Journal of Magnet ism and Magnetic Materials 116 (1992) 80-82 North-Holland

Magnetic ordering in the quasi-one-dimensional induced moment ferro- and antiferromagnets AFeX 3 *

D. Visser a and A. Harrison b

" Department of Physics, Loughborough University of Technology, Loughborough LEI1 3TU, UK t, Inorganic Chemistry Laboratory, Unit,ersity of Oxford, South Parks Road, Oxford OX1 3QR, UK

The ternary halide hexagonal perovskites AFeX 3 shows a local singlet ground state behaviour. Depending on the strength of the exchange constants and the single-ion anisotropy, these systems will show an induced magnetic moment . In this paper we discuss the magnetic ordering behaviour in this series of compounds and the effect on the magnetic ordering due to an applied magnetic field.

1. Introduction

The hexagonal perovskites AFeX 3 ( A = Cs, Rb, T1, N H 4 and X = C I , Br (and l)) show a magnetic ordering behaviour which is strongly dependent on the chemical composition and the subsequent small changes in their crystal struc- ture [1,2]. The quasi one-dimensional structure of the hexagonal perovskite (space group P 6 / 3 m m c ) induces a trigonal distortion in the face-sharing FeX 4- octahedra situated along the c-axis. The combination of the cubic component of the ligand field and the spin-orbi t coupling h on the 5D term of the Fe 2+ ion gives a J = 1 ground state which is further split by the trigonal component, A, of the ligand field into a low-lying doublet state and a singlet ground state.

These systems can be described with the fol- lowing effective Hamiltonian with S = 1:

H = - 2 J ~ S i. Si+ 1 - J' ~ S i" Sj + A ~ ( S/Z) 2 i i c j i

- g~BmHe~ ~ S Z. (1) i

Correspondence to: Dr. D. Visser, Depar tment of Physics, Loughborough University of Technology, Loughborough LE11 3TU, UK. * Paper presented at the International Conference on Mag-

netism (ICM '91), Edinburgh, Scotland, 2 -6 September 1991.

J and J ' are the intrachain and interchain su- perexchange parameters , respectively. A, whose value is positive, denotes the energy gap between the singlet ground state m = 0 and the degener- ate doublet states m - _+ 1, while Hi× represents an externally applied magnetic field.

The Hamiltonian (1) provides in the absence of a magnetic field two different domains:

(a) For T --* 0 and A < 81J I + 12 [ J ' [ the sys- tem has an XY character and is magnetically ordered, e.g. the AFeX 3 compounds with A = Rb, TI, NH 4.

(b) For T ~ 0 and A > 81J I + 12 [ J ' I the sys- tem has a singlet ground state and consequently does not order magnetically. The application of an external field along the c-axis (z-direction) induces Zeeman splitting of the m = _+ 1 states and introduces a long-range magnetic ordering at sufficiently high magnetic fields, e.g. the CsFeX~ salts.

2. Magnetic ordering in AFeCI 3

The intrachain superexchange interaction in the AFeC13 compounds is ferromagnetic. This results in strong magnetic dipolar interactions at low temperatures and has a large influence on the magnetic ordering behaviour [3,4]. Normally the antiferromagnetic intrachain superexchange

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D. Visser, A. Harrison / Ordering in ferro- and antiferromagnets AFeX 3 81

interaction within the triangular lattice of the B ions in the ab plane of the hexagonal perovskite gives rise to a frustrated 120 ° type spin structure. A magnetic Bragg reflection appears at the K

