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The spin precession resonance spectrometer
Nuclear Instruments and Methods 192 (1982) 513-522 North-Holland Publishing Company
513
THE SPIN PRECESSION RESONANCE SPECTROMETER G.P. FELCHER and Lid. CARPENTER Argonne National Laboratory, 9700 S. CassAvenue, Argonne, 1L 60439 USA
Received 30 June 1981
We present the concept of a new neutron scattering instrument to be used at a pulsed neutron source. The machine, which starts as a development of the resonance detector spectrometer and incorporates the basic ideas of spin precession energy analysis, is suited for the study of medium- and high-energy excitations in solids and liquids, particularly at small momentum transfers. The most novel characteristic of its performance is a high resolving power, achieved without appreciable loss of neutron flux. In an alternative operation (and sacrificing resolution) the instrument is capable of separating spin-dependent from spin-independent scattering processes.
1. Introduction The new generation of pulsed spallation neutron sources has, over the conventional neutron sources (reactors), the distinct advantage of a large flux of epithermal neutrons. This enables, in principle, the study of deep inelastic processes in solids and liquids, with the benefit of the neutron scattering technique, which enables one to get at the correlation function from the scattered intensities without resorting to, cumbersome models or to coarse approximations in the evaluation of the matrix elements. It is clear that in order to study processes with an excitation energy 60 neutrons with energy E1 > co have to be employed when 6J i> kT. Furthermore, if the momentum of the induced excitation Q is small as it occurs in many important cases - the conservation laws of energy and momentum require that even the final energy E2 of the scattered neutrons be large. These considerations have prompted the development of a new instrument, the resonance detector spectrometer [1 ] where the neutrons are detected only if the final energy of the neutron matches the energy of a neutron resonance of a n - 7 converting plate. The instrument is very simple and yet powerful: an excitation process in the sample is determined by two quantities, the flight time of the neutron from the pulsed source to the detector, and the energy of the n - 3 ' resonance. The width of the resonance, at best a few hundredths of eV, is adequate in several instances to define the energy E= of the scattered neutron but often it is desirable or imperative to obtain a better 0029-554X/82/0000-0000/$02.75 © 1982 North-Holland
resolution of E2. This is obtained in the present scheme by inserting in the secondary neutron path a spin-precession device, similar to that developed by F. Mezei and J.B. Hayter for their spin-echo spectrometer [2]. The device requires full polarization of the incident beam as well as polarization analysis. We give here a brief description of the mode o f operation and the projected performance of the entire instrument, which we call spin precession resonance spectrometer, together with a brief description of the components needed for its operation. The general areas of solid state physics in which this instrument might be useful are tentatively thought to be similar to those spanned by a high energy chopper spectrometer. They include (1) the study of frequency spectra of crystals, particularly molecular crystals and of phonons in metallic hydrides, in the region of energies />50 meV; (2) the study of high-frequency magnetic excitations (e.g., spin waves and Stoner excitations) in transition metals, alloys, and compounds; (3) the study of magnetic excitations in mixed valence and actinide compounds; (4) measurements of joint densities of electronic states in transition metal and actinide compounds up to "-0.5 eV above the Fermi level; (5) study of spin wave dispersion in amorphous ferromagnetic materials; (6) crystal field excitations.
2. Concept A layout of the resonance detector spectrometer is presented in fig. 1 a. A burst of neutrons at time zero
514
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
y-RAY CASCADE
RESONANCE ~ ,..¢' ABSORBER Fg r~ F~ -
"./: 1~ SAMPLE, /" ) C /
Po,_SE,:,
SOURCE
fsec
Y
DETECTOR
I SPIN FILTER
b
t I = t - (12/02) ;
1----1
~-
+--&
~~NANCE SAMPLEi,/~,/ ~, ABSORBER u,, L ~ " SPIN * FLIPPER
PRECESSION DEVICE
Fig. l. (a) Layout of the resonance detector spectrometer. (b) Components to be added for operation as a spin precession resonance spectrometer.
is emitted from the source. At a subsequent time these neutrons irradiate the sample, which scatters the neutrons at an angle 20 with differential cross section Z (El, E2). The scattered neutrons are measured by the resonance detector only if their energy falls within the energy range where the effective resonance curve D(E) is non-zero. Precisely, the quantities measured at the detector are: t = l l / 0 1 + 12/u2
I(t) = ( o
-
dE1
?
(1)
dE210(El) E(EI, E2)D(E2)
o
X 6(t - ll/vl - 12/v2).
(2)
With an appropriate choice of the instrument's geometry the time of arrival t can be made to define rather well the incident energy El, even if the final energy is not too well defined. This is obtained by making l~, the pathlength of the neutron from source to sample, much larger than the sample-detector distance 12. Since the neutron velocities before and after scattering are comparable the time 12/u2 is small compared to ll/vl and anyway the average value of l=/v2 can be subtracted from the measured time of arrival t. Thus,
l ( t ) ~ , I o ( E 1 ) ( 2 E l / t l ) , F £(E,, E2)D(E2) dE2 , 0
with
(3)
E1 = m/2(lt/tl) 2 •
(4)
The uncertainty in the energy transfer &co is mainly due to the width ~ 2 of the resonance curve D(E2) appearing in the integral of eq. (3). This could be unbearably large; for instance, for a resonance width of 0.1 eV, processes involving 0.5 eV energy transfer are defined with only 20% resolution. However the resolving width &E2 can be compressed making use of the spin properties of the neutron in a precession circuit. Practically this is achieved by adding a number of components to the basic resonance detector spectrometer, whose function we briefly describe, leaving to a later section the discussion of their technical feasibility. a) The primary neutron beam is fully polarized. This is achieved by passing it through a neutron spin filter, which removes neutrons of the unwanted spin for all energies. After the filter, the polarization is maintained along a quantization axis by magnetic guides (for example, the spins are kept normal to the neutron flight path as in fig. lb). We assume for the time being that the neutrons are scattered by the sample without spin flip. b) The resonance detector is spin sensitive. Many of the neutron resonances in the electron volt range are spin dependent: neutron absorption occurs for only one of the two relative orientations of the neutrons spin and the nuclear spin of the n - 7 converting plate (a collection of these is reported [3] in table 1). We assume that the nuclei of the target of tile resonance detector are fully polarized, so that only the scattered neutrons with the same spin state of the primary beam are actually detected. With these definitions, the intensity measured by the detector is given still by eq. (3), with the proviso that all the quantities are relative to one spin state; if this is indicated by + we have:
l+(t) ~ Io(El) 2E--L : tl
£++(E1, E2) D÷(E2) dE2.
(5)
o
With the two additions the instrument is converted into a fully polarized neutron spectrometer. c) A neutron spin precession device is inserted in the flight path (fig. lb) of the scattered neutrons. At its entrance, the neutrons are brought "suddenly" (non-adiabatically) in a magnetic field normal to their quantization axis. The neutron moment precesses around this new field for all the length of the device,
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer Table 1 Spin dependent neutron resonances (from Sailor, ref. 3) Isotope
Target spin
i I s In
9/2
121
Resonant energy
Spin of compound state
1.46 3.86 9.10
5 4 5
Sb
5/2
6.23 15.5
3 2
14SNd
7/2
4.37
3
149Sm
7/2
0.0976 0.87 4.93 8.9
4 4 4 4
lSlEu
5/2
0.327 0.461 1.056 3.37
3 3 3 2
I s s Eu
5/2
2.46
3
lSSGd
3/2
0.0268 2.008 2.568 6.30
2 1 2 2
0.0314 2.825
2 2
lS7Gd lSgTb
161Dy
3/2 3/2
5/2
3.35 4.99 11.14
2 1 2
2.72 3.69 4.33 7.73
3 2 2
163Dy
5/2
1.71
2
16SHo
7/2
3.92 8.1 12.8 18.1
4 3 4 3
167Er
7/2
0.460 0.584 6.1
4 3 3
169Tm
1/2
3.9
1
181Ta
7/2
4.28 10.34
4 3
lSSRe
5/2
187Re
5/2
2.16 5.90 7.20 4.42 11.2
3 2 3 3 2
1911r
3/2
193ir
3/2
19Spt
1/2
0.654 5.36 1.303 11.9
2 2 2 1
515
at whose end the initial field is restored also non-adiabatically (see fig. 2). The final polarization of the neutron depends on the time spent in the device hence on the wavelength of the scattered neutron X2 : P(X2) = cos 27tAX2 ,
(6)
where A = ClpH, and lp is the length of the precession device, H the applied magnetic field. C is a constant; in convenient units C = 7.34 × 10 -3 cm - 1 0 e -I A -1. Basically, the polarization P(X2) gives a function that modulates the effective resonance curve D÷(~2) [see fig. 2]. The product 1/2(1 + P ) ' D ÷ is the effective response of the detector, which has an energy resolution AE2 determined by the period of the precession A rather than the width of the resonance line. The detected intensity is:
I+(t, A) ~Io(E1)2E' f ~++(E1,Ei)D+(E2) tl
0
× [-~(1 + cos 2rrAX2)] dE~ .
