ELSEVIER Physica B 213&214 11995) 167 169

PHYSICA

Magnetic excitations in quasi-one-dimensional hexagonal ABX3-type antiferromagnets

T. Inami a'*, K. Kakurai a, H. Tanaka b, M. Enderle c, M. Steiner 'l

a lnstitutefor Solid State Physics, Universi~,' of Takyo, Roppongi 7-22-1, Minato-ku, Tokyo 106, Japan b Department of Physics, Sophia University. Tokyo, Japan

Clnstitut fiir Technische Physik, Universitiit des Saarlandes, Saarbriicken, German), a Hahn Meitner-lnstitut, Berlin, Germany

Abstract

The magnetic excitations of three ABX3-type quasi-l-D AFs with half-integer spin values are studied. We show that magnetic excitations in S = ~2 systems in the ordered phase at low T are excellently described by the semi-classical linear spin-wave theory. In S = ~ systems however, non-linear terms due to quantum fluctuations are necessary to understand spin dynamics of the system at low T.

In the course of searching for the Haldane gap, it was found that the magnetic excitations of CsNiCI 3, an ABX3-type quasi-one-dimensional quasi {l-D) antifer- romagnet (AF) with S = 1, could not be appropriately described by conventional linear spin-wave (LSW) the- ory [1, 2]. Although this surprising result was explained mainly as an influence of the Haldane gap, which is expected to exist above TN, the origin of the abnormal dispersion is still controversial.

In order to shed some light on this controversy, we have been measuring various ABX3-type AFs of integer spins and half-integer spins by means of inelastic neutron scattering [3]. In this paper, we present our recent studies on the magnetic excitations of three ABX3-type AF's with half-integer spins, CsMnl3, CsMnBr3 and CsVCI3. Hexagonal ABXs-type AF's consist of magnetic chains running along the c-axis. These chains form a tri- angular lattice in the basal plane. The spin Hamiltonian

* Corresponding author.

is written as

H = - J ~ Si 'Sj - J ' Z S,'S~ - D Z (S~)Z, i , j i , k i

where J and J ' are the intrachain and interchain AF couplings, respectively, and D is the single site anisot- ropy. Table 1 summarizes the values of J, J', D, TN and S [4 9]. In all cases, the magnetic structure in the fully ordered state is a collinear arrangement along the chain direction with helical order of pitch (nearly) 120 ° between the chains. The plane of helical order in the easy-plane case (D < 0) is the basal plane and in the case of easy-axis anisotropy (D > 0) they are planes perpen- dicular to the basal plane containing one of the hexag- onal axes.

Inelastic neutron scattering experiments were per- formed on triple-axis spectrometers ISSP-PONTA and HER installed at JRR-3M, JAERI, Tokai, the former at a thermal beam port and the latter on a cold neutron guide. Detailed conditions of the experiments have been or will be reported elsewhere [7-9].

0921-4526.'95/$09.50 c 1995 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 1 9 5 ) 0 0 0 9 3 - 3

168 T. lnami et al. /Physica B 213&214 (1995) 167 169

Table 1 Parameters for the investigated systems

J [K] J ' [K] O [K] TN[K] S

CsMnl3 -9.5" - 0.042 h 0.05 b Tr~ x = 11.4" TN2 = 8.3

CsMnBr3 10.33 c - 0.022 a - 0.14 d 8.4 ~ ~ CsVCI 3 - 145 ~ - 0.08 f - 0.045 f 13.3 ~ ~

aRef. [4], bRef. [7], =Ref. [5], dRef. [8], eRef. [6], rRef. [9].

.=_ 150 E

_,~ 100 e . -

o

0 50

2 0 0 . . . . i , • • ' , i . . . . i . . . .

:(a) CsMnBr3 Q=(0.78 0.78 1) T = 1 . 6 K

} Ei = 5.3 meV" 40'-s-40'-40':

o . . . . . .

0 0.5 1 1.5 Energy [meV]

250 .

200 - t . -

E o 150 -

100- - ~

0

0 5 0 -

0 • 0

• • • i . . . . i . . . . i . . . .

(b) CsVCIz Q=(0.74 0.74 1) T = 1 . 6 K

Ei = 6 . 3 5 m e V 4 0 ' - s - 8 0 ' - 8 0 '

• ' i ] - J i i i i i = , , i . . . .

1 2 3 Energy [meV]

Fig. 1. Typical constant-Q scans for (a) CsMnBr3 and (b) CsVCI3 below TN.

In Fig. 1, we show typical constant-Q scans for CsMnBr3 and CsVCI 3 well below TN at the I-D zone center Q = (r/r/l). The solid lines are least-squares fit results which take account of 1-D dispersion and instru- mental resolution. The asymmetric line shape trailing to the high-energy side is due to the steep 1-D dispersion. The intrinsic line width is negligibly small, and the line shape is resolution limited for CsMnBr3, while we have to include a considerable line width of about 0.2 meV (FWHM) for CsVCI3 to get a reasonably good fit. SW dispersion curves perpendicular to the chain direction are shown in Fig. 2. The solid (and broken) lines are SW dispersion curves calculated within the LSW approximation. The

parameters we used are indicated in the table. In all cases, we observe all SW branches predicted by LSW theory; namely six branches for the easy-axis case (CsMnI3) and three for planar systems (CsMnBr3 and CsVC13). In par- ticular, for the two manganese compounds the agreement between LSW theory and experiment is excellent. In addition to the excitation energies, we also confirmed that the relative intensities and polarization of the branches agree well with the expectations from LSW theory I-7, 8]. These results indicate that in large S (= ~) systems the LSW approximation gives a good description of the spin dynamics at temperatures well below TN.

