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arxiv: 2305.04385 · v2 · submitted 2023-05-07 · ❄️ cond-mat.mes-hall

Lectures on spintronics and magnonics

M. Mazanov , V. A. Shklovskij This is my paper

Pith reviewed 2026-05-24 09:06 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords spintronicsmagnonicsspin transfer torquespin pumpingantiferromagnetic dynamicsspin Hall effectmagnetic resonancespin waves
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The pith

Lectures derive spin transfer torque and spin pumping via scattering matrices while contrasting antiferromagnetic dynamics.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a series of lectures outlining the theoretical concepts of magnonics and spintronics. It recalls background from quantum mechanics and magnetism, then covers classical magnetic dynamics including resonance and spin waves. The main sections address spin currents, torques, and the spin Hall effect. Emphasis is placed on deriving spin transfer torque and spin pumping through the Landauer multi-channel scattering matrix method. The lectures conclude by noting features that set antiferromagnetic dynamics apart from ferromagnetic ones and position antiferromagnets as promising materials.

Core claim

The lectures establish that spin transfer torque and spin pumping follow from the Landauer quantum multi-channel scattering matrix approach, and that antiferromagnetic dynamics possess distinguishing features from ferromagnetic dynamics which make antiferromagnets particularly promising material candidates for spintronics and magnonics.

What carries the argument

The Landauer quantum multi-channel scattering matrix approach, which derives the effects of spin transfer torque and spin pumping.

Load-bearing premise

The reader possesses or can quickly acquire background in quantum mechanics, electrodynamics of continuous media, and basic theory of magnetism.

What would settle it

An experimental measurement showing that spin pumping currents in a multi-terminal device deviate from predictions of the Landauer scattering matrix derivation would challenge the emphasized treatment.

Figures

Figures reproduced from arXiv: 2305.04385 by M. Mazanov, V. A. Shklovskij.

Figure 1.1
Figure 1.1. Figure 1.1: Dependence of P0,l ≡ P(θ,φ) on the direction of measurement (θ, φ) at φ = 0 for the state χ (θ0=π/12,φ0=0) ↑ . The direction of polarization vector in this state is marked as P0. with polarization vectors P1 and P2, |χsupi = |χ1i + |χ2i gives again a state with some polarization vector Psup, |Psup| = 1. An analogy can be drawn with light: a superposition of two waves with circular polarizations of opposi… view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: 2) In an external field (H0 = 0 6 ): the spontaneous magnetization is not completely destroyed at T = Tc , but for usual values of atomic spin (S < 5) it rapidly decreases at T & Tc , so that at high temperatures kT gµBH0S the 4A similar property is inherent in the coefficients of the dynamic force matrix in the theory of crystal lattice vibrations [S6]. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_2_1.png] view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: Dependencies of the relative magnetization σ = M/Ngµ0S of a ferromagnet on the dimensionless temperature τ = T/Tc in the Weiss molecular field theory. The curves are plotted for different atomic spins S = 1/2, 1, 3/2, ..., 10. Left panel: in the absence of an external field, H0 = 0. Right panel: in an external field H0 = 0.1 kTc/gµ0 (coloured solid lines), and at H0 = 0 (gray dashed lines). CONTROL QUEST… view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: Magnetization precession in an external alternating magnetic field H0 + h⊥(t). ESR resonance occurs when the frequency ω of external field h⊥(t) and the frequency ω0 of precession of individual magnetic moments coincide. with the perturbation h(t). Let the susceptibility in the constant field H0 be χ0 (2.34): M0 = χ0H0. (3.1) In an additional weak external alternating field h(t) = h0e −iωt magnetization … view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Limiting forms of an ellipsoid ([6], p. 54). An external constant magnetic field H(t) has components (Hx(t), 0, Hz), where Hx(t) is the high-frequency field, Hz is the constant field. The expression for χ0 can also be derived directly, assuming that a small constant additional field along the x axis only rotates the magnetization vector by a small angle (see [S9]). The resulting resonant precession frequ… view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: To the calculation of effective anisotropy field Ha . The uniaxial symmetry then dictates the form of anisotropy energy: Ea ' Kθ2 , (3.39) where K ≡ K3/2 in Eq.(3.37) (note that constant term has been excluded). Hence, ∂Ea ∂θ eθ ' 2Kθeθ ≡ −MHa eθ. (3.40) Let us take into account the effective magnetic anisotropy field Ha ↑↓ x ↑↑ Mxex in the form of an effective additional demagnetizing field Ha = −Na xMx… view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Spin wave in a ferromagnet. Shown is a section on which one spin wavelength fits. containing the spatial derivatives of the vector m, which now allows us to consider the oscillations of the magnetization not only taking into account the time dispersion m(t), but also spatial dispersion m(r) 3 . In accordance with this, we choose the external variable field h(r, t) in the form of a plane wave, h(r, t) = h… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: The dispersion law for spin waves (4.22). Dispersion curves ω(k, θk) fill the area between the curves ω(k, 0) and ω(k, π/2). In quantum language, spin waves correspond to quasiparticles – magnons 45 [PITH_FULL_IMAGE:figures/full_fig_p045_4_2.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Two types of active spin torques in ferromagnets: dynamic (top panel; schemati￾cally shows a variant of the volume effect in a ferromagnetic metal, M precesses counterclockwise), and current-induced (bottom panel). Blue arrows represent the spins of lattice ions, blue arrows – the spins of conduction electrons, curved arrows – mutual torques acting between them. regime has a distinguished, “exactly integ… view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Passive spin torques in ferromagnets: spin current-induced torque (5.3) (also called the Spin Transfer Torque, STT) (top panel), and induced by diffusion of the near-surface spin density (5.4) (bottom panel). js = Is/S, this moment is inversely proportional to the sample thickness d: Ttransfer ∝ S/V ∝ 1/d. The spin torque (5.4) describes the contribution from the diffusion of the nonequilibrium spin dens… view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: The elementary process underlying spin pumping: spin-flip of an electron (sz = +~/2 → sz = −~/2) with the annihilation of a magnon of uniform magnetization dynamics with spin sz = −~. In this process, only spin is transferred from the electron to the magnetic structure (the linear momentum is transferred to the lattice). Let us consider in more detail the inverse effect of spin pumping – the spin-transfe… view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: The spin pumping three-layer system as viewed in mesoscopic scattering theory. Ferromagnetic scatterer (blue) with dynamically varying magnetization m pumps pure spin currents IsL, IsR into adjacent diffuse normal metal reservoirs N (gray) through ballistic contacts. The scatterer contains the ferromagnet FM (light blue area in the center), as well as areas near the interfaces (dark blue area) of the ord… view at source ↗
Figure 7.1
Figure 7.1. Figure 7.1: The combination of the direct (SHE) and inverse (ISHE) Spin Hall Effects leads to a decrease in the sample resistance by a value δR ∝ −γ 2 . The spin density P ∝ ±γ is accumulated in stripes of width √ Dτs at the opposite edges of the sample. spin density at the sample boundaries by a magnetic field. In a sufficiently strong magnetic field (such that Ω & τ −1 s , H ∼ 5T) [S26], the electron spin precesse… view at source ↗
Figure 8.1
Figure 8.1. Figure 8.1: Equilibrium configurations of light-axis AFM. The light axis and the external magnetic field H0 are directed vertically; the field strength increases from left to right. As a second step towards understanding the spin torques in AFM, we should briefly consider antiferromagnetic resonance (AFMR) and spin waves 77 [PITH_FULL_IMAGE:figures/full_fig_p077_8_1.png] view at source ↗
Figure 8.2
Figure 8.2. Figure 8.2: Two oscillation modes of a light-axis AFM in a configuration depicted in the left panel of Fig.8.1. All vectors representing the order parameters are assumed to be unitary for clarity: m1 and m2 represent sublattice magnetizations, m and n represent the magnetization and the Neel vector of AFM, respectively. in AFM, since these are the type of excitations the spin torques can induce in AFMs, and, convers… view at source ↗
read the original abstract

