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Helimagnetism in Mnbi2se4 Driven by Spin-Frustrating Interactions Between Antiferromagnetic Chains

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Helimagnetism in Mnbi2se4 Driven by Spin-Frustrating Interactions Between Antiferromagnetic Chains crystals Article Helimagnetism in MnBi2Se4 Driven by Spin-Frustrating Interactions Between Antiferromagnetic Chains Judith K. Clark 1,†, Chongin Pak 1,2,†, Huibo Cao 3 and Michael Shatruk 1,2,* 1 Department of Chemistry and Biochemistry, Florida State University, Tallahassee, FL 32306, USA; [email protected] (J.K.C.); [email protected] (C.P.) 2 National High Field Magnetic Laboratory, Tallahassee, FL 32310, USA 3 Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA; [email protected] * Correspondence: [email protected] † Both authors contributed equally to this work. Abstract: We report the magnetic properties and magnetic structure determination for a linear- chain antiferromagnet, MnBi2Se4. The crystal structure of this material contains chains of edge- sharing MnSe6 octahedra separated by Bi atoms. The magnetic behavior is dominated by intrachain antiferromagnetic (AFM) interactions, as demonstrated by the negative Weiss constant of −74 K obtained by the Curie–Weiss fit of the paramagnetic susceptibility measured along the easy-axis magnetization direction. The relative shift of adjacent chains by one-half of the chain period causes spin frustration due to interchain AFM coupling, which leads to AFM ordering at TN = 15 K. Neutron diffraction studies reveal that the AFM ordered state exhibits an incommensurate helimagnetic structure with the propagation vector k = (0, 0.356, 0). The Mn moments are arranged perpendicular to the chain propagation direction (the crystallographic b axis), and the turn angle around the helix ◦ Citation: Clark, J.K.; Pak, C.; Cao, H.; is 128 . The magnetic properties of MnBi2Se4 are discussed in comparison to other linear-chain Shatruk, M. Helimagnetism in antiferromagnets based on ternary mixed-metal halides and chalcogenides. MnBi2Se4 Driven by Spin-Frustrating Interactions Between Keywords: magnetic structure; spin frustration; helimagnet; neutron diffraction Antiferromagnetic Chains. Crystals 2021, 11, 242. https://doi.org/ 10.3390/cryst11030242 1. Introduction Academic Editor: Andrei Frustrated magnetic interactions in crystalline materials result in exotic magnetic phe- Vladimirovich Shevelkov nomena and complex spin textures in magnetically ordered states [1–4]. Low-dimensional magnetic systems feature hierarchical exchange interactions that, in the case of magnetic Received: 1 February 2021 ordering, can lead to the ground state magnetic structure being defined by a combination Accepted: 24 February 2021 of competing exchange coupling pathways rather than by the dominant nearest-neighbor Published: 27 February 2021 interactions [5,6]. A simple example of such behavior can be demonstrated by consid- ering two parallel chains of magnetic moments, with the intrachain exchange coupling Publisher’s Note: MDPI stays neutral (J ) being stronger than the interchain one (J ). In the case of antiferromagnetic (AFM) with regard to jurisdictional claims in 1 2 published maps and institutional affil- exchange, the chains with the exact match in the relative location of their moments form iations. spin ladders (Figure1a) that experience no conflict in setting into an AFM ordered state. If the chains, however, are displaced by half a period in the chain direction (Figure1b), the weaker exchange interactions defined by J2 conflict with the stronger interactions defined by J1, causing spin frustration. The ratio between these exchange constants and the local magnetic anisotropy of the interacting spins will dictate the spin texture attained by the Copyright: © 2021 by the authors. material upon magnetic ordering. The strongest frustration takes place when J = J . But Licensee MDPI, Basel, Switzerland. 1 2 even in the case of well-defined chains, when J dominates, the transverse action of the J This article is an open access article 1 2 distributed under the terms and parameter might lead to the deviation from collinear magnetic ordering along the chain conditions of the Creative Commons and the formation of helical magnetic structures. Attribution (CC BY) license (https:// An ideal one-dimensional (1D) magnet should not exhibit long-range ordering at a creativecommons.org/licenses/by/ finite temperature. Hence, the magnetic ordering in any chain compound depends on the 4.0/). J2/J1 ratio—the smaller this ratio, the lower the AFM ordering temperature (TN) relative Crystals 2021, 11, 242. https://doi.org/10.3390/cryst11030242 https://www.mdpi.com/journal/crystals Crystals 2021, 11, x FOR PEER REVIEW 2 of 9 Crystals 2021, 11, 242 2 of 9 J2/J1 ratio—the smaller this ratio, the lower the AFM ordering temperature (TN) relative to the value that could be