Correlating EUV TMOKE and ARPES measurements to understand the temporal

Transcription

1 Correlaing EUV TMOKE and ARPES measuremens o undersand he emporal and spaial lengh sales underlying ulrafas demagneizaion in ferromagnes Wenjing You 1, Phoebe Tengdin 1, Cong Chen 1, Xun Shi 1 *, Dmiriy Zusin 1, Yinghao Zhang 1, Chrisian Genry 1, Adam Blonsky 1, Mark Keller 2, Peer M. Oppeneer 3, Henry Kapeyn 1, Zhensheng Tao 1 *, Margare Murnane 1 1 Deparmen of Physis and JILA, Universiy of Colorado and NIST, Boulder, Colorado 80309, Unied Saes 2 Naional Insiue of Sandards and Tehnology (NIST), 325 Broadway, Boulder, Colorado 80305, Unied Saes 3 Deparmen of Physis and Asronomy, Uppsala Universiy, Box 516, Uppsala, Sweden *Corresponding auhors: Dr. Xun Shi, xun.shi@olorado.edu, Dr. Zhensheng Tao, zhensheng.ao@jila.olorado.edu; These auhors onribued equally o his work. Absra Timeresolved magneoopial Kerr effe sperosopies provide powerful probes of he spin dynamis in magnei maerials. Moreover, using exreme ulraviole high harmonis ha span he enire Mshell orpion edges, spin dynamis orresponding o individual elemens in alloys or layers in mulilayers an be simulaneously exraed. However, o dae, he disparae spin dynamis ha our a differen dephs in a laserheaed maerial were no disenangled. Here we show ha his spaial averaging masks he rue behavior of he maerial, where maerial a he surfae an go hrough he ferromagneiparamagnei phase ransiion, while deeper layers will no. Here we quaniaively ompare imeresolved ransverse magneoopial Kerr effe measuremens and ime and angleresolved phooemission sperosopy measuremens on nikel. We show ha he riial behavior of he maerial ompleely explains he resuls obained from hese wo experimens, aking ino aoun he hree universal imesales observed, as well as he probing deph for eah mehod. Our findings show ha beause of he exisene of a riial fluene above whih he phase ransiion will our, o undersand he dynamis in magnei maerials boh he iniden fluene and probe deph mus be aken ino aoun. 1

2 In ig. 2A, we plo he magneizaion dynamis measured using TrTMOKE exied by various pump fluenes. rom he resuls, we learly observe ha he remagneizaion ime srongly depends on he pump fluene, onsisen wih previous work(1). In order o quaniaively ompare he measuremens using TrTMOKE and TrARPES resuls, we make hree basi assumpions in our model. irs we assume based on previous observaions of riial behavior ha he eah layer of he maerial behaves in wo disinly differen ways depending on wheher he amoun of orbed fluene is above or below a riial value. Seond, he dynamis of he demagneizaion in eah maerial layer an be desribed by an exponenial deay and biexponenial reovery funion, wih hree universal ime onsans exraed direly from he dynamis of he exhange spliing using TrARPES: a demagneizaion ime, τ demag = 176 fs; a fas reovery ime, τ reover1 = 537 fs; and a slow reovery ime, τ reover2 = 26 ps. Third, o aoun for he effe of sample deph averaging on he ime response of he TMOKE signal, we alulae he dephsensiiviy funion(2, 3) for EUV TMOKE for he firs ime, and apply his weighed deph onribuion funion o alulae he TMOKE signal from he empirially modelled ime dependen behavior a every deph in he maerial. The alulaed dephsensiiviy funion for he differen EUV energies are ploed in ig. 2B. In our model, he bulkaveraged magneizaion ( M ) measured using TMOKE is given as an inegral of he uni magneizaion a eah layer (m) over he probing deph, z: ò ò (, z) W ( z) m dz 0 M ( ) =, (1) W dz 0 ( z) where W(z) is he weighing value as a funion of he deph defined by he deph sensiiviy funion as shown in ig. 2B. The dynamis of he magneizaion of eah layer, m(, z), are 2