(7)
Or in more compact form:
5r+(Xl, A )"~ J ~(Xl, )t2) cos 2rrAX2 dXl
,
(8)
0
where ~ ÷ is the normalized intensity, from which the
GUIDE FIELD l--Ho --I
I I
PRECESSION FIELD H ®
A
1Tl:0~
/
0"
GUIDE POLARIZER FIELD f ABSORBER
/Ho
e
T
['1
~l ; ~ ~ L_] i
: 2rA~,2 A : 7.34x10"3~cmHoe(~-I)
O(X2)1
i[-7~,;---,~ ' 7~,:f,V ',
' )'2
Fig. 2. Top: Conceptual operation of the precession device. From A to B, the magnetic field is normal to the spin quantization axis. Bottom: The effective width of the resonance line compared with the precession period.
516
G.P. Felcher,J.M. Carpenter/ Spin precession resonance spectrometer
cosine-independent terms have been subtracted:
7 ÷ ( k , , A ) = I + ( t , A ) / ( I o ( E D E", / t , ) - 7 ÷()kl, 0 )
(9)
and (~()kl,)k2) "~" Y~,(E1, E2) D(~'2) 2E2/X2 .
(10)
qS()tl, X2) is the quantity that we want to recover from our measurement, since it is directly proportional to the cross section Y,(E1,E2), with factors that can be easily calibrated. ~ X l , X2) is the Fourier transform of the measured intensity ~÷(X~, A). Suppose that a sequence of measurements is performed for different values of the magnetic precession field (i.e., different A's) up to a maximum value. From these we can calculate the quantity: Amax
4)(kl, k2) =
cY÷(kl, A ) cos 2TrAk2 dA
d 0
(ll)
~r+(Xl, A ) = ~ b ( X l , X2i) cos 2rrAX2i,
~b0tl, X2)R0t'2, X2) d)k2 ,
the X2i are determined as the centers of the functions q~(Xl, X;) or equivalently can be determined by least squares fitting a series expression of the form (8a). The only requirement is that the different k i are separated by an interval larger than the ~5)t2 of the resolution function. d) Selection of the spin flip processes. Removing the hypothesis made in section a), we take now ~;(EI, E2) to be not entirely spin independent. For the given neutron spin state of the primary beam, there are two cross sections: 2+-(E1, E2)
with
~-+(EI, f 2 )
(12)
R(X',X2) is a resolution function of width 5X2 ~ 1Mmax. ~Xl,)t2) is then determined within an instrumental resolution constant in wavelength, rather than in the energy of the scattered neutrons. Rather good resolution is obtained even with a modest precession time; for example, to obtain 6X2 = 2 X 1 0 - s A , a magnetic field of 1.3kOe is to be applied over a flight path of 50 cm. The integral in eq. (1 1) can be approximated by a finite number of measurements at different precessing periods A. The minimum precessing period is defined by the reciprocal linewidth of the resonance, A rain = 1/AS2; and all the harmonics have to be taken up to Area x = NAmin. Eq. (11) takes the form: N ~(Xl, ~,2) = ~
(13a)
and two other cross-sections if the spin state of the primary beam is reversed:
0
R0t2, )t2) --Amax 1o [2nAmax(X2 - X2)] •
(Sa)
i
E÷*(fl, f 2 )
oo
= f
duces a blurring of the image of ~(Xl, )k2), assumed as a continuous function. If this function does not present sharp edges it is relatively unimportant to have high resolution. On the other hand, if the signal is made of discrete delta functions, so that eq. (8) can be rewritten:
~+(~k,, nA min) cos 2rmAmin~,2. (1 la) 1
N is the minimum number of measurements to be taken in order to achieve the desired resolution. The treatment given here is a conventional Fourier transformation, identical to the transformation in real space of the X-rays or neutron diffraction data. The truncation in the Fourier integral, due to Amax, intro-
~--(L" 1, E 2 ) .
(13b)
If the precession circuit is not switched on, the instrument is in effect a polarizing spectrometer with polarization analysis. The four cross sections can be independently measured, with the insertion of neutron spin flippers in the primary or in the scattered beams [6]. This makes possible the separation of processes like the coherent and incoherent (nuclear spin incoherence) scattering from liquids: here the coherent cross section is entirely non spin-flip, while the incoherent cross section is one third non spin-flip, two thirds spin-flip (and the relations hold, 22÷÷ =Y:-; S +- = ~-÷). The full separation of the four cross sections is possible only with the precession circuit switched off, hence with the energy resolution of the detector's resonance. With the precession circuit switched on, the information on the spin state of the scattered neutron is lost, in order to attain the compression of the resolution element 2xE2. Rewriting eq. (8) with an explicit indication of the neutron spin history, we have:
7÷(xl, A ) = f
[¢+(Xl, X~) - ¢-(X,, X2)I
o
X cos 2nAX2 dX2
(14a)
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
taken tobe, respectively, 2.79 X 104 and 3.82 X 10 a b for fully polarized nuclei. The probability for a neutron absorption, followed by gamma emission, is presented in fig. 3, for a target thickness o f 4 mm. If the detection efficiency for the gamma cascade is unity, fig. 3 represents the detector function D(E2) , on which we can base the preliminary performance estimates. First, we want to calculate the region of energy and momentum transfers covered by the instrument. The energy transfer is simply 60 = E l - E 2 , while the momentum transfer is defined by:
where ~r÷(kl, A )=l*(t, A )/(Io(E1) El/t~) - ~1 [5r +(hi, 0) +~7-(X~, 0 ) ] ,
(15)
The reversal of the neutron spin in the primary beam provides the intensity: oo
c.'Jr-(k~, A ) : f
[~-+(Xl,
~k2) - -
~--(~,1, ~-2)]
0
X COS 27rA•2 dX2 •
(14b)
These expressions identify the extent of the information that can be eventually obtained by the spin precession resonance spectrometer. In particular, if'- = - ~ r+ [and thus the spin reversal does not provide additional information] unless the sample does not exhibit a natural or induced net magnetization.
Q-
2n
0.2861
x/E1 +E2 - 2x/fflE2 cos20 .
(16)
Where the energies are expressed in eV, and Q in A.-1. The incident energy E~ can assume any value (provided that E~ > E2); the final energy is constrained to be within the range over which the detector function is non-zero. Roughly speaking, this occurs for two energy bands, the first extending from 0.02 to 0.23 eV, the second from 0.81 to 0.93 eV (fig. 3). The region of the (Q, co) space spanned by the detector depends on the scattering angle, and we choose 20 = 8 °, a geometry that would enable us to detect optical modes in the second Brillouin zone of a 3d metal. The (Q, w) space subtended by such detector is depicted in fig. 4. We would like now to evaluate the resolution of the instrument. While a full expression is quite complex, we are interested in obtaining its dependence on 67~2, as this is the most representative quantity in the performance of the instrument. We have already seen how a resolution ~k2 is obtained by the preces-
3. Preliminary performance estimate The analysis of the performance of the spin precession resonance spectrometer requires a proper choice of the spin sensitive resonance detector. No such device has yet been built; actually this is the single item in the proposed instrument whose design will require the most development. However, we have at our disposal a device that conceptually can be utilized as a spin and resonance detector: this is the samarium spin filter developed at Rutherford by Williams [7]. This device is a target of fully polarized 149Sm nuclei, which captures the neutrons of one spin only over an energy range corresponding to the samarium resonance. The device as built is a neutron spin filter; but "for our purpose we "use" it the complementary mode, namely by counting the gamma radiation emitted following the absorption of the neutrons of one spin state. Williams' filter consists of a single crystal o f cerous manganese nitrate (CSMN), with about 6% of the Ce atoms replaced by 1495m. The absorber has a thickness of 4 mm, and a viewing area of 2.5 × 2.5 cm. In the following, we assume that the 149Sm nuclei are completely polarized, and further take into account only the two resonances of lowest energy for which the compound nucleus has s p i n 4 [the 149Sm spin being 7/2]. These occur at laboratory neutron energies E2 = 97.6 and E2 = 873 meV (see table 1), both with a capture width F.r = 60 meV. The peak values of the cross section at these resonances have been
517
A N
w ca Od
0 0
0.2
0.4
0'.6 eV
0.8
1.0
Fig. 3. Effective detector function for a samarium 149 resonance absorber (see text and ref. 7). The bars under the peaks are arbitrarily taken as the effective band width of the resonances.
