Current driven domain wall creation in ferromagnetic nano-wires. Davi R. Rodrigues, 1 Jairo Sinova, 2 and Ar. Abanov 1 1 Department of Physics & Astronomy, Texas A&M University, College Station, Texas 77843-4242, USA 2 Institute of Physics, Johannes Gutenberg Universit¨ at, 55128 Mainz, Germany (Dated: October 27, 2021) We predict the electrical generation and injection of domain walls into a ferromagnetic nano-wire without the need of an assisting magnetic field. Our theory shows that above a critical current jc domain walls are injected into the nano-wire with a period T ∼ (j - jc) -1/2 . In a uniaxial anisotropy geometry this process does not require Dzyaloshinskii-Moria or dipole-dipole interaction and can be done in a simple exchange ferromagnet. We also show that this process and the period exponents are universal and do not depend on the peculiarities of the microscopic Hamiltonian. Recent proposals for the next generation of magnetic mem- ory devices 1–3 rely on the ability to manipulate the position and orientation of the Domain Walls (DW) in ferromagnetic nano-wires by electric current. These proposals have led to an intense research activity in the area of current induced DW dynamics in both anti- and ferromagnets. 4,5 The dynamics of the DW in ferromagnetic nano-wires are well described by a set of simple general equations of the effective coordinates characterising the DW. 6–16 The form of these does not depend on the exact form of the macroscopic magnetic Hamiltonian. Whereas the form of the equations de- scribing the dynamics are universal, the few parameters which the equations depend upon are of course device dependent. These however can be measured in a given nano-wire by spe- cific independent methods and thereafter the DW dynamics are fully deterministic. 17 These developments have led to the possibility of constructing reliable “all electric” non volatile magnetic memory devices. However, in order to manipulate DWs, one needs to first create them. Currently the DWs are injected from one end into a nano-wire by applying of magnetic field. In this work we propose a technique to controllably inject the DWs into nano- wires by DC electric current alone. Hence completing the requirements needed to make an “all electric” DW-dynamics based spintronic device possible. We show that in a simple geometries, for a DC current j above a certain critical current j c , new DWs start to en- ter the nano-wire from the end with a current depended pe- riod: T ∼ (j − j c ) −1/2 . The geometry chosen here as an example is one where the magnetization anisotropy is along the wire and the wire is attached to a ferromagnet with its magnetization perpendicular to the nano-wire, see Fig.1. We show, that under broad conditions this effect does not depend on the details of the microscopic magnetic Hamiltonian and does not require any “twisting” terms in the Hamiltonian, such as Dzualoshinskii-Moria (DMI), or dipole-dipole interactions. We derive what the value of the critical current is and how it depends on the microscopic Hamiltonian. For currents just above the critical the new DW enters the nano-wire slowly, so the process does not depend on dissipation. Below we first discuss the macroscopic magnetic Hamil- tonian with the terms relevant for our proposal. Next, we describe the proposed geometry for the DW injection. Then we discuss the magnetization dynamics in the adiabatic limit. FIG. 1. Geometry for the DW injection in a nano-wire. For currents below j c , when the magnetization is static, we map the one dimensional static problem to a zero dimension dynamical problem and find a conserved quantity associated with translational invariance and find from this the value of the critical current. We next find a general static solution for the currents below critical and show that continued to the unphysical region it ex- hibits an extra DW at the current dependent position. When the current is above j c the position of the unphysical DW slowly changes with time, so that it finally enters the physical domain and appears as a newly generated DW. We calculate the period of this process as a function of current and show that the DWs are produced with a period T ∼ (j − j c ) −1/2 . Finally, we discuss the problem of minimization of Ohmic losses in the injection process as well as the relevance of the presented calculation for the dynamics around a strong pin- ning center relevant to experiments. I. MAGNETIC HAMILTONIAN AND GEOMETRY In order for a DW to be a stable object the magnetic Hamil- tonian must include easy axis anisotropy. We assume for def- initeness that the easy axis anisotropy is directed along the wire. However, we emphasize that the results are also valid for many other cases, as can be shown by a simple change of notations. Also, because DW injection happens at DC currents larger then the currents typically used for DW manipulation, we thus assume that the at the currents of interest the DWs are not pinned by the impurities or nano-wire imperfection. For arXiv:1512.00784v1 [cond-mat.mes-hall] 2 Dec 2015