Evolution of magnetism in topological insulators
Date
2024-08
Authors
Islam, Farhan
Major Professor
Advisor
Vaknin, David
McQueeney, Robert J
Furukawa, Yuji
Kerton, Charles
Zhou, Lin
Committee Member
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Abstract
Topological insulators (TIs) are at the forefront of condensed matter physics due to their unique surface properties, where the surface is conducting while the bulk remains insulating. Introducing magnetism into these materials can lead to novel quantum mechanical phenomena, such as the quantum anomalous Hall effect or axion insulator states, depending on the magnetic ordering. Controlling the magnetic order in TIs is thus a compelling challenge in this field. Typically, transforming a TI into a magnetic TI involves doping or intercalating the material with magnetic elements. However, the role of magnetic defects in these materials is not well understood, primarily due to the random and sparse distribution of magnetic elements in doped systems. Even in magnetic TIs with intercalated magnetic layers, site-mixing can result in a random and sparse distribution of magnetic atoms in certain regions.
In this research, we explore the magnetic interactions that govern magnetic order in such systems by studying dilute magnetic TIs, where the magnetic atoms are randomly and sparsely distributed. We synthesize three different magnetic TIs: 3% Mn-doped Sb₂Te₃, 5% Mn-doped SnTe, and 10% Mn-doped SnTe. Using state-of-the-art inelastic neutron scattering (INS) techniques, we investigate the magnetic interactions relevant to this class of materials.
The 3% Mn-doped Sb₂Te₃ is on the verge of becoming ferromagnetically (FM) ordered. However, our INS experiments confirm that the strongest magnetic interaction within the system is an antiferromagnetic (AFM) superexchange via Mn-Te-Mn linear bonds, an identical configuration to that found in Mn-substituted Sb₂Te₃. Spectral and structure factor evidence show that this strong AFM interaction forms AFM Mn-Te-Mn dimer singlets with an interaction energy scale of approximately 0.67 meV. We also find short-range FM correlations in the adjacent quintuple layers across the van der Waals (vdW) gap. Additionally, we observe nascent evidence of ferromagnetic interaction via a linear chain of Mn-Te-Te-Mn bonds across the vdW gap. Our first-principles calculations using density functional theory (DFT) agree with our experimental results. Moreover, the calculations predict that Mn pairs residing both within the layer and across the vdW gap have FM exchange interactions, while those within the block have AFM exchange interactions. Our findings can be extended to rationalize the magnetic behavior of stoichiometric magnetic TI MnSb₂Te₄ or MnBi₂Te₄. Site-mixing in these materials transforms the system into [(Mn₁₋₂ₓSb₂ₓ)Te][(Sb₁₋ₓMnₓ)₂Te₃] or [(Mn₁₋₂ₓBi₂ₓ)Te]Te[(Bi₁₋ₓMnₓ)₂Te₃], establishing common interactions due to the [(Sb₁₋ₓMnₓ)₂Te₃] block. It has been demonstrated that there is an AFM to FM transition in [(Mn₁₋₂ₓSb₂ₓ)Te][(Sb₁₋ₓMnₓ)₂Te₃] when x > 0.13. Our findings in this research provide a mechanism that rationalizes this transition.
The 5% Mn-doped SnTe displays short-range FM correlations, while the 10% concentration exhibits long-range FM order with a Curie temperature of ≈12 K. The mechanism by which the system transitions to having magnetic order at higher concentrations is not well understood. INS measurements reveal that the strongest interaction in both of these materials is the next-nearest-neighbor (NNN) AFM interaction mediated by Mn-Te-Mn linear bonds. Spectral and structure factor evidence show that this strong AFM interaction forms AFM Mn-Te-Mn dimer singlets with an energy scale of approximately 0.5 meV. While the spectra show evidence of a sharp S = 0 → 1 transition at around 0.5 meV for the 5% concentration, it is broadened for the 10% concentration due to the internal ferromagnetism that exerts an average molecular field, Zeeman-splitting the AFM dimer's energy levels. These dimers are localized and magnetically inactive, and do not contribute to the development of long-range FM order. Our analysis also reveals the presence of NN FM interactions, possibly due to the 90° bond configuration of Mn-Te-Mn, and 8th NN AFM interactions connected via a linear Mn-Te-Sn-Te-Mn bond. However, the inclusion of these interactions, along with the NNN AFM interaction, does not explain the emergence of long-range FM order at higher concentrations. We demonstrate that the 7th nearest-neighbor (NN) FM interaction is crucial for the development of long-range FM order due to its high coordination number of 48. This high number of atoms in its coordination shell allows the 7th NN interaction to percolate long-range FM order even when its interaction strength is weaker than the AFM interaction. Using these interactions, we simulate the magnetic system with atomistic spin dynamics, achieving results that agree with a wide range of experimental data, including the transition from FM correlation to long-range FM order at higher concentrations, the transition temperature for long-range FM order, and the spectroscopic data and their associated structure factors.
Our findings are broadly applicable to a large class of materials, providing a comprehensive framework for understanding and controlling magnetic behavior in topological insulators and similar systems. The insights gained from studying dilute magnetic TIs can be extended to various phenomena in quantum materials. For instance, magnetic defects and impurities play critical roles in a range of effects from the Kondo effect to superconducting pair-breaking, dilute magnetic semiconductors, and even entangled qubits. By understanding the magnetic interactions and the influence of defects in these systems, one may unlock new quantum states of matter and enhance the functionalities of these advanced materials. Thus, our research not only sheds light on the specific mechanisms in TIs but also paves the way for broader applications in the field of quantum materials.
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dissertation