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Synchronous pulsed magnetic fields in muon spin rotation
Physica B 289}290 (2000) 684}688
Synchronous pulsed magnetic "elds in muon spin rotation T. Shiroka , C. Bucci *, R. De Renzi , F. Galli , G. Guidi , G.H. Eaton, P.J.C. King, C.A. Scott Dipartimento di Fisica e Istituto Nazionale per la Fisica della Materia, Universita% di Parma, Parco Area delle Scienze 7a, I-43100 Parma, Italy Rutherford Appleton Laboratory, ISIS Facility, Chilton, Didcot, Oxon OX11 0QX, UK
Abstract One of the advantages o!ered by pulsed-polarized sources of muons, such as the ISIS Facility at RAL (UK), is the possibility to apply external "elds, synchronous to the muon pulse, with a duration as short as a few muon's lifetimes (&20 ls). Here we present a muon spin rotation (lSR) technique in which an external pulsed magnetic "eld and/or "eld gradient, generated by a laminar current-loop method, are applied to investigate new properties. Whereas xeld gradients seem more appropriate for a straightforward imaging of the implantation depth of positive muons in metals, the pulsed uniform magnetic xelds are shown suitable for the direct measurement of the sudden-to-adiabatic cross-over. The latter method is also expected to be applicable to the experimental study of the delayed muonium formation. 2000 Elsevier Science B.V. All rights reserved. PACS: 76.75; 36.10.D; 82.55; 07.55.D Keywords: Muon spin rotation; Pulsed "elds; Field gradients; Muonium
1. Introduction The pulsed time structure of a beam of spinpolarized positive muons (such as the ISIS facility at the Rutherford Laboratory, UK, delivering intense bunches of muons, 80 ns wide, at 50 Hz), is very attractive when synchronous pulsing of magnetic "elds and/or gradients with a low duty-cycle is required. A possible way to generate magnetic "elds or large magnetic "eld gradients in small volumes
* Corresponding author. Tel.: #39-0521-905246; fax: #390521-905223. E-mail address: bucci@"s.unipr.it (C. Bucci).
(as is the case for the thin samples used in lSR experiments) is to employ a laminar current #atloop device [1]. Fig. 1 shows that the current geometry consists of two parallel slabs where a uniform current, with surface density j, #ows in opposite directions. For slab dimensions slightly bigger than the ISIS lSR beam cross section (&90% of the muons within a 30 mm diameter) the fringe e!ects are negligible and the magnetic "eld is calculated by Ampe`re's law. The "eld B is parallel to the surface of the slab and perpendicular to j. The magnetic "eld outside the loop itself is zero, there is a "eld gradient (*B/*x"$k j) inside the forward and back ward current slabs and the "eld is uniform at its maximum value (B "k jd ) in the space between
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 3 1 2 - 4
T. Shiroka et al. / Physica B 289}290 (2000) 684}688
685
Fig. 1. Geometry of currents and magnetic "eld pro"le inside the #at-loop device.
them. Such a device allows a twofold application. The "rst one concerns the "eld gradients: when muons are implanted in the metallic "lm carrying the current, the stopping pro"le of muons (or better, the projected range pro"le) can be measured in a straightforward way since each stopping depth has its own unique label given by the muon precession frequency at that location. So the Fourier transform of the precession signal of even a single lSR experiment will give a direct map of the muon distribution. The second feature deals with the uniform "elds inside the device: when a thin sample is placed inside the loop then the "eld can be switched on with adjustable delays relative to the muons implantation time; the frequency cut-o! in lSR experiments due to the muon pulse-width can be eliminated and delayed muonium formation processes can be detected and studied. 2. lSR measurements of muon range pro5les For a typical `surfacea muon beam of &4 MeV, the thickness of the metallic slab in the #at-loop
device can be chosen larger than the projected range straggling. A copper slab&100 lm thick, for instance, is quite suitable. By pulsing a 150 A current with a+100 ns rise time a uniform "eld gradient of+40 T/m can be generated inside the metallic slab. The frequency pro"le of a single lSR spectrum yields therefore the range and the straggling pro"le of the muons stopped in the "lm, as shown in Fig. 2. The knowledge of the slab thickness and that of the magnetic "eld extreme values (done by adjusting the moderator in such a way as to stop muons either before, as in Fig. 2(d), or after, as in Fig. 2(f ), the region of the gradient) allows a simple conversion of the frequency scale into a length scale. An external uniform "eld of 10 mT, parallel to the "eld generated in the device, conveniently shifts the central frequency. The values we "nd for the range and straggling in Cu are in agreement with those determined by di!erent, although more elaborate, methods [1]. Similar measurements performed on Al and Pb con"rm the Z-dependence of range and straggling.
