*Corresponding author. Fax: 49-30-8062-2523.E-mail address: mezei@hmi.de (F. Mezei).

Physica B 297 (2001) 9}13

Polarimetric neutron spin echo

F. Mezei����*, G. Drabkin���, A. Io!e�

�Berlin Neutron Scattering Center, Hahn}Meitner-Institut, Glienicker Strasse 100, 14109 Berlin, Germany�Los Alamos National Laboratory, MS H805, Los Alamos, NM 87545, USA

�St. Petersburg Nuclear Physics Institute, Russian Academy of Science, Gatchina, Leningrad district, 188350 Russia�Institut fu( r Festko( rperforschung, Forschungszentrum Ju( lich, 52425 Ju( lich, Germany

Abstract

Neutron spin echo (NSE) spectroscopy inherently involves polarization analysis features. Thus, the very principle ofparamagnetic NSE used for the study of magnetically isotropic systems is based on the vector properties of the neutronpolarization change in the scattering, which implies that the incoming and outgoing neutron spin directions are notparallel. Another, conventional polarization analysis feature is the opposite sign of the NSE signal for nuclear andnuclear-spin incoherent scattering, or the signal parallel and perpendicular magnetic #uctuations in the presence ofa strong magnetizing "eld. In these cases the measured NSE spectra are the algebraic sums of two components. In itsactual form, however, NSE does not allow one to investigate spin-#ip and non-spin-#ip scattering channels independent-ly from each other. At the expense of rather moderate loss of signal it is, however, possible to generalize the NSEtechnique for the study of a given channel of spin-dependent scattering processes in the most general sense of neutronpolarimetry. This means to perform inelastic NSE analysis on the partial scattering cross-section corresponding to thetransition from any incoming spin direction P to any outgoing spin direction P�. A method of combining NSE withneutron polarimetry will be described together with a simple example of experimental realization. � 2001 ElsevierScience B.V. All rights reserved.

Keywords: Neutron spin echo; Polarization analysis

1. Introduction

1.1. Types of polarization analysis

Polarization analysis is the most powerful ap-proach in neutron scattering for sorting out contri-butions of di!erent kinds of magnetic origin. Theadditional information on the polarization behav-

ior does not come free: producing a polarized in-coming beam and analysing the scattered beampolarization involves substantial beam intensitysacri"ce, due to the rejection of one neutron spinstate in the polarization process, to the limitedbeam transmission e$ciency of the polarizer andanalyzer, and last but not least, to the number ofdi!erent neutron counts which have to be taken ateach (q, �) point. For this reason, one is well ad-vised to use just the necessary, minimum degree orlevel of polarization analysis in each experiment. Incurrent neutron scattering practice, three such

0921-4526/01/$ - see front matter � 2001 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 8 4 0 - 1

degrees are usual:

(a) One dimensional (1D) (or conventional) polar-ization analysis,

(b) Three directional polarization analysis,(c) Three dimensional (3D) (or generalized) polar-

ization analysis or polarimetry.

First, in the simplest case the incoming beampolarization is parallel to the magnetic "eld direc-tion on the sample, which "eld has a "xed directionand can achieve high absolute values of severalTesla. The scattered beam analysis sorts out thefractions of neutrons scattered without neutron-spin-#ip (NSF) and with (SF), i.e. only the singlespin component of the scattered beam polarizationparallel to both the incoming beam polarizationand the magnetic "eld of the sample is measured.The setup consists of the following components:

Polarizer}�#ip(on or o+ )

NSampleN

� #ip (on or o+ )}Analyzer

Generally, two counts are taken (NSF and SF forone incoming beam polarization), however if thesample is substantially magnetized by the applied"eld, the cross section might also depend on theincoming beam polarization, so these two countswill have to be measured for each incoming beampolarization `upa and `downa.

In case of (b), three directional polarization anal-ysis, the 1D analysis (a) is repeated three times forthree di!erent, mutually perpendicular "eld direc-tions on the sample. This process only makes senseif the sample is not in#uenced by the change of themagnetic "eld direction, i.e. the "elds must remainsmall enough to only polarize the sample to a negli-gible degree. Thus, one NSF and one SF count isneeded at each "eld direction, i.e. alltogether six.This procedure allows to identify magnetic scatter-ing processes in macroscopically isotropic samples,e.g. paramagnets or randomly oriented, multido-main antiferromagnets. (Ferromagnets with ran-domly oriented domains would depolarize thebeam, so the method cannot be applied for them.)The experimental set-up is as in case (a) but thedirection of the guide "eld on the sample is freelyadjustable into various directions.