518
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer t00~
~
~
-~ .
.
.
.
.
.
.
!
i
0 . 0 9 7 6 eV Resonance
I0
..... / : - ~
upper band ....
E = 0 . 9 3 0 eV ,
i,
:~/~----~7~, ~ E = 0.814 eV
I0
E f = 0 . 2 3 5 eV T
~ >
lower band
~t 4i
0.1
2
2
O0
0.2
0.~4 W, eV
----016
0.8
Fig. 4. ~, Q range covered by the two resonances of samarium-149 for a detector set at 20 = 8° from the primary beam.
sion method in the case of one resonance; the extension to the present case of two resonances is trivial. (Notice that, since the resonances are far apart, their separation comes about in a natural way; if the sample can be said to have no excitations with energies greater than 0 . 8 1 - 0 . 2 3 = 0.58 eV then the two bands are separated in time-of-flight.) The energy and momentum resolution are given by:
QAQ
_
4712
(0"2861) s 6X2
=
[1: Eal/2 +E~/:)
O.---2-ff~
6.2 - - ~ -
o'.~
--
0'.6
~p oV
Fig. 5. Limits of the energy resolution for the two lowest samarium-149 resonance lines. The precession device is assumed 50 cm long, with a maximum field of 2 kOe.
with the following definitions: S(EO is the source function. It has been assumed to have the following shape [8] : E S ( E t ) = S N • G 5.3 L-~T
exp(-E/ET)
Et(~/E~ - x / E z c o s 2 0 ) (17a)
+ E : ( x / E : - x/E1 cos 20)~
~
~
[~ -1
2
0%
aX2.
(17b)
Numerical calculation o f Aw was performed with the following parameters: A~,2 = 2 X 10 -3 A; Ii = 7 m, 12 = 1 m. The results are shown in fig. 5. While for the lower band the neglected terms in the resolution (due to the geometry; time of the neutron burst etc.) are comparable to 6X2, this is the controlling factor for the upper band. Scattered intensities. For each element E l , E2 the number of neutrons collected in unit time is:
N(E1, E2) =S(EI) T(E O ~1 Y.(E1, E2) ~2 T(E2)D(E2) (18)
+ E[1 +
(5ET/E) 7]
"
(19)
Where for the maximum o f the spectrum ET = 0.035 eV; G is a normalization constant equal to 3 X 10 -4 in consistent units and SN is the time-averaged neutron production rate which was taken as 3 X 10 Is neutrons/s (design current for the Intense Pulsed Neutron Source at Argonne National Laboratory). T(EO is the transmission through the spin filter. If this is made o f almost fully polarized hydrogen the transmission is, over the region o f interest, almost constant, and equal to 0.2 for 95% neutron polarization. ~21 is the angle subtended by the sample. If its cross section is 2.5 X 2.5 cm, at a distance o f 7 m from the source, ~Zl = 10 -6 st.
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
~22 is the angle subtended by the detector. If its cross section is 2.5 × 2.5 cm, at a distance of 1 m from the sample, ~22 = 6 × 10 -4 sr. T(E2) is the transmission through the spin precession devices. On the average the spin of half of the neutrons is turned down, hence it is not detected by the counter; thus T(E2) = 0.5. D(E2) is the detector function, as presented in fig. 3. E(E1,E2) is the scattering power of the sample, and can be written as follows:
Z(E1, E2) = x/(E21E1) Zo(a, co),
(20)
519
RESOLUTIONELEMENT:
10,
!
I
/>0.1 9
/// I
iI
t / 7 6
c; 5
where E0 is finite over a fixed resolution element AQ, ACO.
4
We can now calculate the number of neutrons detected following the Q, • scattering process:
3
/
f
// / /
2 eV
N(Q,
AQ Ac~ = f
dE~
co+0.025 eV
×
j
t -co+~to/2
N(E~, E2)
dE:
(21)
~ 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
~,eV
E1 --to--Awl2
when El, E: are not independent variables [see eq. (16)], and the limits of El were chosen for convenience. The intensity depends linearly on the value of Z0, the macroscopic cross-section of the sample per unit area. In terms of the microscopic cross section a ( a , co):
Y~o(Q,w) =No(Q, w) l,
0
(22)
where N is the number of cells per unit volume, and l the sample thickness. Suppose that o has a value of the order of 10 -4 b/sr/meV per unit cell, which is a typical cross section for high-frequency photon spectra, at least for some co, Q range. Let ustake the cell as cubic, with an edge 4 A long; and the thickness I be 2.5 cm [admittedly a rather thick sample]. With these numbers, we can calculate the number of neutrons scattered within a resolution element AQ, Aeo. If we put A~o = 5 meV, AQ = 0.75 A -1 we obtain the neutron counts presented in fig. 6. Comparison with other spectrometers. The spin precession resonance spectrometer utilizes a broad band of incident neutron energies, and detects the scattered neutrons within a fairly wide range of energies. For this reason the instrument has very high luminosity, thus offsetting the neutron losses due to the polarizing devices (which lower the efficiency by
Fig. 6. C o n t o u r s of counting rate (neutrons/min) in the resonance detector. Sample cross section 10 .-4 b/sr/meV over the indicated resolution function. For the source flux, instrum e n t geometry and sample shape, see text.
an order of magnitude) and partially offsetting the constraint due to the small area of the detector. The instrument is operated as a Fourier spectrometer, hence the statistical errors on the recovered signal ¢(~1, ?~2) [see eq. (11)] are not independent. However in this as in other spin precession devices [4] the Fourier modulation is exact, since it does not depend on the perfection of mechanical components. The chopper spectrometer has quite different characteristics. It starts selecting a very narrow band in the incident energy spectrum, so that the neutron count on a fixed detector area is considerably lower than for the spin precession resonance spectrometer. However, in this case the addition of other detecting elements is simple and relatively cheap: and thus a drastic improvement can be achieved both in the counting rate and in the ¢o-Q region spanned. Only when the region of the energy-momentum space to be scanned is confined to large w, small Q is this improvement not satisfactory: in this case the scattering is confined anyway to the region of small 20 angles,
G.P. Felcher, J.M. Carpenter/Spin precession resonance spectrometer
52(!
and furthermore detectors must have reasonable efficiency for high neutron energies. The resonance detector spectrometer does not have any conceptual advantage over the spin precession resonance spectrometer. In order to keep the effective linewidth of the resonance detector narrow, the n - 7 converting plate must not absorb more than about 10% of the neutron beam at the resonant energy. Thus the efficiency for the two instruments is comparable, while the substantial improvement in resolution favors the spin precession resonance spectrometer. However, the resonance detector spectrometer is a comparatively simple machine, and the understanding of its performance and capabilities is a necessary stepping stone in the development of the more sophisticated devices described here.
with ytterbium. Here high proton polarization is attained due to the coupling of the proton spins with the magnetic impurity ytterbium (kept polarized by an external magnetic field) by a method called "spin refrigeration" [12]. The device is expected to achieve ~75% proton polarization in an easily reachable sample environment (temperature ~1.1 K; applied magnetic field ~14 kOe). In these conditions, 18c~ of the neutrons of 100 meV energy should be transnritted, with a final polarization of 95%.. b) Neutron spin flipper: It must be capable of flipping the spin of the neutrons irrespective of their energies. A device with these characteristics has been successfully demonstrated already [ 13]. c) Spin precession unit: The circuits hitherto built [4] are effective for quasi-monochromatic radiation. For a "white" neutron beanr a scheme such as that presented in fig. 7 should be satisfactory. The neutron spin is kept aligned along a magnetic field H t transverse to its flight path. Immediately before the start of the precession circuit, the guide field lit is tipped to 45 ° (with respect to the flight path axis) by the insertion of a current coil. The neutron spin is now also aligned at 45 ° , and remains so after crossing a thin superconducting sheet. At the right side of the superconducting sheet, which allows the non-adiabatic change of the field direction, the applied magnetic field is normal to the neutron spin direction. This precesses in an effective field f~ Hp(l) dl, after which the insertion of a second superconducting sheet allows the restoration of the primary magnetic situation. (For tire neutron spin presented in fig. 7, the final state is almost antiparallel to the original state.) The device as presented requires two non-adia-
4. Technical development The design of the spin precession resonance spectrometer requires the acquisition of state of the art technology. The task is less formidable than it nfight appear at a first glance, since all the individual components have been already partially or fully developed for different purposes, as it appears from the following list: a) neutron spin filter: Several devices have been developed recently [ 9 - 1 2 ] which polarize a white beam. In all these devices the spin filter consits of a target material which contains a high concentration of polarized hydrogen nuclei. In the scheme followed at Argonne, and presently under testing, the target is a crystal of hydrated yttrium ethyl sulfate doped
MAGNETIC
FIELDPROFILE Hz:Ht Hz Ht
T
Hp Hz
l Hz=Hp HZH~H9
T~Hx!
