Spin resonance studies of the quasi-one-dimensionalHeisenberg antiferromagnet Cs2CuCl4

J.M. Schrama a,*, A. Ardavan a, A.V. Semeno a, P.J. Gee a, E. Rzepniewski a,J. Suto a, R. Coldea a, J. Singleton a, P. Goy b

a Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UKb Abmm, 52 rue Lhomond, 75005 Paris, France

Abstract

Measurements of the magnetic-®eld dependent millimetre-wave response of Cs2CuCl4, a quasi-one-dimensional

Heisenberg antiferromagnet, are presented. The evolution of the electron spin resonance between high temperatures

(the paramagnetic regime) and temperatures below TN, at which there is an onset of long-range magnetic order (the

antiferromagnetic regime), is studied for a range of crystal orientations. The magneto-optical data suggest that there

is an onset of local magnetic order at temperatures considerably higher than TN as determined from neutron scattering

measurements, and that the evolution towards a long-range ordered state is gradual. A phenomenological model that

describes the general features is suggested. Ó 1998 Elsevier Science B.V. All rights reserved.

Keywords: Electron spin resonance; Quasi-one-dimensional Heisenberg antiferromagnet; CS2CuCl4

The compound Cs2CuCl4 has an orthorhombiccrystal structure of the b-K2SO4 type (space groupPnma �D2h

16�); the lattice parameters at 0.3 K area � 9:65 �A, b � 7:48 �A and c � 12:35 �A [1±3].The unit cell contains four CuCl2ÿ

4 tetrahedraand the corresponding eight Cs� ions. Each ofthe four independent Cu2� ions carries a spin of 1

2

[1±3]. Magnetic susceptibility measurements [4]suggest that Cs2CuCl4 behaves like a quasi-one-di-mensional S � 1

2Heisenberg antiferromagnet with

TN � 0:6 K. A detailed study using neutron scat-tering has con®rmed this and has allowed the mag-netic structure in the ordered state to be

determined [1±3]. The predominant exchange in-teraction is between neighbouring Cu spins lyingin chains along the crystalline b-axis; the exchangepath is Cu±Cl±Cl±Cu. The intrachain interactionbetween neighbouring spins, J , is antiferromagnet-ic. There are four independent chains through eachunit cell and the spins on neighbouring chains aredisplaced along the b-axis by b=2. Due to the anti-ferromagnetic interchain interaction, J 0, a spin onone chain interacts equally with two spins on theneighbouring chain. Thus the symmetry of the in-terchain exchange interaction leads to frustrationof the simple antiferromagnetic ordering and caus-es an incommensurate cycloidal ordering of thespins with the plane of rotation lying in the chaindirection [1±3]. The ordering wavevector isq � 0:472b�, where b� is the reciprocal lattice vec-tor in the b-direction; successive spins along achain are at an angle of 169:92� to one another.

Physica B 256±258 (1998) 637±640

* Corresponding author. Fax: 44 1865 272400; e-mail: mar-

ije.schrama@magd.ox.ac.uk

0921-4526/98/$ ± see front matter Ó 1998 Elsevier Science B.V. All rights reserved.

PII: S 0 9 2 1 - 4 5 2 6 ( 9 8 ) 0 0 5 2 8 - 6

The spins in neighbouring chains rotate in oppo-site senses. The cycloid planes are canted at an an-gle of 17� 3� to the b±c plane [1±3]. Onapplication of a steady magnetic ®eld along thea-axis (perpendicular to the plane in which thespins lie), the spins partially align in the directionof the ®eld. The ordering remains cycloidal in theb±c plane, with the same period as in the zero ®eldcase. A ®eld of 11 T along the a-axis is su�cient tofully align the spins [1±3]. Application of a mag-netic ®eld stronger than 1.66 T along the c-axis(i.e.in the plane in which the spins lie) destroysthe magnetic order; full ferromagnetic alignmentis found above 8 T [1±3].

Measurement of spin resonance in magneticsystems can provide useful information about thestructure and interactions present [5,6]. In orderto investigate the magnetism in Cs2CuCl4 further,the magneto-optical response of single crystalswas measured using a combination of transmissionand cavity techniques. An ABmm Millimetre-waveVector Network Analyser (MVNA) providedsource and detection [7]. Single crystals, orientedby X-ray di�raction, were measured in several ex-perimental con®gurations. Magnetic ®elds weresupplied either by a superconducting magnet orby an electromagnet which allowed rotation ofthe magnetic ®eld in the horizontal plane. Lowtemperatures were achieved using a combinationof 3He and 4He cryostats and a specially modi®eddilution refrigerator.

