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The recently discovered spin Seebeck effect refers to a spin current induced by a temperature gradient in a ferromagnetic material. It combines spin degrees of freedom with caloric properties, opening the door for the invention of new, spin caloritronic devices. Using spin model simulations as well as an innovative, multiscale micromagnetic framework we show that magnonic spin currents caused by temperature gradients lead to spin transfer torque effects, which can drag a domain wall in a ferromagnetic nanostructure towards the hotter part of the wire. This effect opens new perspectives for the control and manipulation of domain structures.

The established methods for the numerical evaluation of magnetic material properties exist only in certain limits, including first-principles methods, spin models, and micromagnetics. In the present paper, we introduce a multiscale modeling approach, bridging the gaps between the three approaches above. The goal is to describe thermodynamic equilibrium and nonequilibrium properties of magnetic materials on length scales up to micrometers, starting from first principles. In the first step, we model, as an example, bulk FePt in the ordered Llo phase by using an effective, classical spin Hamiltonian that was constructed earlier on the basis of firstprinciples methods. The next step is to simulate this spin model by using the stochastic Landau-LifshitzGilbert equation. The temperature dependent micromagnetic parameters, which are evaluated with these atomistic simulations, are consequently used to develop a many macrospin micromagnetic approach, based on the Landau-Lifshitz-Bloch equation. As an example, we calculate the magnetization dynamics following a picosecond heat pulse resembling pump-probe experiments.

We investigate the origin of the spin Seebeck effect in yttrium iron garnet (YIG) samples for film thicknesses from 20 nm to 50 μm at room temperature and 50 K. Our results reveal a characteristic increase of the longitudinal spin Seebeck effect amplitude with the thickness of the insulating ferrimagnetic YIG, which levels off at a critical thickness that increases with decreasing temperature. The observed behavior cannot be explained as an interface effect or by variations of the material parameters. Comparison to numerical simulations of thermal magnonic spin currents yields qualitative agreement for the thickness dependence resulting from the finite magnon propagation length. This allows us to trace the origin of the observed signals to genuine bulk magnonic spin currents due to the spin Seebeck effect ruling out an interface origin and allowing us to gauge the reach of thermally excited magnons in this system for different temperatures. At low temperature, even quantitative agreement with the simulations is found. The thermal excitation of a spin current by a temperature gradient is commonly called the spin Seebeck effect (SSE) which is detected by the inverse spin Hall effect (ISHE) [1,2], leading to a thermovoltage similar to the charge analogue, the Seebeck effect. Experimental evidence of the SSE, first in ferromagnetic metals [3], and later, both in semiconductors [4] and in insulators [5][6][7][8], has brought up the question about the origin of the SSE. Of particular interest for spin caloritronics is the observation of the SSE in insulators, which allows us to generate pure spin currents in insulating systems.However, the underlying mechanism, properties, and the origin of the observed signals have been highly controversial. Thermally induced magnonic spin currents have been suggested as the origin [9,10], based on the presence of the effect in magnetic insulators, which excludes charge currents as the source. Despite this explanation of the origin of the effect, direct experimental evidence has not been reported. While parasitic interface effects [11] were suggested as an alternative source of the SSE due to a polarization of the paramagnetic detector layer [12], generally, the observed effects are now primarily attributed to magnonic spin currents [13,14].Time resolved experiments trying to address the problem by probing the temporal evolution of the SSE have obtained contradictory results: For film thickness up to 61 nm, no cut-off frequency due to an intrinsic limitation by the SSE was observed [15]. In contrast, for μm thick films, a characteristic rise time was found, and a finite magnon propagation length of the order of several 100 nm was put forward as a possible explanation [16,17]. This clearly calls for study to reveal the origin of this discrepancy as it underlies the fundamental mechanism of the SSE and to determine the intrinsic length scale.To clarify the origin of the measured SSE signals, we present a detailed study of the relevant length scales of the longitudinal SSE (LSSE) coveri...