X
,.';-A'
A f
,
NEUTRON SPIN PROFILE SUPERCONDUCTING SHEET ( Ht= 0 )
Hz: Ht
T
UUU
VVVU
i
Ht Hz
i
,
,,.::.;,
i i
/
3'
t-_-,,
SUPERCONDUCTING SHEET ( HI =0)
Fig. 7. Preliminary design of the spin precession device. The superconducting sheets provide the decoupling of the magnetic fielc inside and outside the precessor. The precession is switched off by reversing the current in the coils between the two superconducting sheets.
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
batic processes at the superconducting sheets; adiabatic variations of the field elsewhere. The efficiency of the superconducting sheets as neutron spin flippers (180 ° rotation) has been demonstrated by Schneider al I.L.L. [14]. d} Spin-sensitive resonance detector: Of all the components of the spin precession resonance spectrometer, this is the one that requires most development: it requires the combining of two devices now in existence, namely the neutron spin resonance filter [7] and the resonance detector [1]. For this reason only some preliminary considerations will be given here. The performance requirements for the spin-sensitive resonance detector are quite different from those of a neutron spin resonance filter. In the latter, the transmission of the neutrons of the two spin states is given by [15]; T ÷ = exp(-K) exp(aK)
(23)
T- = e x p ( - ~ ) exp(-~K) with K = oANd ;
ct = PPN ,
(24)
where o A is the absorption cross-section for unpolarized neutrons, N the number, of nuclei per unit volume and d the thickness of the filter. PN is the nuclear polarization, and p is a statistical weighting factor which takes the values p = - 1 if the compound nucleus has spin (1 - 1/2) and p = I/(1 + 1) if the compound nucleus has spin (I + 1/2) (1 is the spin state of the absorbing nucleus). The polarization of the transmitted beam is: PT
T ÷- T~T ÷ -+ T
tanhax
(25)
hence it can be brought as close to PT = 1 as desired, at the expense of the transmitted intensity. In contrast the polarization of the absorbed beam is PA = (1 -- T ÷) - (1 - T - ) _ sinh aK (1 + T ÷ ) + ( I - T - ) expK-coshtax
521
would entail a large Q, co area. The broadening of the E2 range can be obtained by constructing an absorber composed of different absorbing nuclei; provided that all resonances occur for the same neutron spin state. With this method more neutron counts are obtained for a given cross-section o(Q, 6o) AQ A ~ . However, the statistics of the signal is not necessarily better, since the cross-section is obtained by Fourier analysis of N data sets (each with its own statistics) and the broadening of the covered E2 range demands a larger number of data sets. As its is common to all broad range spectrometer (as the Fourier chopper, the pseudorandom chopper) the choice of a proper E2 range depends on the problem at hand. Up to now we have assumed an indiscriminate detection of a multi-resonance absorber. No energy analysis is required in the gamma detectors which measure the cascade of gammas (on the order of ten quanta) emitted by the absorber. The system is quite efficient, and can be further improved by a coincidence circuit which discriminates against background events. A possible alternative to this procedure is to discriminate in energy the gamma radiation emitted by the absorber. Since each excited nucleus has some characteristic low energy capture gamma line this system of detection separates the spectra of the different nuclei of which the n - 3 ' converting plate is composed. Higher selectivity is achieved at the expense of efficiency. Both schemes are presently under testing at the Rutherford Laboratory [16]. Finally, the physical and the chemical form of the resonance target needs a considerable amount of research. Williams is currently experimenting with a 149SmCos permanent magnet [17]. If a permanent magnet material cannot be obtained with the most suitable target nuclei, a possible alternative is the choice of ferromagnetic (or ferrimagnetic) alloys, with low coexcitivity so that magnetic saturation can be achieved in a low magnetic field. In this class might fall splat-cooled rare-earth-indium alloys.
(26) 5. Summary
This function peaks at K = 0 (zero thickness) to give a maximum polarization PA = a; and the practical useful thickness is proportional to 1/(1 - a). Thus, the requirement of high nuclear polarization is very stringent for the absorbing target. In the operation of the spin precession resonance spectrometer it might be convenient to have a detector that covers a wide E2 range: since this in turn
We have illustrated the concept of the spin precession resonance spectrometer, a neutron instrument conceived for a pulsed neutron source. Its basic purpose is to study high energy, low m o m e n t u m transfer excitations in condensed matter; excitations that can be determined with good energy resolution - without sacrificing intensity - thanks to the principles of
522
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
spin-precession spectroscopy already developed for the spin-echo spectrometer as well as for proposed novel instruments [18]. The number of potential applications has been only summarily analyzed, and indeed part of the scope of this note is to stimulate suggestions. The construction of the instrument should not present unsurmountable difficulties, but some of its components have still to be fully developed. Part of this effort would benefit the whole areas of polarized neutron research, especially at pulsed neutron sources. In fact is conceivable that the ultimate instrument would be a hybrid, since the spin precession circuit and the resonance detector occupy only a portion of the scattering area, and the remaining solid angle might be "filled" with conventional energy and spin analyzers in the thermal range of the neutron energies. The authors would like to thank Drs. W.G. Williams, R.N. Sinclair and J.B. Hayter for several enlightening discussions.
References [1] D.R. Allen, E.W.J. Mitchell and R.N. Sinclair, J. Phys. E., in press. [2] F. Mezei (editor) Neutron Spin Echo Proceedings, Grenoble 1979 (Springer Verlag, Lecture Notes in Physics No. 128, 1980).
[3] [4] [5] [6]
V.C. Sailor, B.N.L. Report No. 13624 (1 May 1964). F. Mezei, Z. Physik 225 (1972) 146. J.B. Hayter, Z. Physik B 31 (1978) 117. R.M. Moon, T. Riste and W.C. Koehler, Phys. Rev. 181 (1969) 920. 17] F.t:. Freeman and W.G. Williams, J. Phys. E: Sci. lnstrum., 11 (1978)459. [8] J.M. Carpenter, D.L. Price and N.J. Swanson, ANL report 78-88 (November 1978). [9] V.I. Lushchikov, Yu.V. Yaran and F.L. Shapiro, Soviet J. of Nuclear Physics 10 (1970) 664. A more recent instrument utilizing an LMN crystal has been built by G.T. Jenkin at I.L.L. (Institute Lave-Langevin Technical Report, February t 977). [10] G.A. Keyworth, J.R. Lemley, C.E. Olsen, F.T. Seibel, J.W.T. Dabbs and N.W. Hill, Phys. Rev. C8 (1973) 2352. [11] S. Hiramatsu, S. Isagawa, S. lshimoto, A. Masaike, K. Morimoto, S. Funahaski, Y. Hamaguchi, N. Minakawa and Y. Yamaguchi, J. Phys. Japan 45 (1978) 949. [12] J. Button-Shafer, R. Lichti and W.H. Potter, Phys. Rev. Letters 39 (1977) 677. [13] T.J.L. Jones and W.G. Williams, Rutherford laboratory report RL-77-079/A (July 1977). [ 14 ] Private communication. [15] W.G. Williams, Rutherford neutron division internal n~emorandum, (November 1979). [16] R.N. Sinclair, private communication. [17] W.G. Williams,private communication. [18] Y. Ito, M. Nishi and K. Motoya, Technical report of ISSP, A 1062 (1980).
