msr: muon spin relaxation, rotation, resonance Mark Telling ISIS Facility

Transcription

1 SR: un spin relaxatin, rtatin, resnance Mark Telling ISIS Facility e-ail:

2 Lecture 5 : Overview Prperties f the un S what is SR? The SR ethd Generalised respnse: the un Generalised respnse: uniu Generalised respnse: uniu-substituted radical Where n earth can yu d SR? Muns at the ISIS facility Getting uns int yur saple

3 Selected references Mun Spin Rtatin Spectrscpy Principles and Applicatins A.Schenck, Ada Hilger Ltd, Bristl and Bstn,1985 Mun Science: Muns in Physics, Cheistry and Materials S.L Lee, R Cywinski, S.H Kilcyne (eds). Institute f Physics Pub., 1999 Muns and Pins in Materials Research J.Chappert and R.I.Grynszpan (eds), Elsevier Science Publishers, B.V., 1984

4 Prperties f the un PROPERTY VALUE Mass Spin μ = e = p S μ = ½ Charge +e Magnetic Ment Gyragnetic factr Average Lifetie μ μ = 3.183μ p = μ B γ μ = khz/g τ μ = 2.197μs

5 Evlutin f Spin Plarisatin, P(t) S what is SR? SR : Mun Spin R = relaxatin, rtatin r resnance Mun Science, S.L Lee et al (eds). IOP, 1999 Unlike neutrns, SR is a LOCAL prbe f atter The un sits between ats The technique relies upn the fact that: The uns entering the saple are ALL spin plarised The un decays after 2.2 s and eits a psitrn preferentially alng its final spin directin Experiental dataset : tie dependent evlutin f the un bea spin plarisatin Fr f this evlutin, G(t), tells us sething abut the nature f a aterials internal agnetic r electrnic envirnent P(t) = (P(t=0) x G(t))+Bck

6 Why use SR?

7 Areas f applicatin

8 Psitrn cunts Psitrn cunts Plarisatin, P(t) The SR ethd Detectr Arrays 1 tie saple psitin un bea Backward, B Frward, F Assue: tie Spin plarised uns are iplanted in saple Spins reain plarised (aligned) fr the life tie f the un Psitrns are eitted ONLY alng the spin directin If we nralise t the un decay we get P(t) = 1 tie

9 In reality there is an angular distributin f psitrn eissin i.e. W(q) = 1 + a.cs(q) where a = the asyetry f the distributin saple : silver un bea Backward, B Frward, F Assue: Spin plarised uns are iplanted in saple Spins reain plarised (aligned) fr the life tie f the un Psitrns are eitted asyetrically Then in the FORWARD AND BACKWARD detectrs we get.

10 Psitrn cunts In reality there is an angular distributin f psitrn eissin i.e. W(q) = 1 + a.cs(q) where a = the asyetry f the distributin Assuing: tie Spin plarised uns are iplanted in saple Spins reain plarised (aligned) fr the life tie f the un Psitrns are eitted asyetrically Then in the FORWARD AND BACKWARD detectrs we get.

11 Asyetry / A In reality there is an angular distributin f psitrn eissin i.e. W(q) = 1 + a.cs(q) where a = the asyetry f the distributin tie Assuing: Spin plarised uns are iplanted in saple Spins reain plarised (aligned) fr the life tie f the un Psitrns are eitted asyetrically and ur experiental 100% spin plarisatin value fr t=0 is actually A = 0.3

12 What happens when a + iplants in a saple? Well, depending n the aterial (etal, insulatr, rganic, liquid ) ne f three things can ccur: 1. The un, Mu +, sits in the saple and decays with a ean lifetie f 2.2s 2. It cbines with an electrn t fr uniu, Mu. ; a radiactive light istpe f hydrgen 3. The Mu reacts with the saple t fr a uniu-substituted radical, RMu. Respnse t applied external agnetic field Experiental signatures f situatins 1-3 at t=0 1. The uns shuld retain their full spin plarisatin (A=0.3) 2. 50% f the plarisatin (asyetry ) is lst initially but restred by applying B ext alng + spin directin 3. Mre r less than 50% f the initial plarisatin can be lst if RMu is fred

13 Asyetry / A Generalised respnse fr: the un the uns sit at a specific crystallgraphic site between ats and sense a static internal agnetic field 0.3 AG( t) t) 2 ) tie B = Cbalt with a nuclear diple ent f nuclear agnetns R = Yttriu with a nuclear diple ent f nuclear agnetns If the un senses a net static internal agnetic field (arising fr the ats nuclear diple ents) AND there is a internal field cpnent perpendicular t the un spin then the un will rtate (Larr precess) while it decays In this case, dividing psitrns cllected in the back and frward detectrs will result in G(t) = GAUSSIAN FORM