1 0), of the Brillouin zone. The mag- point, Q (3 netic dipolar ordering tends towards M-point or- dering at Q (½00). In RbFeC13 one finds a deli- cate interplay between dipolar and superex- change forces resulting in a magnetic ordering behaviour which takes place first by adopting a helical spin structure; the IC1 phase with the satellites positioned on the K - M line of the Bril- louin zone, changing over into a sinusoidal one; the IC 2 phase with the satellites on the K - F line and finally locking into the 120 ° type triangular spin array; the C phase at the K point [5]. T1FeC13 undergoes structural phase transitions which fi- nally results in a magnetic lattice in which the Fe 2+ ions are arranged similar to those of the low-temperature phase of RbFeBr 3 (space group P63cm) [6]. The inequivalence in the interchain superexchange interactions causes the magnetic structure to stabilise in the helical IC 1 phase with a temperature- independent k vector. The value for k = (0.3200.3200) shows that this magnetic structure is nearly commensurate with the C phase. The details of the nuclear structure of ND4FeC13 are strongly influenced by the rota- t ion/ l ibrat ional behaviour of the NH~- group. Thermodiffraction data and DSC measurements showed that a structural phase transition occurs from hindered rotational to free rotor behaviour at about 400 K. At about 35 K a further struc- tural phase transition takes place related tO the ordering of the NH~ groups. Both phases are strongly related to the hexagonal perovskite structure at T > 400 K. At low temperatures mag- netic scattering is detected around positions re- lated to Q (~ ~ 0) of the simple hexagonal lattice. This relates to a K point type ordering.

Long-range magnetic ordering can be induced in CsFeC13 by applying a magnetic field along the c-axis [7]. At T = 0.7 K and H = 3.7 T a similar behaviour has been observed as in CsFeBr 3. However, the magnetic field changes the mag- netic domain distribution while the helical mag- netic (IC 1) phase represents only a short-range magnetic order. A similar short-range ordered

phase has been observed in TIFeC13 at 2.0 K < T < 2.5 K.

3. Magnetic ordering in AFeBr 3 and CsFeI 3

The AFeBr 3 compounds have an antiferro- magnet intrachain superexchange interaction, thus the magnetic dipolar exchange interactions are less important and one expects the 120 ° type magnetic ordering. RbFeBr 3 undergoes a struc- tural phase transition a t Tph = 108 K which causes one of the linear chains to move slightly along the c-axis [6]. This causes an inequivalence of su- perexchange pathways in the basal plane which results in a release of the frustration. The mag- netic ordering in this case involves first a partially ordered phase in which one out of the three chains in the magnetic unit cell is disordered. Finally at T = 2.0 K the full magnetic ordering is built up in the form of a modified triangular spin structure [8]. ND4FeBr 3 undergoes a similar mag- netic ordering process; however, the magnetic ordering does not take place at the H point, Q (½ ~1 1) but at the A point, Q (½01) of the BZ. This has been related to a larger distortion of the low-temperature crystal structure of NDaFeBr 3 [9].

Polymorphic behaviour has been reported for T1FeBr 3 [10]. The orthorhombic NH4CdC13 type structure as well as the hexagonal perovskite structure can be obtained. The hexagonal phase shows a structural phase transition at 657 K. The low-temperature phase has the same crystal structure as the low-temperature phase of RbFeBr 3. No information is available on the magnetic ordering, but a similar behaviour to that of RbFeBr 3 is expected.

A powder neutron diffraction study of CsFeI 3 at 4.2 K [11] shows that this compound is magnet- ically ordered in a 120 ° type triangular magnetic structure. From magnetic susceptibility studies a T N = 10(1) K was deduced. CsFeI 3 is the only AFeI 3 hexagonal perovskite which crystal struc- ture is stable. For smaller A + ions a AzFeI 4 phase will be formed.

CsFeBr 3 is a singlet ground state system and does not show magnetic order for T---, 0. How-

82 D. Visser, A. Harrison / Ordering in ferro- and antiferromagnets AFeX~

Table 1 Magnetic phases and phase transition temperatures of the hexagonal AFeX 3 ternary halides

Compound T N Comment Reference

CsFeCl 3 H induced [7] 0.7 IC t at H = 3.8 T

IC 2 at H = 3.94 T C, K point at

H - 4.55 T RbFeCI 3 2.50 (5) IC t [5]

