Speed limit of FePt spin dynamics on femtosecond timescales
J. Mendil, P. C. Nieves, O. Chubykalo-Fesenko, J. Walowski, M. Münzenberg, T. Santos, S. Pisana
UUltrafast demagnetization in FePt
Speed limit of FePt spin dynamics on femtosecond timescales
J. Mendil, P. C. Nieves, O. Chubykalo-Fesenko, J. Walowski, M. M¨unzenberg, a) T.Santos, and S. Pisana I. Physikalisches Institut, Universit¨at G¨ottingen, Friedrich-Hund Platz 1,37077 G¨ottingen, Germany Instituto de Ciencia de Materiales de Madrid, CSIC, Cantoblanco,28049 Madrid, Spain San Jose Research Center, HGST, a Western Digital Company,3403 Yerba Buena Rd., San Jose, California 95135, USA (Dated: 6 November 2018)
Magnetization manipulation is becoming an indispensable tool for both basic andapplied research. Theory predicts two types of ultrafast demagnetization dynamicsclassified as type I and type II. In type II materials, a second slower process takesplace after the initial fast drop of magnetization. In this letter we investigate thisbehavior for FePt recording materials with perpendicular anisotropy. The magneti-zation dynamics have been simulated using a thermal micromagnetic model basedon the Landau-Lifshitz-Bloch equation. We identify a transition to type II behaviorand relate it to the electron temperatures reached by the laser heating. This slowingdown is a fundamental limit to reconding speeds in heat assisted reversal.PACS numbers: Valid PACS appear hereKeywords: Ultrafast demagnetization, FePt, perpendicular anisotropy, LLB modeling a) Electronic mail: corresponding author: [email protected] a r X i v : . [ c ond - m a t . m t r l - s c i ] J un ltrafast demagnetization in FePtThe FePt Ll alloy represents the most important material for novel concepts in magneticrecording due to its high magnetic anisotropy, which ensures long-time thermal stability ofnanometer sized bits . Thin films of FePt with perpendicular anisotropy and small grain sizesare the most promising candidate for heat-assisted magnetic recording, which could reachstorage densities beyond 1 Tb/inch . Patterning continuous FePt into individual bits canin principle extend recording densities to 100 Tb/inch . The ultimate magnetic recordingapplications will also require faster bit switching. However, non-deterministic fractioningin ultrafast magnetization reversal can limit the switching speed in recording schemes, andthus has inspired fundamental research for nearly two decades . Recently a new concept ofultrafast all-optical magnetic recording with an unprecedented switching timescale below 1ps was suggested . This opened new possibilities to reduce the speed limit established by thespin-orbit coupling timescale to that governed by the much stronger exchange interaction.Here we show that in FePt fractioning limits the ultimate switching speed through criticalfluctuations at the high electron temperatures following femtosecond laser excitation.Even though CoPt was among the first thin film systems investigated since the discoveryof ultrafast demagnetization in 1996 by Beaurepaire et al. , most investigations were centeredon samples with in-plane anisotropy, so that little is known about the behavior of materialswith perpendicular anisotropy. A notable exception is ferrimagnetic CoFeGd, which wasstudied in all-optical ultrafast switching triggered by a single laser pulse . The modelingof this mechanism involves the complex interaction of the two spin subsystems and is stillunder debate. To enable progress in high-speed and high-capacity magnetic storage devices,a fundamental understanding of the ultrafast demagnetization dynamics in these materialsis required.Recent work of Koopmans et al. suggests the classification of materials as ”fast” (or typeI) and ”slow” (or type II) based on the ratio T C /µ at , where µ at is the magnetic momentumper atom and T C is the Curie temperature. In both cases, there is an initial sub-picosecondfast demagnetization. However, in the first case the fast femtosecond demagnetization isfollowed by a magnetization recovery (as in Ni ), while in the latter a second slower de-magnetization takes place. The recovery occurs on the timescale on the order of 50 ps andmore (as in Gd ). According to this classification FePt should be regarded as a fast mag-netic