14 Asyetry / A S what happens when the uns sit at a specific crystallgraphic site between ats and sense a static internal agnetic field and an external agnetic field, B ext > internal field is applied alng the un spin directin 0.3 tie B = Cbalt with a nuclear diple ent f nuclear agnetns R = Yttriu with a nuclear diple ent f nuclear agnetns If the un senses a net static internal agnetic field (arising fr the ats nuclear diple ents) AND there is a internal field cpnent perpendicular t the un spin then the un will rtate while it decays Result : NO DEPOLARISATION...applicatin f B ext can be used t test that the un is sensing a static envirnent

15 Asyetry / A The beauty f silver the uns sit at a specific crystallgraphic site between ats and sense a static internal agnetic field 0.3 tie Fr silver: the atic nuclear diple ent ( nuclear agnetns) is VERY SMALL As a result the uns precess very little befre they decay t psitrns and full spin plarisatin is alst aintained as a functin f tie Silver is therefre a very useful aterial fr which t ake saple hlders The signal fr any uns iplanting in an Ag saple hlder will just lk like a flat backgrund cntributin

16 The beauty f silver In practice, t deterine G(t) we relate the nuber f psitrns detected in the frnt and back detectr banks accrding t eqn. C The calibratin factr, a, is required t ensure bth banks are equally efficient and t crrect fr the saple psitin relative t the tw detectr arrays a is deterined by applying a 20G field perpendicular t the un spin directin. The uns Larr precess abut the 20G applied field, pinting first frward and then backward. Hwever, there is inial spin deplarisatin due t the sall silver at nuclear diple ent a is crrect when applicatin f eqn. C gives a signal that scillates syetrically abut the tie axis. A(t) = a G z (t) = N F - αn B N F + αn B C

17 Asyetry / A S what happens when the uns sit at a specific crystallgraphic site between ats and the internal agnetic field sensed changes with tie since it arises fr electrns hpping n and ff f ats (i.e. itinerant electrn agnetis) 0.3 AG( t) t)) tie If the uns sense a net dynaic internal agnetic field (arising fr the agnetic ent n each f the ats fluctuating as electrns hp n and ff n ats) AND there is an internal field cpnent perpendicular t the un spin then the uns will rtate while they decay. In this case dividing psitrns cllected in the back and frward detectrs will result in G(t) = LORENTZIAN FORM

18 ExpDecOsc f ( t) t)cs( t + ) 2 GauOsc f ( t) t) 2)cs( t + ) Abraga Cn spin plarisatin decay functins 2 f ( t) c ) (exp( t c ) 1+ t c ))cs( t + ) ExpDecOsc f ( t) t)cs( t + ) ExpDecOsc 2 2 StaticKubTyabe f ( t) A(exp( t) 2)((1 ( t) f )(2 ( t) 3) A+ exp( 1 3) t)cs( t + ) 2 GauOsc f ( t) t) 2)cs( t + ) 2 GauOsc StrexpExp f ( t) t) ) f ( t) t) 2)cs( t + ) Abraga GausDec 2 Abraga 2 f ( t) t) ) f ( t) c ) (exp( t c ) 1+ t c ))cs( t + ) 2 f ( t) c ) (exp( t c ) 1+ t c ))cs( t + ) 2 2 ExpDecMun f ( t) t) StaticKubTyabe f ( t) A(exp( t) 2)((1 ( t) )(2 3) + 1 3) StaticKubTyabe 2 f ( t) A(exp( t) 2 2)((1 ( t) )(2 3) + 1 3) MunFInteractin Ipleents equatin (3) StrexpExp in reference Brewer et al, f ( t) t) ) Physical StrexpExp Review B 33(11) f ( t) At exp( del t) the ) 2 un respnse under the GausDec fratin f the FμF species f ( t) t) ) 2 GausDec f ( t) t) ) DynaicKubTyabe Fitting fr the paraeters ExpDecMun A, σ and ν (the initial f ( t) t) asyetry, ExpDecMun relaxatin rate and hp f ( t) rate, respectively) t) MunFInteractin Ipleents equatin (3) in reference Brewer et al, using nuerical integratin techniques MunFInteractin Ipleents equatin Physical (3) in reference Review B Brewer 33(11) et al, t del the Physical Review B 33(11) un respnse under t del the fratin the f the FμF species Fr the functins abve: un respnse under the fratin f the FμF species DynaicKubTyabe Fitting fr the paraeters A, σ and ν (the initial and are in s -1 is in radians DynaicKubTyabe Fitting fr the paraeters asyetry, A, σ relaxatin and ν (the rate initial and hp rate, respectively) asyetry, relaxatin using rate nuerical and hp rate, integratin respectively) techniques using nuerical integratin techniques is in MHz (nte MHz/Gauss) Fr the functins abve:

