Journal Club for January 2025: Interplay of Mechanics with Quantum Mechanics in Materials for Quantum Technologies

Interplay of Mechanics with Quantum Mechanics in Materials for Quantum Technologies

Swarnava Ghosh* and Tanvir Sohail

National Center for Computational Sciences

Oak Ridge National Laboratory, Oak Ridge, United States.

 *email: ghoshs@ornl.gov

Introduction

In recent years, there has been flourishing research on quantum and spintronic materials. This undertaking is primarily driven by interest and excitement of utilizing exotic phenomena in these materials for novel future generation quantum technologies. Although promising, yet success has been partial. This is because a comprehensive understanding of these materials beyond the perfect crystalline unit cell is often lacking. This makes correlating theoretical predictions with observations in experimentally synthesized materials difficult. In particular the role of defects and strain in these materials and their manifestation on the quantum phenomena is not well understood. From a theoretical point of view, this understanding is primarily limited by methods that can accurately capture the quantum phenomena at small length/time scale which are very computationally expensive and linking them with meso or higher -scale methods for device scale simulations. This brief blog post aims to discuss some of the recent and ongoing work and some of the opportunities and challenges in this field of research. 

Magnetic Topological Insulators

Topological insulators (TI) are a new class of materials which conduct electricity on the surface but act as insulators on the interior. They have bulk gaps but metallic surface/ edge states with linear dispersion protected by the time reversal symmetry (TRS). opens up new possibilities in condensed matter physics. It allows researchers to explore a wide range of new phenomena, such as the existence of robust, protected edge states that remain insensitive to perturbations. This has also paved the way for the development of innovative electronic devices that promise to be more efficient and versatile than traditional technologies.  Research has focussed on exploring the combination of magnetism and topology through techniques such as doping and capping, leading to the creation of a range of fascinating new states with exotic properties. See Figure 1. 

Figure 1: Some future perspectives on magnetic topological insulators [1]. Heterostructure and defect engineering can be used to realize exotic quantum phenomena serving the potential for developing next generation electronics.

Magnetic topological insulators (MTI) are compounds where some of the atoms have an intrinsic magnetic moment. MnBi2Te4 (MBT) is the first synthesized intrinsic magnetic Topological Insulator. This is because Mn is magnetic, and the ground state is anti-ferromagnetic. Magnetic TIs are important from a technological point of view such as quantum computing. We refer the reader to Ref [1] for an understanding of the field of magnetic topological insulators.

Figure 2: a) shows the crystal structure of MnBi2Te4. b) and c) show the presence and random distribution of Mn-Sb antisite defects in both MnSb2Te4 crystals from STEM and STM. a) taken from Ref [5] and b) and c) taken from Ref [3].

The MBT class of materials exhibit remarkable properties such as quantum anomalous Hall effect (QAHE), the quantized magnetoelectric effect, and can be used in fields such as spintronics and quantum computing. MBT is a van der Waals material that consists of septuple layers (SLs) which are arranged as Te-Bi-Te-Mn-Te-Bi-Te (See Figure 2a).  A large magnetization in MBT is due to the magnetic order of Mn atoms. The magnetic properties of MBT vary depending on the layer number, with even-numbered layers exhibiting antiferromagnetism and odd-numbered layers showing ferromagnetism. These magnetizations are affected by external factors such as temperature and strain and defects. See Figure 2b.

In this post, we discuss the strain-dependent magnetic properties of MBT. Strain variation from the ideal structure can significantly affect the magnetic properties, as previous studies have shown that strain can alter the magnetic phase transitions and enhance the magnetic moments of materials. By understanding the effects of strain on magnetism, we can better understand the critical behavior resulting from the correlation between structure (strain) and magnetism. 

Figure 3: a) shows the different magnetic configurations for MnBi2Te4. The magnetic moments are on the Mn atom. b) shows the differences in energy between the ferromagnetic states and the different antiferromagnetic states for various cases of Hubbard U parameter. c) shows the magnetic moment on the Mn atom for different choices of U parameter. d) and e) shows the magnetic phase diagram for different cases of strain. All figures taken from Ref [2]

Figure 3a shows the magnetic configurations of the MBT septuple layer. In total four magnetic configurations are chosen. First is Ferromagnetic (FM) ordering where all the magnetic moments on the Mn atom points in the same direction. The next are the antiferromagnetic type (AFM) ordering where the magnetic moments on Mn atoms are oriented along opposite directions, resulting in net zero magnetization. In the case of MBT, there are three possible AFM configurations as shown in Figure 3b. Strain and defects can switch the magnetic configurations in these materials. We use first-principles calculations to calculate these effects. As these materials exhibit strong electronic correlation, Density Functional Theory (DFT) is not accurate in simulating these materials. However Hubard correction can be added to DFT to predict properties of correlated systems with increased accuracy. This is also known as DFT+U formalism in literature, and setting U=0 recovers the DFT value. As seen from Figure 3, the value of U chosen strongly influences the calculated magnetic moments and energy differences between the different magnetic states. Furthermore, the optimal value of U can change with strain itself.