In this series of lectures, we discuss the basic theoretical concepts of magnonics and spintronics. We first briefly recall the relevant topics from quantum mechanics, electrodynamics of continuous media, and basic theory of magnetism. We then discuss the classical theory of magnetic dynamics: ferromagnetic and antiferromagnetic resonance, dynamic susceptibilities, and spin waves. We open the main discussion with phenomena of spin and exchange spin currents, spin torques, the spin Hall effect, and the spin Hall and Hanle magnetoresistance. Special emphasis is given to the effects of spin transfer torque and spin pumping, where we follow the celebrated derivation utilizing Landauer quantum multi-channel scattering matrix approach. Finally, we outline the most important features distinguishing antiferromagnetic dynamics from ferromagnetic one, which make antiferromagnets particularly promising material candidates for spintronics and magnonics.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 0 minor

Summary. The manuscript consists of lecture notes reviewing established theoretical concepts in magnonics and spintronics. It recalls background material from quantum mechanics, electrodynamics of continuous media, and basic magnetism; covers classical magnetic dynamics including ferromagnetic and antiferromagnetic resonance, dynamic susceptibilities, and spin waves; discusses spin and exchange spin currents, spin torques, the spin Hall effect, and spin Hall/Hanle magnetoresistance; provides a detailed presentation of spin transfer torque and spin pumping via the Landauer quantum multi-channel scattering matrix approach; and outlines distinguishing features of antiferromagnetic versus ferromagnetic dynamics that make antiferromagnets promising for applications.

Significance. If the presentations and derivations remain accurate, the notes constitute a useful pedagogical resource that consolidates standard material with emphasis on the Landauer-based treatment of spin transfer torque and spin pumping, plus the practical distinctions of antiferromagnets. Such structured lecture material can aid training of students and researchers entering the field.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the lecture notes and for recommending acceptance. The report accurately captures the scope and pedagogical intent of the manuscript.

Circularity Check

0 steps flagged

No significant circularity; pedagogical review of standard results

full rationale

The document is lecture notes that recall background material and follow the established Landauer multi-channel scattering-matrix derivation for spin-transfer torque and spin pumping (explicitly described as the 'celebrated derivation' from prior literature). No new first-principles derivation, fitted parameter, or uniqueness claim is advanced whose validity reduces to the paper's own inputs or self-citations. All load-bearing steps are external standard results; the paper is self-contained against external benchmarks and therefore receives score 0.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

As a review of established physics, the content relies on standard axioms and parameters from quantum mechanics and magnetism theory without introducing new free parameters, ad hoc axioms, or invented entities.

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Works this paper leans on

59 extracted references · 59 canonical work pages · 2 internal anchors

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