Ultrafast Demagnetization After Femtosecond Laser

Authors: Manfred Fähnle Theodoros Tsatsoulis Christian Illg Michael Haag Benedikt Y Müller Lifa Zhang

Publish Date: 2017/01/23

Volume: 30, Issue: 5, Pages: 1381-1387

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Abstract

When exciting a ferromagnetic film with a femtosecond optical laser pulse then there is a partial demagnetization within a few hundred fs This means that the angular momentum of the electronic system is transferred to the lattice This transfer is calculated by describing the lattice degrees of freedom as spinphonon eigenmodes which have a sharp angular momentum Possible other lattice degrees of freedom are mentioned but not considered explicitly For Ni and Fe the calculated amount of transfer of angular momentum to the spinphonon eigenmodes is rather smallWhen a ferromagnetic film is excited by a laser pulse of length of 30–100 fs the sample is partially demagnetized within a few hundred fs with a following remagnetization on a longer time scale 1 2 Recently it has been discussed both theoretically 3 4 and experimentally 5 that very short pulses 5–6 fs of higher intensity lead to a demagnetization on time scales of the order of just 5 to 35 fs At present this is the fastest possible macroscopic manipulation of the magnetization in solids Such ultrafast processes are of great importance for advanced data storage and data manipulation devices based on magnetism if remagnetization to the original state is avoided This is the case for ultrafast alloptical switching of ferrimagnetic compounds 6 or antiferromagnetically coupled ferromagnetic multilayers 7 by which the magnetization can be switched in a reproducible manner by a femtosecond circularly polarized optical laser pulse The two effects ultrafast demagnetization and alloptical switching are certainly related to each other Therefore it is of great interest to figure out the mechanisms of ultrafast demagnetizationAlthough ultrafast demagnetization is investigated worldwide both experimentally and theoretically since 1996 a detailed understanding of the underlying physical processes is still lacking and several models compete A possible mechanism is the superdiffusive transport of excited electrons mainly with majority spin orientation from the conducting ferromagnetic film to a conducting substrate 8 In the following we consider the situation with a nonconducting substrate for which the superdiffusive transport may lead to an inhomogeneous distribution of the magnetization in the film but not to a reduction of the total magnetic moment of the film Other possible mechanisms are spinflip scatterings of the excited electrons at other electrons 9 10 at phonons 11 or at magnons 12 13 The spinflip scatterings change the electronic spin and orbitalangular momentum leading to the demagnetization Thereby the electronic angular momentum has to be transferred to other degrees of freedomTo describe the transfer of angular momentum one had to take into account in principle explicitly the coupling of the sample to the whole surroundings However a simplification arises because on the fs time scale a process in the ferromagnetic sample can lead to reactions only within a very limited spatial distance from the sample In a first step one therefore could try to model the system by a Hamiltonian which contains all degrees of freedom of the lattice of the sample ie to assume that the electronic angular momentum is mainly transferred to the lattice An example for lattice degrees of freedom would be local elastic twists in the sample as reactions on local torques twists which have certainly small amplitudes but which may have angular momentum which add up in the whole sample However these degrees of freedom are very complicated to be described mathematically Another example for lattice degrees of freedom are collective motions of the atoms which on an appropriately long time scale are described by phonons and the scattering of electrons at phonons has been discussed in the literature see eg 11 So far however only the change of the occupation numbers of the electronic states by electronphonon scatterings and hence the contribution of electronphonon scatterings to ultrafast demagnetization has been calculated By these theories also the occupation numbers of phononic states have been determined The transfer of the angular momentum from the electronic system to the lattice via electronphonon scattering has never been calculated explicitly The reason is that usually the lattice dynamics are described by linearly polarized phonons which do not have a sharp angular momentum and for which the expectation value of the angular momentum is zero 14 Therefore it is not possible to calculate the change of the phononic angular momentum from the above discussed change of the phononic occupation numbers The first idea to cope with this problem is to construct circularly or