Fig. 1(a) shows the temperature dependence ofthe transmission of a resonant cavity containinga single crystal of Cs2CuCl4 at a frequency of48.5 GHz. The steady magnetic ®eld was alignedalong the c-axis and the sample was situated in amagnetic ®eld antinode with the oscillatory ®eldlying in the a±b plane. At 4.2 K, well above the or-dering temperature, there is a single, comparative-ly narrow resonance. As the temperature falls toaround 2 K, the resonance becomes broader andshallower. At 1 K, it has shifted to a slightly higher®eld and broadened further, and an additional res-onance becomes resolvable at a lower ®eld. At 0.6K, the temperature at which neutron measure-ments indicate complete ordering, the two reso-nances are clear and distinct. Similar shifts andsplittings of the resonance lineshapes are also ob-

served as a function of temperature when the stea-dy magnetic ®eld is aligned along the a- andb-axes; there is insu�cient space to present thesedata here.

Measurements of the temperature dependenceof the lineshape made in a dilution refrigerator re-veal no further changes in the lineshape betweenthe temperatures of 0.7 and 0.1 K.

Fig. 1(b) shows the resonance positions as afunction of frequency when the steady magnetic

Fig. 1. (a) The temperature dependence of the transmission of a

cavity containing a single crystal of Cs2CuCl4. The steady mag-

netic ®eld is aligned along the c-axis. The traces are normalised

and o�set for clarity. The measurement frequency is 48.5 GHz.

(b) Resonance positions as a function of frequency when the

steady magnetic ®eld is parallel to the crystalline c-axis at 4.2

and 0.6 K. Note that there are two resonances at 0.6 K. The

lines are ®ts to the data. The corresponding g-factors, calculat-

ed from the gradients of the straight line ®ts, are indicated on

the plot.

638 J.M. Schrama et al. / Physica B 256±258 (1998) 637±640

®eld is applied along the crystalline c-axis and theoscillatory ®eld is in the a±b plane, at 4.2 and 0.6K. Note that there are two resonances at 0.6 K.The g-factors (shown on the plots) are evaluatedfrom the gradients of the straight line ®ts. The res-onance ®eld position is proportional to the mea-surement frequency at 4.2 K. This behaviour isexpected for a collection of uncoupled moments;at this temperature the system is paramagnetic.At 0.6 K, the extrapolation of both straight line®ts cross the ®eld axis away from the origin. Thisis strongly suggestive of the presence of an internale�ective ®eld and therefore some long range mag-netic ordering.

It is a general feature of the data that no split-ting of the line is observed for con®gurations inwhich the oscillatory magnetic ®eld is alignedalong a single crystal axis (for example, in the mea-surements employing a rectangular cavity geome-try allowing precise alignment of the sample withrespect to the millimetre-wave ®eld). This suggeststhat the system has a strongly anisotropic excita-tion spectrum.

In order to investigate this anisotropy further,measurements of the detailed angle dependence ofthe resonances were made. An electromagnet,which could be rotated in the horizontal plane,supplied the steady ®eld. The sample was placedin a cylindrical cavity, with resonance frequency43 GHz, such that the oscillatory magnetic ®eldwas vertical and along a single crystal axis, per-pendicular to the steady ®eld at all times.Fig. 2(a) shows the cavity transmission for arange of steady ®eld directions at a temperatureof 0.7 K, with the oscillatory magnetic ®eld paral-lel to the c-axis. The resonance position is strong-ly angle dependent, varying between 0.75 T whenthe steady magnetic ®eld is aligned along the a-axis to 1.3 T when it is along the b-axis. Thesharp resonance at 1.53 T is due to DPPH, ag � 2 marker substance that is useful for ®eld cal-ibration. Fig. 2(b) shows the resonance positionsas a function of angle at 0.7 and at 4.2 K. Thesolid line shows a ®t to the behaviour expectedin an anisotropic paramagnetic system [5]. Thelow temperature data are not well described bythis theory; this is a further consequence of theformation of magnetic order.

The results of the magneto-optical measure-ments can be summarised as follows:· At temperatures well above the transition tem-

perature, TN, a single paramagnetic resonanceline is seen. Its width and intensity increaseswith decreasing temperature.

