arXiv:cond-mat/0604610v1 [cond-mat.mtrl-sci] 26 Apr 2006 neulbimaedsrbdby about described displacements are Rotational equilibrium 9). an 8; spin 7; are of 4; studies position, magnetooptical dynamics(3; most equilibrium for point an starting the about oscillator harmonic where rqec ffroantcrsnne(M)ad2 and (FMR) resonance ferromagnetic of frequency t hrceitcrlxto time. relaxation characteristic its of ain oeage ol emaue ont 0.1 to down measured ro- be Faraday could of angles equivalent x-ray Cone High soft tation. the geometry measurement. 2), transmission by the XMCD(1; provided is for contrast necessary magnetic resolution tial magnetic x-ray (XMCD). time-resolved dichroism using circular time-domain measured the been has in GHz, 2.3 at field microwave low-power 1.0 iedmi esrmn fdie ermgei resonanc ferromagnetic driven of measurement Time-domain eovdmaueeto ermgei eoac na in Ni resonance of layer ferromagnetic single of above. measurement and GHz resolved 1 at devices electronic spin technological of switching modern the response the underpin relaxation In and resonance magnetism. context, of study the in h aduLfht L)euto() ie nS as SI in given equation(5), (LL) Landau-Lifshitz reflectivity.the XMCD previous in in fields achieved step pulsed we pulsed in than using work(4) better present an magnitude are sup- jitter of resolutions phase order timing source, and Motional of excitation 4). experiments(3; effects an the as phase- pressing microwaves using provided CW is locked resolution temporal Improved where reoclain,dsrbn h oino hsdamped this of motion the describing oscillations, Free h Leuto a elnaie o ml rotations small for linearized be can equation LL The w noain aealwdterttoa n spa- and rotational the allowed have innovations Two nti etr edmntaeatm-adelement- and time- a demonstrate we Letter, this In topic venerable a is (FMR) resonance Ferromagnetic ngnrl antzto yaisaedsrbdby described are dynamics magnetization general, In M d ◦ ~ dt M M oin rvnwt otnoswv (CW) wave continuous a with driven motion, FMR ) about ω λ = 0 2 nne(M)i igelyro Ni of layer dy single magnetization a of in measurement (FMR) time-resolved onance a present We 2018) 18, July (Dated: La National Brookhaven Source, Arena Light A. Synchrotron D. National and Kao, C.-C. Vescovo, E. Physics, Applied of Department Program, Science Bailey Materials E. W. and Guan Y. H,vrfigbscepcain o rvnresonance. driven a amp for and expectations phase basic a the verifying temporal of GHz, characterization high allowed The usin has transmission. quantitatively technique in and (XMCD) directly dichroism measured cular be could moments steL eaainrt nsec in rate relaxation LL the is = − µ µ H ~ ∂ 0 0 2 2 ∂t | γ as φ γ 2 ( 2 81 H t | ) Fe eff ( M + 19 ( λ H × ovninl o-nl ( low-angle Conventional, . ∂φ eff H ∂t ( ) t ) + − + M M ω λ s φ s 2 0 2 (6). ) ; φ ( ( ω M t 0 0 = ) × − si h circular the is is 81 1 M . Fe , 19 × ml-nl ( Small-angle . H ) ∼ , /λ 0.1- (2) (1) ◦ is . < iueo rvnFRmto t2.3 at motion FMR driven of litude φ where eso a eepesdas: expressed be can cession H hs h phase the Thus, susceptibility, (6). and (5) parameter-free Eqs. a with for comparison allowing linewidth, field the through ueet h damping the surement, using over, n oE.() h edsetrsnnelnwdhhas linewidth resonance field-swept at The points (4). half-power Eq. to ing n ( ing (2 otoa otedmninesdmigconstant damping dimensionless the to portional ihrsett h rv edge hog hneof change a through goes field lag drive 90 phase the to the respect points, with half-power these tween r oeesl en hs aeawidth a shape have line These Lorenzian seen. the easily of more points are inflection the tion, iersle -a antccir- magnetic x-ray time-resolved g 1 0 oaoy po,NwYr 11973 York New Upton, boratory, oubaUiest,NwYr,NwYr 10027 York New York, New University, Columbia drttoa estvt fo this of of sensitivity rotational nd aisdrn ermgei res- ferromagnetic during namics ◦ y / fisedtemto sfre yatases cfield ac transverse a by forced is motion the instead If M bopini ie yteiaiaypr fthe of part imaginary the by given is absorption FMR hs eainhp a o etse iety More- directly. tested be now can relationships These nlc-n(eiaie eeto fmcoaeabsorp- microwave of detection (derivative) lock-in In ◦ rcsino lmna i Fe Ni, elemental of precession ) x ( exp ( √ t codn oE.(5). Eq. to according α = ) 3) A ≪ φ αω/γ iωt ∂ 0 H 2 ≈ ∂t 1), = φ y = ) 0 ( 2 µ in-situ 1) While (10). t ( x ( exp λ ) | ω 0 2 | χ γ φ 0 2 + φ a hsb xrse as expressed be thus can ′′ 2 0 δ 0 − λ M ln h fdiigfield, driving rf the along , λ iωt | n h mltd fdie M pre- FMR driven of amplitude the and | = = ω ∂φ s x [ exp tan M mcoaeasrto)mea- absorption) (microwave FMR H 2 ∂t ,tersos sgvnas given is response the ), A p √ ) ( µ y 2 2 t 0 3 0 δ ( ) + i ovn q 3 using (3) Eq. Solving . ∆ ω ( µ = + α ωt 0 2 λ λ H 0 2 γ − ω 2 = ω 1 ω + 2 a eetmtddirectly estimated be can 0 2 / 0 2 − ω M 2 φ 2 λ/ A δ − ω 2 λω ( [( e s ] then )], 2 = ) t ( ω ∆ = ) 2 ω µ 0 2 + 2 H 0 M − , αω/γ pp λ A s ω 2 . x ( exp γ ω 2 o o damp- low for ) ) 2 ietypro- directly , . − iωt iωλ H µ y 0 ) δ ∆ accord- , , ] . of H φ α ( Be- . pp t φ = ) (3) (7) (5) (6) (4) ( = t ) 2

