Magnetic Neutron Scattering

Transcription

1 Magntc utron Scattrng Martn Rottr Insttut für Physkalsch Chm, Unvrstät Wn Martn Rottr ESY Wntr School 005

2 Contnts Introucton: utrons an Magntsm Elastc Magntc Scattrng Inlastc Magntc Scattrng Martn Rottr ESY Wntr School 005

3 utrons an Magntsm Macro-Magntsm: Soluton of Maxwll s Equatons Engnrng of lctromagntc vcs Mcromagntsm: Doman Dynamcs, Hystrss Atomc Magntsm: Instrnsc Magntc Proprts MFM mag Mcromagntc smulaton. 0 - m 0-3 m 0-5 m 0-7 m 0-9 m 0 - m Hall Pro VSM SUID MOKE MFM MR FMR µsr S Martn Rottr ESY Wntr School 005 3

4 Bragg s Law n Rcprocal Spac Ewal Sphr π/λ O a * k c * θ sn Θk θ k Incomng utron Scattr utron

5 Sngl Crystal Dffracton E HMI, Brln k O Martn Rottr ESY Wntr School 005 5

6 Th Scattrng Cross Scton Scattrng Cross Sctons Total σ umr of scattr nutrons pr sc Incnt nutron flux tm tm ara tot ara Dffrntal σ Ω umr of scattr nutrons pr sc nto angl lmnt Ω Incnt nutron flux. Ω Doul Dffrntal σ ΩE umr of... an wth nrgs twn E Incnt nutron flux. E Ω an E E Scattrng Law σ ΩE k S, k S... Scattrng functon Unts: arn0-8 m ca. uclar raus Martn Rottr ESY Wntr School 005 6

7 σ ΩE k Martn Rottr Ps P < > n sn; Hnt s ESY Wntr n; f δ E School k π f, s M n M nutron mass k wavvctor s n > Spn stat of th nutron P sn Polarsaton >, f> Intal-,fnalstat of th targts E,E f Enrgs of - P thrmal populaton of stat > H nt Intracton -oprator S. W. Lovsy Thory of utron Scattrng from Conns Mattr,Oxfor Unvrsty Prss, 984 E f

8 Martn Rottr ESY Wntr School Intracton of utrons wth Mattr H nuc H mag H nt n n n nuc M H ~ R r s I r δ π H s n ˆ ˆ nt β n nuc M H ~ s I R π n B n n mag c m c m H B s A A A r µ P P { } n n B mag g gf H J s R ˆ ˆ 8 ~ πµ n n r H H n 3 r r

9 Unpolars utrons - Van Hov Scattrng functon S, ˆ ˆ ˆ > < > < > < Ω f f f P E E M k k E f f β δ π σ no nuclar orr - <I>0: { } { } > < > < Ω 0 ~ ~ 4 * * 0 ~ ~, 0,,, ˆ ˆ T t t nuc T t t mag nuc mag I I t S J t J gf gf t S S k k S mc k k E R R R R δ π π δ γ σ β α αβ αβ αβ β α αβ 4 * * W W l nuc I I S R R δ δ ~ t t u R R { } { } W W T T l mag J gf J gf S > < > < R R β α δ Splttng of S nto lastc an nlastc part nl mag l mag mag nl nuc l nuc nuc S S S S S S

10 utron Dffracton 4 * W W l nuc I I S R R δ Lattc G wth ass B: k k B G R... Isotop-ncohrnt-Scattrng Spn-ncohrnt-Scattrng Inpnnt of : B B W W B l nuc I I S B 4, *, δ δ δ δ B B Lattcfactor Structurfactor on lmnt B : Ω nc l nuc nc l nuc I I π σ π σ σ 4 c π σ

11 S l mag S l nuc coh σ ΩE δ δ k γ k mc Magntc Dffracton αβ δ αβ ˆ α * ˆ β S R R Martn Rottr ESY Wntr School 005 { } { R R gf < J > gf } < J > α Dffrnc to nuclar scattrng: Formfactor Polarsatonfactor { gf } ˆ T, k k β αβ mag S nuc T,... no magntc sgnal at hgh angls ˆ δαβ α β... only momnt componnts normal to contrut

12 Formfactor g F κ < 0 > < g > Martn Rottr ESY Wntr School 005

13 Atomc Lattc Magntc Lattc frro antfrro Martn Rottr ESY Wntr School 005 3

14 Atomc Lattc Magntc Lattc frro antfrro Martn Rottr ESY Wntr School 005 4

15 Atomc Lattc Magntc Lattc frro antfrro Martn Rottr ESY Wntr School 005 5

16 Th ol Prz n Physcs 994 In 949 Shull show th magntc structur of th MnO crystal, whch l to th scovry of antfrromagntsm whr th magntc momnts of som atoms pont up an som pont own.

