2020
DOI: 10.1103/physrevb.101.161403
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Chiral ferromagnetism beyond Lifshitz invariants

Abstract: We consider a contribution w ch to the micromagnetic energy density that is linear with respect to the first spatial derivatives of the magnetization direction. For a generalized 2D Rashba ferromagnet, we present a microscopic analysis of this contribution and, in particular, demonstrate that it cannot be expressed through Lifshitz invariants beyond the linear order in the spin-orbit coupling strength. Effects of terms in w ch beyond Lifshitz invariants on the phase diagram of magnetic states and spin waves di… Show more

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Cited by 26 publications
(18 citation statements)
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“…Here, the Levi-Civita symbol, αβγ , is introduced to convert the third-order DMI tensor in Lifshitz invariant presentation [65] to a second-order tensor and V M is the volume of the unit cell of the ferromagnetic film. Eq.…”
Section: Phenomenological Modelingmentioning
confidence: 99%
“…Here, the Levi-Civita symbol, αβγ , is introduced to convert the third-order DMI tensor in Lifshitz invariant presentation [65] to a second-order tensor and V M is the volume of the unit cell of the ferromagnetic film. Eq.…”
Section: Phenomenological Modelingmentioning
confidence: 99%
“…Phenomenologically, the free energy density of an inhomogeneous DM interaction can be written as [23,[43][44][45],…”
Section: Dm Interactions In Terms Of Correlation Functionsmentioning
confidence: 99%
“…In another approach, the origin of DM interactions is attributed to a Doppler shift due to an intrinsic spin current induced by SOC [20]. Several different approaches based on the Berry phase formalism and the spin-spin correlation functions have been developed recently to compute the DM interactions of realistic band structures in both FM and AFM systems in equilibrium [21][22][23][24][25]. Equilibrium DM interaction might be enhanced and even induced in magnetic thin films by breaking the inversion symmetry via, e.g., sandwiching a magnetic slab between two different layers, using proximity effects in heavy-metal (HM) and magnetic film heterostructures [26][27][28][29][30], or applying electric gate voltages and lattice strains [31][32][33].…”
Section: Introductionmentioning
confidence: 99%
“…Some of us also mentioned this in Ref. [28]. Here by n we denote the unit vector of the local magnetization direction.…”
mentioning
confidence: 93%