686
T. Shiroka et al. / Physica B 289}290 (2000) 684}688
Fig. 2. Polarization (left) and its Fourier transform (right) for Cu (top scale: implantation depths x). Cu moderator was 178.4 mg/cm in (a), 89.2 mg/cm in (b) (dotted vertical lines delimit currents slab) and 44.6 mg/cm in (c).
In view of possible experiments with the recently developed epithermal muons [2,3], separate tests of the device were performed by using thin "lms. This type of measurements is important since for muon energies below 1 keV the expected ranges are smaller than 100 nm, data are still scarce and available simulation codes [4] will need to be compared to experiments. Various thicknesses between 18 nm Al and 100 nm Cu have been tested with currents up to 250 A and proved the stability of the "lms and the uniformity of the magnetic "eld gradients [1]. 3. lSR experiments with delayed 5elds The same synchronous pulsing principle can be used to perform experiments when the muon implantation in a sample inside the central volume of
the device (where the "eld is quite uniform) is made before the current pulse is applied. In this way, the cut-o! frequency of the main beam can be appreciably extended, the new limit being set by the timeto-digital converters of the adopted electronics. To prove the viability of the method a quartz sample in which muons thermalize as free muons (10%) and muonium atoms (90%) was used. The results in three typical cases are shown in Fig. 3. A pulsed "eld, transverse to the initial muon polarization, which reaches its steady value before the muon pulse arrival, as in Fig. 3(a), is equivalent to a constantly applied "eld and, since the muonium frequency in e.g. &2 mT (28 MHz) exceeds the ISIS passband limit, the Mu signal is lost. The lower precession frequency of k> is well within the bandwidth and therefore its signal still observable. If, on the other hand, the pulse is started after the arrival of muons, no dephasing is introduced
T. Shiroka et al. / Physica B 289}290 (2000) 684}688
687
Fig. 3. Asymmetry signal for di!erent delays of the pulsed transverse "eld. Magnetic "eld is switched on before (a), at the end of the muon pulse (b) and 850 ns after the muon pulse arrival (c). The initial variable frequency signal, due to the gradual increase of the transverse "eld, is shown in the inset.
and full asymmetry can be measured also for muonium, regardless of the amplitude B. In particular, in Fig. 3(c) B is delayed by 850 ns. This experiment suggests the possibility of studying delayed muonium formation processes and reactions, similarly or alternatively to the existing pulsed RF Resonance Technique [5,6]. Indeed, a debated and still largely unanswered question deals with the time scale over which these formation mechanisms take place. Up to now the unique sign of thermal (or delayed) processes has been the existence of missing fractions of muonium/radical signals [7]. This technique is expected to shed new light on these phenomena since in a delayed formation process the deferred application of a transverse magnetic "eld will recover the precession phase coherence (otherwise lost in a constantly applied "eld). The experimental set-up includes a constant "eld, parallel to the initial muon polarization, B . By varying its intensity, we can suitably lock the
polarization of the incoming muons before the transverse "eld is switched on. This con"guration o!ers also the unique opportunity to test the sudden-versus-adiabatic condition [8,9] while observing, in real time, the evolution of the muon spins. There exists a straightforward parallel with the similar case in NMR [10,11]. The adiabatic cross-over measurements for Mu and k> were performed for longitudinal "eld values in the range 0.1:B :2 mT. Raw data, similar to those of Fig. 3(b), con"rm that k> and Mu lSR signals lose their asymmetry amplitude as B is increased, and the adiabatic regime is reached, due to the consequent reduction of the muon-spin precession cone aperture. Changes in muonium amplitude are far more dramatic than those for free muons, due to their di!erent gyromagnetic ratios c. After normalization of the measured amplitudes one obtains the curves shown in Fig. 4.
