Magnon spin transport driven by the magnon chemical potential in a magnetic insulator (1604.03706v1)

Abstract: We develop a linear-response transport theory of diffusive spin and heat transport by magnons in magnetic insulators with metallic contacts. The magnons are described by a position dependent temperature and chemical potential that are governed by diffusion equations with characteristic relaxation lengths. Proceeding from a linearized Boltzmann equation, we derive expressions for length scales and transport coefficients. For yttrium iron garnet (YIG) at room temperature we find that long-range transport is dominated by the magnon chemical potential. We compare the model's results with recent experiments on YIG with Pt contacts [L.J. Cornelissen, et al., Nat. Phys. 11, 1022 (2015)] and extract a magnon spin conductivity of $\sigma_{m}=5\times10^{5}$ S/m. Our results for the spin Seebeck coefficient in YIG agree with published experiments. We conclude that the magnon chemical potential is an essential ingredient for energy and spin transport in magnetic insulators.

• The paper demonstrates that the magnon chemical potential drives long-range spin transport in YIG with an estimated conductivity of 5×10^5 S/m.
• The paper develops diffusion equations for spin and heat currents using a linearized Boltzmann approach, elucidating key magnons relaxation dynamics.
• The paper introduces a novel interface spin mixing conductance via finite element modeling of Pt|YIG|Pt systems, aligning theory with experimental data.

Investigating Magnon Spin Transport in Magnetic Insulators

This paper presents a comprehensive theoretical framework for analyzing diffusive spin and heat transport mediated by magnons in magnetic insulators with metallic contacts. The authors utilize a linear-response transport theory, underpinned by a linearized Boltzmann equation approach, to derive fundamental expressions governing magnon dynamics in these systems. This work is especially relevant to understanding magnon transport phenomena in yttrium iron garnet (YIG), a prominent magnetic insulator, at room temperature.

Key Contributions and Results

The paper provides several significant contributions to the field of spin caloritronics, notably the treatment of the magnon chemical potential as a driver of long-range magnon spin transport under diffusive conditions. The primary findings can be summarized as follows:

1. Magnon Spin Conductivity: The authors postulate that the magnon chemical potential significantly influences magnon spin transport. For YIG, they estimate a magnon spin conductivity of $\sigma_m = 5 \times 10^5$ S/m, derived from comparative analysis with experimental data involving Pt contacts.
2. Spin and Heat Equations: The paper articulates diffusion equations for magnon-driven spin and heat currents, highlighting relaxation times and length scales. This theoretical perspective elucidates how the magnon chemical potential plays a paramount role, especially where inelastic magnon scattering predominates over magnon-phonon interactions.
3. Interface Spin Conductance: A novel parameterization of the interface spin mixing conductance, $g_s$, is introduced, emphasizing its importance in experimental configurations such as the Pt|YIG|Pt trilayer systems. The effective conductance is determined to be a fraction of the traditional mixing conductance, signifying partial transmission of spin currents at interfaces.
4. Finite Element Modeling: The paper employs finite element methods to model the two-dimensional geometry of the Pt|YIG|Pt interface, revealing insights into the magnon chemical potential distribution and its decay, which aligns well with experimental observation for contact separations, supporting the proposed theoretical constructs.

Theoretical and Practical Implications

This work advances the understanding of magnon transport by proposing a refined notion of equilibrium states in magnetic systems under the influence of external perturbations. It challenges earlier models by asserting the relevance of non-equilibrium magnon chemical potential. The resulting theoretical findings hold significant implications for both experimental analysis and the development of spintronic devices:

• Device Engineering: For spintronic and magnonic device engineering, understanding the parameters governing magnon transport is critical for optimizing the efficiency and functionality of devices utilizing magnetic insulator interfaces.
• Future Theoretical Developments: This paper sets a foundation for future theoretical studies that might extend the linearized framework to account for external factors like temperature gradients, anisotropic materials, or interface spin resistances, to better correlate with a broader range of experimental scenarios.

Speculation on Future Developments

As interest in spin-based technologies grows, understanding the fundamental parameters influencing magnon transport becomes crucial. Future research could explore more complex materials systems or more sophisticated models accounting for quantum effects or non-linear dynamics. Furthermore, explore scaling laws in nanoscale systems or low-temperature phenomena, possibly unveiling new physics at these extremes.

In essence, this paper contributes a detailed theoretical pathway to comprehend and exploit magnon-mediated transport phenomena, catalyzing advancements in both theoretical physics and spintronic applications.