Tight-binding theory of spin-spin interactions, Curie temperatures, and quantum Hall effects in topological (Hg,Cr)Te in comparison to non-topological (Zn,Cr)Te, and (Ga,Mn)N

Abstract

Earlier theoretical results on $p$-$d$ and $d$-$d$ exchange interactions for zinc-blende semiconductors with ${\mathrm{Cr}}^{2+}$ and ${\mathrm{Mn}}^{3+}$ ions are revisited and extended by including contributions beyond the dominating ferromagnetic (FM) superexchange term [i.e., the interband Bloembergen-Rowland-Van Vleck contribution and antiferromagnetic (AFM) two-electron term], and applied to topological Cr-doped HgTe and non-topological (Zn,Cr)Te and (Ga,Mn)N in zinc-blende and wurtzite crystallographic structures. From the obtained values of the $d$-$d$ exchange integrals $J_{ij}$, and by combining the Monte-Carlo simulations with the percolation theory for randomly distributed magnetic ions, we determine magnitudes of Curie temperatures $T_{\text{C}}(x)$ for ${\mathrm{Zn}}_{1-x}{\mathrm{Cr}}_x\mathrm{Te}$ and ${\mathrm{Ga}}_{1-x}{\mathrm{Mn}}_x\mathrm{N}$ and compare to available experimental data. Furthermore, we find that competition between FM and AFM $d$-$d$ interactions can lead to a spin-glass phase in the case of ${\mathrm{Hg}}_{1-x}{\mathrm{Cr}}_x\mathrm{Te}$. This competition, along with a relatively large magnitude of the AF $p$-$d$ exchange energy $N_0\beta$ can stabilize the quantum spin Hall effect, but may require the application of tilted magnetic field to observe the quantum anomalous Hall effect in HgTe quantum wells doped with Cr, as confirmed by the Chern number determination.

arXiv comment19 pages, 11 figures

References in corpus (38)

• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Hole-mediated ferromagnetism in tetrahedrally coordinated semiconductors
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Dilute ferromagnetic semiconductors: Physics and spintronic structures
• Quantum Anomalous Hall Effect in Hg${}_{1-y}$Mn${}_y$Te Quantum Wells
• Colloquium: Quantum anomalous Hall effect
• Progress and prospects in magnetic topological materials
• Origin and control of high-temperature ferromagnetism in semiconductors
• Band structure of semimagnetic Hg1-yMnyTe quantum wells
• Spin-dependent phenomena and device concepts explored in (Ga,Mn)As
• Conductance of a helical edge liquid coupled to a magnetic impurity
• Quantum anomalous Hall effect driven by magnetic proximity coupling in all-telluride based heterostructure
• Part-per-million quantization and current-induced breakdown of the quantum anomalous Hall effect
• Realistic Tight Binding Model for the Electronic Structure of II-VI Semiconductors
• Hole states in wide band-gap diluted magnetic semiconductors and oxides
• Modifications and Extensions to Harrison's Tight-Binding Theory
• Zero-field quantum anomalous Hall metrology as a step towards a universal quantum standard unit system
• Experimental probing of exchange interactions between localized spins in the dilute magnetic insulator (Ga,Mn)N
• High-energy spectroscopic study of the III-V nitride-based diluted magnetic semiconductor Ga${}_{1-x}$Mn${}_x$N
• Phase diagram and critical behavior of the random ferromagnet $G{a}_{1-x}M{n}_{x}N$
• Origin of low-temperature magnetic ordering in Ga1-xMnxN
• Magnetic properties of GaMnAS from an effective Heisenberg Hamiltonian
• Stretching magnetism with an electric field in a nitride semiconductor
• Quantum anomalous Hall edge channels survive up to the Curie temperature
• Emergent quantum Hall effects below $50$ mT in a two-dimensional topological insulator
• Optical investigation of electronic states of Mn4+ ions in p-type GaN
• Electron-hole contribution to the apparent s-d exchange interaction in III-V diluted magnetic semiconductors
• The influence of electrostatic potentials on the apparent s-d exchange energy in III-V diluted magnetic semiconductors
• Momentum-resolved spin splitting in Mn-doped trivial CdTe and topological HgTe semiconductors
• Effects of s,p - d and s - p exchange interactions probed by exciton magnetospectroscopy in (Ga,Mn)N
• Effects of charge dopants in quantum spin Hall materials
• Superexchange dominates in magnetic topological insulators
• Theory of ferromagnetism driven by superexchange in dilute magnetic semiconductors
• Ubiquitous impact of localised impurity states on the exchange coupling mechanism in magnetic topological insulators
• Quantitative theory of backscattering in topological HgTe and (Hg,Mn)Te quantum wells: acceptor states, Kondo effect, precessional dephasing, and bound magnetic polaron
• CdTe and HgTe doped with V, Cr, and Mn -- prospects for the quantum anomalous Hall effect
• Thermodynamic perturbation theory for non-interacting quantum particles with application to spin-spin interactions in solids

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• Role of magnetic doping in topological HgTe and application of the Gram-Schmidt method for computing impurity states in quantum wells