Caloric Phenomena and Stirling-Cycle Performance in Heisenberg- Kitaev Magnon Systems

Abstract

We investigate the Stirling-cycle performance of a Heisenberg--Kitaev magnonic medium with Dzyaloshinskii--Moriya (DM) interactions. Using linear spin-wave theory, we show the DM interaction preserves spectral symmetry, yielding even caloric responses and symmetric Stirling engine efficiency. In contrast, bond-dependent Kitaev exchange asymmetrically distorts the magnonic density of states, enabling distinct direct and inverse caloric effects. Consequently, Kitaev-driven cycles achieve significantly higher efficiencies than DM-driven protocols, approaching a high-performance saturation regime for negative couplings. This establishes exchange-anisotropic magnets as highly tunable platforms for nanoscale solid-state energy conversion.

Figures (12)

• Figure 1: Schematic illustration of the magnonic system defined on a hexagonal lattice. For the numerical calculations, the nanoribbon is periodic along the $x$ direction and finite along the $y$ direction. The magnetic unit cell, with nearest-neighbor distance $a_0$, is enclosed by a dashed black box, where the positions of the sites within each sublattice are identified. The corresponding nearest-neighbor vectors $\boldsymbol{\delta}_x$, $\boldsymbol{\delta}_y$, and $\boldsymbol{\delta}_z$ are highlighted. The blue and red sites denote the sublattices $\mathcal{A}$ and $\mathcal{B}$, respectively.
• Figure 2: (Color online) Magnon band structure $\varepsilon_{\bm k,n}$ for $\mathcal{N}_s=30$. (a) Fixed $K=0$ and two values of the DM interaction: $D=0.20$ (solid) and $D=0.40$ (dashed). (b) Fixed $D=0$ and two values of the Kitaev exchange: $K=0.20$ (solid) and $K=0.40$ (dashed).
• Figure 3: (Color online) Normalized magnon density of states $g(\varepsilon)$ used in the thermodynamic calculations: (a) $g(\varepsilon)$ at fixed $K=0.00$ for $D=\{0.00,\pm 0.30,\pm 0.40\}$ (positive $D$ shown with solid lines and negative $D$ with dotted lines); (b) $g(\varepsilon)$ at fixed $D=0.00$ for $K=\{0.00,\pm 0.30,\pm 0.40\}$ (positive $K$ shown with solid lines and negative $K$ with dotted lines), truncated at $\varepsilon \le 5.2$ for numerical stability near the upper band edge. In both panels the DOS is normalized to the total number of single--particle states $N_{\mathrm{states}}=2\mathcal{N}_s=60$
• Figure 4: Stirling cycle in the $S(\lambda,T)$--$T$ plane for a bosonic working medium, where the control parameter $\lambda\in\{K,D\}$ is modulated quasistatically. The vertical branches correspond to the isothermal strokes at $T_H$ and $T_L$, whereas the upper and lower curved branches correspond to the isoparametric processes at fixed $\lambda_1$ and $\lambda_2$, respectively. Red arrows denote heat absorbed by the working medium, whereas blue arrows indicate heat released to the reservoirs.
• Figure 5: Magnonic entropy $S_M(D,T)$ as a function of temperature for different values of the Dzyaloshinskii–Moriya interaction $D$, with $J = -1$ and $K = 0$.