Entropy-driven phase transition in a non-collinear antiferromagnet due to higher-order exchange interactions

Abstract: The triple-Q state arises due to the superposition of three symmetry equivalent spin spirals stabilized by higher-order exchange interactions. It has been predicted more than 20 years ago but was only recently discovered in a Mn monolayer on the Re(0001) surface. To date little is known about the thermodynamic properties of this intriguing non-coplanar spin state. Here, we reveal a low-temperature phase transition between the triple-Q and the row-wise antiferromagnetic state in this system via Monte Carlo simulations based on an atomistic spin model parametrized by density functional theory. By modeling the free energy landscape in terms of thermal excitations we derive an analytical expression of the partition function, which allows us to prove that the phase transition is driven by entropy. The predicted phase transition is not unique to Mn/Re(0001) but appears for a wide range of magnetic interaction parameters and is expected to occur also for other multi-Q states.

• The paper finds that the entropy-driven phase transition between triple-Q and RW-AFM states is induced by higher-order exchange interactions.
• The authors employ Monte Carlo simulations backed by DFT-based parameters to model and analyze the free energy landscape.
• The study demonstrates that entropic effects favor the RW-AFM state above 32.7 K, emphasizing the role of thermal excitations in ultra-thin antiferromagnets.

Entropy-Driven Phase Transition in Non-Collinear Antiferromagnets

Introduction

This paper explores the emergence of a phase transition in non-collinear antiferromagnets driven by entropy, focusing on the triple-Q (3Q) state in a Mn monolayer on a Re(0001) surface. Utilizing Monte Carlo (MC) simulations based on an atomistic spin model parameterized by density functional theory (DFT), the study identifies a low-temperature phase transition between the 3Q state and the row-wise antiferromagnetic (RW-AFM) state. The authors model the free energy landscape using thermal excitations to derive an analytical expression for the partition function, proving that the phase transition is prominently driven by entropy.

Atomistic Spin Model

Addressing the 3Q state emergence requires incorporating higher-order exchange interactions (HOI) beyond the standard Heisenberg model. These HOIs, although typically smaller than pair-wise exchanges, significantly alter the magnetic ground state by breaking degeneracies between single-Q and multi-Q states. A classical extended Heisenberg Hamiltonian models the system:

$$H = -\sum_{i,j}J_{ij}(m_i \cdot m_j) - \sum_i K_i(n \cdot m_i)^2 - ... \sum_{i,j,k,l}F_{ijkl}(m_i \cdot m_j)(m_k \cdot m_l) ...$$

The parameters are derived from previous DFT calculations for a Mn monolayer on a Re(0001) surface, neglecting minor contributions from dipole-dipole interactions and the Dzyaloshinskii-Moriya interaction.

Monte Carlo Simulations and Observations

Monte Carlo simulations reveal both the triple-Q state and RW-AFM state as significant configurations.

Figure 1: Representations of RW-AFM and 3Q state in real and reciprocal space, demonstrating distinct components in their spin-structure factor.

Figure 2: Phase transition from the 3Q to the RW-AFM state, indicating shifts in temperature dependence and SSF prominence.

Figure 3: Energy landscape around the 3Q and the RW-AFM state, highlighting Hessian eigenmodes around local minima and stationary points.

With DFT parameters, simulations showcase the 3Q state at low temperatures transitioning to an RW-AFM state at higher temperatures, underscoring HOI's influence on free energy configurations.

Analytical Approaches: Partition Function and Free Energy

The framework extends traditional harmonic approximations to include unstable Hessian eigenmodes, enabling calculation of partition functions and state functions like free energy, entropy, and internal energy.

Figure 4: Thermodynamic state functions across the phase transition, with entropy differences calculated between states.

For low temperatures, the free energy of the 3Q state is lower, but at $T_c=32.7$ K, the RW-AFM gains favor due to entropic advantages, manifesting as a temperature-driven transition.

Phase Diagrams and Variability

Phase stability checks across various magnetic interaction parameters corroborate the transition's robustness.

Figure 5: Phase diagrams show SSF variations with magnetic interaction strengths, confirming robust phase boundaries.

MAE and four-spin interactions notably shift transition temperatures, demonstrating the delicate balance of entropic and energetic factors.

Conclusion

The paper confirms the role of entropy in governing phase transitions between 3Q and RW-AFM states via HOI, with far-reaching implications for understanding the thermodynamics of ultra-thin antiferromagnetic films. The extended harmonic approach proves valuable, potentially aiding the design of new materials with targeted magnetic properties. Future exploration could address structural factors affecting state energy discrepancies, enhancing predictive accuracy in experimental contexts.