513
THE SPIN PRECESSION RESONANCE SPECTROMETER G.P. FELCHER and Lid. CARPENTER Argonne National Laboratory, 9700 S. CassAvenue, Argonne, 1L 60439 USA
Received 30 June 1981
We present the concept of a new neutron scattering instrument to be used at a pulsed neutron source. The machine, which starts as a development of the resonance detector spectrometer and incorporates the basic ideas of spin precession energy analysis, is suited for the study of medium- and high-energy excitations in solids and liquids, particularly at small momentum transfers. The most novel characteristic of its performance is a high resolving power, achieved without appreciable loss of neutron flux. In an alternative operation (and sacrificing resolution) the instrument is capable of separating spin-dependent from spin-independent scattering processes.
1. Introduction The new generation of pulsed spallation neutron sources has, over the conventional neutron sources (reactors), the distinct advantage of a large flux of epithermal neutrons. This enables, in principle, the study of deep inelastic processes in solids and liquids, with the benefit of the neutron scattering technique, which enables one to get at the correlation function from the scattered intensities without resorting to, cumbersome models or to coarse approximations in the evaluation of the matrix elements. It is clear that in order to study processes with an excitation energy 60 neutrons with energy E1 > co have to be employed when 6J i> kT. Furthermore, if the momentum of the induced excitation Q is small as it occurs in many important cases - the conservation laws of energy and momentum require that even the final energy E2 of the scattered neutrons be large. These considerations have prompted the development of a new instrument, the resonance detector spectrometer [1 ] where the neutrons are detected only if the final energy of the neutron matches the energy of a neutron resonance of a n - 7 converting plate. The instrument is very simple and yet powerful: an excitation process in the sample is determined by two quantities, the flight time of the neutron from the pulsed source to the detector, and the energy of the n - 3 ' resonance. The width of the resonance, at best a few hundredths of eV, is adequate in several instances to define the energy E= of the scattered neutron but often it is desirable or imperative to obtain a better 0029-554X/82/0000-0000/$02.75 © 1982 North-Holland
resolution of E2. This is obtained in the present scheme by inserting in the secondary neutron path a spin-precession device, similar to that developed by F. Mezei and J.B. Hayter for their spin-echo spectrometer [2]. The device requires full polarization of the incident beam as well as polarization analysis. We give here a brief description of the mode o f operation and the projected performance of the entire instrument, which we call spin precession resonance spectrometer, together with a brief description of the components needed for its operation. The general areas of solid state physics in which this instrument might be useful are tentatively thought to be similar to those spanned by a high energy chopper spectrometer. They include (1) the study of frequency spectra of crystals, particularly molecular crystals and of phonons in metallic hydrides, in the region of energies />50 meV; (2) the study of high-frequency magnetic excitations (e.g., spin waves and Stoner excitations) in transition metals, alloys, and compounds; (3) the study of magnetic excitations in mixed valence and actinide compounds; (4) measurements of joint densities of electronic states in transition metal and actinide compounds up to "-0.5 eV above the Fermi level; (5) study of spin wave dispersion in amorphous ferromagnetic materials; (6) crystal field excitations.
2. Concept A layout of the resonance detector spectrometer is presented in fig. 1 a. A burst of neutrons at time zero
514
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
y-RAY CASCADE
RESONANCE ~ ,..¢' ABSORBER Fg r~ F~ -
"./: 1~ SAMPLE, /" ) C /
Po,_SE,:,
SOURCE
fsec
Y
DETECTOR
I SPIN FILTER
b
t I = t - (12/02) ;
1----1
~-
+--&
~~NANCE SAMPLEi,/~,/ ~, ABSORBER u,, L ~ " SPIN * FLIPPER
PRECESSION DEVICE
Fig. l. (a) Layout of the resonance detector spectrometer. (b) Components to be added for operation as a spin precession resonance spectrometer.
is emitted from the source. At a subsequent time these neutrons irradiate the sample, which scatters the neutrons at an angle 20 with differential cross section Z (El, E2). The scattered neutrons are measured by the resonance detector only if their energy falls within the energy range where the effective resonance curve D(E) is non-zero. Precisely, the quantities measured at the detector are: t = l l / 0 1 + 12/u2
I(t) = ( o
-
dE1
?
(1)
dE210(El) E(EI, E2)D(E2)
o
X 6(t - ll/vl - 12/v2).
(2)
With an appropriate choice of the instrument's geometry the time of arrival t can be made to define rather well the incident energy El, even if the final energy is not too well defined. This is obtained by making l~, the pathlength of the neutron from source to sample, much larger than the sample-detector distance 12. Since the neutron velocities before and after scattering are comparable the time 12/u2 is small compared to ll/vl and anyway the average value of l=/v2 can be subtracted from the measured time of arrival t. Thus,
l ( t ) ~ , I o ( E 1 ) ( 2 E l / t l ) , F £(E,, E2)D(E2) dE2 , 0
with
(3)
E1 = m/2(lt/tl) 2 •
(4)
The uncertainty in the energy transfer &co is mainly due to the width ~ 2 of the resonance curve D(E2) appearing in the integral of eq. (3). This could be unbearably large; for instance, for a resonance width of 0.1 eV, processes involving 0.5 eV energy transfer are defined with only 20% resolution. However the resolving width &E2 can be compressed making use of the spin properties of the neutron in a precession circuit. Practically this is achieved by adding a number of components to the basic resonance detector spectrometer, whose function we briefly describe, leaving to a later section the discussion of their technical feasibility. a) The primary neutron beam is fully polarized. This is achieved by passing it through a neutron spin filter, which removes neutrons of the unwanted spin for all energies. After the filter, the polarization is maintained along a quantization axis by magnetic guides (for example, the spins are kept normal to the neutron flight path as in fig. lb). We assume for the time being that the neutrons are scattered by the sample without spin flip. b) The resonance detector is spin sensitive. Many of the neutron resonances in the electron volt range are spin dependent: neutron absorption occurs for only one of the two relative orientations of the neutrons spin and the nuclear spin of the n - 7 converting plate (a collection of these is reported [3] in table 1). We assume that the nuclei of the target of tile resonance detector are fully polarized, so that only the scattered neutrons with the same spin state of the primary beam are actually detected. With these definitions, the intensity measured by the detector is given still by eq. (3), with the proviso that all the quantities are relative to one spin state; if this is indicated by + we have:
l+(t) ~ Io(El) 2E--L : tl
£++(E1, E2) D÷(E2) dE2.
(5)
o
With the two additions the instrument is converted into a fully polarized neutron spectrometer. c) A neutron spin precession device is inserted in the flight path (fig. lb) of the scattered neutrons. At its entrance, the neutrons are brought "suddenly" (non-adiabatically) in a magnetic field normal to their quantization axis. The neutron moment precesses around this new field for all the length of the device,
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer Table 1 Spin dependent neutron resonances (from Sailor, ref. 3) Isotope
Target spin
i I s In
9/2
121
Resonant energy
Spin of compound state
1.46 3.86 9.10
5 4 5
Sb
5/2
6.23 15.5
3 2
14SNd
7/2
4.37
3
149Sm
7/2
0.0976 0.87 4.93 8.9
4 4 4 4
lSlEu
5/2
0.327 0.461 1.056 3.37
3 3 3 2
I s s Eu
5/2
2.46
3
lSSGd
3/2
0.0268 2.008 2.568 6.30
2 1 2 2
0.0314 2.825
2 2
lS7Gd lSgTb
161Dy
3/2 3/2
5/2
3.35 4.99 11.14
2 1 2
2.72 3.69 4.33 7.73
3 2 2
163Dy
5/2
1.71
2
16SHo
7/2
3.92 8.1 12.8 18.1
4 3 4 3
167Er
7/2
0.460 0.584 6.1
4 3 3
169Tm
1/2
3.9
1
181Ta
7/2
4.28 10.34
4 3
lSSRe
5/2
187Re
5/2
2.16 5.90 7.20 4.42 11.2
3 2 3 3 2
1911r
3/2
193ir
3/2
19Spt
1/2
0.654 5.36 1.303 11.9
2 2 2 1
515
at whose end the initial field is restored also non-adiabatically (see fig. 2). The final polarization of the neutron depends on the time spent in the device hence on the wavelength of the scattered neutron X2 : P(X2) = cos 27tAX2 ,
(6)
where A = ClpH, and lp is the length of the precession device, H the applied magnetic field. C is a constant; in convenient units C = 7.34 × 10 -3 cm - 1 0 e -I A -1. Basically, the polarization P(X2) gives a function that modulates the effective resonance curve D÷(~2) [see fig. 2]. The product 1/2(1 + P ) ' D ÷ is the effective response of the detector, which has an energy resolution AE2 determined by the period of the precession A rather than the width of the resonance line. The detected intensity is:
I+(t, A) ~Io(E1)2E' f ~++(E1,Ei)D+(E2) tl
0
× [-~(1 + cos 2rrAX2)] dE~ .
