ,1,

0,I

Io.

0 I0 I d

0, ,

0

0 I 10

I '0

com or!' I I 000, I 00 0 00

, I 9L=220 lineI ,

1""z' '1"",26('L----,':----':------'--~--Jo

3

10

9Qi'ag 8

~ 7aul 6G:

~ 5~a~ 4

13

b. Ig , Rb Ni BrJ

<J 12 I

0, Hie

g11 II 24.02GHz,

::i: I T",=2350K

a 10 00'

T",=27,47Kg 00 I

00· II

'" 9 ~o 00

:~~ , I

~ 8 I F o.0lf3 , , 9,=220 lineex: 7

I I, I

01...-.7",.1 1 .T., rI ,

I , I I

o 5 10 15 20 25 30 35 40

TEMPERATURE (K}

10

CII Cs Mn /J

9 II HieI

8 0, 9.26 GHz"iii' 01a TN1= 11.42Kg 0

7 0 T"z=8.20K:J::.<> 0

a 60

0

ul 8

G: s I

~5 8 I

0 I

<: 0 I0

~ 40 I

<1' ~a .I 1'000012 a> 0

0: 3 If , I 91=200 line, II I

2, I

of1""z: :TN1 rI ,

0 5 10 15 20 25TEMPERATURE (K)

Fig . 1. The temperalure dependence of the resonance field forthe applied field perpendicular to the c-axis in (a) CsNiBr3•(b)

RbNiBr3 and (c) CsMnI).

dence of the resonance field of the "'I-mode for CsNiBr3,RbNiDr3 and CsMnI 3. Their magnetic parameters arelisted in table 1.

Fig. 1 shows the ·resonance field for 11.1 c as afunction of temperature. The measurements have beenperformed at X-band (::::: 9 GHz) for CsNiBr3 andCsMnI3 and at K-band (::::: 24 GHz) for RbNiBr3' Thelinewidth of RbNiBr3 measured at X-band is largerthan 5 kOe in the low-temperature phase, which mayarise from the domains in the c-plane. The accuratedata for RbNiDr3 could not be taken at X-band .

The fields for resonance in these substances show asimilar temperature variation to each other. As tempera­ture is increased in the low-temperature phase, theresonance field shifts toward the high-field side andshows a tendency to diverge at the lower transitionpoint TN 2• i.e.• the "'I-mode softens. For CsNiBr3 andRbNiBr3 the paramagnetic resonance mode is continu­ously connected to a resonance mode in the inter­mediate phase and the ESR spectrum shows no anomalyat the higher transition point TNt. As the temperature islowered in the intermediate phase, the resonance fieldshifts steeply toward the high-field side.

For CsMnI 3 the well-resolved ESR spectrum couldnot be observed in the intermediate phase, because ofthe broadening of the linewidth . The temperature varia­tion of the field for resonance in the paramagneticphase of CsMnI 3 is similar to those of CsNiBr3 andRbNiBr3' and shows no critical behaviour near TNt.

When an external field is applied along the c-axis in theparamagnetic phase in these compounds, the ESR spec­trum broadens out at TNt without noticeable shift ofthe resonance position.

We discuss mainly the ESR spectrum in the low-tem­perature phase. As for the definitions of the sublatticemagnetizations, resonance modes, exchange fields, etc.which are used in the discussion, see I. With increasingtemperature the magnitudes of the sublattice magnetiza­tions decrease and the angle between M 2 (or l'tf3, l'tfs,M 6 ) and the c-axis becomes smaller [12]. When anapplied field is perpendicular to the c-axis, the sub­lattice magnetizations M, and M4 (or M2 and Ms, andM3 and M6 ) which couple strongly with each other aresymmetric with respect to the applied field. In such casethe resonance condition of the "'t-mode is always ex­pressed as "'/Y = H. Hence the shift of the resonancefield is not explained by the temperature variation ofthe sublattice magnetization. That is to say, the shift of

1/. Tanaka I ESR in hexagonal ARX) antiferromagnets 253

nal field and decreases steeply with increasing thefluctuation angle. The whole ESR spectrum is given bythe superposition of the spectra coming from the re­gions which have different fluctuation angles and reso­nance frequencies. Consequently, the average field forresonance shifts toward the high-field side. When thefrequency of the fluctuations is larger than the distribu­tion of the resonance frequencies, the whole ESR spec­trum has a Lorentzian shape by the motional narrowingeffect. We think that the shift of the resonance field ofthe "'I-mode is caused by the local rotational fluctua­tions of the triangular spin structure around the c-axis.The temperature variation of the shift in the low-tem­perature phase seems to indicate that the fluctuationsare enhanced with increasing temperature and at TN2

the distribution of the local spin planes becomes iso­tropic with respect to the c-axis. The average spinstructure is given by the spatial and time average of thelocal triangular structures. Accordingly, with increasingtemperature in the low-temperature phase, the magni­tude of the sublattice magnetizations AI2 , MJ , Als and""6 .which cant from the c-axis becomes smaller incomparison with that of M I and "'14 which are parallelto the c-axis, and the angle between M 2 (or ""J' M s,·/'116) and the c-axis decreases, At TN2 the angle becomeszero and the ferrimagnetic spin structure along thec-axis is realized in the c-plane,

