Thickness-Dependent Magnon Spin Transport

• Thickness-dependent magnon spin transport is the modulation of angular momentum transfer via spin waves in magnetic films as thickness varies, affecting dimensional regimes.
• Adjustments in film thickness impact magnon diffusion lengths, scattering rates, and density of states, with enhanced transport in quasi-2D systems and suppression in ultrathin layers.
• These thickness effects underlie advanced spintronic and caloritronic device operations by enabling tunable spin propagation and thermal management at the nanoscale.

Thickness-dependent magnon spin transport describes how the propagation, relaxation, and conversion of magnonic spin currents—the transfer of angular momentum via quantized spin-wave excitations—are fundamentally altered as the thickness of magnetic films or multilayers is varied, especially as systems transition between three-dimensional (3D), quasi-3D, and two-dimensional (2D) regimes. In both ferromagnetic and antiferromagnetic insulators, control over layer thickness modulates magnon mean free paths, density of states, interfacial scattering, and dimensionality, resulting in profound changes in spin propagation length and efficiency. These effects underpin the operation of a broad class of spintronic and spin-caloritronic devices, and understanding their thickness dependence is pivotal as materials and devices reach the nanoscale limit.

1. Magnon Spin Transport and Diffusive Regimes

Magnon spin transport arises from the creation and propagation of non-equilibrium magnon populations, which can be injected electrically (e.g., via the spin Hall effect) or thermally (via the spin Seebeck effect, SSE). The diffusive transport of magnons in a film of thickness $d$ is governed by the interplay between the magnon spin diffusion length $\lambda_s$ and the energy relaxation length $\lambda_T$, which dictate how far magnons and their associated spin or energy imbalances propagate before being relaxed by scattering.

The prevailing transport regime is set by the relative magnitude of $d$ compared to $\lambda_s$ and $\lambda_T$:

• For $d \gg \lambda_s$, magnon propagation saturates—the magnon spin current is limited by internal relaxation rather than thickness.
• For $d \sim \lambda_s$ or $d \sim \lambda_T$, the observable spin current or thermal signal exhibits non-trivial dependence, often showing peaks or crossovers as distinct transport channels dominate.
• For $d \ll \lambda_s$, transport is ballistic or quasi-ballistic, and finite-size and interfacial effects become dominant.

The magnon density of states (DOS) also undergoes a qualitative crossover: in thick films, it mirrors the 3D bulk, but in ultrathin films, it reduces to a 2D DOS, strongly influencing the phase space for scattering and thereby the magnon diffusion length (Myhre et al., 4 Sep 2025, Wei et al., 2021).

2. Impact of Thickness on Magnon Diffusion Length

As magnetic film thickness is reduced, several key behaviors emerge:

• Quasi-3D to Quasi-2D Crossover: Simulations in prototypical antiferromagnetic insulators (AFIs) such as hematite reveal a sharp enhancement of the magnon diffusion length at a critical thickness, dictated by the magnon excitation energy and the effective dimensionality. Below this crossover, the effective scattering phase space contracts, and $\lambda_s$ can increase up to ~4x compared to the bulk (see Fig. 1 in (Myhre et al., 4 Sep 2025)). This phenomenon appears in both the easy-axis and easy-plane magnetic phases and is governed by the DOS transition: $g^{AF}_2(E) \propto |E|$ (2D) versus $g^{AF}_3(E) \propto |E|\sqrt{E^2-E_0^2}$ (3D).
• Ultrathin Film Enhancement: In yttrium iron garnet (YIG) thin films, when the thickness approaches a few nm (at or below the magnon thermal wavelength), only a few perpendicular standing spin wave modes are occupied, leading to a giant increase in the magnon spin conductivity $\sigma_m$; in the strict 2D limit, $\sigma_m\approx 1$ S at room temperature (Wei et al., 2021). Such enhancement arises because the lowest subband dominates the transport, and the phase space for scattering collapses, prolonging the mean free path.
• Suppression by Surface and Defect Scattering: Conversely, in atomically thin van der Waals antiferromagnets such as MnPS$_3$, decreasing thickness leads to strong suppression of the magnon diffusion length due to the increase in surface-to-volume ratio, which amplifies impurity and surface-defect scattering (Xing et al., 2019). In ultrathin antiferromagnetic Cr$_2$O$_3$ films, disorder from point defects—especially oxygen vacancies—inhibits magnon propagation for $d > 3$ nm, with $\lambda_m$ shrinking to a few nm (Keagy et al., 26 May 2025).
• Exponential and Non-monotonic Scaling: For magnetic multilayers or NM/FM/NM structures, the spin signal decays exponentially with the spacer or AFI thickness, characterized by a material and temperature-dependent $\lambda_s$ (Baldrati et al., 2018). In YIG and similar systems, the thickness dependence of the SSE or magnon Peltier effect may be fitted phenomenologically as $V_{\mathrm{SSE}} \propto 1-\exp(-L/2\lambda)$ for diffusion-limited propagation (Guo et al., 2015), but often requires a more sophisticated Boltzmann or drift-diffusion approach to capture boundary and interface conditions (Daimon et al., 2019, Prakash et al., 2017).