(7)
Or in more compact form:
5r+(Xl, A )"~ J ~(Xl, )t2) cos 2rrAX2 dXl
,
(8)
0
where ~ ÷ is the normalized intensity, from which the
GUIDE FIELD l--Ho --I
I I
PRECESSION FIELD H ®
A
1Tl:0~
/
0"
GUIDE POLARIZER FIELD f ABSORBER
/Ho
e
T
['1
~l ; ~ ~ L_] i
: 2rA~,2 A : 7.34x10"3~cmHoe(~-I)
O(X2)1
i[-7~,;---,~ ' 7~,:f,V ',
' )'2
Fig. 2. Top: Conceptual operation of the precession device. From A to B, the magnetic field is normal to the spin quantization axis. Bottom: The effective width of the resonance line compared with the precession period.
516
G.P. Felcher,J.M. Carpenter/ Spin precession resonance spectrometer
cosine-independent terms have been subtracted:
7 ÷ ( k , , A ) = I + ( t , A ) / ( I o ( E D E", / t , ) - 7 ÷()kl, 0 )
(9)
and (~()kl,)k2) "~" Y~,(E1, E2) D(~'2) 2E2/X2 .
(10)
qS()tl, X2) is the quantity that we want to recover from our measurement, since it is directly proportional to the cross section Y,(E1,E2), with factors that can be easily calibrated. ~ X l , X2) is the Fourier transform of the measured intensity ~÷(X~, A). Suppose that a sequence of measurements is performed for different values of the magnetic precession field (i.e., different A's) up to a maximum value. From these we can calculate the quantity: Amax
4)(kl, k2) =
cY÷(kl, A ) cos 2TrAk2 dA
d 0
(ll)
~r+(Xl, A ) = ~ b ( X l , X2i) cos 2rrAX2i,
~b0tl, X2)R0t'2, X2) d)k2 ,
the X2i are determined as the centers of the functions q~(Xl, X;) or equivalently can be determined by least squares fitting a series expression of the form (8a). The only requirement is that the different k i are separated by an interval larger than the ~5)t2 of the resolution function. d) Selection of the spin flip processes. Removing the hypothesis made in section a), we take now ~;(EI, E2) to be not entirely spin independent. For the given neutron spin state of the primary beam, there are two cross sections: 2+-(E1, E2)
with
~-+(EI, f 2 )
(12)
R(X',X2) is a resolution function of width 5X2 ~ 1Mmax. ~Xl,)t2) is then determined within an instrumental resolution constant in wavelength, rather than in the energy of the scattered neutrons. Rather good resolution is obtained even with a modest precession time; for example, to obtain 6X2 = 2 X 1 0 - s A , a magnetic field of 1.3kOe is to be applied over a flight path of 50 cm. The integral in eq. (1 1) can be approximated by a finite number of measurements at different precessing periods A. The minimum precessing period is defined by the reciprocal linewidth of the resonance, A rain = 1/AS2; and all the harmonics have to be taken up to Area x = NAmin. Eq. (11) takes the form: N ~(Xl, ~,2) = ~
(13a)
and two other cross-sections if the spin state of the primary beam is reversed:
0
R0t2, )t2) --Amax 1o [2nAmax(X2 - X2)] •
(Sa)
i
E÷*(fl, f 2 )
oo
= f
duces a blurring of the image of ~(Xl, )k2), assumed as a continuous function. If this function does not present sharp edges it is relatively unimportant to have high resolution. On the other hand, if the signal is made of discrete delta functions, so that eq. (8) can be rewritten:
~+(~k,, nA min) cos 2rmAmin~,2. (1 la) 1
N is the minimum number of measurements to be taken in order to achieve the desired resolution. The treatment given here is a conventional Fourier transformation, identical to the transformation in real space of the X-rays or neutron diffraction data. The truncation in the Fourier integral, due to Amax, intro-
~--(L" 1, E 2 ) .
(13b)
If the precession circuit is not switched on, the instrument is in effect a polarizing spectrometer with polarization analysis. The four cross sections can be independently measured, with the insertion of neutron spin flippers in the primary or in the scattered beams [6]. This makes possible the separation of processes like the coherent and incoherent (nuclear spin incoherence) scattering from liquids: here the coherent cross section is entirely non spin-flip, while the incoherent cross section is one third non spin-flip, two thirds spin-flip (and the relations hold, 22÷÷ =Y:-; S +- = ~-÷). The full separation of the four cross sections is possible only with the precession circuit switched off, hence with the energy resolution of the detector's resonance. With the precession circuit switched on, the information on the spin state of the scattered neutron is lost, in order to attain the compression of the resolution element 2xE2. Rewriting eq. (8) with an explicit indication of the neutron spin history, we have:
7÷(xl, A ) = f
[¢+(Xl, X~) - ¢-(X,, X2)I
o
X cos 2nAX2 dX2
(14a)
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
taken tobe, respectively, 2.79 X 104 and 3.82 X 10 a b for fully polarized nuclei. The probability for a neutron absorption, followed by gamma emission, is presented in fig. 3, for a target thickness o f 4 mm. If the detection efficiency for the gamma cascade is unity, fig. 3 represents the detector function D(E2) , on which we can base the preliminary performance estimates. First, we want to calculate the region of energy and momentum transfers covered by the instrument. The energy transfer is simply 60 = E l - E 2 , while the momentum transfer is defined by:
where ~r÷(kl, A )=l*(t, A )/(Io(E1) El/t~) - ~1 [5r +(hi, 0) +~7-(X~, 0 ) ] ,
(15)
The reversal of the neutron spin in the primary beam provides the intensity: oo
c.'Jr-(k~, A ) : f
[~-+(Xl,
~k2) - -
~--(~,1, ~-2)]
0
X COS 27rA•2 dX2 •
(14b)
These expressions identify the extent of the information that can be eventually obtained by the spin precession resonance spectrometer. In particular, if'- = - ~ r+ [and thus the spin reversal does not provide additional information] unless the sample does not exhibit a natural or induced net magnetization.
Q-
2n
0.2861
x/E1 +E2 - 2x/fflE2 cos20 .
(16)
Where the energies are expressed in eV, and Q in A.-1. The incident energy E~ can assume any value (provided that E~ > E2); the final energy is constrained to be within the range over which the detector function is non-zero. Roughly speaking, this occurs for two energy bands, the first extending from 0.02 to 0.23 eV, the second from 0.81 to 0.93 eV (fig. 3). The region of the (Q, co) space spanned by the detector depends on the scattering angle, and we choose 20 = 8 °, a geometry that would enable us to detect optical modes in the second Brillouin zone of a 3d metal. The (Q, w) space subtended by such detector is depicted in fig. 4. We would like now to evaluate the resolution of the instrument. While a full expression is quite complex, we are interested in obtaining its dependence on 67~2, as this is the most representative quantity in the performance of the instrument. We have already seen how a resolution ~k2 is obtained by the preces-
3. Preliminary performance estimate The analysis of the performance of the spin precession resonance spectrometer requires a proper choice of the spin sensitive resonance detector. No such device has yet been built; actually this is the single item in the proposed instrument whose design will require the most development. However, we have at our disposal a device that conceptually can be utilized as a spin and resonance detector: this is the samarium spin filter developed at Rutherford by Williams [7]. This device is a target of fully polarized 149Sm nuclei, which captures the neutrons of one spin only over an energy range corresponding to the samarium resonance. The device as built is a neutron spin filter; but "for our purpose we "use" it the complementary mode, namely by counting the gamma radiation emitted following the absorption of the neutrons of one spin state. Williams' filter consists of a single crystal o f cerous manganese nitrate (CSMN), with about 6% of the Ce atoms replaced by 1495m. The absorber has a thickness of 4 mm, and a viewing area of 2.5 × 2.5 cm. In the following, we assume that the 149Sm nuclei are completely polarized, and further take into account only the two resonances of lowest energy for which the compound nucleus has s p i n 4 [the 149Sm spin being 7/2]. These occur at laboratory neutron energies E2 = 97.6 and E2 = 873 meV (see table 1), both with a capture width F.r = 60 meV. The peak values of the cross section at these resonances have been
517
A N
w ca Od
0 0
0.2
0.4
0'.6 eV
0.8
1.0
Fig. 3. Effective detector function for a samarium 149 resonance absorber (see text and ref. 7). The bars under the peaks are arbitrarily taken as the effective band width of the resonances.