688
T. Shiroka et al. / Physica B 289}290 (2000) 684}688
Fig. 4. Experimental results for the adiabatic cross-over of Mu (䊐) and k> (*) as a function of the longitudinal magnetic "eld. Lines represent the results of numerical calculations. The frequency scales for Mu and k> refer to the corresponding precession in the steady-state total "eld B.
The sudden to adiabatic cross-over occurs in the range B "0.3}0.6 mT for muonium whereas, as expected, k> undergoes the same transition at much higher "elds } by extrapolation } close to 10 mT. Note that the drop of the measured asymmetry is not a passband e!ect (there is no intrinsic frequency resolution limitation) but simply re#ects the "nite "eld switching velocity.
4. Conclusions Pulsed muon beams lend themself to a variety of techniques which take advantage of their pulsed time structure. We have found that the synchronous and/or delayed application of magnetic "elds or gradients, by using a laminar current device, o!ers many possibilities while holding an intrinsic technical simplicity. In addition, the #at-loop device provides the unique feature of producing a "eld/gradient only where required (i.e. on the sample), with negligible "eld values outside the device, thus avoiding interferences with the transport and focusing of muons. This becomes important especially when perform-
ing lSR experiments with epithermal muons. Moreover, the gradient method allows still unknown features of energy loss at epithermal energies [4] to be explored through range and straggling measurements. An interesting application of this pulsed procedure, is expected to be in the study of delayed muonium formation and/or reactions; the sudden regime is the most appealing since it allows switching to a precession mode with a large precession cone at the desired time. The presence of an additional static longitudinal "eld would preserve the large initial muon-spin polarization, thus allowing investigation in two important cases: (a) when local random static "elds are present in the host material, (b) when muonium radicals subject to transferred hyper"ne interaction with host nuclei are formed. The comparison of standard lSR to NMR becomes very stimulating when pulsed techniques, such as the present one and RF resonance, are involved. Unlike the sophisticated NMR pulsed methods, the work ahead in lSR is still in need of developments both technical and conceptual.
References [1] T. Shiroka, C. Bucci, R. De Renzi, G. Guidi, G.H. Eaton, P.J.C. King, C.A. Scott, Nucl. Instr. and Meth. B 152 (2}3) (1999) 241. [2] E. Morenzoni, F. Kottmann, D. Maden, B. Matthias, M. Meyberg, Th. Prokscha, Th. Wutzke, U. Zimmermann, Phys. Rev. Lett. 72 (1994) 2793. [3] G. Allodi et al., Appl. Magn. Res., in press. [4] M. Mayer, W. Eckstein, Nucl. Instr. and Meth. B 94 (1994) 22. [5] S.R. Kreitzman et al., Phys. Rev. Lett. 61 (1988) 2890. [6] S.P. Cottrell, S.F.J. Cox, J.S. Lord, C.A. Scott, Appl. Magn. Res. 15 (1998) 469. [7] L.D.A. Siebbeles, W.M. Bartczak, M. Terrissol, A. Hummel, J. Phys. Chem. A 101 (1997) 1619. [8] D. Bohm, Quantum Theory, Prentice-Hall, Englewood Cli!s, NJ, 1960 (Chapter 20). [9] A. Messiah, Quantum Mechanics, Academic Press, New York, 1966 (Chapter 18). [10] A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, 1961. [11] C.P. Slichter, Principles of Magnetic Resonance, 3rd Edition, Springer, Berlin, 1990.
