Spin-dependent transport in antiferromagnetic tunnel junctions P. Merodio, A. Kalitsov, H. Béa, Vincent Baltz, M. Chshiev To cite this version: P. Merodio, A. Kalitsov, H. Béa, Vincent Baltz, M. Chshiev. Spin-dependent transport in anti- ferromagnetic tunnel junctions. Applied Physics Letters, American Institute of Physics, 2014, 105, pp.122403. 10.1063/1.4896291. hal-01683647 HAL Id: hal-01683647 https://hal.archives-ouvertes.fr/hal-01683647 Submitted on 19 May 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. APPLIED PHYSICS LETTERS 105, 122403 (2014) Spin-dependent transport in antiferromagnetic tunnel junctions P. Merodio, 1, a) A. Kalitsov, 1,2 H. B ea, 1 V. Baltz, 1 and M. Chshiev 1, a) 1Univ. Grenoble Alpes, INAC-SPINTEC, F-38000 Grenoble, France; CNRS, SPINTEC, F-38000 Grenoble, France; and CEA, INAC-SPINTEC, F-38000 Grenoble, France 2MINT Center, University of Alabama, Box 870209, Tuscaloosa, Alabama 35487, USA (Received 8 July 2014; accepted 8 September 2014; published online 22 September 2014) We investigate the behaviour of spin transfer torque (STT) and tunnelling magnetoresistance (TMR) in epitaxial antiferromagnetic-based tunnel junctions using tight binding calculations in the framework of the Keldysh formalism. We find that the STT out-of-plane component exhibits a staggered spatial distribution similar to its in-plane component. This behaviour is specific to the use of a tunnel barrier and significantly differs from the out-of-plane torques reported in previous works using a metallic spacer. Additionally, we show that unlike conventional ferromagnetic-based tunnel junctions, the TMR can increase with applied bias and reach values comparable to typical magnetoresistances found for usual spin valves. VC 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4896291] Antiferromagnets (AFs)-based spintronics is a branch of PM/AF multilayers 13 makes the observation of STT in AF a science that explores spin dependent transport devices using technological challenge. Indirect mechanisms such as the AFs instead of ferromagnets (F). 1,2 It is currently considered study of exchange bias variations at F/AF interfaces due to as a significant exploratory topic in spintronics 3–6 since AFs the effect of a spin polarized current on the spin orientation exhibit no stray fields, which is beneficial for ultimate down- of the AF interfacial layer 14 are thus a convenient tool for size scalability. In particular, a first theoretical toy model studying STT in AF. showed AF spin transfer torque (STT) and giant magnetore- Apart from spin-valve structures using metallic spacers, sistance (GMR) for metallic AF/PM/AF multilayers,7 where usual F-based spintronics takes advantage since long of tunnel PM stands for a paramagnetic metallic spacer. The authors barriers (B). 15 Whereas GMR relies on spin dependent scatter- considered crystalline uncompensated F monolayers with ing at interfaces, tunnel magnetoresistance (TMR) rather relates staggered AF order (i.e., two alternating F sublattices with to spin dependent densities of states. In addition, tunnel barriers opposite magnetizations). Furthermore, unlike the pioneering filter the wave vectors’ angles of incidence of incoming elec- theoretical works on STT in F multilayers, 8,9 which predict trons, which lowers the effect of dephasing in three dimensional torques exerted by a spin polarized current close to the inter- systems (3-D). 16 In effect, the tunneling current distribution face between a F and a nonmagnetic metal, STT is expected over the two-dimensional Brillouin zone (corresponding to the to act cooperatively through the entire volume of the AF wave vector component parallel to the barrier interface, kjj ) is electrodes. This feature together with the absence of shape strongly localized in certain regions. For instance, STT is anisotropy in AFs explain that lower critical currents for mostly determined by electrons with perpendicular incidence 17 magnetization switching are predicted for epitaxial AFs and decreases quickly with kjj in F tunnel junctions. compared to the typical values for Fs. We investigate the behaviour of STT and TMR in AF- The STT picture proposed in Ref. 7 arises from changes based tunnel junctions using tight binding calculations in the in the exchange field experienced by localized moments due framework of the Keldysh formalism both for 1-D and 3-D to their magnetic interaction with nonequilibrium spin den- geometries. Due to the use of tunnel barriers, we anticipate sities originated by conduction