518
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer t00~
~
~
-~ .
.
.
.
.
.
.
!
i
0 . 0 9 7 6 eV Resonance
I0
..... / : - ~
upper band ....
E = 0 . 9 3 0 eV ,
i,
:~/~----~7~, ~ E = 0.814 eV
I0
E f = 0 . 2 3 5 eV T
~ >
lower band
~t 4i
0.1
2
2
O0
0.2
0.~4 W, eV
----016
0.8
Fig. 4. ~, Q range covered by the two resonances of samarium-149 for a detector set at 20 = 8° from the primary beam.
sion method in the case of one resonance; the extension to the present case of two resonances is trivial. (Notice that, since the resonances are far apart, their separation comes about in a natural way; if the sample can be said to have no excitations with energies greater than 0 . 8 1 - 0 . 2 3 = 0.58 eV then the two bands are separated in time-of-flight.) The energy and momentum resolution are given by:
QAQ
_
4712
(0"2861) s 6X2
=
[1: Eal/2 +E~/:)
O.---2-ff~
6.2 - - ~ -
o'.~
--
0'.6
~p oV
Fig. 5. Limits of the energy resolution for the two lowest samarium-149 resonance lines. The precession device is assumed 50 cm long, with a maximum field of 2 kOe.
with the following definitions: S(EO is the source function. It has been assumed to have the following shape [8] : E S ( E t ) = S N • G 5.3 L-~T
exp(-E/ET)
Et(~/E~ - x / E z c o s 2 0 ) (17a)
+ E : ( x / E : - x/E1 cos 20)~
~
~
[~ -1
2
0%
aX2.
(17b)
Numerical calculation o f Aw was performed with the following parameters: A~,2 = 2 X 10 -3 A; Ii = 7 m, 12 = 1 m. The results are shown in fig. 5. While for the lower band the neglected terms in the resolution (due to the geometry; time of the neutron burst etc.) are comparable to 6X2, this is the controlling factor for the upper band. Scattered intensities. For each element E l , E2 the number of neutrons collected in unit time is:
N(E1, E2) =S(EI) T(E O ~1 Y.(E1, E2) ~2 T(E2)D(E2) (18)
+ E[1 +
(5ET/E) 7]
"
(19)
Where for the maximum o f the spectrum ET = 0.035 eV; G is a normalization constant equal to 3 X 10 -4 in consistent units and SN is the time-averaged neutron production rate which was taken as 3 X 10 Is neutrons/s (design current for the Intense Pulsed Neutron Source at Argonne National Laboratory). T(EO is the transmission through the spin filter. If this is made o f almost fully polarized hydrogen the transmission is, over the region o f interest, almost constant, and equal to 0.2 for 95% neutron polarization. ~21 is the angle subtended by the sample. If its cross section is 2.5 X 2.5 cm, at a distance o f 7 m from the source, ~Zl = 10 -6 st.
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
~22 is the angle subtended by the detector. If its cross section is 2.5 × 2.5 cm, at a distance of 1 m from the sample, ~22 = 6 × 10 -4 sr. T(E2) is the transmission through the spin precession devices. On the average the spin of half of the neutrons is turned down, hence it is not detected by the counter; thus T(E2) = 0.5. D(E2) is the detector function, as presented in fig. 3. E(E1,E2) is the scattering power of the sample, and can be written as follows:
Z(E1, E2) = x/(E21E1) Zo(a, co),
(20)
519
RESOLUTIONELEMENT:
10,
!
I
/>0.1 9
/// I
iI
t / 7 6
c; 5
where E0 is finite over a fixed resolution element AQ, ACO.
4
We can now calculate the number of neutrons detected following the Q, • scattering process:
3
/
f
// / /
2 eV
N(Q,
AQ Ac~ = f
dE~
co+0.025 eV
×
j
t -co+~to/2
N(E~, E2)
dE:
(21)
~ 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
~,eV
E1 --to--Awl2
when El, E: are not independent variables [see eq. (16)], and the limits of El were chosen for convenience. The intensity depends linearly on the value of Z0, the macroscopic cross-section of the sample per unit area. In terms of the microscopic cross section a ( a , co):
Y~o(Q,w) =No(Q, w) l,
0
(22)
where N is the number of cells per unit volume, and l the sample thickness. Suppose that o has a value of the order of 10 -4 b/sr/meV per unit cell, which is a typical cross section for high-frequency photon spectra, at least for some co, Q range. Let ustake the cell as cubic, with an edge 4 A long; and the thickness I be 2.5 cm [admittedly a rather thick sample]. With these numbers, we can calculate the number of neutrons scattered within a resolution element AQ, Aeo. If we put A~o = 5 meV, AQ = 0.75 A -1 we obtain the neutron counts presented in fig. 6. Comparison with other spectrometers. The spin precession resonance spectrometer utilizes a broad band of incident neutron energies, and detects the scattered neutrons within a fairly wide range of energies. For this reason the instrument has very high luminosity, thus offsetting the neutron losses due to the polarizing devices (which lower the efficiency by
Fig. 6. C o n t o u r s of counting rate (neutrons/min) in the resonance detector. Sample cross section 10 .-4 b/sr/meV over the indicated resolution function. For the source flux, instrum e n t geometry and sample shape, see text.
an order of magnitude) and partially offsetting the constraint due to the small area of the detector. The instrument is operated as a Fourier spectrometer, hence the statistical errors on the recovered signal ¢(~1, ?~2) [see eq. (11)] are not independent. However in this as in other spin precession devices [4] the Fourier modulation is exact, since it does not depend on the perfection of mechanical components. The chopper spectrometer has quite different characteristics. It starts selecting a very narrow band in the incident energy spectrum, so that the neutron count on a fixed detector area is considerably lower than for the spin precession resonance spectrometer. However, in this case the addition of other detecting elements is simple and relatively cheap: and thus a drastic improvement can be achieved both in the counting rate and in the ¢o-Q region spanned. Only when the region of the energy-momentum space to be scanned is confined to large w, small Q is this improvement not satisfactory: in this case the scattering is confined anyway to the region of small 20 angles,
G.P. Felcher, J.M. Carpenter/Spin precession resonance spectrometer
52(!
and furthermore detectors must have reasonable efficiency for high neutron energies. The resonance detector spectrometer does not have any conceptual advantage over the spin precession resonance spectrometer. In order to keep the effective linewidth of the resonance detector narrow, the n - 7 converting plate must not absorb more than about 10% of the neutron beam at the resonant energy. Thus the efficiency for the two instruments is comparable, while the substantial improvement in resolution favors the spin precession resonance spectrometer. However, the resonance detector spectrometer is a comparatively simple machine, and the understanding of its performance and capabilities is a necessary stepping stone in the development of the more sophisticated devices described here.
with ytterbium. Here high proton polarization is attained due to the coupling of the proton spins with the magnetic impurity ytterbium (kept polarized by an external magnetic field) by a method called "spin refrigeration" [12]. The device is expected to achieve ~75% proton polarization in an easily reachable sample environment (temperature ~1.1 K; applied magnetic field ~14 kOe). In these conditions, 18c~ of the neutrons of 100 meV energy should be transnritted, with a final polarization of 95%.. b) Neutron spin flipper: It must be capable of flipping the spin of the neutrons irrespective of their energies. A device with these characteristics has been successfully demonstrated already [ 13]. c) Spin precession unit: The circuits hitherto built [4] are effective for quasi-monochromatic radiation. For a "white" neutron beanr a scheme such as that presented in fig. 7 should be satisfactory. The neutron spin is kept aligned along a magnetic field H t transverse to its flight path. Immediately before the start of the precession circuit, the guide field lit is tipped to 45 ° (with respect to the flight path axis) by the insertion of a current coil. The neutron spin is now also aligned at 45 ° , and remains so after crossing a thin superconducting sheet. At the right side of the superconducting sheet, which allows the non-adiabatic change of the field direction, the applied magnetic field is normal to the neutron spin direction. This precesses in an effective field f~ Hp(l) dl, after which the insertion of a second superconducting sheet allows the restoration of the primary magnetic situation. (For tire neutron spin presented in fig. 7, the final state is almost antiparallel to the original state.) The device as presented requires two non-adia-
4. Technical development The design of the spin precession resonance spectrometer requires the acquisition of state of the art technology. The task is less formidable than it nfight appear at a first glance, since all the individual components have been already partially or fully developed for different purposes, as it appears from the following list: a) neutron spin filter: Several devices have been developed recently [ 9 - 1 2 ] which polarize a white beam. In all these devices the spin filter consits of a target material which contains a high concentration of polarized hydrogen nuclei. In the scheme followed at Argonne, and presently under testing, the target is a crystal of hydrated yttrium ethyl sulfate doped
MAGNETIC
FIELDPROFILE Hz:Ht Hz Ht
T
Hp Hz
l Hz=Hp HZH~H9
T~Hx!
