Extreme asymmetry of N\'eel domain walls in multilayered films of the dilute magnetic semiconductor (Ga,Mn)(As,P)

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Extreme asymmetry of Néel domain walls in multilayered films of the dilute magnetic semiconductor (Ga,Mn)(As,P)

V. K. Vlasko-Vlasov, W.-K. Kwok, S. Dong, X. Liu, M. Dobrowolska, and J. K. Furdyna

Phys. Rev. B 98, 180411(R) – Published 29 November 2018

Abstract

We report on unconventional perfectly shaped, fully asymmetric $\sim 90^{\circ}$ Néel domain walls in multilayered films of the diluted ferromagnetic semiconductor (Ga,Mn)(As,P) with a stepwise variation of P doping. Our results contradict micromagnetic calculations, which favor symmetric domain walls due to crystallographic anisotropy and stray field energy. We demonstrate that both the puzzling uniaxial in-plane anisotropy in the tetragonal multilayered film and the asymmetry of the domain walls could result from Dzyaloshinskii-Moriya interactions that are enhanced by the multiple sharp interfaces between the layers and from anisotropic nonrelativistic exchange coupling. Our finding shows that digital variations of composition during the molecular beam epitaxy can be used to tune the anisotropy and chirality of magnetic multilayers.

Received 27 August 2018
Revised 29 October 2018

DOI:https://doi.org/10.1103/PhysRevB.98.180411

Physics Subject Headings (PhySH)

Dzyaloshinskii-Moriya interaction Magnetic anisotropy Magnetic coupling Magnetic domains Magnetism Magneto-optical effect

Magnetic multilayers Magnetic semiconductors

Magnetization measurements

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

V. K. Vlasko-Vlasov and W.-K. Kwok

Materials Sciences Division, Argonne National Laboratory, Argonne, Illinois 60439, USA

S. Dong, X. Liu, M. Dobrowolska, and J. K. Furdyna

Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA

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Vol. 98, Iss. 18 — 1 November 2018

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Figure 1
(a)–(c) Magneto-optical images of the nucleation and growth of domains during perpendicular remagnetization at $T = 5 K$ . The orientation of the easy axes EA1 and EA2 and the crystal axes is shown in (d). The sample has three etched $150 \times 150 μ m$ square apertures and a slit with sides parallel to [110] and $[1 \bar{1} 0]$ (white lines). The yellow lines indicate scratches in the sample. The sample is initially polarized into a monodomain state (not shown) with $M_{1} | | - E A 1$ (black arrow) by application of $H = 1 kOe | | [\bar{1} 00]$ and switching off $H$ . (a)–(c) present subsequent images in $H | | [010]$ after subtraction of the initial polarized $M_{1}$ state picture to enhance the contrast of new domains. Rhombus-shaped domains with $M_{2} | | EA 2$ (white arrows) appear and grow with increasing $H$ . They have bright and dark $90^{\circ} + 2 α$ domain walls (DWs) oriented along EA1 and EA2. Domains nucleating at the scratches have zigzag boundaries. The DW bright and dark contrast reveals up and down directed stray fields due to + and $-$ magnetic charges at the DWs (e). Visualization of the stray fields at the edges of the apertures allows monitoring of the $M$ components in adjoining areas. In the subtracted image (c), the square aperture and the slit sides where the magnetic charge inverts sign, become visible upon the expansion of $M_{2}$ domains as sketched in (f). Our MOI resolution is $\sim 2 μ m$ , but the stray fields diverge in a range wider than 2 µm.
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Figure 2
(a), (b) Magneto-optical images of two-stage axial remagnetization at $T = 5 K$ . Images of the same area as in Fig. 1 are referenced to the initial monodomain $M_{1}$ state with $M_{1} | | E A_{2}$ (black arrow) formed after application of $H | | [010]$ . Subsequent application of $H | | [1 \bar{1} 0]$ promotes nucleation and growth of domains with $M_{2} | | EA 1$ (white arrows) (a). These domains have bright and dark boundaries associated with magnetic charges sketched in (c). In this first remagnetization stage, the $M_{2}$ domains have $90^{\circ} - 2 α$ DWs. At larger $H$ , the $M_{2}$ domains expand and form a monodomain state (not shown) where then new domains with $M_{3} | | - EA 2$ (blue arrows) appear and grow (b). These domains have bright and dark bottom- and top-side boundaries associated with the magnetic charges sketched in (d). In the second rotation stage, the $M_{3}$ domains have $90^{\circ} + 2 α$ DWs. For both stages the DWs are oriented along EA1 and EA2.
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Figure 3
Sketch of symmetric and asymmetric 90° Néel domain walls. In the symmetric case (a), magnetic charges $ρ_{m}$ change sign across the DW, whereas they have one sign in the asymmetric Néel wall (b). Details of the $ρ_{m}$ distribution are presented in the Supplemental Material [12]. The range of stray fields $H_{s}$ for (b) is much larger, similar to $H_{s}$ of a charged line decaying with distance as $1 / R$ , compared to a dipole of $+ / -$ lines with $H_{s} \sim 1 / R^{2}$ in (a). Blue arrows show magnetization vectors in the domains and inside the Néel DW.
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Figure 4
Sketch of asymmetric Néel domain walls modified by Dzyaloshinskii-Moriya interactions. $M_{1} | | E A_{1}$ in the initial state and $M_{2} | | E A_{2}$ in the nucleating domain are both in the film plane. Due to the DMI, magnetization in the Néel DW tilts slightly out of the plane, as shown by ellipses with their small axis along the film normal $Z$ . Within the DWs, $M$ rotates in the film plane and out of plane as shown in (b) and (c). Magnetic charges in the DWs shown by + and $-$ are defined by the asymmetric in-plane rotation of $M$ , while the $M_{z}$ contribution is small. All the DWs around the nucleating domain have the same CCW chirality for rotation from $M_{2}$ to $M_{1}$ .
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Physical Review B

covering condensed matter and materials physics

Extreme asymmetry of Néel domain walls in multilayered films of the dilute magnetic semiconductor (Ga,Mn)(As,P)

V. K. Vlasko-Vlasov, W.-K. Kwok, S. Dong, X. Liu, M. Dobrowolska, and J. K. Furdyna

Phys. Rev. B 98, 180411(R) – Published 29 November 2018

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Physical Review B

covering condensed matter and materials physics

Extreme asymmetry of Néel domain walls in multilayered films of the dilute magnetic semiconductor (Ga,Mn)(As,P)

V. K. Vlasko-Vlasov, W.-K. Kwok, S. Dong, X. Liu, M. Dobrowolska, and J. K. Furdyna

Phys. Rev. B 98, 180411(R) – Published 29 November 2018

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