Most complete information is delivered by 3Dpolarization analysis, or polarimetry, in which caseone determines the probability P(S, S�) for a neu-tron to emerge from the scattering sample with anarbitrary spin direction vector S�, after having ar-rived with an arbitrary incoming spin directionvector S [1}3]. Due to the linear dependence of thecross sections on the neutron spin vector, a quan-tum mechanical necessity in view of the s"�

�value

of the neutron spin, it can be shown that the P func-tion can be expressed in terms of 16 independentcorrelation functions depending on (q, �) [4]. Thecomponents of a 3D polarization analysis set-upare the following:

Polarizer}�#ip (rotation)

NSampleN

� #ip (rotation)}Analyzer

The main di$culty of realizing 3D polarizationanalysis is to make sure that all the three compo-nents of the polarization vector of both incomingand outgoing beams are maintained in the appar-atus. This can be achieved only in a zero or nearlyzero "eld environment around the sample, in orderto make sure that the precessions of the spin com-ponents perpendicular to an eventual guide "eld donot run out of phase due to di!erences in velocityand/or in #ight path between various neutrons inthe beam. In this respect neutron spin echo (NSE) isa 3D polarization analysis technique, actually withthe neutron velocity di!erences been taken particu-lar care of by the echo e!ect. Nevertheless, thecombination of NSE and polarimetry is not quitestraightforward, since they require potentially dif-ferent spin manipulations around the sample. Inwhat follows, we will consider the way to getaround this obstacle.

2. Polarization analysis aspects of neutron spin echo

The sequence of neutron spin operations ina NSE set-up is as follows:

Polarizer}

�/2#ip}Precession}(�#ip)}

NSampleN

10 F. Mezei et al. / Physica B 297 (2001) 9}13

}Precession}�/2#ip}

Analyzer

One can consider this as a special case of polariza-tion analysis. The polarizer, �/2 #ipper and pre-cession "eld on the incoming side represent similarneutron spin manipulations as in polarimetry (case(c) above). Quite the same way, the analyzer ispreceded by the combined spin operations pre-cession and �/2 #ip. This particular set-up performsa peculiar polarization analysis: an echo signal willbe observed for neutrons whose spin direction isre#ected about an axis in the precession plane (i.e.perpendicular to the magnetic "eld) at the sampleregion, and those with their spin rotated in thatplane will give no echo signal (i.e. end up in a de-polarized beam). The combination of these twoelementary operations covers all linear operationsof direction vectors in a plane. It has been shown[5], that the P�"!q(qP) Halpern}Johnson rela-tion for the scattered beam polarization of para-magnets is equivalent to the sum of re#ecting half ofthe spin vector and rotating by � the other halfabout an axis perpendicular to the momentumtransfer vector q in the plane of the neutron spinprecessions (if q is lying within this plane). Thus theparamagnetic scattering gives an echo signal of �

�of

the possible maximum spin modulation amplitude(i.e. a degree of NSE polarization of 50%) withoutany other spin manipulation in the sample region.In contrast, both the nuclear coherent and isotopicincoherent (P�"P) and the nuclear spin incoherent(P�"!P/3) scattering correspond to pure rotation(by 0 and 1803, respectively), thus in order to pro-duce an NSE signal one has to place a perfectspin-direction re#ector, i.e. a � #ipper close to thesample.

NSE also produces a similar e!ect to conven-tional 1D polarization analysis. The NSE signalwill have opposite signs for NSF scattering (03 spinrotation) and SF scattering (1803 spin rotation), soif the sample displays both scattering e!ects theNSE signal will be the di!erence of the coherentspectrum (intermediate scattering function I

���(q, t))

and of the nuclear spin incoherent spectrumI��

(q, t):

I(q, t)"I���

(q, t)!I��

(q, t).

If the two spectra cover very di!erent NSE timedomains, one has a chance to separately analyzethem. However, if they vary over the same timedomain, the di!erence spectrum gives little inde-pendent information on one or the other contribu-tions. We can encounter the same situation in NSEwork with a high magnetic "eld on the sample(so-called ferromagnetic NSE) concerning the NSFand SF magnetic scattering contributions.

In sum, NSE is very e$cient to single out Hal-pern}Johnson (e.g. paramagnetic) scattering pro-cesses by the peculiar polarization analysis featureit implies, but in its usual form it does not allow usto separately investigate the spectra S��(q, �) in thevarious scattering channels, form spin state � tospin state � (where � and � stand for `upa and`downa in 1D polarization analysis and for anychosen spin direction vector in 3D polarimetry). Toachieve this, we have to e!ectively decouple, makeindependent of each other the NSE spin manipula-tions and those spin operations involved in polar-ization analysis.

