Research ArticlePHYSICS

Giant facet-dependent spin-orbit torque and spin Hall conductivity in the triangular antiferromagnet IrMn3

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Science Advances  30 Sep 2016:
Vol. 2, no. 9, e1600759
DOI: 10.1126/sciadv.1600759
  • Fig. 1 ST-FMR measurement of Embedded Image in p-IrMn3.

    (A) Illustration of the ST-FMR experimental setup where Hext is the external field, M is the magnetization of the permalloy layer (yellow), and τH and τST are the torques on M due to the Oersted field created by the RF charge current and the spin current in the Ir1−xMnx layer (green), respectively. (B) ST-FMR spectra measured on a ~60 Å IrMn3/~60 Å Py sample at a frequency varying from 9 to 12 GHz. (C) ST-FMR spectrum measured at 9 GHz. The black solid lines are the fits with Lorentzian functions. The red and green solid lines represent the symmetric and antisymmetric Lorentzian fits, respectively. (D) Frequency dependence of measured Embedded Image of ~60 Å IrMn3/~60 Å Py. (E) ST-FMR spectra measured on these devices with different thicknesses of IrMn3 at 11 GHz. Inset: Thickness dependences of the symmetric and antisymmetric components of Vmix. (F) Thickness dependence of measured Embedded Image for IrMn3/~60 Å Py. Error bars correspond to 1 SD in (D) and (F).

  • Fig. 2 Dependence of Embedded Image and HB on Mn concentration in Ir1−xMnx/Py bilayers.

    (A) Embedded Image measured at 11 GHz for polycrystalline bilayers of ~60 Å Ir1−xMnx/~60 Å Py versus the Mn concentration x. (B) In-plane exchange bias field for polycrystalline bilayers of ~60 Å Ir1−xMnx/~60 Å Py versus the Mn concentration x. Note that HB was measured after the films were annealed in an in- plane field of 1 T for 30 min at 300°C. Error bars correspond to 1 SD in (A).

  • Fig. 3 Structural characterization of IrMn3.

    (A) The XRD measured on 100 Å (001) IrMn3 (blue line), (111) IrMn3 (cyan line), and p-IrMn3 films (black line). Each film is capped with a TaN layer with a thickness of 20 Å. (B to D) High-resolution transmission electron micrographs of 40 Å (001) IrMn3, (111) IrMn3, and p-IrMn3, with 60 Å Py/20 Å TaN capping layers.

  • Fig. 4 Facet-dependent Embedded Image in crystalline Ir1−xMnx.

    (A) Embedded Image as a function of IrMn3 thickness for (001)-oriented (olive circles), (111)-oriented (blue circles), and polycrystalline-oriented (cyan circles) films. (B) Embedded Image as a function of Mn concentration for (001), (111), and p-Ir1−xMnx. Error bars correspond to 1 SD in (A) and (B).

  • Fig. 5 In-plane exchange bias field and Embedded Image in crystalline Ir1−xMnx after annealing in in-plane magnetic field.

    In-plane exchange bias field and Embedded Image as a function of annealing temperature for (001) IrMn3 (A and C) and (111) IrMn3 (B and D). The thickness of IrMn3 is 43 Å. Squares and circles indicate positive and negative in-plane magnetic field (1 T) during annealing (30 min), respectively.

  • Fig. 6 Modulation of the Embedded Image in crystalline Ir1−xMnx after annealing in a perpendicular magnetic field.

    Embedded Image for (001) (A) and (111) (B) IrMn3/60 Å Py bilayers as a function of IrMn3 thickness measured sequentially in the following: an as-grown device, a device annealed in a 1-T perpendicular field (60 min), a device annealed in an in-plane 1-T field (30 min), and a device annealed in a −1-T perpendicular field (60 min). (C) Exchange bias field measured in (001) and (111) IrMn3/60 Å Py bilayers as a function of IrMn3 thickness after the unpatterned films were annealed in-plane in a 1-T field (30 min) using vibrating sample magnetometry. The annealing field was aligned along the (001) axis for the (001)-oriented samples. The exchange bias field was also measured in the same devices used in (A) and (B) via magnetoresistance measurements (see fig. S8). Error bars correspond to 1 SD in (A) and (B).

  • Fig. 7 Chiral noncollinear antiferromagnetic orders and corresponding anomalous Hall conductivity and SHC.

