Dr. Rocio Yanes (Universidad de Salamanca)
Introduction The ability to control the motion of magnetic structures, like domain walls (DW), is a key point in the development of many spintronic and magnetic devices. The traditional ways to control their motion areis by means ofusing magnetic fields and spin polarized currents. MAlso, magnetic domain motion driven by temperature gradients hasave been also shown in theoretical [1,2] and experimental  works, opening the door to use thermal control of domain wall in future spintronicmagnonics devices. On the other hand, the possibility to control the magnetic properties using mechanical stress is currently being investigated with promising results [4,5]. In this work we will focus in these two ways to control the dynamics of magnetic textures, studying: 1) the dynamics of complex magnetic textures, like spin spirals or skyrmions, induced by thermal gradients. 2) the possibility to use acoustic waves as the driven force for the DW motion. Motionvement induced by temperature gradients The existence of a temperature gradient in the system induces a non-equilibrium populationsituation of magnons. The density of magnons excited in the hotter isare larger than that in the cold section of the system, leading to a flow of magnons from the hotter area to the colder one. When the magnons pass through the DW, they transfer angular momentum to the DW and as a consequence of that effect the DW moves to the colder area. Recently, F. Schlickeiser et. al have proposed that in parallel to the transfer angular momentum other mechanism may exist responsible of the movement of magnetic structures into a temperature gradient. Such mechanism is related to the maximization of the entropy of the system by displacing the DW from the colder to the hotter area . In our work, we analyze the dynamics of two dimensional non-collinear magnetic textures subject to a temperature gradient. In order to do that, numerical calculations of the dynamics of a helical spin spiral (HSS), a skyrmion lattice and isolated skyrmions are carried out in atomistic spin models with the stochastic Landau-Lifshitz-Gilbert equation of motion. Fig1: Helical spin spiral (HSS) velocity versus temperature gradient for, α=0.2. The open symbols present our numerical data, the lines are from linear fits to the positive and negative temperature gradient dT/dx. Our findings show that in systems with spin spirals the lack of mirror symmetry leads to the effect that the velocity of the moving spiral depends on the sign of the temperature gradient with respect to the chirality of the HSS. This result is clearly shown in the Fig. 1, where the velocity of a left-handed helical spin spiral (HSS) versus the temperature gradient is displayed for a value of the damping constant, α=0.2. .The data points (empty symbols) are from the numerical simulations while the lines represent linear fits to the positive and negative temperature gradient , dT/dx . Furthermore, we observe that the movement of isolated skyrmions is determined by the temperature gradient and the Magnus force, and in the case of a lattice of skyrmions the interaction between skyrmions plays a fundamental role. Motionvement induced by acoustic waves In our study of the mechanical control of the DW motion we use micromagnetic simulations to investigate whether it is possible to move a DW using mechanical waves, a possibility that has been suggested recently . To do that we have developed a novel numerical scheme to solve both: magnetization dynamics and elastodynamics equations self-consistently, similar to the one presented in  but using a finite difference scheme. We consider a Ni nanowire of a rectangular cross section (50 x 20 nm) with a head to head DW in the middle. Circularly polarized elastic waves are excited ion one end of the nanowire by imposing a periodic deformation of amplitude uo and frequency ʋ=10Ghz. The mechanical excitation induces magneto-elastic waves (MEW). When they reach the DW they excite it, exerting a torque on such magnetic texture which induces a movement of the DW towards the source of the elastic excitation. This result is clearly shown in the Fig. 2, where the x-component of the averaged magnetization (which is related to the position of the DW) is plotted as a function of time for several values of the amplitude of the mechanical excitation. Fig1: Time evolution of the averaged x-component of the magnetization of the nanowire as a function of the amplitude uo of the acoustic excitation. Acknowledgments This work was partially supported by No. SA090U16 from the Junta de Castilla y Leon. References  D. Hinzke and U. Nowak, Phys. Rev. Lett, 107 (2011) 027205.  P. Yan et al, Phys. Rev. Lett, 107 (2011) 177207.  W. J. Jiang et al. Phys. Rev. Lett, 110 2013) 177207.  V. Sampath et al, Nano Lett. 16 (2016) 5681.  Na Lei et al, Nat. Comm. 4 (2012) 2386.  F. Schlickeiser et al Phys. Rev. Lett, 113 (2014) 097201.
Dr. Rocio Yanes (Universidad de Salamanca)
Dr. Denise Hinzke (Universitat Konstanz) Prof. Luis López Díaz (Universidad de Salamanca) Mr. Moretti Simone (Universidad de Salamanca) Dr. Ulrich Nowak (Universitat Konstanz) Mr. Voto Michele (Universidad de Salamanca)