elliptically polarized phonon states with nonzero angular momentum by a linear combination of linearly polarized transverse phonon states 14 But linear combinations are stationary states only if the two combined states are degenerate which is the case only for special phonon wave vectors q in highsymmetry directions of the phononBrillouin zone and the formalism of electronphonon scatterings requires stationary states In isotropic systems like amorphous materials the degeneracy is given for arbitrary q and therefore it is possible to generate stationary phonon states with welldefined angular momentum 15 But this does not help to describe the angular momentum transfer during demagnetization experiments which are mainly performed for crystalline ferromagnetic films In the present paper the collective dynamics of the ferromagnetic lattice are described by magnetoelastic spinphonon modes which will be introduced in the next section and which carry a welldefined angular momentum Within the framework of an electronspinphonon scattering Hamiltonian we calculate for the first time explicitly the transfer of angular momentum from the electronic system to the lattice during ultrafast demagnetizationRate of change of the electronic angular momentum a the phononic angular momentum b and the relative error of the total angular momentum conservation c for a 40 × 40 × 40 kgrid a smearing parameter of σ = 0025 mRy and different spinphonon interaction parameters λ z in units of GHz for Ni left Rate of change of the electronic angular momentum d the phononic angular momentum e and the relative error of the total angular momentum conservation f for a 30 × 30 × 30 kgrid a smearing parameter of σ = 0033 mRy and different spinphonon interaction parameters λ z in units of GHz for Fe rightObviously the total angular momentum is not conserved when using a nonisotropic Hamiltonian and therefore the speed of demagnetization is not determined by the need for angular momentum conservation It is determined by the magnitude of the energy which is injected from the laser pulse to the electronic system and which drives the system out of equilibrium the farer the larger this injected energy is In the present paper we have calculated the demagnetization rates for the time directly after the action of the laser pulse The rates evolve with time first because the deviation from an equilibrium situation becomes smaller and second because the value of λ z decreases during demagnetization Our guess is that the angular momentum transfer does change strongly with time The calculated rate of change frac mathrm dJtext elmathrm dt gives a rate of change frac mathrm dMmathrm dt of the electronic magnetic moment per atom which is about 2mu Bfrac mathrm dJtext elmathrm dt This can be compared to experimental values for frac mathrm dMmathrm dt From ref 25 one can learn that for Ni after a laser fluence which raises the electron temperature to 1000 K the demagnetization rate is frac mathrm dMmathrm dt=01 mu B/100~ text fs atom and from ref 12 we get frac mathrm dMmathrm dt=02 mu B/100 text ~fs atom for Fe which compares to our calculated values for λ z = 006 GHz of frac mathrm dMmathrm dt= 004mu B/100~ text fs atom for Ni and for λ z = 023 GHz of frac mathrm dMmathrm dt= 0013mu B/100~ text fs atom for Fe Of course we cannot expect a perfect agreement between our theoretical values and the experimental values because we considered from the various contributions to ultrafast demagnetization just the contributions of spinflip scatterings of electrons at spinphononsWe have calculated for Ni and Fe the transfer of angular momentum from the spin system to the lattice after excitation of the system with a fs optical laser pulse The transfer is due to the scattering of the excited electrons at the spinphonon eigenmodes which carry a welldefined angular momentum Thereby we have used a Hamiltonian which is not isotropic as all the Hamiltonians used in the literature to describe ultrafast demagnetization For realistic values of a parameter describing the strength of the spinphonon interaction only a very small part of the change of the electronic angular momentum is transferred to the lattice For a more realistic description of the whole situation one should include in the Hamiltonian other degrees of freedom to which the angular momentum can be transferred in a first step other degrees of freedom for the lattice dynamics We have given suggestions for more realistic lattice degrees of freedomOpen AccessThis article is distributed under the terms of the Creative Commons Attribution 40 International License http//creativecommonsorg/licenses/by/40/ which permits unrestricted use distribution and reproduction in any medium provided you give appropriate credit to the original authors and the source provide a link to the Creative Commons license and indicate if changes were made

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