Theory of Spin Diode Effect Piotr Ogrodnik Warsaw University of Technology and Institute of Molecular Physics Polish Academy of Sciences NANOSPIN Summarizing Meeting, Kraków, 11-12th July 216
Outline: o What is the spin diode effect? o Analytical model o Applications: TMR/GMR/AMR structures o Extensions of the model GMR nanowire o Summary
What is the spin diode effect? The idea is very simple (A. Tulapurkar et al., Nature 438, 33-342 (2) ) magnetoresistive element: AMR, GMR, TMR Then we pass the a.c. current through this element If the current is the source of driving force for magnetization dynamics then we can measure Vdc (spin diode voltage) that results from the mixing of a.c. current and oscillating resistance of the element. 1-1 1 1 V dc Time RF current:.. Oscillating resistance: R(t) Spin diode DC voltage:..
Model (1) What is measured? Output voltage: a.c. current oscillating resistance The amplitude of resistance changes: cos ΔR ; ) TMR, GMR structures: the angle between two magnetic moments AMR structures: the angle between magnetic moment and current density vector
Model (2) AMR: 2Δsin cos % &' (%Δ sin cos )*+ I TMR /GMR: 1 2 Δsin % &' (%Δ 4 sin )*+ The goal is to calculate -. for specific system -. may be derived from LLG/LLGS equation
Model (3) Calculations : < =>>?@ A A B A C A D A 'EFG A HC A IJ Magnetic energy: magneto--crystalline anisotropy shape anisotropy Zeeman-like Interactions Interlayer coupling Magnetoelastic energy Interaction with Oersted field (in the case:?3< = K) STT term in standard form for multilayer systems i.e. 1 2 3 1 2 31 1 2 31 or for non-uniform magnetization distribution: 4 67 38 9 : 67 ; (magnetization distribution within the sample has to be assumed), Such a torque effectively acts on averaged magnetic moment of the sample 1 (macrospin with nonhomogenities..)
Model (4) LLG equation in spherical coordinates with STT Slonczewski-like and field-like terms: We assume that magnetic moment oscillates harmonically around stationary point, so the solutions for two angles describing 1 are in the form:
Model () Linearization of RHS Ψ - phase shift between 1 and driving-force (a.c. current)
if dynamics is driven by Oersted field, we use derivatives with respect to M EJ (instead of % )
- symmetric contribution to the Vdc lineshape - antisymmetric contribution to the Vdc lineshape
Applications(1): TMR nanopillar with perpendicular anisotropy first comparison with the experiment. Energy with perpendicular anisotropy: A = N 2 cos sin sino 1 C M JPQ S U U V W X S U Y Z[S U N 2 -is V bias voltage dependent
Application (2) GMR structure in CIP configuration Ziętek et al., Phys. Rev. B 91, 1443 (21)
Application (3) GMR sample in CIP configuration (the influence of IEC on the out-of-resonance Vdc signal driven by Oersted field) Ziętek et al., APL 17, 12241 (21) V dc (mv) - -1 - -1 1 7 1 8 1 9 1 1 1 7 1 8 1 9 1 1 1 7 1 8 1 9 1 1 H coup (Oe) Frequency (Hz) - -1 Cu layer thickness (nm) - 1.8 2. 2.2 2.4 2.6 Additional energy term (IEC): A 'EFG 1 M 'EFG 196 Oe 61 Oe 32 Oe RKKY interaction
Extension of the spin diode model - GMR nanowires. Motivation : Cu (7 nm) spacer Thin (nm) magnetic (Co) layer Thick(2nm ) magnetic (Co) layer
Results relations of dispersion Thin layer (fixed nm) The best fits: 1 1 1 1 2 1 1 Magnetic Field Oe 2 1 1 Magnetic Field Oe thick layer: d = 1 nm, K = 2 kj/m3, Ms= 1.4 T thin layer: d = nm, K = 3kJ/m3, Ms = 1.3 T Spacer thickness: 3 nm (corresponding to dipolar coupling fields: 6 Oe (in thick layer) and 113 Oe (in thin layer) thick layer: d = 1 nm, K = 3 kj/m3, Ms= 1.4 T thin layer: d = nm, K = 2kJ/m3, Ms = 1.3 T Spacer thickness: 3 nm (corresponding to dipolar coupling fields: 6 Oe (in thick layer) and 113 Oe (in thin layer)
Thick layer = 1 nm 1 1 1 1 2 1 1 Magnetic Field Oe 2 1 1 Magnetic Field Oe More realistic Cu thickness = 7 nm dipolar fields are large... and with reduced magnetocrystalline anisotropy (in both layers ~.1 kj/m3) 1 More realistic: thick layer = 2 nm Thick layer, and thin layer: K = 1 J/m3 Ms=.9 T 1 2 1 1 Magnetic Field Oe Best fit for: Spacer thickness: 17. nm (corresponding to dipolar coupling fields: 67 Oe (in thick layer) and 36 Oe (in thin layer) The conclusion from f(h) within macrospin model: The best fit is for thick layer (~1nm) and very thick Cu spacer (3 nm) with very high magnetocrystalline anisotropy (2-4kJ/m3) and high saturation magnetization (1.3-1.4 T).
Spin diode voltage Vdc a.u. 2 1 1 2 Vdc lineshapes (for the best f(h) fit): Dynamics driven only by STT: H 4 6 8 1 12 Frequency 2 Oe GHz Spin diode voltage Vdc a.u. Spin diode voltage Vdc a.u. H 1 Oe 1. 1 13 1. 1 13 2. 1 13 4 6 8 1 12 without coupling -> peaks still symmetric H 1 Oe..4.3.2.1.1 4 6 8 1 12
Vdc lineshapes (for the best f(h) fit): Dynamics driven only by Oersted field: H 2 Oe H 1 Oe Spin diode voltage Vdc a.u. 4 2 2 4 6 4 6 8 1 12 Spin diode voltage Vdc a.u..6.4.2.2.4.6 4 6 8 1 12 Playing with the parameters (phase shift, amplitudes of STT and Oersted field) makes possible to get lineshapes similar to experimental ones. Spin diode voltage Vdc a.u. 1 1 1 H 12 Oe 2 4 6 8 1 12 Spin diode voltage Vdc a.u.....1 H 1 Oe 4 6 8 1 12
Summary (short): In some cases the model (macrospin) agrees well with the experimental results However, in the case of strongly coupled layers the theoretical analysis becomes very difficult because of number of free parameters