material. However, more recently it has been shown that in Ni both behaviors can beobserved, depending on the amount of deposited energy . Thus, the question of whether2ltrafast demagnetization in FePt FIG. 1. Sample characteristics: schematics and sample structure of the granular FePt recordingmedia a) and thin film b) as measured by transmission electron microscopy (TEM). c) Ultrafastmagnetization dynamics for both cases after femtosecond laser excitation. Solid line: analyticalthree temperature model to obtain τ M . Both can be described with sets of identical parameters.d) The reflectivity dynamics from which the exponential decay τ E and e) the electron temperature T e are obtained. f) The relaxation time τ E for the electron temperature and τ M for the ultrafastdemagnetization is given below for a set of pump fluences. FePt can behave as ”fast” or ”slow” under specific laser excitation is an open question. Inaddition, for thin films and granular media the contributions of spin currents to the ultrafastdemagnetization dynamics cannot be neglected . In this work, we use isolating substratesand cap layers to minimize these effects. The ultrafast demagnetization dynamics of a FePt3ltrafast demagnetization in FePtcontinuous film sample and a high anistropy granular recoding medium is investigated. Atransition from type I to type II is found, triggered by the laser fluence. We pinpoint theelectron temperature reached by the laser heating as the underlying mechanism in FePt.We have studied a 3 nm-thick continuous FePt thin layer ( H C = 200 mT) and 7 nm-thick AgCuFePt-C granular recording media ( H C = 2 . film to ensurethat it remains smooth and continuous during the fabrication process . The granular filmhas a 3 nm protective carbon overcoat, a small amount of Ag to reduce the FePt Ll orderingtemperature, and a small amount of Cu to lower the T C . The whole structure from bottom totop is glass/NiTa/MgO/FePt/SiO (glass/NiTa/MgO/AgCuFePt-C/carbon overcoat). Thecontinuos film sample has a Curie temperature of 650 K, a saturation magnetization M s =1070 emu/cm , a maximum anisotropy constant K u,max = 2 . · erg/cm , and an averageanisotropy constant K u,av = 1 . · erg/cm . The presented data are obtained by fluence-dependent all-optical pump-probe experiments. In Fig. 1 c) the time-resolved magneto-optical Kerr effect (∆ θ K /θ K, ) is shown for the granular FePt recording media as well as thedata for the continuous FePt layer. Besides the absolute scale, both can be described usingidentical parameters of the analytical solution of a rate equation model shown as a continuousline: the microscopic mechanisms on the nanometer lenght scale dominate the dynamics ona femtosecond time scale. This leads to identical spectra for the continous film and granularmedia. Spin currents transmitted through the carbon interfaces have no influence on thedynamics on the picosecond scale here. Moreover for the granular structure in case of therecording media, the larger H C and different K u does not alter the magnetization dynamics.The energy scale of the magnetic anisotropy K u < in steps of 5 mJ/cm . Themagneto-optical Kerr rotation of the probe beam is measured and its time delay relative tothe pump beam is varied. Similarly, the time resolved reflectivity is detemined. The decayof the reflectivity signal is fitted to a simple exponential function before characteristic stresswaves set in (Fig. 1 d)), according to R ( t ) ∼ exp ( − t/τ E ). The results are presented in Fig.4ltrafast demagnetization in FePt
5 m J / c m D e l a y t i m e ( p s )
Kerr rotation Dq K/ q K,0
FIG. 2. Ultrafast demagnetization dynamics of FePt: spin dynamics measured by the Kerr set-upat increasing laser fluence in steps of 5 mJ/cm from 5 mJ/cm (upper curve) to 40 mJ/cm (lowercurve). The detail on the femtosecond timescale is shown with expanded scale on the left side. τ E that represents the relaxationtime of the electron temperature. Experimentally, the value for τ E ∼ .The Kerr rotation is extracted from that of opposite external field direction in order toremove all non-magnetic and thus symmetric contributions . To get the absolute degreeof demagnetization, the Kerr signal is scaled to hysteresis measurements at two states ofreference; one at negative delay ( θ K ∼ M z, ) and the other at a time delay that shows thelowest magnetization (∆ θ K,min ∼ ∆ M z,min ). The pulse shape is assumed to be Gaussian5ltrafast demagnetization in FePt M( τ )M FIG. 3. Micromagnetic Landau-Lifshitz-Bloch model: the magnetization is described by theaverage over 900 thermal macrospins with a lateral cubic discretization of ∆ = 3 nm with peri-odic boundary conditions. Each cell represents thermodynamic average over atomistic magneticmoments (shown schematically on the right side). Within each cell, the precession and relaxationalong and around the quantization direction (the longitudinal relaxation M ( τ ) and the rotation ofthe individual macrospin on the nanometer sized element) are taken into account. and has a full width at half maximum of τ p = 40 fs. The repetition rate of the laser systemis 250 kHz and thus every 4 µ s a pulse excites the sample. A magnetic field of µ H = 200mT perpendicular to the film plane, parallel to the easy axis, is applied. The magnetizationdynamics ∆ M z (Kerr rotation angle ∆ θ K ) is presented in Fig. 2. The first rapid demag-netization, τ M , occurs at a timescale below 1 ps in the range 0.15-0.3 ps, increasing withthe laser pump fluence. Also the remagnetization timescale slows down as a function of theincident fluence. Finally a second, slower demagnetization with the absence of recovery isfound above a fluence of 30 mJ/cm . Thus, a transition from type I to type II as classifiedin Ref. is observed for FePt.To understand the behavior, we model the ultrafast magnetization dynamics under ex-ternal laser excitation by a thermal process of electronic origin . The model considers thatwithin a timescale of the order of 10 fs the electrons are thermalized and can be describedby a quasi-equilibrium electron temperature T e ( t ), coupled to the phonon and spin systems.A multi-macrospin model is used with cubic discretization elements with a lateral size of∆ = 3 nm (and thus a volume of V = ∆ ) as illustrated in Fig. 3. The thermal dynamicsof the spin system within each cell is described macroscopically within the Landau-Lifshitz-Bloch (LLB) micromagnetic formalism . For the present simulation, a system of 30 × × x and y directions is used. Then every6ltrafast demagnetization in FePt T C = 6 5 0 KT C = 6 5 0 KT C = 6 5 0 K 1 5 m J / c m
5 m J / c m Electron temperature Te (K)
D e l a y t i m e ( p s )
FIG. 4. Simulation of the electron temperature T e , shown as a function of the laser pump fluence(from 5 mJ/cm (upper curve) to 40 mJ/cm (lower curve), in steps of 5 mJ/cm . The 2T modelis based on the set of parameters presented in Table I. The parameters are extracted from thereflectivity dynamics (Fig. 1). Within the shaded area marked in the left panel, the electrontemperature exceeds the Curie temperature. single macrospin m i = M i /M e (0) is described using the LLB equation for a finite spin S that reads : d m i dt = γ [ m i × H ieff ] − γ ˜ α (cid:107) m i ( m i · H ieff ) m i (1)+ γ ˜ α ⊥ m i [ m i × [ m i × ( H ieff + ζ i, ⊥ )]] + ζ i,ad . M i is the spin polarization (thermal average of atomistic spins over the volume V at7ltrafast demagnetization in FePttemperature T ), M e ( T ) is its equilibrium value and M e (0) is the maximum spin polarizationat T = 0 o K and M e (300 o K ) = M s . The value of M e ( T ) is evaluated in the mean-field ap-proximation (MFA) via the Brillouin function. For FePt, it has been shown that the bestfit for the temperature-dependent experimentally measured magnetization is obtained withthe spin value S = 3 /
2. The effective field H ieff = H + H i,A + H i,EX + H J is comprised of ap-plied, anisotropy, micromagnetic exchange, and internal exchange fields. The micromagneticanisotropy field H i,A = − χ ⊥ ( m i,x e x + m i,y e y ) is determined by the perpendicular suscep-tibility ˜ χ ⊥ = ∂m/∂H ⊥ . Experimental and theoretical results report that in FePt theanisotropy scales with magnetization as K ∼ m . . Thus, we use ˜ χ ⊥ = M s (0) / K (0) m . .The micromagnetic exchange field is defined as H i,EX = A i ( T ) m i M s (cid:52) (cid:88) j ( m j − m i ) (2)where j goes over neighboring elements and A ( T ) is the micromagnetic exchange stiffness,for FePt it has been shown to scale with the magnetization as A ( T ) ∼ m . , where A (0) = 2 . · − erg/cm, thus, we use A i ( T ) = A (0) m . i . The internal exchange field H J results from the thermal average of atomic spins, comprising a sufficiently large discretizationvolume V in the MFA. At low temperatures, it is responsible for keeping the magnetizationmagnitude constant. It is described by the following expression: H J = χ (cid:107) (cid:16) − m i m e (cid:17) m i T (cid:46) T C − χ , (cid:107) (cid:16) T C T − T C ) m i (cid:17) m i T (cid:38) T C . (3)Here ˜ χ (cid:107) = ∂m/∂H || represents the longitudinal susceptibility, evaluated in the MFA as˜ χ (cid:107) = µ βB (cid:48) S ( ξ e )1 − βS J B (cid:48) S ( ξ e ) ; ξ e = 3 ST C m e ( S + 1) T (4)where B (cid:48) () stands for the derivative of the Brillouin function. The relationship between theinternal exchange parameter J (also related to A ( T = 0 K), see Ref. ) and T C is given by T C = S ( S + 1) J / k B where k B is the Boltzmann’s constant. The stochastic fields ζ i, ⊥ and ζ i,ad are given by (cid:10) ζ ki, ⊥ (0) ζ lj, ⊥ ( t ) (cid:11) = 2 | γ | k B T (cid:0) ˜ α ⊥ − ˜ α (cid:107) (cid:1) M s V ˜ α ⊥ δ ij δ kl δ ( t ) (5) (cid:10) ζ ki,ad (0) ζ lj,ad ( t ) (cid:11) = 2 | γ | k B T ˜ α (cid:107) M s V δ ij δ kl δ ( t ) (6)8ltrafast demagnetization in FePtwhere i and j denote the macrospin number and k and l denote its Cartesian components x , y , and z . Finally, the longitudinal and transverse relaxation parameters are ˜ α (cid:107) = λ T T c q s sinh(2 q s ) ˜ α ⊥ = λ (cid:20) tanh( q s ) q s − T T C (cid:21) (7)where λ is the microscopic relaxation parameter that couples the spin dynamics to the elec-tron temperature, defined by the microscopic spin scattering rate, and q s = 3 T C m e / [2( S +1) T ].The magnetization dynamics is coupled to the electron temperature T e ( t ). In turn, theelectron temperature within the two temperature model (2T) is coupled to the lattice tem-perature T ph ( t ) via rate equations: C e d T e d t = − G e − ph ( T e − T ph ) + P ( t ) − C e ( T e − T room ) τ ph C ph d T ph d t = G e − ph ( T e − T ph ) . (8)Here C e and C ph denote the specific heat of the electrons and the lattice, respectively, G e − ph is the coupling constant determining the energy exchange between the electron andlattice systems, and τ ph is the heat diffusion time to the substrate. For C e , the free electronapproximation is used resulting in C e = γ e T e . C ph is set constant, since FePt has a Debyetemperature well below the room temperature T room . The laser absorbed power is definedby P ( t ) = I F exp [ − ( t/τ p ) ] proportional to the laser pump fluence F . The time resolvedreflectivity reveals that the change of electron temperature depends linearly on the changein reflectivity . Thus, we assume that the lacking parameters of the 2T model can beextracted from the measured reflectivity at the lowest pump fluence F = 5 mJ/cm . Thelong-term diffusion timescale τ ph is obtained from the long-term magnetization behavior.The proportionality constant I is estimated by fitting of the experimental demagnetizationvalue at 30 ps, and the coupling-to-the bath parameter λ via matching the maximum de-magnetization value. Note that the value obtained for λ is similar to those used previouslyfor the simulations of FePt and corresponds to an enhanced spin scattering rate at hightemperatures.The determination of the material specific constants such as γ e and G e − ph is crucialfor a proper simulation of the demagnetization process. Two approaches were performed,resulting in a high and low electron temperature (see Supplementary Materials). First,9ltrafast demagnetization in FePt TABLE I. Overview of all constants relevant for the simulation in the case of high electron tem-perature. γ e λ I G el − ph C ph τ ph S (J/m K ) (a.u.) (s − ) (W/m K) (Jm − K − ) (ps) ( (cid:126) )110 0.1 5.0 · · ·