Then, the following relationship can be derived as 0.20 1 √3∆Hpp = ∆H1 2 = ∆H 1 , (8) 0.8 MCD (a.u.) / √ 2 |φ0| 3 XAS1 XAS2 0.10 where ∆H 1 denotes the linewidth defined by the half- 0.6 (a) Fe 2 |φ0| amplitude points. Time-resolved XMCD (TR-XMCD) measurements of 0.4 0.00

XAS (a.u.) MCD magnetization motion during FMR precession were car- ried out at Beamline 4-ID-C of Advanced Photon Source 0.2 -0.10 in Argonne, IL. The circular dichroism signal was ob- 690 700 710 720 730 740 tained in transmission, using photon helicity ~σ switching (~σ, with an incident angle of 38◦ from normal, and with Photon Energy (eV) in-plane projection along ˆy) at the elliptical undulator 1.2 0.20

for fixed static applied field HB. The transmitted inten- MCD (a.u.) sity was read at a soft x-ray sensitive photodiode and normalized to an incident intensity at a reference grid. 0.8 XAS1 0.10 Transmission measurements require an x-ray transpar- (b) Ni XAS2 ent sample and substrate. For time-resolved measure- 0.4 0.00 ments, x-ray transparent RF field delivery system is also XAS (a.u.) MCD necessary. The Ni81Fe19(25nm)/Cu(2nm) thin film sam- ple was deposited onto a Si/Si3N4 membrane using UHV 0.0 -0.10 magnetron sputtering at a base pressure of 4 10−9 Torr. 840 850 860 870 880 890 × The sample was placed in the center of a hollow mi- Photon Energy (eV) crowave resonator. Uniform precession of the magneti- zation was excited at 2.3 GHz by a CW low-power mi- FIG. 1 (a)L2,3-edge transmission XAS and MCD spectra of crowave field, synchronized with variable delay to APS Fe in Ni81Fe19;(b)L2,3-edge transmission XAS and MCD spec- x-ray photon bunches (88 MHz). Microwave absorption tra of Ni in Ni81Fe19. was measured in-situ, using standard lock-in techniques, detecting reflected power at the resonator. Orthogonal Helmholtz coils were used to apply longitudinal bias field HB ˆx or transverse bias field HT ˆy. Ni 1.0 Fe Element-specific XMCD hysteresis loops were taken as a function of transverse bias field HT to obtain a calibra- 0.5 tion for magnetization angle φ. Photon energies were (°) set to the L3 peaks for Fe (707.5 eV) and Ni (852.0 0.0 eV) to measure Fe and Ni XMCD signals, respectively. Ni,Fe