The local rotational fluctuations of the triangularstructure round the external field also seems probable.However, it does not change the resonance condition ofthe "'I-mode. The mixture of the local rotationalfluctuations around the external field and the c-axisgives rise to a remarkable shift of the resonance field ofthe "'I-mode.

Next we discuss shortly the ESR spectra in theintermediate and paramagnetic phases. With decreasingtemperature in these phases the resonance field forJl ..1 c shifts toward the high-field side. The shift is notexplained by the intrachain short range spin correlationeffect discussed by Nagata and Tazuke (16), because theobserved direction of the shift is different from thatpredicted by their theory. There is a model of theintermediate phase such that the spins in two-third ofchains are antiferromagnetically ordered along the c-axisand the spins in the rest of chains are paramagnetic.This spin structure is called the partially disorderedstructure. In general the anti ferromagnetic resonancemode for the collinear spin structure in the easy-axisanisotropy case is accompanied by the finite gap energy.Therefore the shift toward the high-field side in theintermediate phase is not interpretable in terms of theresonance of the collinearly ordered spins. The magneticmoment of the ordered spins induced by the externalfield yields an effective field acting on the spins in the

1045'

30 '

40'

0'10'

20'

8

10

8

Q) 60'0~

"-<;

4::l

2

00 4 6

H (IOJOe)

Fig. 2. The resonance condition of the "'I-mode for variousfluctuation angles, where the intrachain and interchain ex­change fields and the anisotropy field are taken as 400, 3 and 2kOe, respectively. The inset shows the configuration of thesublattice spins for Il s: c in the low-temperature phase and its

rotational fluctuations round the c-axis .

the resonance field is not explainable in terms of theaverage spin structure.

On the frequency-field diagram the shift of theresonance field toward the high-field side is interpretedas the decrease of the slope of the "'I-branch withoutgap energy. The disappearance of the gap is characteris­tic of the triangular spin structure in a plane includingthe c-axis. Thus the ESR signal comes from the regionin which the spin moments form locally the triangularstructure.

The motion of the triangular spin structure corre­sponding to the "'I-mode is rotation round the c-axis.Therefore it seems probable that the local rotationalfluctuations of the triangular structure round the c-axisas illustrated in the inset of fig. 2 couples with the"'I-mode, so that the "'I-mode softens. Fig. 2 shows howthe resonance conditions of the region changes, when alocal region of the triangular structure fluctuates aroundthe c-axis. In fig. 2 the magnitude of the fluctuations isrepresented by the angle between the external field andthe normal of the spin plane, which we call the fluctua­tion angle . The intrachain and interchain exchange fieldsand the anisotropy field have been taken as 400, 3 and 2kOe, respectively.

The cofiguration of spins for the finite fluctuationangle is not the equilibrium state. In the low frequencyrange in comparison with the gap of the "'s-mode, thefrequency of the "'I,mode is in proportion to the exter-

254 II. Tanaka / ESR in hexagonal ABXJ antiferromagnets

paramagnetic chains through the interchain exchangeinteraction. Although the effective field reduces theexternal field, its magnitude is of order of IJI IXoll/(gJLn)2 =:: (J1/JO)Jl ::;1O- 2H, where Jo and J I are theexchange constants in a chain and between chains,respectively, and Xo the susceptibility per spin in theordered chains. Hence the shift of the resonance field inthe intermediate phase is not explained in terms of theresonance of the paramagnetic spins in the partiallydisordered structure.

Although we have no clear explanation for the mech­anism of the shift of the resonance field near the highertransition point TN I , we think that the interchain shortrange spin correlation and the relaxation process areresponsible for the shift. When the triangular spin struc­tures are locally constructed by the interchain shortrange correlation in the paramagnetic or intermediatephase, and their directions are distributed about thec-axis, the resonance fields of the wt-moue for thesestructures are located on the high-field side. If theparamagnetic resonance mode and the wl·mode for thelocal triangular structure are mixed by the relaxationprocess, the resonance field of the whole spectrum shiftstoward the high-field side. By such a mechanism theshift near TNI may be caused.

This work has been done in collaboration with Prof.K. Nagata, Prof. K. lio, Mr. S. Teraoka, Mr. Y. Saitoand Mr. E. Kakehashi in Tokyo institute of Technology,to whom the author expresses his sincere thanks.

References

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