X
,.';-A'
A f
,
NEUTRON SPIN PROFILE SUPERCONDUCTING SHEET ( Ht= 0 )
Hz: Ht
T
UUU
VVVU
i
Ht Hz
i
,
,,.::.;,
i i
/
3'
t-_-,,
SUPERCONDUCTING SHEET ( HI =0)
Fig. 7. Preliminary design of the spin precession device. The superconducting sheets provide the decoupling of the magnetic fielc inside and outside the precessor. The precession is switched off by reversing the current in the coils between the two superconducting sheets.
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
batic processes at the superconducting sheets; adiabatic variations of the field elsewhere. The efficiency of the superconducting sheets as neutron spin flippers (180 ° rotation) has been demonstrated by Schneider al I.L.L. [14]. d} Spin-sensitive resonance detector: Of all the components of the spin precession resonance spectrometer, this is the one that requires most development: it requires the combining of two devices now in existence, namely the neutron spin resonance filter [7] and the resonance detector [1]. For this reason only some preliminary considerations will be given here. The performance requirements for the spin-sensitive resonance detector are quite different from those of a neutron spin resonance filter. In the latter, the transmission of the neutrons of the two spin states is given by [15]; T ÷ = exp(-K) exp(aK)
(23)
T- = e x p ( - ~ ) exp(-~K) with K = oANd ;
ct = PPN ,
(24)
where o A is the absorption cross-section for unpolarized neutrons, N the number, of nuclei per unit volume and d the thickness of the filter. PN is the nuclear polarization, and p is a statistical weighting factor which takes the values p = - 1 if the compound nucleus has spin (1 - 1/2) and p = I/(1 + 1) if the compound nucleus has spin (I + 1/2) (1 is the spin state of the absorbing nucleus). The polarization of the transmitted beam is: PT
T ÷- T~T ÷ -+ T
tanhax
(25)
hence it can be brought as close to PT = 1 as desired, at the expense of the transmitted intensity. In contrast the polarization of the absorbed beam is PA = (1 -- T ÷) - (1 - T - ) _ sinh aK (1 + T ÷ ) + ( I - T - ) expK-coshtax
521
would entail a large Q, co area. The broadening of the E2 range can be obtained by constructing an absorber composed of different absorbing nuclei; provided that all resonances occur for the same neutron spin state. With this method more neutron counts are obtained for a given cross-section o(Q, 6o) AQ A ~ . However, the statistics of the signal is not necessarily better, since the cross-section is obtained by Fourier analysis of N data sets (each with its own statistics) and the broadening of the covered E2 range demands a larger number of data sets. As its is common to all broad range spectrometer (as the Fourier chopper, the pseudorandom chopper) the choice of a proper E2 range depends on the problem at hand. Up to now we have assumed an indiscriminate detection of a multi-resonance absorber. No energy analysis is required in the gamma detectors which measure the cascade of gammas (on the order of ten quanta) emitted by the absorber. The system is quite efficient, and can be further improved by a coincidence circuit which discriminates against background events. A possible alternative to this procedure is to discriminate in energy the gamma radiation emitted by the absorber. Since each excited nucleus has some characteristic low energy capture gamma line this system of detection separates the spectra of the different nuclei of which the n - 3 ' converting plate is composed. Higher selectivity is achieved at the expense of efficiency. Both schemes are presently under testing at the Rutherford Laboratory [16]. Finally, the physical and the chemical form of the resonance target needs a considerable amount of research. Williams is currently experimenting with a 149SmCos permanent magnet [17]. If a permanent magnet material cannot be obtained with the most suitable target nuclei, a possible alternative is the choice of ferromagnetic (or ferrimagnetic) alloys, with low coexcitivity so that magnetic saturation can be achieved in a low magnetic field. In this class might fall splat-cooled rare-earth-indium alloys.
(26) 5. Summary
This function peaks at K = 0 (zero thickness) to give a maximum polarization PA = a; and the practical useful thickness is proportional to 1/(1 - a). Thus, the requirement of high nuclear polarization is very stringent for the absorbing target. In the operation of the spin precession resonance spectrometer it might be convenient to have a detector that covers a wide E2 range: since this in turn
We have illustrated the concept of the spin precession resonance spectrometer, a neutron instrument conceived for a pulsed neutron source. Its basic purpose is to study high energy, low m o m e n t u m transfer excitations in condensed matter; excitations that can be determined with good energy resolution - without sacrificing intensity - thanks to the principles of
522
G.P. Felcher, J.M. Carpenter / Spin precession resonance spectrometer
spin-precession spectroscopy already developed for the spin-echo spectrometer as well as for proposed novel instruments [18]. The number of potential applications has been only summarily analyzed, and indeed part of the scope of this note is to stimulate suggestions. The construction of the instrument should not present unsurmountable difficulties, but some of its components have still to be fully developed. Part of this effort would benefit the whole areas of polarized neutron research, especially at pulsed neutron sources. In fact is conceivable that the ultimate instrument would be a hybrid, since the spin precession circuit and the resonance detector occupy only a portion of the scattering area, and the remaining solid angle might be "filled" with conventional energy and spin analyzers in the thermal range of the neutron energies. The authors would like to thank Drs. W.G. Williams, R.N. Sinclair and J.B. Hayter for several enlightening discussions.
References [1] D.R. Allen, E.W.J. Mitchell and R.N. Sinclair, J. Phys. E., in press. [2] F. Mezei (editor) Neutron Spin Echo Proceedings, Grenoble 1979 (Springer Verlag, Lecture Notes in Physics No. 128, 1980).
[3] [4] [5] [6]
V.C. Sailor, B.N.L. Report No. 13624 (1 May 1964). F. Mezei, Z. Physik 225 (1972) 146. J.B. Hayter, Z. Physik B 31 (1978) 117. R.M. Moon, T. Riste and W.C. Koehler, Phys. Rev. 181 (1969) 920. 17] F.t:. Freeman and W.G. Williams, J. Phys. E: Sci. lnstrum., 11 (1978)459. [8] J.M. Carpenter, D.L. Price and N.J. Swanson, ANL report 78-88 (November 1978). [9] V.I. Lushchikov, Yu.V. Yaran and F.L. Shapiro, Soviet J. of Nuclear Physics 10 (1970) 664. A more recent instrument utilizing an LMN crystal has been built by G.T. Jenkin at I.L.L. (Institute Lave-Langevin Technical Report, February t 977). [10] G.A. Keyworth, J.R. Lemley, C.E. Olsen, F.T. Seibel, J.W.T. Dabbs and N.W. Hill, Phys. Rev. C8 (1973) 2352. [11] S. Hiramatsu, S. Isagawa, S. lshimoto, A. Masaike, K. Morimoto, S. Funahaski, Y. Hamaguchi, N. Minakawa and Y. Yamaguchi, J. Phys. Japan 45 (1978) 949. [12] J. Button-Shafer, R. Lichti and W.H. Potter, Phys. Rev. Letters 39 (1977) 677. [13] T.J.L. Jones and W.G. Williams, Rutherford laboratory report RL-77-079/A (July 1977). [ 14 ] Private communication. [15] W.G. Williams, Rutherford neutron division internal n~emorandum, (November 1979). [16] R.N. Sinclair, private communication. [17] W.G. Williams,private communication. [18] Y. Ito, M. Nishi and K. Motoya, Technical report of ISSP, A 1062 (1980).