340 3/2 G e − ph = 1 . · W/m K is assumed and thus in the range of Cu, Mo, and Pt . Then,the fitting to the reflectivity relaxation rate, measured at F = 5 mJ/cm , gives γ e = 110J/m K . This value is of the order reported for Au and Cu but is much smaller than thecorresponding value for Ni and hence produces a high electron temperature. The final setof parameters is presented in Table I. The corresponding simulated electron temperatureis shown in Fig. 4. The electron temperature decay fitted to the same exponential decayfunction as in the experiment and the relaxation time τ E shows a reasonable agreementwith the experiment for all fluences (Fig. 1 f)). In the second case, a coupling constant G e − ph = 1 . · W/m K, similar to Ni is assumed which gives γ e = 1700 J/m K , moreproper to transition metals, and thus about one order of magnitude larger than in the firstcase. As a consequence, a lower electron temperature (with the maximum value up to 1000K) is reached.The results for the integration of the set of the LLB equations, coupled to the 2T model,with the set of parameters from Table I are presented in Fig. 5 for all fluences. As in theexperiment, the simulations show a transition between type I and type II behavior. Theagreement is found in the demagnetization values ∆ M/M (300 K ) = 0 . − . τ M = 0 . − . T e stays nearthe Curie temperature T C for several picoseconds this transition is found. From the theoryof phase transitions, we know that at such temperatures the dynamics will be characterized10ltrafast demagnetization in FePt t y p e I It y p e I 1 5 m J / c m
5 m J / c m Magnetization D Mz/ Mz,0
D e l a y t i m e ( p s )
FIG. 5. Ultrafast demagnetization dynamics obtained by integration of the LLB micromagneticmodel coupled to the 2T model (Fig. 4). The model data are shown with increased laser fluencefrom top to bottom in steps of 5 mJ/cm from 5 mJ/cm (upper curve) to 40 mJ/cm (lowercurve). The detailed view on the femtosecond timescale is shown with expanded scale on the leftside. by an increased dominance of magnetization fluctuations. Particularly, the divergence ofcorrelation lengths leads to slowing down of correlation times . We find that the char-acteristics of type II materials are related to a non-deterministic fractioning into dynamicspin excitations. In the experiment (Fig. 2) the relative decay is deviating for the two high-est laser fluences, in comparison to the model (Fig. 5). This discrepancy is related to thedecrease of the magnetization at negative delay due to the accumulation of the high pump11ltrafast demagnetization in FePtpower, which is not taken into acount in the LLB model.In summary, by means of the time-resolved Kerr magnetometry we have investigatedultrafast magnetization dynamics in FePt thin films with perpendicular anisotropy. Ourresults indicate that the amount of the absorbed energy plays a crucial role in the characterof the ultrafast demagnetization in FePt. The measurements reveal a transition from typeI to type II behavior. Our experimental results are modeled in terms of the micromagneticLLB model, coupled to the 2T model. Within this framework, we find that transition to typeII behavior is a consequence of high electron temperature. We identify that at large pumpfluences the resulting electron temperature remains close to the Curie temperature and isleading to critical magnetization fluctuations responsible for this transition. This non-deterministic spin dynamics is responsible for a speed limtitation of the magnetic responseto the laser pulse. Note that this is defined not only by the laser fluence, but also by thenature of the FePt’s density of states at the Fermi level defining the increase in electrontemperature. Our results open possibilities for ultrafast control of the demagnetization inFePt, the most promising candidate for future magnetic recording applications. Importantly,we have shown that we are able to manipulate the degree of demagnetization and its ultrafastrates. We propose that for efficient writing the degree of heating and its speed have to bebalanced by varying the amount of the energy deposited.Acknowledgments: we thank A. McCallum for providing a sample and TEM image, O.Mosendz for a TEM image and U. Atxitia for his help with the theory. Research at G¨ottingenUniversity was supported by German Research Foundation (DFG) through SFB 602, MU1780/ 6-1 Photo-Magnonics and SPP 1538 SpinCaT. Research in Madrid was supported bythe European Community’s Seventh Framework Programme under grant agreement NNP3-SL-2012-281043 (FEMTOSPIN) and the Spanish Ministry of Science and Innovation underthe grant FIS2010-20979-C02-02. REFERENCES A. Moser and D. Weller, in
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