electrons. This is in contrast unusual behaviours compared to AF-based spin-valves with with the widely used theoretical framework for F systems, metallic spacers, as described below. where the basic idea is that the precession of an electron Fig. 1 sketches a typical tunnel junction layer structure. about the magnetization of a F yields to a change in this The semi-infinite leads are modelled as a chain of uncom- magnetization by conservation of angular momentum, equal pensated localized spins with translational invariance in the to the imbalance of inward and outward spin fluxes. Due to plane perpendicular to the electron flow (y axis). We use a the vanishing magnetization in AF metals, this formalism single band tight binding Hamiltonian for the itinerant elec- can only be applied locally. trons with a hopping parameter t ¼ À 1 eV in all regions. The STT has been experimentally shown, for instance, with insulating spacer is a barrier of N B sites (respectively layers) layered ferromagnetic contacts with metallic spacers10 ,11 and for 1-D (respectively 3-D) with a spin-independent on-site 12 with a scanning tunneling microscope. These experimental energy eB ¼ 5 eV. The spin-dependent on-site energy in the works are based on the variation in the resistance of the dif- leads is the sum of the s-like orbital energy e0 and the spin ferent F structures. However, the difficulty to pin the order splitting D, which accounts for the s-d magnetic interaction parameter of an AF element along a reference direction to- between itinerant spins and localized moments. The absolute gether with the dwarfed magnetoresistance observed in AF/ value of the spin splitting D is constant, but alternates in sign for a given spin from one site(layer) to the next one due to a) Electronic addresses: [email protected] and [email protected] the alternating orientation of the localized magnetic 0003-6951/2014/105(12)/122403/5/$30.00 105, 122403-1 VC 2014 AIP Publishing LLC This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 132.168.11.98 On: Tue, 07 Oct 2014 09:55:16 122403-2 Merodio et al. Appl. Phys. Lett. 105, 122403 (2014) FIG. 1. Layouts of the tunnel junction modified from Ref. 8 for AF leads. (Top) Scheme of the left and right semi-infinite AF electrodes separated by the non- 0 magnetic insulating spacer of N B atomic layers. The order parameter M of the right lead points along the z direction, while the order parameter M of the left lead is rotated by an angle h around the y axis in the plane parallel to the AF/B interface. The on-site torques delivered in the right lead are represented by the in-plane (Tjj ) and out-of-plane ( T?) components. The vector decomposition of the spin current densities is depicted in the barrier (Q ij ). (Middle) Schematic illustration of the two AF sublattices of up and down localized spins whose magnetic interaction with itinerant electrons is modeled by the staggered spin split- ting D. Sites in the left lead, barrier, and right lead are denoted, respectively, by unprimed Greek, Latin, and primed Greek letters. (Bottom) Schematic picture of the density of states in the AF leads and the potential profile within the junction. The lower and upper bands for a given spin are separated by a gap of 2 D. eB is the spin-independent on-site energy in the barrier, and V is the potential applied through the junction. The Fermi level is set at E F ¼ 0 and is indicated by the lower dashed line. moments within the AF leads. In particular, localized up where e is the elementary charge and kjj labels the Bloch (similarly for down) spins build up a magnetic sublattice in state in each translationally invariant layer. Since coherent which the spin-dependent on-site energy reads transport is considered here, we assume transverse momen- "ð#Þ e ¼ e0 À ðþÞ D. Thus, the magnetic properties of each AF tum conservation. In the case of a 1-D junction, the prefactor D et et k are embedded in the spin-splitting . In addition, the exis- 8p3h in Eq. (1) becomes 2ph since the integration in the jj tence of two sublattices within the AF leads opens a gap in states is not necessary. the density of states (DOS) equal to 2 D (see Fig. 1). The essential block to calculate the projections of the ^< However, since AFs do not exhibit any macroscopic magnet- lesser Green function Gp;q into layers p and q for the whole ^r ization, majority and minority bands are not split. structure is the retarded Green function gp;q for isolated leads The charge current density J is calculated in the right lead and barrier.