We present results of detailed experimental and theoretical studies of all-optical magnetization reversal by single circularly-polarized laser pulses in ferrimagnetic rare earth-transition metal (RE-TM) alloys Gd x Fe 90−x Co 10 (20% < x < 28%). Using single-shot time-resolved magneto-optical microscopy and multiscale simulations, we identified and described the unconventional path followed by the magnetization during the reversal process. This reversal does not involve precessional motion of magnetization but is governed by the longitudinal relaxation and thus has a linear character. We demonstrate that this all-optically driven linear reversal can be modeled as a result of a two-fold impact of the laser pulse on the medium. First, due to absorption of the light and ultrafast laser-induced heating, the medium is brought to a highly nonequilibrium state. Simultaneously, due to the ultrafast inverse Faraday effect the circularly polarized laser pulse acts as an effective magnetic field of the amplitude up to ∼20 T. We show that the polarization-dependent reversal triggered by the circularly polarized light is feasible only in a narrow range (below 10%) of laser fluences. The duration of the laser pulse required for the reversal can be varied from ∼40 fs up to at least ∼1700 fs. We also investigate experimentally the role of the ferrimagnetic properties of GdFeCo in the all-optical reversal. In particular, the optimal conditions for the all-optical reversal are achieved just below the ferrimagnetic compensation temperature, where the magnetic information can be all-optically written by a laser pulse of minimal fluence and read out within just 30 ps. We argue that this is the fastest write-read event demonstrated for magnetic recording so far.

Thermally driven domain wall (DW) motion caused solely by magnonic spin currents was forecast theoretically and has been measured recently in a magnetic insulator using magneto optical Kerr effect microscopy. We present an analytical calculation of the DW velocity as well as the Walker breakdown within the framework of the Landau Lifshitz Bloch equation of motion. The temperature gradient leads to a torque term acting on the magnetization where the DW is mainly driven by the temperature dependence of the exchange stiffness, or in a more general picture by the maximization of entropy. The existence of this entropic torque term does not rest on the angular momentum transfer from the magnonic spin current. Hence, even DWs in antiferromagnets or compensated ferrimagnets should move accordingly. We further argue that the entropic torque exceeds that of the magnonic spin current.Spin caloritronics is a new field of research focused on the combined transport of spin, charge, entropy, and energy in magnetic systems [1]. A good example for a spin caloritronic phenomenon is the spin Seebeck effect, the occurrence of spin currents or spin accumulation due to temperature gradients, which was discovered first in metallic ferromagnets [2]. Later on, this effect was also found in dilute magnetic semiconductors [3] and even in insulators [4]. In the latter case the existence of the spin Seebeck effect can only be explained by pure magnonic spin currents not resting on any charge transport.Spin caloritronic phenomena call for an exploitation in magnetic devices. In Ref.[5] the existence of thermally driven domain wall (DW) motion in a temperature gradient was demonstrated by computer simulations based either on the stochastic Landau-Lifshitz-Gilbert equation of motion for an atomistic spin model or-in a more micromagnetic picture-on the Landau-Lifshitz-Bloch (LLB) equation of motion for a thermally averaged spin polarization. The microscopic explanation for DW motion in temperature gradients rests on the diffusive motion of magnons from the hot end of a nanowire towards the colder end [6] and the transfer of angular momentum pushing the wall in the direction opposite to the magnonic spin current. Theoretical investigations based on these arguments give estimates for the DW velocity which can be achieved [7][8][9][10].In this work we will focus on a more thermodynamic point of view. At finite temperature T a DW is a thermodynamic object where the free energy ΔFðTÞ is the thermodynamic potential that is minimized. The free energy of the DW can be expressed as the difference between a magnetic system with DW minus the free energy of the same system without DW [11]. It is connected to the internal energy ΔU of the wall and its entropy ΔS via ΔF ¼ ΔU − TΔS. The temperature dependence of the different thermodynamic potentials are illustrated in Fig. 1 for a DW in a high anisotropic material. The calculations are from Ref. [11] for an atomistic spin model for FePt. However, the general features of a DW free energy do not depend on the ...

The Landau-Lifshitz-Bloch equation is a formulation of dynamic micromagnetics valid at all temperatures, treating both the transverse and longitudinal relaxation components important for high-temperature applications. In this paper we discuss two stochastic forms of the Landau-Lifshitz-Bloch equation. Both of them are consistent with the fluctuation-dissipation theorem. We derive the corresponding Fokker-Planck equations and show that only the stochastic form of the Landau-Lifshitz-Bloch equation proposed in the present paper is consistent with the Boltzmann distribution at high temperatures. The previously used form does not satisfy this requirement in the vicinity of the Curie temperature. We discuss the stochastic properties of both equations and present numerical simulations for distribution functions and the average magnetization value as a function of temperature.

The switching of rare-earth-based ferrimagnets triggered by thermal excitation is investigated on the basis of an atomistic spin model beyond the rigid-spin approximation, distinguishing magnetic moments due to electrons in d and f orbitals of the rare earth. It is shown that after excitation of the conduction electrons a transient ferromagneticlike state follows from a dissipationless spin dynamics where energy and angular momentum are distributed between the two sublattices. The final relaxation can then lead to a new state with the magnetization switched with respect to the initial state. The time scale of the switching event is to a large extent determined by the exchange interaction between the two sublattices.