    (A) Schematic diagram of two chiral AF orderings, AF1 and AF2, of the Mn moments in the (111) plane of IrMn3. As illustrated, spin-up and spin-down electrons feel opposite fictitious fields because of spin-orbit coupling. Thus, their trajectories will be in opposing transverse directions. Because of the underlying antiferromagnetic lattice, the induced transverse currents from opposite spins (j, j) are not equal in amplitude. Let us suppose that j > j for AF1. When reversing the spins, for example, by a time reversal operation, an opposite spin chirality is realized as AF2. The time reversal operation simultaneously reverses the spin and velocity. Thus, the deflection direction for the electron with a given spin does not change. However, the relative amplitude of these currents change, that is, j < j, because of the inversed spin chirality. Therefore, AF1 and AF2 exhibit opposite anomalous Hall current jAH and the same spin Hall current js. (B and C) Ab initio calculations of the anomalous Hall conductivity (AHC) (σxy) and SHC Embedded Image with respect to chemical potential. The charge-neutral point is set to zero. Here, the x, y, and z axes correspond to the crystallographic directions Embedded Image, Embedded Image, and [111], respectively (see the Supplementary Materials). Because AF1 and AF2 can be transformed into each other by a mirror reflection or a time reversal operation, they exhibit opposite signs of AHC but the same sign of SHC.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/9/e1600759/DC1

    Supplementary Materials and Methods

    fig. S1. Thickness dependence of the effective SHA, Formula, for Ir1−xMnx.

    fig. S2. Frequency dependence of the effective SHA, Formula, for Ir1−xMnx.

    fig. S3. Frequency dependence of Formula for (001) IrMn3 (top), (111) IrMn3 (middle), and p-IrMn3 (bottom).

    fig. S4. ST-FMR signals measured on d IrMn3/60 Å Py at an RF frequency of 9 GHz.

    fig. S5. XRD measured on Ir1−xMnx films with a thickness of 100 Å.

    fig. S6. Magnetization Ms versus in-plane magnetic field obtained for Py on (001) IrMn3 (left), (111) IrMn3 (middle), and p-IrMn3 (right) measured from vibrating sample magnetometry.

    fig. S7. Exchange bias field for IrMn3.

    fig. S8. Exchange bias field measured in (001) and (111) IrMn3/60 Å Py bilayers as a function of IrMn3 thickness after the devices were annealed in-plane in a 1-T field (30 min) via magnetoresistance measurement.

    fig. S9. Formula as a function of Cu and Au insertion layers for (001)- and (111)-oriented IrMn3/Py bilayers, respectively.

    fig. S10. Ab initio band structure of IrMn3.

    table S1. Summary of SHA, SHC, and resistivity of Ir1–xMnx based ST-FMR devices in as-deposited, unannealed films.

    table S2. AHC and SHC tensors.

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Materials and Methods
    • fig. S1. Thickness dependence of the effective SHA, θeff SH, for Ir1−xMnx.
    • fig. S2. Frequency dependence of the effective SHA, θeff SH, for Ir1−xMnx.
    • fig. S3. Frequency dependence of θeff SH for (001) IrMn3 (top), (111) IrMn3 (middle), and p-IrMn3 (bottom).
    • fig. S4. ST-FMR signals measured on d IrMn3/60 Å Py at an RF frequency of 9 GHz.
    • fig. S5. XRD measured on Ir1−xMnx films with a thickness of 100 Å.
    • fig. S6. Magnetization Ms versus in-plane magnetic field obtained for Py on (001) IrMn3 (left), (111) IrMn3 (middle), and p-IrMn3 (right) measured from vibrating sample magnetometry.
    • fig. S7. Exchange bias field for IrMn3.
    • fig. S8. Exchange bias field measured in (001) and (111) IrMn3/60 Å Py bilayers as a function of IrMn3 thickness after the devices were annealed in-plane in a 1-T field (30 min) via magnetoresistance measurement.
    • fig. S9. θeff SH as a function of Cu and Au insertion layers for (001)- and (111)- oriented IrMn3/Py bilayers, respectively.
    • fig. S10. Ab initio band structure of IrMn3.
    • table S1. Summary of SHA, SHC, and resistivity of Ir1–xMnx–based ST-FMR devices in as-deposited, unannealed films.
    • table S2. AHC and SHC tensors.

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