· At temperatures approaching (but still above)the ordering temperature, the lineshape beginsto change. For certain orientations of the sam-ple with respect to the steady and oscillatorymagnetic ®elds, the paramagnetic resonancesplits into two. The extrapolations of the reso-nance position versus frequency plots acquirenon-zero axis intercepts.

· The properties depend strongly on sample ori-entation with respect to the steady and oscilla-tory magnetic ®elds.

Fig. 2. (a) The evolution of the the spin resonance as the orien-

tation of the steady magnetic ®eld is varied. At ÿ20�, the steady

®eld is parallel to the b-axis, at �70� it is parallel to the a-axis.

The traces are o�set for clarity. The temperature is 0.7 K. The

sharp resonance at 1.53 T is due to DPPH. (b) Resonance po-

sitions as a function of angle at (�) 4.2 K and (�) 0.7 K. The sol-

id line is a ®t to the theory of an anisotropic paramagnetic

system.

J.M. Schrama et al. / Physica B 256±258 (1998) 637±640 639

These results indicate a situation in which themagneto-optical properties vary gradually as thetransition temperature is approached. This wouldappear to be in contradiction with the results ofneutron scattering experiments, which show asharp phase transition at TN [3]. The discrepancylies in the di�erences between the techniques.

In a neutron elastic scattering measurement, thewavevector of the neutrons is varied; scatteringpeaks are detected when the neutron wavevectormatches an ordering wavevector in the sample.In an inelastic scattering measurement, the chan-ges of neutron energy and wavevector give the en-ergy and wavevector of excitations in the sample[8]. Spin resonance is a small-wavevector inelasticmeasurement; photons, whose wavelengths arevery large compared to the spin separation, are ab-sorbed. Thus the measurement gives informationabout the magnetic excitations at the zone centrein a magnetic ®eld.

With this picture, it is possible to explain thegeneral features of the magneto-optical spectra.As a material is cooled towards its transition tem-perature, regions of local order appear, as nearestneighbouring spins become more likely to be cor-related. The length scale over which spins are cor-related is known as the correlation length [9]. Asthe temperature falls, the correlation length in-creases; at the transition temperature, it becomesin®nite.

The spin resonance positions move as the tem-perature falls; this indicates that the energies ofthe magnetic-®eld-dependent small-wavevectormagnetic excitations change as the correlationlength increases. The increasing correlation lengthmight also be expected to have an e�ect on thedensity of states for small-wavevector excitations.An increase in the density of states would shortenthe excitation lifetime and hence broaden the reso-nance linewidth, as observed.

No splitting of the spin resonance was observedfor experimental con®gurations in which the

millimetre-wave ®eld was aligned along a singlecrystal axis. This suggests that the low-wavevectorexcitation energies are anisotropic. When there areoscillatory ®eld components along several crystal-line directions, excitations of di�erent energies oc-cur leading to splitting of the spin resonance.

Work is in progress to calculate the small-wave-vector excitations in the Cs2CuCl4 spin system, fora quantitative comparison with the observations ofthe spin resonance measurements. On the experi-mental front, measurements of spin resonance attemperatures below 100 mK are in progress usinga dilution refrigerator. This gives access to infor-mation about the excitations well inside the or-dered state, and how they evolve across themagnetic phase boundary, and it will possibly al-low the measurement of traditional antiferromag-netic resonance [10].

Acknowledgements

This work is supported by EPSRC, the RoyalSociety and the TMR programme of the EC.

References

[1] R. Coldea et al., J. Phys. Condens. Matter 8 (1996) 7473.

[2] R. Coldea et al., Phys. Rev. Lett. 79 (1997) 151.

[3] R. Coldea, D.Phil thesis, Oxford University, 1997.

[4] R.L. Carlin et al., J. Appl. Phys. 57 (1985) 3351.

[5] C.P. Poole, Electron Spin Resonance, Interscience, New

York, 1967.

[6] A. Abragam, B. Bleaney, Electron Paramagnetic Reso-

nance of Transition Ions, Clarendon Press, Oxford, 1970.

[7] French Patent CNRS-ENS 1989; US Patent no. 5 119 035,

1992.

[8] G. Burns, Solid State Physics, Academic Press, New York,

1990.

[9] J.M. Yeomans, Statistical Mechanics of Phase Transitions,

Oxford Science Publications, 1992.

[10] M. Hagiwara et al., J. Phys.: Condens. Matter 8 (1996)

7349.

640 J.M. Schrama et al. / Physica B 256±258 (1998) 637±640