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Physica B 356 (2005) 56–59

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Polarized inelastic neutron scattering in the quasi-one-dimensional antiferromagnet KCuF3

B. Lakea, D.A. Tennantb, S.E. Naglerc,�

aClarendon Laboratory, Parks Road, Oxford OX1 3PU, UKbSchool of Physics and Astronomy, University of St. Andrews, St. Andrews KY16 9SS, UK

cOak Ridge National Laboratory, Condensed Matter Science Division and Center for Neutron Scattering, Oak Ridge,

TN 37831-6393, USA

Abstract

The material KCuF3 is a prototypical example of a weakly coupled S ¼ 1/2 Heisenberg antiferromagnetic chain

system. The inter-chain coupling leads to antiferromagnetic order at low temperatures. In the ordered state theory

predicts that the low-energy spin dynamics exhibits an unusual gapped longitudinal mode. Here we report polarized

inelastic scattering measurements of the excitations in KCuF3. A weak magnetic field is utilized to prepare a single

domain state with the spins aligned in the scattering plane but perpendicular to the chain direction. This configuration

enables a clean measurement of the longitudinal magnetic response as spin-flip scattering.

r 2004 Elsevier B.V. All rights reserved.

PACS: 75.10.Jm; 75.10.Pq; 75.30.Ds; 78.70.Nx

Keywords: Quantum magnets; Longitudinal modes; Low dimensional

Magnetic excitations in low-dimensional quan-tum magnetic systems can differ dramatically fromthose found in the corresponding classical spinsystems. The natural excitations of the S ¼ 1/2nearest neighbour Heisenberg antiferromagneticchain (HAFC) are S ¼ 1/2 spinons [1]. Theseoccur in pairs, and the resulting spectrum as

e front matter r 2004 Elsevier B.V. All rights reserve

ysb.2004.10.046

ng author. Tel.: +1865 574 5240; fax:

.

ss: naglerse@ornl.gov (S.E. Nagler).

observed in neutron scattering is a triply degen-erate continuum [2–8]. In contrast, the excitationsof classical antiferromagnetic spin systems withnearest neighbour Heisenberg exchange are doublydegenerate transverse spin waves [9]. When S ¼ 1/2 HAFCs are weakly coupled to each other anordered antiferromagnetic state results at lowtemperatures. In this state, the low-energy excita-tions are doubly degenerate transverse spin waves.Theoretical calculations treating the inter-chaininteractions in the random phase approximation

d.

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B. Lake et al. / Physica B 356 (2005) 56–59 57

(coupled-chain RPA, [10,11]) predict the existenceof a gapped longitudinal mode. Such a mode ispurely a quantum mechanical effect since in thecorresponding classical spin systems longitudinalresponse arises from multiple spin waves alone [12].Many of the principal features described

above can be investigated experimentally insuitable model materials such as the insulatingantiferromagnet KCuF3, a tetragonal system(a ¼ b ¼ 4.1 A, c ¼ 3.9 A) with chains of antifer-romagnetically-coupled S ¼ 1/2 Cu2+ ions run-ning along the c-axis. The nearest neighbour intra-chain exchange constant is Jc ¼ 17meV [13], withthe lower bound of the excitation continuumfollowing the des Cloizeaux–Pearson dispersionrelation for the HAFC [14], oq ¼ pJc|sin q|. Weak,ferromagnetic inter-chain interactions whereJa ¼ JbE�10�2Jc lead to an antiferromagneticallyordered state at low temperatures, with TN ¼ 39Kfor crystals of polytype A [15] including the samplediscussed in this paper. In the ordered state, thespins are aligned perpendicular to the crystal-lographic c-axis [13]. In the absence of a magneticfield, within the a– b plane the easy axis directionsare (1, 1, 0) or (1,�1, 0) [14]. Applying a modestmagnetic field of roughly 0.5 T within the a– b

plane is sufficient to rotate the spins into a singledomain with all spins pointing perpendicular tothe applied field [16,17].The presence of the spinon continuum scattering

in KCuF3 has been verified experimentally innumerous inelastic neutron-scattering experiments[4–7], in particular using pulsed-neutron chopperspectrometers. The magnetic scattering at tem-peratures above TN is clearly dominated by thisspectrum. A careful measurement using triple-axisspectrometry was carried out to characterize thelow-temperature magnetic excitations in the neigh-bourhood of the ordering wave vector [18]. Theresults were consistent with the theoretical predic-tions of a gapped longitudinal fluctuation inKCuF3, but the measurements were difficult andcomplex, in part because the presence of phononmodes impedes a clean measurement of themagnetic spectrum. The intensity associated withthe longitudinal mode is quite subtle. As the inter-chain interactions vanish the dynamic responsemust approach the pure one-dimensional limit,

implying that for very weakly coupled chains thelongitudinal intensity will be extremely broad andnot observable as a distinct peak in neutronscattering [19]. On the other hand, the mode willhave vanishing intensity in the limit of stronginter-chain interactions. For these reasons, a fullypolarized inelastic measurement has been carriedout which allows an unambiguous identification ofthe longitudinal magnetic scattering in KCuF3.Preliminary results of this measurement arereported here.The same single crystal of KCuF3 employed in