Synchronous pulsed magnetic "elds in muon spin rotation T. Shiroka , C. Bucci *, R. De Renzi , F. Galli , G. Guidi , G.H. Eaton, P.J.C. King, C.A. Scott Dipartimento di Fisica e Istituto Nazionale per la Fisica della Materia, Universita% di Parma, Parco Area delle Scienze 7a, I-43100 Parma, Italy Rutherford Appleton Laboratory, ISIS Facility, Chilton, Didcot, Oxon OX11 0QX, UK
Abstract One of the advantages o!ered by pulsed-polarized sources of muons, such as the ISIS Facility at RAL (UK), is the possibility to apply external "elds, synchronous to the muon pulse, with a duration as short as a few muon's lifetimes (&20 ls). Here we present a muon spin rotation (lSR) technique in which an external pulsed magnetic "eld and/or "eld gradient, generated by a laminar current-loop method, are applied to investigate new properties. Whereas xeld gradients seem more appropriate for a straightforward imaging of the implantation depth of positive muons in metals, the pulsed uniform magnetic xelds are shown suitable for the direct measurement of the sudden-to-adiabatic cross-over. The latter method is also expected to be applicable to the experimental study of the delayed muonium formation. 2000 Elsevier Science B.V. All rights reserved. PACS: 76.75; 36.10.D; 82.55; 07.55.D Keywords: Muon spin rotation; Pulsed "elds; Field gradients; Muonium
1. Introduction The pulsed time structure of a beam of spinpolarized positive muons (such as the ISIS facility at the Rutherford Laboratory, UK, delivering intense bunches of muons, 80 ns wide, at 50 Hz), is very attractive when synchronous pulsing of magnetic "elds and/or gradients with a low duty-cycle is required. A possible way to generate magnetic "elds or large magnetic "eld gradients in small volumes
* Corresponding author. Tel.: #39-0521-905246; fax: #390521-905223. E-mail address: bucci@"s.unipr.it (C. Bucci).
(as is the case for the thin samples used in lSR experiments) is to employ a laminar current #atloop device [1]. Fig. 1 shows that the current geometry consists of two parallel slabs where a uniform current, with surface density j, #ows in opposite directions. For slab dimensions slightly bigger than the ISIS lSR beam cross section (&90% of the muons within a 30 mm diameter) the fringe e!ects are negligible and the magnetic "eld is calculated by Ampe`re's law. The "eld B is parallel to the surface of the slab and perpendicular to j. The magnetic "eld outside the loop itself is zero, there is a "eld gradient (*B/*x"$k j) inside the forward and back ward current slabs and the "eld is uniform at its maximum value (B "k jd ) in the space between
0921-4526/00/$ - see front matter 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 2 6 ( 0 0 ) 0 0 3 1 2 - 4
T. Shiroka et al. / Physica B 289}290 (2000) 684}688
685
Fig. 1. Geometry of currents and magnetic "eld pro"le inside the #at-loop device.
them. Such a device allows a twofold application. The "rst one concerns the "eld gradients: when muons are implanted in the metallic "lm carrying the current, the stopping pro"le of muons (or better, the projected range pro"le) can be measured in a straightforward way since each stopping depth has its own unique label given by the muon precession frequency at that location. So the Fourier transform of the precession signal of even a single lSR experiment will give a direct map of the muon distribution. The second feature deals with the uniform "elds inside the device: when a thin sample is placed inside the loop then the "eld can be switched on with adjustable delays relative to the muons implantation time; the frequency cut-o! in lSR experiments due to the muon pulse-width can be eliminated and delayed muonium formation processes can be detected and studied. 2. lSR measurements of muon range pro5les For a typical `surfacea muon beam of &4 MeV, the thickness of the metallic slab in the #at-loop
device can be chosen larger than the projected range straggling. A copper slab&100 lm thick, for instance, is quite suitable. By pulsing a 150 A current with a+100 ns rise time a uniform "eld gradient of+40 T/m can be generated inside the metallic slab. The frequency pro"le of a single lSR spectrum yields therefore the range and the straggling pro"le of the muons stopped in the "lm, as shown in Fig. 2. The knowledge of the slab thickness and that of the magnetic "eld extreme values (done by adjusting the moderator in such a way as to stop muons either before, as in Fig. 2(d), or after, as in Fig. 2(f ), the region of the gradient) allows a simple conversion of the frequency scale into a length scale. An external uniform "eld of 10 mT, parallel to the "eld generated in the device, conveniently shifts the central frequency. The values we "nd for the range and straggling in Cu are in agreement with those determined by di!erent, although more elaborate, methods [1]. Similar measurements performed on Al and Pb con"rm the Z-dependence of range and straggling.