3. Decoupling NSE and polarization analysis.

A "rst successfully demonstrated and appliedexample of making NSE independent of undesirede!ects of the sample on the neutron spin polariza-tion has been described by Farago and Mezei [6],who investigated magnon dynamics in the fer-romagnetic phase of Fe, i.e. when the sample com-pletely depolarizes the beam and all informationcontained in the neutron spin polarization is lost.They have used Larmor precessions to preparea "ne intensity modulated (in contrast to the usualspin direction modulated) incoming beam, whichhas been analyzed by an identical Larmor-pre-cession-based intensity modulator (intensity-modulated NSE). The setup corresponds to thefollowing spin manipulation sequence:

Polarizer}

�/2#ip}Precession}�/2#ip}

Analyzer

NSampleN

F. Mezei et al. / Physica B 297 (2001) 9}13 11

Fig. 1. Schematic layout of an intensity modulated NSE experi-ment [6].

Fig. 3. Critical scattering spectra in Fe as directly measured byintensity-modulated NSE. The inset shows the S(q, �) spectrumcorresponding to the ¹

�!3 K curve [6].

Fig. 2. Example of neutron wavelength distribution of the in-coming beam at the sample in the intensity modulated NSEset-up in Fig. 1.

Polarizer}

�/2#ip}Precession}�/2#ip}

Analyzer

and it is shown in more detail in Fig. 1. Fig. 2 showsan example of the resulting intensity modulatedincoming beam.

The intensity modulation looses 50% of the in-formation compared to Larmor precessions, sincethe cosine projection of the spin rotation we have todo with does not distinguish between forward andbackward rotations here. For this reason the NSEsignal will have �

�of the full modulation amplitude.

Fig. 3. shows the NSE and the derived energy spectraof magnons in Fe just below ¹

�, which are the

smallest energy magnons probably ever observed [6].This instrument con"guration can easily be com-

pleted by 1D or 3D polarization analysis capabilityby placing the spin manipulation devices requiredfor these purposes and reviewed above around thesample, i.e. between the analyzer}polarizer pair

closest to the sample:

Polarizer}

�/2#ip}Precession}�/2#ip}

Analyzer

NSample & Polarimeter(1D or 3D)N

Polarizer}

�/2#ip}Precession}�/2#ip}

Analyzer

12 F. Mezei et al. / Physica B 297 (2001) 9}13

Such a con"guration has also been proposed byLebedev and Gordeev in 1985 [7].

Here the decoupling between NSE and polariza-tion analysis is achieved by transforming the ordi-nary NSE spin direction modulation into intensitymodulation. The way this is achieved by a polarizer}�/2 #ip}precession }�/2 #ip}polarizer sequence(note that polarizers and analyzers physically arethe same devices) in the incoming beam leaves uswith a conventionally, uniformly `upa polarized(and intensity modulated) beam. The "rst elementof the outgoing beam manipulation is spin analysis.So one can apply all the polarization analysisschemes around the sample and perform a polar-ization analysis selection of a neutron scatteringchannel between any two spin vector states � and� simultaneously with the NSE inelastic analysis,the latter being independently carried out by theintensity modulation. For example by just addinga � #ipper next to the sample allows us to do NSEanalysis of NSF and SF scattering processes inde-pendently one after the other.

4. Conclusion

Both NSE and polarization analysis use the sametool, the neutron spin polarization direction at thesample to extract information on the scatteringprocesses. With the exception of paramagnetic scat-tering, this single tool cannot do both jobs at thesame time. By transcoding the neutron wavelength

information into intensity modulation it has beenexperimentally shown 15 years ago, that NSE canbe made independent of what happens to the neu-tron spin at the sample (e.g. depolarization in a fer-romagnet). This technique opens up the possibilityto use the neutron polarization information aroundthe sample in conventional 1D polarization analy-sis or in more general 3D polarimetric selection ofspeci"c scattering processes (such as NSF and SFin the simplest case) while performing NSE inelasticanalysis via the intensity modulation at the sametime. Beyond the enhanced complexity of the set-upand the experiment, there of course is another priceto pay for the extra information, the additionalpolarizer}analyzer pair close to the sample (cf.Fig. 1) costs quite some intensity, whatever polariz-ing system is used: supermirrors, crystals, polarized�He. Potentially progress with �He polarizing "l-ters will minimize this intensity loss for thermalneutron work.

References

[1] M.Th. Rekveldt, J. Phys. Collq. C 1 (1971) 579.[2] G. Drabkin, A. Okorokov, V. Runov. JETP Lett. 5 (1972)

324.[3] F. Tasset, Physica B 156}159 (1989) 627.[4] F. Mezei, Physica B 137 (1986) 417.[5] A.P. Murani, F. Mezei, in: F. Mezei (Ed.), Neutron Spin

Echo, Springer, Berlin, 1980, p. 104.[6] B. Farago, F. Mezei, Physica B 136 (1986) 627.[7] V. Lebedev, G. Gordeev, JTP Lett. 11 (1985) 820.

F. Mezei et al. / Physica B 297 (2001) 9}13 13