3. Role of Interfacial, Structural, and Defect Effects

Interface and defect engineering critically affect the thickness dependence of magnon spin transport:

• Interface/Free Surface Electronic States: In metallic ferromagnets such as Co$_2$FeAl (CFA), thinner films show enhanced contribution from interface or surface states, which increase electron and magnon scattering, shorten magnon mean free paths, and modify spin-dependent resistivities (Wang et al., 2012).
• Disorder-Induced Suppression: In AFI films, even minor deviations from ideal stoichiometry (e.g., oxygen vacancies in Cr$_2$O$_3$) act as strong scattering centers for magnons, truncating spin current propagation to a characteristic attenuation length that may be only a few nm (Keagy et al., 26 May 2025). This introduces a thickness threshold, above which magnon spin transport is suppressed due to disorder, independent of nominal crystallinity or homoepitaxy.
• Spin Mixing Conductance and Magnon Transmission: The transparency and spin mixing conductance at the FM|NM or AFI|NM interface govern the frequency-dependent transmission of magnon spin current. The spin Seebeck signal's peak temperature and amplitude are highly sensitive to interfacial scattering, and the ability of low-energy magnons to traverse the interface (Guo et al., 2015).

4. Theoretical Frameworks and Modeling Approaches

The quantitative description of thickness-dependent magnon spin transport relies on several foundational models:

• Drift-Diffusion and Boltzmann Models: Magnon transport is often described by coupled diffusion equations for magnon spin and energy densities, incorporating relaxation rates due to magnon-magnon, magnon-phonon, and non-magnon-conserving (e.g., Gilbert damping) processes. Typical forms are

$$\frac{\partial^2 n_m}{\partial x^2} = \frac{n_m}{\lambda_m^2}$$

and related continuity equations for magnetothermal currents (Prakash et al., 2017, Troncoso et al., 2019).

• Density of States-Driven Crossovers: The dimensional crossover is characterized by comparing critical energies $|E_c| = \sqrt{\pi^2 L_z^2 C^2 A |A_h| + E_0^2}$ (Myhre et al., 4 Sep 2025). DOS reduction in the quasi-2D regime reduces magnon-magnon scattering, enhancing $\lambda_m$; this is manifest in both stochastic micromagnetic simulations and direct experiment.
• Suppression Functions and MFP Distributions: The longitudinal SSE in thin YIG films can be modeled via suppression functions $S(x)$, following the Fuchs–Sondheimer or exponential forms, convolved with the magnon mean free path (MFP) distribution. The full, reconstructed MFP distribution from experimental thickness scaling reveals that LSSE is contributed to by magnons with a wide spectrum of path lengths; simple single-valued models are insufficient (Chavez-Angel et al., 2016).
• Interfacial Boundary Conditions: Solutions to $\mu_m(x) = A e^{x/\lambda_m} + B e^{-x/\lambda_m}$ with appropriate boundary conditions (e.g., $\mu=0$ at spin sinks or $\partial \mu/\partial x = 0$ at insulating interfaces) are used to capture the interfacial magnon accumulation and resultant temperature drops in multilayer structures (Tang et al., 15 Oct 2024).