686
T. Shiroka et al. / Physica B 289}290 (2000) 684}688
Fig. 2. Polarization (left) and its Fourier transform (right) for Cu (top scale: implantation depths x). Cu moderator was 178.4 mg/cm in (a), 89.2 mg/cm in (b) (dotted vertical lines delimit currents slab) and 44.6 mg/cm in (c).
In view of possible experiments with the recently developed epithermal muons [2,3], separate tests of the device were performed by using thin "lms. This type of measurements is important since for muon energies below 1 keV the expected ranges are smaller than 100 nm, data are still scarce and available simulation codes [4] will need to be compared to experiments. Various thicknesses between 18 nm Al and 100 nm Cu have been tested with currents up to 250 A and proved the stability of the "lms and the uniformity of the magnetic "eld gradients [1]. 3. lSR experiments with delayed 5elds The same synchronous pulsing principle can be used to perform experiments when the muon implantation in a sample inside the central volume of
the device (where the "eld is quite uniform) is made before the current pulse is applied. In this way, the cut-o! frequency of the main beam can be appreciably extended, the new limit being set by the timeto-digital converters of the adopted electronics. To prove the viability of the method a quartz sample in which muons thermalize as free muons (10%) and muonium atoms (90%) was used. The results in three typical cases are shown in Fig. 3. A pulsed "eld, transverse to the initial muon polarization, which reaches its steady value before the muon pulse arrival, as in Fig. 3(a), is equivalent to a constantly applied "eld and, since the muonium frequency in e.g. &2 mT (28 MHz) exceeds the ISIS passband limit, the Mu signal is lost. The lower precession frequency of k> is well within the bandwidth and therefore its signal still observable. If, on the other hand, the pulse is started after the arrival of muons, no dephasing is introduced
T. Shiroka et al. / Physica B 289}290 (2000) 684}688
687
Fig. 3. Asymmetry signal for di!erent delays of the pulsed transverse "eld. Magnetic "eld is switched on before (a), at the end of the muon pulse (b) and 850 ns after the muon pulse arrival (c). The initial variable frequency signal, due to the gradual increase of the transverse "eld, is shown in the inset.
and full asymmetry can be measured also for muonium, regardless of the amplitude B. In particular, in Fig. 3(c) B is delayed by 850 ns. This experiment suggests the possibility of studying delayed muonium formation processes and reactions, similarly or alternatively to the existing pulsed RF Resonance Technique [5,6]. Indeed, a debated and still largely unanswered question deals with the time scale over which these formation mechanisms take place. Up to now the unique sign of thermal (or delayed) processes has been the existence of missing fractions of muonium/radical signals [7]. This technique is expected to shed new light on these phenomena since in a delayed formation process the deferred application of a transverse magnetic "eld will recover the precession phase coherence (otherwise lost in a constantly applied "eld). The experimental set-up includes a constant "eld, parallel to the initial muon polarization, B . By varying its intensity, we can suitably lock the
polarization of the incoming muons before the transverse "eld is switched on. This con"guration o!ers also the unique opportunity to test the sudden-versus-adiabatic condition [8,9] while observing, in real time, the evolution of the muon spins. There exists a straightforward parallel with the similar case in NMR [10,11]. The adiabatic cross-over measurements for Mu and k> were performed for longitudinal "eld values in the range 0.1:B :2 mT. Raw data, similar to those of Fig. 3(b), con"rm that k> and Mu lSR signals lose their asymmetry amplitude as B is increased, and the adiabatic regime is reached, due to the consequent reduction of the muon-spin precession cone aperture. Changes in muonium amplitude are far more dramatic than those for free muons, due to their di!erent gyromagnetic ratios c. After normalization of the measured amplitudes one obtains the curves shown in Fig. 4.