Figure 3 also shows the effect of strain on the magnetic phase diagram in MBT for U=3eV and U optimized for strain. The optimization is done using Diffusion Monte Carlo simulations (a more accurate but expensive method than DFT for correlated systems, see Reference [2] for details of the computation). We see that strain can strongly influence the magnetic ground state in these materials and can switch the magnetic state from FM to AFM. Furthermore, the optimized U with strain is more accurate in estimating the magnetic ground state. We refer the reader to Reference [2] for more details.

Magnetic Skyrmions

Magnetic skyrmions are chiral spin structures showing a whirling configuration of spins. This is shown in Figure 4. Skyrmions are observed in certain magnetic materials such as B20 compounds, magnetic thin films. Skyrmions have a unique, stable spin configuration that can be manipulated with much less energy than conventional magnetic domain walls. This makes them attractive for potential applications in spintronic devices (devices which are based on transfer of spins rather than electronic charge) and magnetic data storage. There are different types of skyrmions. The main types are 1) Bloch type skyrmion where the magnetic spins point in a circular fashion in the plane of the material. These are found in 3D materials such as B20 helimagnets 2) Neel-type skyrmions where the magnetic spins point in a circular fashion around the core but out of the plane of the material. These are observed in magnetic multilayers. 3) Antiskyrmions, similar to skyrmions but with opposite topological charge. Figure 3 shows the different types of skyrmions. We refer the reader to Refs [3,4] for an overview of the field. 

Figure 4: Magnetic spin textures for three different types of skyrmions. Adapted from Ref [6]. 

The primary mechanism by which skyrmions are stable is due to asymmetric magnetic exchange interactions from non-collinear magnetism. This is also known as Dzyaloshinskii-Moria interaction (DMI). Figure 5 schematically shows the DMI interaction for a multilayer. The materials hosting skyrmions also have defects present. The concentration of defects is low; few parts per million for vacancies to few percent for dopants few lines per cm2 for dislocations. Defects and strain not only interact with the motion of skyrmions but can also alter its geometry as shown in Fig. 5. These can in turn affect the motion and stability of skyrmions. A clear understanding of the interaction of skyrmions with defects is an open problem.

Figure 5: a) shows spin orientations in a magnetic skyrmion. b) Schematic of the Dzyaloshinskii–Moriya Interaction (DMI) at the interface between a ferromagnetic metal (grey) and a metal with strong spin orbit coupling (SOC) (blue). The DMI vector D12 is related to the triangle formed by two magnetic sites in the ferromagnetic layer and an atom with large SOC in the metal layer. The direction of DMI is perpendicular to the plane of the triangle. c) Micromagnetic simulations of current driven skyrmion motion on a track. A promising candidate for future spintronic storage or logic device. d) Lattice strain and defects can have a profound effect on the static and dynamic properties of skyrmions. As shown, skyrmions can be deformed by strain. a) b) & c) adapted from [4].  

Opportunities and Challenges

Accurate physics based muli-scale modeling is largely open, particularly for magnetic quantum materials and spintronic materials where a comprehensive understanding of the changes in transport of spin and spin structures due to changes in magnetic interactions and energy landscape from perturbations caused by strain, defects and disorder remain yet unexplored.

Furthermore, first principles informed comprehensive phenomenological models of these materials that account for strain, defects and disorder does not exist. Though spin dynamics, phase-field and micromagnetic simulations of magnetic spin structures have been pursued, accurate Density Functional Theory (DFT) informed atomistic spin dynamics, meso-scale micromagnetic and phase-field simulations incorporating the effects of strain, disorder and defects have not been undertaken.

References

1. Tokura, Yoshinori, Kenji Yasuda, and Atsushi Tsukazaki. "Magnetic topological insulators." Nature Reviews Physics 1, no. 2 (2019): 126-143.

2. Ghosh, Swarnava, Jeonghwan Ann, Seoung-Hun Kang, Dameul Jeong, Markus Eisenbach, Young-Kyun Kwon, Fernando A. Reboredo, Jaron T. Krogel, and Mina Yoon. "Optimizing Density Functional Theory for Strain-Dependent Magnetic Properties of MnBi2Te4 with Diffusion Monte Carlo." arXiv preprint arXiv:2408.03248 (2024).

3. Liu, Yaohua, Lin-Lin Wang, Qiang Zheng, Zengle Huang, Xiaoping Wang, Miaofang Chi, Yan Wu et al. "Site mixing for engineering magnetic topological insulators." Physical Review X 11, no. 2 (2021): 021033.

4. Fert, Albert, Vincent Cros, and Joao Sampaio. "Skyrmions on the track." Nature nanotechnology 8, no. 3 (2013): 152-156.

5. Du, Mao‐Hua, Jiaqiang Yan, Valentino R. Cooper, and Markus Eisenbach. "Tuning Fermi levels in intrinsic antiferromagnetic topological insulators MnBi2Te4 and MnBi4Te7 by defect engineering and chemical doping." Advanced Functional Materials 31, no. 3 (2021): 2006516.

6. Criado, Juan C., Sebastian Schenk, Michael Spannowsky, Peter D. Hatton, and L. A. Turnbull. "Simulating anti-skyrmions on a lattice." Scientific Reports 12, no. 1 (2022): 19179.

   Acknowledgements

   This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725.