The saturation values of XMCD signals are taken to be φ -0.5 φ = φ = 90◦. F e Ni ± -1.0 L2,3-edge XAS and MCD spectra have been measured in transmission for both Fe and Ni in Ni81Fe19. High- quality spectra are obtained here, as shown in our pre- 0.0 0.5 1.0 1.5 2.0 vious work at NSLS, Beamline U4B(2). Fig. 1(a) shows Time (ns) Fe transmission XAS spectra for both photon helicity di- rections, with the difference. Corresponding spectra for FIG. 2 TR-XMCD measurement of Fe and Ni magnetization Ni are shown in Fig. 1(b). precession at resonance, 37 Oe at 2.3 GHz. Solid lines are Time- and element-resolved XMCD measurements of sinusoidal fits of the Fe and Ni data sets separately. magnetization precession at resonance are presented in Fig. 2. XMCD signals were taken as a function of delay time and converted into time-dependent elemen- Hres (37 Oe) to 4 ∆Hpp off resonance (5 Oe). A ∼ × tal magnetization angles φF e(t) and φNi(t) for Fe and clear variation in the amplitude of driven FMR motion Ni, respectively(4). Precessional oscillations are clearly φF e(t), and its phase, compared with the RF excitation seen. Fe and Ni moments are found to precess together field, can be seen. within instrumental resolution, improved here to 2 ps The key result of this letter is presented in Fig. 4(b). and <0.1◦. ± Verifying basic expectations of a driven resonance, we Time-resolved XMCD measurements of magnetization can clearly see a 90◦ phase shift generated through the precession off resonance are presented in Fig. 3. Applied adjustment of ω0 (through longitudinal bias field HB) to fields were selected according to in-situ measured FMR ω, and a Lorentzian variation of the precessional am- spectra (Fig. 4(a)), spanning the resonance condition ≪plitude. Both behaviors are in excellent agreement with 3

In conclusion, we have measured driven ferromagnetic H = 37 Oe B resonance (FMR) precession in the time domain using H = 32 Oe B time-resolved XMCD. Precessional phase and amplitude, H = 29 Oe B lumped together in microwave absorption measurement,

HB = 26 Oe could be measured directly, providing a vivid illustration

HB = 22 Oe of damped oscillator behavior.

HB = 19 Oe

HB = 16 Oe

XMCD (a.u) The authors thank Carl Patton for a critical reading of

HB = 11 Oe this manuscript, and David J. Keavney (APS) for beam-

HB = 5 Oe line support. This work was partially supported by the Army Research Office with Grant No. ARO-43986-MS- 0.0 0.5 1.0 1.5 2.0 YIP, and the National Science Foundation with Grant Time (ns) No. NSF-DMR-02-39724. Use of the Advanced Photon Source was supported by the U.S. Department of Energy, FIG. 3 TR-XMCD measurement of Ni81Fe19 magnetization Office of Science, Office of Basic Energy Sciences, under precession off resonance at Fe L3 edge. Solid lines are sinu- soidal fits. Contract No. W-31-109-Eng-38. the linearized model (Eqs. (5) and (6)). No empirical parameters have been used apart from Hy0; λ is esti- mated as 1.80 GHz directly from the in-situ measured FMR spectra (Fig. 4(a)) using Eq. (7). We verify di- rectly the relationship in Eq. (8), with √3 separating the peak-to-peak, 1/2 power (90◦ phase shift), and 1/2 amplitude linewidths.

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