3 generally defined as an exponenial deay and biexponenial reovery funion wih is groundsae magneizaion equals o 1: m (, z) ï ì1, í ïî 1+ A = ( < 0) demag reove r1 reove r2 ( z) e [ A ( z) A ( z) ] e A ( z) e, ( ³ 0), (2) where A 1 and A 3 represen he ampliudes of he demagneizaion and he seond slow remagneizaion a differen maerial deph (z). We noe ha Eq. (1) is normalized o he groundsae magneizaion. In Eq. (2), we onsider he riial behavior of he magneizaion dynamis a differen deph by assuming ha A 3 is a linear response funion of he orbed pump fluene a z [(z)] above he riial orbed fluene ( ): [ ( z) < ] [ ( z) ], ( z) ³ ì0, A ( z) = í. (3) 3 îb3 [ ] Here, B 3 in Eq. (3) is a proporionaliy onsan of he linear behavior. A he same ime, we also assume A 1 is linearly depends on he orbed pump fluene: A 1 (z)=b 1 (z), whih is suppored by he fa ha he maximum demagneizaion measured by TrTMOKE inreases linearly as a funion of he pump fluene (see ig. 2A). Here we define he orbed fluene a eah deph (z) z o be ( ) d z = e, where is he surfae orbed fluene and d» 13 nm is he peneraion deph of he 800 nm pump laser. We noe ha in order o direly ompare resuls from TrTMOKE and TrARPES, in whih he IR pump is iniden on he sample wih differen angles (normal inidene for ARPES and 48 degrees relaive o normal for TMOKE), we define he fluene as he surfae orbed fluene by expliily aking he refleiviy of IR pump on Ni surfae (R) ino aoun: ( R) = 1 wih in he iniden fluene. The refleiviy for normal inidene in 3

4 is ~0.75, while i hanges o ~0.64 when he inidene angle is 48 degrees relaive o normal, whih is also onfirmed by insiu refleiviy measuremens. Wih our model desribed above, we fi he magneizaion dynamis wih differen pump fluenes o Eqs. (1), (2) and (3) aking only B 1, B 3 and as he fiing parameers. The fiing resuls are ploed as he solid lines in ig. 2A. Amazingly, exellen agreemen an be ahieved beween he model resuls and experimenal measuremens for a range of differen pump fluenes, whih v our model. The parameers for he opimal fiing are lised in Table 1. In ig. 2C, we plo A 3 a differen orbed fluenes in dire omparison wih he riial behavior of he exhange spliing observed in TrARPES experimens, showing onsisen riial orbed fluene in boh experimens. A he same ime, our model shows ha he fluenedependen remagneizaion ime observed in TrTMOKE experimens an be essenially explained by a dephaveraging, where pars of he maerial near he surfae undergo a phase ransiion wih slow reovery dynamis, while layers deeper wihin he maerial exhibi only he fas reovery dynamis. These dynamis are learly illusraed in ig. 3A and B, where we plo he evoluion of he magneizaion in boh spae and ime afer he laserpulse exiaion. 4

5 igure 2. (A) Ulrafas demagneizaion in Ni measured using he TrTMOKE mehod, when exied by differen orbed laser fluenes ( ). The daa are normalized o he groundsae magneizaion and are offse by 0.3 for differen laser fluenes for illusraion purposes only. The solid lines are he model resuls aking he deph dependene of he orbed laser fluene, as well as he riial behavior and assoiaed universal ime onsans ino aoun. (B) The dephsensiiviy funion alulaed for EUV TMOKE measuremens on Ni onsidering EUV phoon energies 64.3 and 67.3 ev(3). (C) The exraed values of A 3 in dire omparison o he experimenally measured hange of exhange spliing as a funion of he orbed pump laser fluene obained from TrARPES measuremens. The experimenally observed values of he riial orbed fluene are onsisen in boh TMOKE and ARPES measuremens. 5

6 igure 3. (A) Evoluion of he magneizaion in Ni as a funion of boh ime and spae for a orbed pump fluene = mj/m 2 a he sample surfae. The dashed lines represen he onours for onsan magneizaion. (B) Same as (A) wih he surfae orbed fluene = mj/m 2. The slow reovery dynamis due o riial behavior an be learly observed for he sample surfae region where he orbed fluene is higher han he riial orbed fluene = 0.44 mj/m 2. Table 1. iing parameers for he magneizaion dynamis a differen fluenes using Eqs. (1), (2) and (3). (mj/m 2 ) B 1 B

7 Referenes 1. B. Koopmans, G. Malinowski,. Dalla Longa, D. Seiauf, M. ähnle, T. Roh, M. Cinhei, M. Aeshlimann, Explaining he paradoxial diversiy of ulrafas laserindued demagneizaion. Na. Maer. 9, (2009). 2. S. Valenia, A. Gaupp, W. Guda, H. C. Merins, P. M. Oppeneer, D. Abramsohn, C. M. Shneider, araday roaion spera a shallow ore levels: 3p edges of e, Co, and Ni. New J. Phys. 8, 254 (2006). 3. G. Traeger, L. Wenzel, A. Huber, Compuer experimens on he informaion deph and he figure of meri in magneoopis. Phys. Sa. Sol. 131, 201 (1992). 7