hypothetically expected from the strength of the intrachain ex- change coupling. A well-studied example of an AFM Heisenberg chain is (Me4N)[MnCl3] to the value that could be hypothetically expected from the strength of the intrachain 2+ exchange(Me = methyl). coupling. The A well-studied large interchain example ofseparation an AFM Heisenberg of 9.15 Å chain between is (Me4N)[MnCl the S = 35/2] Mn ions, as (Mecompared = methyl). to The the large much interchain shorter separation intrachain of 9.15 distance Å between of 3.25 the S Å,= 5/2 effectively Mn2+ ions, isolates as the chains comparedof the Mn to spins. the much As shorter a result, intrachain the experimental distance of 3.25 T Å,N = effectively 0.84 K is isolates substantially the chains smaller than the oftemperature the Mn spins. of As 76 a result, K calculated the experimental from TtheN = mole 0.84 Kcular is substantially field theory smaller based than theon the intrachain temperature of 76 K calculated from the molecular field theory based on the intrachain exchange value of J1 = –6.3 K (estimated from high-temperature magnetic susceptibility exchange value of J1 = –6.3 K (estimated from high-temperature magnetic susceptibility measurements)measurements) [7]. [7]. The strongThe stro quasi-1Dng quasi-1D nature of nature magnetic of coupling magnetic in (Me coupling4N)[MnCl in3] (Me4N)[MnCl3] allowedallowed observation observation of temperature-dependent of temperature-dependent soliton excitations soliton bothexcitations above and both below above and below T , making it a unique 1D magnetic system [8]. TNN, making it a unique 1D magnetic system [8]. FigureFigure 1. 1.Two Two chains chains of magnetic of magnetic moments moments with antiferromagnetic with antiferromagnetic (AFM) exchange (AFM) coupling exchange both coupling both within (J ) and between (J ) the chains. While all pairwise AFM interactions can be satisfied in the within 1(J1) and between2 (J2) the chains. While all pairwise AFM interactions can be satisfied in the ar-rangementarrangement (a ),(a spin), spin frustration frustration develops develops in the arrangement in the arrangement (b) due to the(b) half-period due to the shift half-period be- shift be- tween the chains. This shift results in the orientation of spins that conflicts with the AFM ex-change tween the chains. This shift results in the orientation of spins that conflicts with Table 2. (the con- constant J (the conflicting interactions are highlighted in red). flicting interactions1 are highlighted in red). As the distance between the chains decreases, the J2 exchange pathway begins to play a moreAs notable the distance role. Thus, between (MeNH3 the)[MnCl chains3(H2 O)decreases,2] and Cs[MnCl the J23 (Hexchange2O)2] exhibit pathway AFM begins to play ordering at 4.1 K [9] and 4.9 K [10], respectively. In K MnS and K MnSe , with even closer a more notable role. Thus, (MeNH3)[MnCl32(H2O)2 2] and2 Cs[MnCl2 3(H2O)2] exhibit AFM or- arranged chains, the TN value increases to 17 K, and the J1 value was estimated to be above –14dering K [11 ].at The 4.1 spin K [9] frustration and 4.9 observed K [10], inrespectively. these two structures In K2 leadsMnS to2 and a helical K2MnSe magnetic2, with even closer structure,arranged with chains, the moments the TN beingvalue perpendicular increases to to 17 the K, chain and propagationthe J1 value direction. was estimated to be above –14 HelimagneticK [11]. The spin ordering frustration can be expected observed in other in th quasi-1Dese two systemsstructures with leads the relative to a helical magnetic spinstructure, arrangement with the of Figure moments1b. Spin being frustration perpendi affordedcular by to such the chain a configuration propagation can direction. lead toHelimagnetic incommensurate ordering magnetic structures,can be expected resulting inin two-dimensional other quasi-1D vortex systems domain with the relative walls that are not typically seen in bulk magnetic systems [12]. Such vortex domain walls arespin sensitive arrangement to external of currents, Figure thus1b. Spin creating frustration prospects afforded for leveraging by such magnetoelectric a configuration can lead couplingto incommensurate in helimagnets formagnetic applications structures, in low-power resulting devices andin rapid-accesstwo-dimensional memory. vortex domain wallsMany that mixed-metal are not typically ternary halidesseen in and bulk chalcogenides magnetic systems feature chain-like [12]. Such structural vortex domain walls motifsare sensitive of the magnetic to external transition currents, metal ions.thus Forcrea manyting ofprospects these compounds, for leveraging however, magnetoelectric the magnetic structures remain unknown. The interesting fundamental properties of chaincoupling magnets, in helimagnets such as the observation for applications of soliton excitationsin low-power and helimagnetism
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