Spintronic oscillators can be realized by considering two ferromagnets separated by a normal metal or a ultrathin (<1.2nm) insulator. One of the ferromagnets act as polarizer while the other, namely the free layer, is designed in order that a large enough spin-polarized current can modify its magnetic state. In particular, if the negative damping exactly compensates the magnetic losses related to the Gilbert damping a self oscillation of the magnetization can be excited.[1][2][3] In the literature, different kind of devices have been studied, spin-valves where the current is injected uniformly into the free layer, point contact geometries or nanowire where the current is injected locally into the free layer via a nanocontact. Here we have investigated the dynamical properties of a nanowire spintronic oscillator[4] (2500x100x6nm3) where the polarizer (100x100nm2) is in a vortex state localized in the center of the nanowire (see inset of Fig. 1(a), the arrows indicates the in-plane component of the magnetization and the red color denotes the out of plane magnetization). An in-plane field of 50mT is applied to introduce a shift in the vortex core location. The initial configuration of the magnetization is uniform and aligned along the -x direction. Our results are based on the numerical solution of the Landau-Lifshitz-Gilbert-Slonczweski equation.[3] First, we have studied the self-oscillation properties driven by dc spin-polarized current density. Fig. 1(a) (main panel) and (b) show the oscillation frequency and power (computed as integrated output power) of the y-component of the magnetization as a function of the current density, respectively. The Hopf bifurcation found at the critical current is sub-critical, the oscillation power is finite and there is a current region where a co-existence of a limit cycle and of a fixed point of dynamics is present. The oscillation frequency of the x-component is twice the one of the y-component and this means that in the GMR-signal are present two harmonics. We have also studied the wave profile finding a non-propagating spin wave in the wire. Fig. 1(c) displays the profile of the spin wave in the contact (the x-axis represents the cell number). In micromagnetic simulations, we have used 5x5x6nm3 micromagnetic cells for the discretization. For three different current densities indicated in Fig.1(a): JA=0.65x108A/cm2, JB=0.70x108A/cm2, and JC=0.75x108A/cm2. The found results are also confirmed by investigating the dynamics in strips long 5000nm. We also computed the FMR-spectrum (see main panel of Fig. 1(d)) by applying a microwave field linearly polarized (1mT) in the plane y-z perpendicular to the static configuration of the magnetization (-x). As it can be observed, the FMR frequency (around 7.95GHz) is larger than the oscillation frequency. The FMR spectrum obtained as a response of a weak microwave current is qualitatively very similar to the field-driven FMR. Basically our results indicate that it is possible to compute the FMR computation of an extended nanostripe by a injecting a non-uniform and localized spin-polarized current. This approach can be used to characterize experimentally spin wave eigenmodes in low field regime where a collinear configurations are generally achieved in case of uniform polarizer.[5] We also computed and compare the wave vector as function of the current frequency with no thermal fluctuations for the case of uniform and non uniform polarizer as displayed in the inset of Fig. 1(d). Our results indicate that, as the frequency approaches the FMR frequency, the wave vector is finite in the case of non-uniform polarizer and tends to be almost zero (excitation of the uniform mode) in the case of uniform polarizer.

### Nanowire spin-torque oscillator with non-uniform polarizer: a micromagnetic study

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*GIORDANO, ANNA;SIRACUSANO, GIULIO;AZZERBONI, Bruno;FINOCCHIO, Giovanni*

##### 2014-01-01

#### Abstract

Spintronic oscillators can be realized by considering two ferromagnets separated by a normal metal or a ultrathin (<1.2nm) insulator. One of the ferromagnets act as polarizer while the other, namely the free layer, is designed in order that a large enough spin-polarized current can modify its magnetic state. In particular, if the negative damping exactly compensates the magnetic losses related to the Gilbert damping a self oscillation of the magnetization can be excited.[1][2][3] In the literature, different kind of devices have been studied, spin-valves where the current is injected uniformly into the free layer, point contact geometries or nanowire where the current is injected locally into the free layer via a nanocontact. Here we have investigated the dynamical properties of a nanowire spintronic oscillator[4] (2500x100x6nm3) where the polarizer (100x100nm2) is in a vortex state localized in the center of the nanowire (see inset of Fig. 1(a), the arrows indicates the in-plane component of the magnetization and the red color denotes the out of plane magnetization). An in-plane field of 50mT is applied to introduce a shift in the vortex core location. The initial configuration of the magnetization is uniform and aligned along the -x direction. Our results are based on the numerical solution of the Landau-Lifshitz-Gilbert-Slonczweski equation.[3] First, we have studied the self-oscillation properties driven by dc spin-polarized current density. Fig. 1(a) (main panel) and (b) show the oscillation frequency and power (computed as integrated output power) of the y-component of the magnetization as a function of the current density, respectively. The Hopf bifurcation found at the critical current is sub-critical, the oscillation power is finite and there is a current region where a co-existence of a limit cycle and of a fixed point of dynamics is present. The oscillation frequency of the x-component is twice the one of the y-component and this means that in the GMR-signal are present two harmonics. We have also studied the wave profile finding a non-propagating spin wave in the wire. Fig. 1(c) displays the profile of the spin wave in the contact (the x-axis represents the cell number). In micromagnetic simulations, we have used 5x5x6nm3 micromagnetic cells for the discretization. For three different current densities indicated in Fig.1(a): JA=0.65x108A/cm2, JB=0.70x108A/cm2, and JC=0.75x108A/cm2. The found results are also confirmed by investigating the dynamics in strips long 5000nm. We also computed the FMR-spectrum (see main panel of Fig. 1(d)) by applying a microwave field linearly polarized (1mT) in the plane y-z perpendicular to the static configuration of the magnetization (-x). As it can be observed, the FMR frequency (around 7.95GHz) is larger than the oscillation frequency. The FMR spectrum obtained as a response of a weak microwave current is qualitatively very similar to the field-driven FMR. Basically our results indicate that it is possible to compute the FMR computation of an extended nanostripe by a injecting a non-uniform and localized spin-polarized current. This approach can be used to characterize experimentally spin wave eigenmodes in low field regime where a collinear configurations are generally achieved in case of uniform polarizer.[5] We also computed and compare the wave vector as function of the current frequency with no thermal fluctuations for the case of uniform and non uniform polarizer as displayed in the inset of Fig. 1(d). Our results indicate that, as the frequency approaches the FMR frequency, the wave vector is finite in the case of non-uniform polarizer and tends to be almost zero (excitation of the uniform mode) in the case of uniform polarizer.##### Pubblicazioni consigliate

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