2.35 (5) IC z 1.95 (5) C, K p o i n t

TIFeCI3 2.05 (3) IC t this work ND4FeCI 3 1.7 (2) M point this work CsFeBr 3 H induced this work

1.65(5) C, H p o i n t at H = 3.9 T

RbFeBr 3 5.5 (5) partially ordered [6] 2.0 (1) modified C, H point this work

TIFeBr 3 like RbFeBr 3 ND4FeBr 3 4.8 (2) partially ordered [9]

2.8 (2) A point CsFeI 3 10 ( l) C, H point [11]

has little effect on TN. However, the transition temperature from the partially ordered phase to the modified triangular structure is strongly influ- enced and increases rapidly. This indicates that the applied magnetic field couples with the non- magnetically ordered sites in the partially ordered phase and induces a magnetic moment, likewise magnetic ordering is induced in the singlet ground state compounds.

A general picture of the magnetic phase dia- grams of the AFeX 3 compounds in an applied magnetic field has been obtained by specific-heat studies [13].

The new information provided in this paper has been obtained from powder and single-crystal neutron diffraction experiments carried out at the Institut Laue-Langevin, Grenoble and the Hahn Meitner Institut, Berlin. The full details of these experiments will be published elsewhere.

ever, magnetic ordering can be induced as in CsFeC13 by applying a magnetic field along the c-axis. In comparison to CsFeC13, CsFeBr3 orders at higher temperatures and at lower magnetic fields than CsFeCI 3. This is directly related to slightly different anisotropy and exchange values. Only the long-range magnetic order in this case involves the 120 ° type magnetic structure. A sum- mary of the magnetic phases and ordering tem- peratures is given in table 1.

4. The effect of a magnetic field, H II c, on the ordered magnetic phases of the AFeX 3 com- pounds

The magnetic ordering in RbFeCl 3 in the presence of a magnetic field applied along the c-axis was studied by Wada et al. [5]. In this case the magnetic field enhances the exchange field. Consequently the factors which induce the in- commensurate ordering become less important which results finally in the formation of the com- mensurate 120 ° type C phase. This effect is well demonstrated in the random singlet magnetic ground state system Rbl_xCsxFeC13 [12].

For the antiferromagnetic linear chain RbFe- Br3, the application of a magnetic field up to 5 T

Acknowledgements

The authors wish to thank the UK SERC for financial support and the Institut Laue-Langevin for providing the neutron beam facilities.

References

[1] D. Visser and A. Harrison, J. de Phys. 49 (1988) C8-1467. 12] H. Yoshizawa, W. Kozukue and H. Hirakawa, J. Phys.

Soc. Jpn. 49 (1980) 144. [3] H. Shiba, Solid State Commun. 41 (1982)511. [4] N. Suzuki, J. Phys. Soc. Jpn. 52 (1983) 1383. [5] N. Wada, K. Ubukoshi and H. Hirakawa, J. Phys. Soc.

Jpn. 51 (1982) 283. [6] M. Eibschutz, G.R. Davidson and D.E. Cox, AIP Conf.

Proc. 18 (1973) 386. [7] W. Knop, M. Steiner and P. Day, J. Magn. Magn. Mater.

31-34 (1983) 1033. W. Knop, Thesis, TU Berlin (1985) unpublished.

[8] N. Suzuki and M. Shirai, Physica B 136 (1986) 346. D. Visser, B. Dorner and A. Harrison, J. Appl. Phys. 69 (1991) 6232.

[9] A. Harrison, C.V. Stager and D. Visser, J. Appl. Phys. 69 (1991) 5998.

[10] N. Jouini, L. Guen and M. Tournoux, Mater. Res. Bull. 17 (1982) 1421.

[11] H.W. Zandbergen, Thesis, University of Leiden (1981) unpublished.

[12] A. Harrison, D. Visser, P. Day, W. Knop and M. Steiner, J. Phys. C 19 (1986) 6811.

[13] T. Haseda, N. Wada, M. Hata and K. Amaya, Physica B 108 (1981) 841.