On the other hand, the results on CsVCI3 with S = ~2 show deviations from LSW theory even at the lowest T. The spectra at the 1-D zone center, taken with coarse resolution (see Fig. 3(bJ), are dominated by broad scatter- ing around 6 meV, which displays hardly any dispersion along the [1 1 0] direction. Furthermore the SW branch (designated as x y l in Fig. 2(c) shows minima at Q = (0 0 1) and (~ 13 1) instead of maxima as expected from LSW theory. These experimental findings can be under- stood within the framework of a quantum mechanical SW calculation taking into account higher-order terms, as performed by Ohyama and Shiba recently. They pointed out that in ABX3-type AF's a large quantum correction to LSW theory appears due to the one-dimen- sionality and helical ordering [10]. They showed that considerable two-magnon scattering is observed along the 1-D zone center Q = (r/r/1) and that, owing to the one-magnon- two-magnon interaction, the SW disper- sion is affected, as is observed in this experiment. We therefore conclude that the deviations from the LSW theory in the S = ~2 system are caused by non-linear quantum-fluctuation terms. The broad peak in Fig. 3(b) is then interpreted as being due to two-magnon excita- tions. As shown in Fig. 3(b), this two-magnon excitation in CsVCI 3 depends only weakly on temperature., A large two-magnon peak which exists at 1.6 K remains almost unchanged up to 40 K ( ~ 3 TN), and with further in- creasing temperature gradually dampens with its peak position moving to the high-energy side.

T. Inami et al. / Physica B 213&214 (1995) 167-169 169

2.5

2

¢1 t-" u.l

0.5

, . . . . , . . . . , . . . . , . . . . , . . . . ,

(a) CsMnl3 4 . 3 K ~ Q=I,I,~I) (3:=-(1 1 1)

0.1 0.2 0.3 0.4 0.5 lq

6 0 0

5 0 0

i 400

300

(3 2 0 0

100

I

.~~,~.,. 0.5 1 1.5 2 2 .5

Energy[meV]

ti6~ ' Cs~,Cb ~(b' 0 ~ ) ' / [- 2 - m a g n o n

~ " l l - r n a g n o n ,I. E f=14 .TmeV

" ~ 0 - E l= 14 7 meV~ .-- ~ 40'-40 '-s-4ff-417 ¢/~ " e e - [ * * ° =%~o 4 0 K

. . . . . . . • - - . . .

- 0 [ . . U . . . . . . . . . . . . . ..,.0.: 0 L t o o

0 2 4 6 8 10 12 14 Energy[meV]

2 ~-'(l~i csMn l~r3 :11(~K . . . . . . . . . 1 o Q=(-~ I ,-'rl 1)

¢ -

0 J . . . . I ,

0.1 0.2 0.3 0.4 05 11

i(C) CsVCI3 1.6K 6 r o Q=( 'q -q 1) •

! L - " ~ - o=-(1-,i 1-n 11 5 : ' z ~ , \ . ~ * o=-(11 1)

• o-.-, ~ - o - <~.~ " ~ ~ -o--e - - .o.-_ ..../ LU 2

1

0 01 0.2 0.3 0.4 0.5

I1

Fig. 2. SW dispersion curves perpendicular to the chain direction for (a) CsMnI3, (b) CsMnBr3 and (c) CsVCI3 below TN. Solid lines and broken lines are SW dispersion calculated from LSW theory. Dotted dashed lines in (c) are guides to the eye.

In the planar S = ~ CsMnBr3, two magnon scattering has been reported at T = 4.2 K [5]. In Fig. 3(a) the temperature dependences of the excitation spectrum measured at Q = (00 1) for CsMnBr3 is shown. In con- trast to CsVC13 there is no significant two-magnon scat- tering at the lowest T, but a broad peak appears with increasing temperature around 1.5 meV. This broad peak

Fig. 3. Temperature dependence of magnetic excitations at Q = (001) for (a) CsMnBr3 and (b) CsVC13.

can be attributed to the classical two-magnon process, which is expected to have a T z dependence.

In conclusion, the spin dynamics of half-integer ABX3- type AF's can be well understood in the frame of SW theory including higher-order I / S expansion terms. The non-linear terms are essential in both planar cases. In S = ~2 CsVCI3 non-linear terms due to quantum fluctu- ations are important even at the lowest T, while in S = CsMnBr3 non-linear terms due to thermal fluctuations are essential at finite temperatures.

We would like to thank Y. Kawamura and S. Watanabe for technical assistance and Tohoku Univer- sity for the use of the orange cryostat.

R e f e r e n c e s

[1] K. Kakurai, M. Steiner, R. Pynn and J.K. Kjems, J. Phys.: Condens. Matter 3 (1991) 715.

I-2] R.M. Morra, W.J.L. Buyers, R.L Armstrong and K. Hirakawa, Phys. Rev. B 38 (1988) 543.

[3] K. Kakurai, Physiea B 180&181 (1992) 153. [4] A. Harrison, M.F. Collins, J. Abu-Dayyeh and C.V. Stager,

Phys. Rev. B 43 (1991) 679. 1-5] U. Falk, A. Furrer, H.U. Giidel and J.K. Kjems, Phys. Rev.

B 35 (1987) 4888. [6] S. Itoh, Y. Endoh, K. Kakurai and H. Tanaka, Phys. Rev.

Lett. to be published. [7] T. lnami, K. Kakurai, H. Tanaka, M. Enderle and M,

Steiner, J. Phys. Soc. Japan 63 (1994) 1530. 1-8] T. Inami and K. Kakurai, in preparation. [9] T. lnami, K. Kakurai and H. Tanaka, in preparation.

[10] T. Ohyama and H. Shiba, J. Phys. Soc. Japan 62 (1993) 3277.