17 Arrangmnt of Magntc Momnts n Mattr Paramagnt Frromagnt Antfrromagnt An many mor... Frrmagnt, Hlmagnt, Spnglass...collnar, commnsurat tc. Martn Rottr ESY Wntr School 005 7

18 GCu T 4 K M [00] T R 0 K q /3 0 Magntc Structur from utron Scattrng Rottr t.al. J. Magn. Mag. Mat Martn Rottr ESY Wntr School 005 8

19 Cu Magntc Phasagram Fl along -rcton 4 F FM µ 0 H T F AF AF AF T K Martn Rottr ESY Wntr School 005 9

20 Complx Structurs AF Martn Rottr ESY Wntr School 005 0

21 Complx Structurs F Martn Rottr ESY Wntr School 005

22 Complx Structurs F Martn Rottr ESY Wntr School 005

23 Cu Magntc Phasagram H F3 F c F a AF LnsExprmnt ColorsThory Martn Rottr ESY Wntr School 005 3

24 Inlastc Magntc Scattrng Drachsnspktomtr PADA Dynamk magntschr Systm:. Magnonn. Krstallflr 3. Multpolar Anrgungn Martn Rottr ESY Wntr School 005 4

25 Martn Rottr ESY Wntr School k k G hkl q q G k k hkl M k M k Thr Axs Spctromtr TAS

26 PADA TAS for Polarz utrons at th FRM-II, Munch Martn Rottr ESY Wntr School 005 6

27 PADA TAS for Polarz utrons at th FRM-II, Munch am-channl monochromatorshlng wth platform Can wth computr work-placs an lctroncs sconary spctromtr wth surrounng raoprotcton, 5 Tsla / 30mK Cryomagnt Martn Rottr ESY Wntr School 005 7

28 Movmnt of Atoms [Soun, Phonons] Brockhous Th ol Prz n Physcs 994 E /a Martn Rottr ESY Wntr School 005 8

29 Movmnt of Spns - Magnons 53 H J S S MF - Zman Ansatz for S/ T.3 K Martn Rottr ESY Wntr School 005 9

30 Movmnt of Spns - Magnons 53 H J S S T.3 K Bohn t. al. PRB Martn Rottr ESY Wntr School

31 H Movmnt of Spns - Magnons J S S 53 a T.3 K Bohn t. al. PRB Martn Rottr ESY Wntr School 005 3

32 Movmnt of Chargs - th Crystal Fl Concpt 4f charg nsty E Hamltonan H cf lm, B m l O m l J Martn Rottr ESY Wntr School 005 3

33 Cu Crystal Fl Exctatons orthorhomc, T 6.5 K, 3 : J9/, Kramrs-on Gratz t. al., J. Phys.: Con. Mat Martn Rottr ESY Wntr School

34 Cu - 4f Charg Dnsty m < ˆ ρ r > R4 f r cnmθ n < On J > T Z nm Ω n 0,,4,6 m 0,..., n T00 T40 K Martn Rottr ESY Wntr School

35 Martn Rottr ESY Wntr School Calculat Magntc Exctatons an th utron Scattrng Cross Scton, ˆ ˆ δ γ σ αβ αβ β α αβ mag S mc k k E Ω / χ kt S, } { } {, W W nl mag S gf gf S αβ π αβ B B { } * z z z βα αβ αβ χ χ χ,,, T H T H n n J J J J J > > < >< > < < ε ε χ χ χ χ β β α α αβ Lnar Rspons Thory, MF-RPA B J lm m l m l J g O B H J J H J J, µ

36 F3 F3: masur sprson was ftt to gt xchang constants J Cu F AF

37 950 Movmnts of Atoms [Soun, Phonons] 970 Movmnt of Spns [Magnons]? Movmnt of Ortals [Ortons] a orton Dscrpton: quarupolar hghr orr ntractons H, lm m m C O J O J l l Martn Rottr ESY Wntr School

38 M. Martn Rottr, Insttut für physkalsch ESY Chm, Wntr School Unvrstät 005 Wn 38

39 McPhas - th Worl of Rar Earth Magntsm McPhas s a program packag for th calculaton of magntc proprts of rar arth as systms. Magntzaton Magntc Phasagrams Magntc Structurs Elastc/Inlastc/Dffus utron Scattrng Cross Scton Martn Rottr ESY Wntr School

40 Crystal Fl/Magntc/Ortal Exctatons Magntostrcton an much mor... Martn Rottr ESY Wntr School

41 McPhas runs on Lnux an Wnows an s avalal as frwar. McPhas s ng vlop y M. Rottr, Insttut für Physkalsch Chm, Unvrstät Wn, Austra M. Dorr, R. Schlr, Insttut für Fstkörprphysk, Tchnsch Unvrstät Drsn, Grmany P. Fa né Hoffmann, Forschungszntrum Jülch, Grmany S. Rottr, Wn, Austra Important Pulcatons rfrncng McPhas: M. Rottr, S. Kramp, M. Lownhaupt, E. Gratz, W. Schmt,. M. Pyka, B. Hnnon, R. v..kamp Magntc Exctatons n th antfrromagntc phas of Cu Appl. Phys. A74 00 S75 M. Rottr, M. Dorr, M. Lownhaupt, P. Svooa, Molng Magntostrcton n RCu Compouns usng McPhas J. of Appl Physcs M. Rottr Usng McPhas to calculat Magntc Phas Dagrams of Rar Earth Compouns J. Magn. Magn. Mat Martn Rottr ESY Wntr School 005 4