688
T. Shiroka et al. / Physica B 289}290 (2000) 684}688
Fig. 4. Experimental results for the adiabatic cross-over of Mu (䊐) and k> (*) as a function of the longitudinal magnetic "eld. Lines represent the results of numerical calculations. The frequency scales for Mu and k> refer to the corresponding precession in the steady-state total "eld B.
The sudden to adiabatic cross-over occurs in the range B "0.3}0.6 mT for muonium whereas, as expected, k> undergoes the same transition at much higher "elds } by extrapolation } close to 10 mT. Note that the drop of the measured asymmetry is not a passband e!ect (there is no intrinsic frequency resolution limitation) but simply re#ects the "nite "eld switching velocity.
4. Conclusions Pulsed muon beams lend themself to a variety of techniques which take advantage of their pulsed time structure. We have found that the synchronous and/or delayed application of magnetic "elds or gradients, by using a laminar current device, o!ers many possibilities while holding an intrinsic technical simplicity. In addition, the #at-loop device provides the unique feature of producing a "eld/gradient only where required (i.e. on the sample), with negligible "eld values outside the device, thus avoiding interferences with the transport and focusing of muons. This becomes important especially when perform-
ing lSR experiments with epithermal muons. Moreover, the gradient method allows still unknown features of energy loss at epithermal energies [4] to be explored through range and straggling measurements. An interesting application of this pulsed procedure, is expected to be in the study of delayed muonium formation and/or reactions; the sudden regime is the most appealing since it allows switching to a precession mode with a large precession cone at the desired time. The presence of an additional static longitudinal "eld would preserve the large initial muon-spin polarization, thus allowing investigation in two important cases: (a) when local random static "elds are present in the host material, (b) when muonium radicals subject to transferred hyper"ne interaction with host nuclei are formed. The comparison of standard lSR to NMR becomes very stimulating when pulsed techniques, such as the present one and RF resonance, are involved. Unlike the sophisticated NMR pulsed methods, the work ahead in lSR is still in need of developments both technical and conceptual.
References [1] T. Shiroka, C. Bucci, R. De Renzi, G. Guidi, G.H. Eaton, P.J.C. King, C.A. Scott, Nucl. Instr. and Meth. B 152 (2}3) (1999) 241. [2] E. Morenzoni, F. Kottmann, D. Maden, B. Matthias, M. Meyberg, Th. Prokscha, Th. Wutzke, U. Zimmermann, Phys. Rev. Lett. 72 (1994) 2793. [3] G. Allodi et al., Appl. Magn. Res., in press. [4] M. Mayer, W. Eckstein, Nucl. Instr. and Meth. B 94 (1994) 22. [5] S.R. Kreitzman et al., Phys. Rev. Lett. 61 (1988) 2890. [6] S.P. Cottrell, S.F.J. Cox, J.S. Lord, C.A. Scott, Appl. Magn. Res. 15 (1998) 469. [7] L.D.A. Siebbeles, W.M. Bartczak, M. Terrissol, A. Hummel, J. Phys. Chem. A 101 (1997) 1619. [8] D. Bohm, Quantum Theory, Prentice-Hall, Englewood Cli!s, NJ, 1960 (Chapter 20). [9] A. Messiah, Quantum Mechanics, Academic Press, New York, 1966 (Chapter 18). [10] A. Abragam, The Principles of Nuclear Magnetism, Clarendon Press, Oxford, 1961. [11] C.P. Slichter, Principles of Magnetic Resonance, 3rd Edition, Springer, Berlin, 1990.