Robust topological Hall effect driven by tunable noncoplanar magnetic state in Mn-Pt-In inverse tetragonal Heusler alloys

Bimalesh Giri, Arif Iqbal Mallick, Charanpreet Singh, P. V. Prakash Madduri, Françoise Damay, Aftab Alam, and Ajaya K. Nayak

Phys. Rev. B 102, 014449 – Published 28 July 2020

Abstract

Manipulation of magnetic ground states by effective control of competing magnetic interactions has led to the finding of many exotic magnetic states. In this direction, the tetragonal Heusler compounds consisting of multiple magnetic sublattices and crystal symmetry favoring chiral Dzyaloshinskii-Moriya interaction (DMI) provide an ideal base to realize nontrivial magnetic structures. Here we present the observation of a large robust topological Hall effect (THE) in the multisublattice ${Mn}_{2 - x} PtIn$ Heusler magnets. The topological Hall resistivity, which originates from the nonvanishing real space Berry curvature in the presence of nonzero scalar spin chirality, systematically decreases with decreasing the magnitude of the canting angle of the magnetic moments at different sublattices. With help of first-principle calculations, magnetic and neutron diffraction measurements, we establish that the presence of a tunable noncoplanar magnetic structure arising from the competing Heisenberg exchanges and chiral DMI from the $D_{2 d}$ symmetry structure is responsible for the observed THE. The robustness of the THE with respect to the degree of noncollinearity adds up a new degree of freedom for designing THE based spintronic devices.

Received 17 December 2019
Revised 9 July 2020
Accepted 9 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.014449

Physics Subject Headings (PhySH)

Ferrimagnetism Spin texture Topological Hall effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Bimalesh Giri¹, Arif Iqbal Mallick², Charanpreet Singh¹, P. V. Prakash Madduri¹, Françoise Damay³, Aftab Alam², and Ajaya K. Nayak^1,*

¹School of Physical Sciences, National Institute of Science Education and Research, HBNI, Jatni-752050, India
²Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
³Laboratoire Léon Brillouin, CEA-CNRS, CEA Saclay, 91191 Gif-sur-Yvette, France

^*ajaya@niser.ac.in

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Vol. 102, Iss. 1 — 1 July 2020

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Images

Figure 1
First-principle calculation of magnetic structures for ${Mn}_{2 - x} PtIn$ . Total energy (with reference to $E_{θ = 180^{\circ}}$ ) versus canting angle $θ$ of the Mn moment in (a) ${Mn}_{2} PtIn$ , (b) ${Mn}_{1.5} PtIn$ , and (c) MnPtIn. The alignment of magnetic moment of each Mn atom in different magnetic sublattices are shown in the inset of the respective figures. In case of ${Mn}_{2} PtIn$ (space group $I \bar{4} m 2$ ), Mn occupies two positions: ${Mn}_{2 b}$ (magenta balls) and ${Mn}_{2 d}$ (blue balls). For ${Mn}_{1.5} PtIn$ (space group $I \bar{4} 2 m$ ) and MnPtIn (space group $I \bar{4} 2 m$ ) the Mn sits at ${Mn}_{2 a}$ (violet balls), ${Mn}_{2 b}$ (magenta balls), ${Mn}_{4 d}$ (blue balls), and ${Mn}_{8 i}$ (red balls). For all cases In and Pt atoms are represented by green and yellow balls, respectively.
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Figure 2
(a) Field dependence of magnetization loops measured at 2 K for ${Mn}_{2 - x} PtIn$ . The inset shows compositional dependent magnetization at a field of 5 T. (b) Temperature dependence of magnetization $M (T)$ measured in zero field cooled (ZFC, open symbols) and field cooled (FC, closed symbols) modes in an applied field of 0.1 T for ${Mn}_{2 - x} PtIn$ . The $M (T)$ data for $x = 0.9$ and 1.0 are multiplied by a factor of 3 and 30, respectively, for a clear view.
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Figure 3
Field dependence of Hall resistivity ( $ρ_{y x}$ ) measured at different temperatures for (a)–(f) ${Mn}_{2} PtIn$ , (g) ${Mn}_{1.5} PtIn$ , and (h) ${Mn}_{1.2} PtIn$ . The open and closed symbols represent experimental data with field sweep in $+ H \to - H$ and $- H \to + H$ , respectively. The solid lines corresponds to the total calculated Hall resistivity as described in the main text. (i) Field dependence of the real component of AC susceptibility, $χ^{'} (H)$ measured at 5 K.
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Figure 4
(a) Topological Hall resistivity ( $ρ_{y x}^{T}$ ) calculated at different temperatures for ${Mn}_{2} PtIn$ . The open and closed symbols represent experimental data with field sweep in $+ H \to - H$ and $- H \to + H$ , respectively. The inset shows calculated $ρ_{y x}^{T}$ at 5 K for ${Mn}_{1.5} PtIn$ (filled circles) and ${Mn}_{1.2} PtIn$ (filled stars) in $μ Ω cm$ . (b) Maximum value of $ρ_{y x}^{T}$ as a function of temperatures (solid symbols) taken from the field dependent $ρ_{y x}^{T}$ data.
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Figure 5
(a) Neutron diffraction patterns for ${Mn}_{1.5} PtIn$ measured at different temperatures. For a clear view of the major magnetic reflections the patterns are shown in the $2 θ$ range of 22 to 50 deg. (b) Temperature variation of normalized integrated intensity for the three major magnetic reflections (101), (200), and (004). (c) Rietveld refinement of the neutron diffraction patterns at 300 and 1.5 K for ${Mn}_{1.5} PtIn$ . (d) Temperature dependence of net magnetic moment of site-specific Mn atoms at different sublattices as depicted by different symbols.
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Figure 6
(a) Unit cell for ${Mn}_{2} PtIn$ representing Mn moments at different lattice planes. Mn-In and Mn-Pt lattice planes are shown in light magenta color marked by 1 and light blue color marked by 2 and 3, respectively. Solid angle sustained by three moments $S_{1}, S_{2}$ , and $S_{3}$ is shown in dark yellow color. (b) Upper panel: Solid angle $Ω$ subtended by three noncoplanar spins $S_{i}, S_{j}, S_{k}$ that gives a fictitious magnetic field in both upward and downward direction (blue arrows) in the absence of any chiral DMI. Lower panel: Fixed chirality in the presence of DMI.
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