19 Asyetry / A Generalised respnse fr: uniu Exaple: QUARTZ, Brewer, Hyp. Int. 8 (1981) Muns can cuple t unpaired electrns t fr uniu uniu is a light istpe f hydrgen Strength f cupling between un-electrn is given by hyperfine cupling cnstant, A Signature : 50% f initial spin plarisatin is lst but full spin plarisatin can be recvered by applying an external agnetic field strng enugh t decuple the unelectrn External Field Fr uniu B eff = 1500 Gauss Fr uniu A = 4.46 GHz h D and h M are un / uniu fractins. e (28 GHz/T) and (0.13 GHz/T) are gyragnetic ratis f electrn / un A replarisatin that gives A f 4.46 GHz is an indicatin f uniu fratin

20 Generalised respnse fr: a uniated radical Exaple: BENZENE, Rduner, Hyp. Int. 65(1) (1991) If uniu is fred and the syste cnsists f duble bnds then a uniu-substituted radical ay fr Here the hyperfine cupling cnstant extracted fr replarisatin is sensitive t the lcal radical envirnent Infratin abut lcal dynaics at the radical site can be extracted using a ethd: LEVEL CROSSING RESONANCE Here, the external field is applied and swept acrss the agnetic field, B eff, assciated with a cupling cnstant f A Integrated psitrn cunts ver a cnstant tie range and pltting this integral value as functin f field Fr uniu B eff = 1500 Gauss A 4460 MHz

21 Generalised respnse fr: a uniated radical Exaple: BENZENE, Rduner, Hyp. Int. 65(1) (1991) If uniu is fred and the syste cnsists f duble bnds then a uniu-substituted radical ay fr Here the hyperfine cupling cnstant extracted fr replarisatin is sensitive t the lcal radical envirnent Infratin abut lcal dynaics at the radical site can be extracted using a ethd: LEVEL CROSSING RESONANCE Here, the external field is applied and swept acrss the agnetic field, B eff, assciated with a cupling cnstant f A Integrated psitrn cunts ver a cnstant tie range and pltting this integral value as functin f field

22 Where n earth can yu d SR? Triuph, Canada ISIS, UK PSI, Switzerland J-PARC, Japan Fr ni3.eu/un-research/

23 Muns at the ISIS Facility 25 neutrn instruents and 7 un instruents Welces ~ 2000 researchers, perfring ~ 800 experients, resulting in ver 400 publicatins/yr

24 The RIKEN-RAL Mun Facility Largest UK-Japan science cllabratin First uns in 1994 Fur experiental areas used fr: Cndensed atter physics Technique develpent High energy uns fr pressure studies Laser stiulatin extic ethds

25 The Eurpean Mun Facility

26 surface un prductin at ISIS Mun prductin target is ade f graphite which is hit by 5% f the ISIS prtn bea the ther 95 % creates spallatin neutrns Prtn bea heating raises graphite teperature ~ 900 K but the cllisin prcess creates pins, Se pins stp in graphite and decay t + Thse + stpping at graphite surface escape and are channelled t the experiental areas SURFACE MUON BEAM = 100% SPIN POLARISED

27 The MUON Spectreter : MUSR at ISIS side view frnt view

28 Ultiately sensitive? The frequency respnse At ISIS, uns dn t arrive in the saple at ne tie. Due t the pulsed nature f the un prductin prcess there is a spread f arrival ties If the uns sense an internal field, a un arriving in the saple at tie t = 1 will start t precess befre a un arriving at psitin t = 2 enters the saple The result is that even befre the easureent begins the tw uns will be ut f phase and plarizatin is lst The larger the internal field, the faster the precessin frequency f the uns BUT als the wrse this initial dephasing beces. There will be a precessin frequency abve which all spin plarizatin will be lst

29 Getting the uns int yur saple Unlike neutrns, yu want as any uns interacting with Hrizntal Hr the saple as pssible Electragnetic devices are incrprated int a un bea line t steer the bea nt the saple Steering is perfred in bth the hrizntal and vertical directins relative t the un bea directin and by Vertical varying the current supplying the device Steering curves are perfred using, fr exaple, a highly deplarising saple (i.e. haeatite). The bea is centred when the easured asyetry is at a iniu

30 Sall saple? N prble, use fly past! Unlike neutrns, yu want as any uns interacting with the saple as pssible Fr large quantities f aterial ne usually unts the saple n a 3c x 3c Ag plate the saple is s large that very few uns stp in the Ag Fr sall saple quantities this is nt ideal since, as shwn in A, the large uncvered / expsed Ag surface area gives rise t a sizable backgrund ter Instead, the saple is suspended n a sall Ag needle, as shwn in B, and thse uns that dn t hit the saple fly past This ethd can reduce the backgrund cntributin t a easureent alst t zer A B

31 Range curves Muns strike the saple at 0.25c. They are slwed via cllisin with the saple and/r the saple envirnent If a saple is t thin = uns will pass straight thrugh! There is a certain thickness/distance, r range ver which uns will land in the saple T ptiise the nuber f uns iplanted in a thin saple, etal fils can be used t degrade the un energy and create a range curve fr ISIS, uns are stpped in aterials with a ttal surface density f ~ 120 g/c 2 Fe 2 O 3