5. Applications and Device-Level Implications

Thickness-dependent magnon spin transport has direct consequences for the design and optimization of spintronic, spin-caloritronic, and magnetothermal nano-devices:

• Magnon Transistors and Logic Circuits: The ability to tune the diffusion length via thickness (and thereby enter the quasi-2D regime) enables low-dissipation, long-range magnon conduits, especially in AFIs and high-quality thin YIG films (Wei et al., 2021, Myhre et al., 4 Sep 2025).
• Thermal Switches and Magnetothermal Resistance (mMTR): In FM/NM multilayers, thickness controls the interfacial magnon accumulation and consequent additional thermal resistance—the mMTR effect—which can reach large ratios ($\sim 40\%$) and be used for robust, all-solid-state magnetically switchable thermal devices (Tang et al., 15 Oct 2024).
• Robust Spin Transport in Disordered Systems: Films above a defect-controlled thickness threshold ($\sim$3 nm for Cr$_2$O$_3$) will suppress long-range magnon propagation, imposing constraints for designing AFI-based devices requiring coherence over extended distances (Keagy et al., 26 May 2025).
• Topological Spin Transport: In chiral magnonic edge modes, thickness and edge geometry control the interplay between bulk and robust edge transport, especially under non-Hermitian control schemes that use sublattice-dependent spin–orbit torque to modulate damping and amplification (Gunnink et al., 10 Jan 2024).

6. Thickness-Driven Crossovers and Universalities

The crossover from 3D to quasi-2D magnon transport constitutes an emergent universal feature, with broad ramifications:

• Diffusion Length Scaling: As thickness $t$ decreases below a critical value set by the magnon excitation spectrum, diffusion lengths become dramatically enhanced due to reduced phase space for magnon–magnon and magnon–phonon scattering. This is observed in both AFI (hematite, Cr$_2$O$_3$) and FI (YIG, CFA) systems, as well as in van der Waals antiferromagnets (MnPS$_3$).
• Non-Universal Role of Scattering: While ideal, clean systems support enhanced transport in thin limits, defect or surface impurity scattering sharply suppresses the mean free path in practical ultrathin materials, creating a non-universal thickness dependence governed by extrinsic disorder.
• Dimensionality and Phase Control: The phenomenon is robust across magnetic phases (easy-axis, easy-plane), and in multi-component materials (ferrimagnets, antiferromagnets) where multiple magnon branches and polarization states contribute (Myhre et al., 4 Sep 2025, Zeng et al., 13 Jun 2024).

7. Summary Table: Thickness Dependence of Key Parameters

System Type	Thin-Film Behavior	Critical Thickness (nm)	Key Mechanism
YIG (ferromagnet)	Enhancement of $\sigma_m$, up to 2D regime	$\sim$3–5	Subband occupancy, 2D DOS
Hematite (AFI)	$\lambda_s$ up $\sim$4x in 2D regime	$\sim$20–25	DOS-driven scattering reduction
MnPS$_3$ (AFM, vdW)	$\lambda_m$ decreases with $t$	$<$10	Surface-impurity scattering
Cr$_2$O$_3$ (AFI)	Complete suppression for $t > 3$	3	Defect-limited attenuation
NiO (epitaxial)	$\lambda_{MSDL}$ typically $\sim$1–4	N/A (bulk-like films)	Interface/mode matching

Critical thickness reflects either quasi-2D crossover (enhanced transport) or disorder-limited cutoff (suppressed transport) depending on system.

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Thickness-dependent magnon spin transport is governed by a subtle interplay between intrinsic magnetic dynamics, dimensionality-induced quantum effects, boundary and interface conditions, and extrinsic disorder. Control over film thickness therefore provides an essential degree of freedom for tuning spin propagation in next-generation spintronic and caloritronic devices, with major ramifications for nanoscale thermal management, nonvolatile memory, logic architectures, and the manipulation of coherent or topological spin currents.