previous experiments [4–7] was mounted in acryomagnet and aligned with the crystallographicb-axis perpendicular to the scattering plane of thefull polarization analysis HB1 triple-axis spectro-meter [20] at the Oak Ridge High Flux IsotopeReactor. A flat FeSi monochromator produced anincident polarized neutron beam which, afterscattering from the specimen, was analysed by aHeusler crystal. The spectrometer collimationused was 480–monochromator–1200–sample–800–analyzer–2400–detector. Measurements were gen-erally carried out using a fixed scattered neutronenergy Ef ¼ 30.5meV.Measurements on magnetic Bragg peaks con-

firmed that a field of 0.8 T along the crystal-lographic b direction was sufficient to align thespins along the a-axis. In this field the flippingratio was found to be 12.5 in the elastic config-uration, with a weak variation with energytransfer.With the sample in a single domain ordered

state with spins aligned along a, the longitudinalmagnetic fluctuations appear in the correlationfunction Saa(Q, o). Both of the terms Sbb(Q, o)and Scc(Q, o) represent transverse magneticfluctuations. Since the applied field defines theneutron polarization axis parallel to the b direc-tion, the terms Saa(Q, o) and Scc(Q, o) contributeto spin-flip scattering, and the non-spin-flipscattering has contributions from Sbb(Q, o) andnon-magnetic fluctuations [20].Fig. 1 shows the inelastic neutron scattering

observed in constant-Q scans at the antiferromag-netic point Q ¼ (0, 0, 1.5). At this wave vector thegeometrical term in the neutron scattering cross-section ensures that there is no contribution to

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KCuF3 (0,0,1.5)spin-flip (longitudinal)

Energy (meV)

5 10 15 20 25 30

Cou

nts

/ M30

0

20

30

40

50

T = 6 KT = 200 K

KCuF3 (0,0,1.5)non-spin-flip (transverse)

Energy (meV)

5 10 15 20 25 30

Cou

nts

/ M30

0

20

30

40

50

T = 6 KT = 200 K

(a)

(b)

Fig. 1. Polarized inelastic neutron scattering in KCuF3 at the

wave vector (0, 0, 1.5). The upper panel (a) depicts the spin-flip

scattering at T ¼ 6K (open circles) and T ¼ 200K (triangles).

The lower panel (b) shows the corresponding non-spin-flip

scattering. The data shown are uncorrected. The solid and

dashed lines are included as guides to the eye. See the text for

further details.

B. Lake et al. / Physica B 356 (2005) 56–5958

the scattering from Scc(Q, o). Therefore the spin-flip scattering arises from Saa(Q, o) alone, andcontains only the longitudinal magnetic response.The non-spin-flip scattering contains non-mag-netic scattering as well as transverse magnetic

response corresponding to Sbb(Q, o). Theupper panel Fig. 1(a) shows spin-flip scatteringat temperatures T ¼ 6K (open circles) andT ¼ 200K (triangles). The lower panel, Fig. 1(b),shows the corresponding non-spin-flip scans. Theraw data presented here have not been correctedfor incomplete polarization or background.The low temperature spin-flip data clearly shows

a peak near the energy transfer 16meV. Thisconfirms the previous identification [18] of thisscattering as a longitudinal mode. Furthermore, theabsence of this mode above TN is in accord with theidentification of this longitudinal mode as thatpredicted by the theory of weakly coupled chains[10,11]. The non-spin-flip scattering is qualitativelydifferent. At low temperatures there is strongscattering near the elastic position, which arisesprincipally from the low energy transverse magneticspin-waves that lie within the resolution volume ofthe measurement. The scattering goes through alocal minimum near 15meV and increases, showinga broad peak at energy transfers between 20 and30meV. In the ordered state the spinon-continuumscattering should appear at energies above the scaleof the inter-chain interactions, and although there isa phonon contribution it is likely that a significantamount of the low temperature spectral weightabove 20meV is magnetic continuum scattering.There is some evidence for a longitudinal contribu-tion to this scattering in an asymmetry or ashoulder in the 6K longitudinal scattering. AtT ¼ 200K the non-spin-flip scattering shows adramatically reduced contribution from the lowenergy spin waves, and a pair of peaks at 17 and25meV consistent within resolution with thoseidentified previously [18] as phonons. This inter-pretation is consistent with the polarization and T

dependence observed in the present experiment.The measurements reported here remove any

remaining ambiguity concerning the presence of alow temperature longitudinal mode in KCuF3. Thepower of polarized inelastic scattering for thestudy of quantum fluctuations is clearly illustrated,and as improved spectrometers and neutronsources become available one can be confidentthat the technique will grow in importance. A fullaccount of the experiments described here will bepublished elsewhere.

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B. Lake et al. / Physica B 356 (2005) 56–59 59

We thank G. Shirane for the loan of the crystal,and G. B. Taylor and S. Moore for experttechnical assistance. ORNL is operated by UT-Battelle LLC., under Contract no. DE-AC05-00OR22725 with the US Department of Energy.

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