Phase separations and nematicity of transition metal impurities

Tomasz Dietl^1,2

¹International Research Centre MagTop, Institute of Physics, Polish Academy of Sciences, PL-02668 Warsaw, Poland

²WPI-Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japandietl@MagTop.ifpan.edu.pl

Semiconductors [1] and topological materials [2] doped with transition metal elements attract considerable attention due to the fascinating physics and nonospintronic functionalities associated with exchange coupling between band carries and localized spins. However, there is a growing amount of pieces of evidence that d-shells of magnetic impurities contribute also to bonding, which can affect their spatial distribution and modify key properties, such as magnetic ordering temperature [3]. It has recently been experimentally demonstrated that the resulting phase separation (spinodal decomposition) can be anisotropic and result in the hitherto puzzling rotational symmetry breaking (i.e., nematic characteristics) revealed in a certain class of dilute magnetic semiconductors [4]. This finding put in a new light a possible origin of nematicity in other systems, such as unconventional superconductors and modulation-doped semiconductor quantum wells, in which rotational symmetry breaking has so far been assigned to the unidirectional spontaneous ordering of spin, orbital or charge degrees of freedom.

[1] T. Dietl and H. Ohno, Rev. Mod. Phys. 86, 187–251 (2014).

[2] Y. Tokura, K. Yasuda, and A. Tsukazaki, Nature Rev. Phys. 1, 126–143 (2019).

[3] T. Dietl, K. Sato, T. Fukushima, A. Bonanni, M. Jamet, A. Barski, S. Kuroda, M. Tanaka, Phan Nam Hai, H. Katayama-Yoshida, Rev. Mod. Phys. 87, 1311–1376 (2015).

[4] Ye Yuan, R. Hübner, M. Birowska, Chi Xu, Mao Wang, S. Prucnal, R. Jakieła, K. Potzger, R. Böttger, S. Facsko, J. A. Majewski, M. Helm, M. Sawicki, Shengqiang Zhou, and T. Dietl, Phys. Rev. Materials 2, 114601 (2018).

Keywords: crystallographic phase separation, chemical phase separation, spinodal decomposition, nematicity, dilute magnetic semiconductors

This work has been supported by the Foundation for Polish Science through the IRA Programme financed by the EU within SG OP Programme.

A high-pressure study of a black phosphorus crystal leads to a rich phase diagram,
including a Lifshitz-type semiconductor-semimetal transition, a Weyl semimetal, and
superconductivity as well as structural phase transitions. Transport properties and
quantum oscillations under high pressure provide critically valuable information to
understand the physics behind these new phases. These properties have been measured
reliably under hydrostatic pressure and magnetic field with a large-volume apparatus.
Superconductivity in the A7 phase has been found to exhibit the largest
magnetoresistance effect in its normal state so far. The BCS superconductivity in the A7
phase as identified by the experiment can be accounted for by a first-principles
calculation.

Topology of defects in ordered states of matter is determined by dimensionality and symmetry properties of the order parameter. Larger number of variables needed to describe an ordered state gives rise to a greater diversity and complexity of topological defects, a prominent example being the A-phase of superfluid ³He. The order parameter describing non-collinear antiferromagnetic orders in the swedenborgite, CaBaCo₂Fe₂O₇, and Fe-langasite, Ba₃TaFe₃Si₂₄O₁₄, is an SO(3) matrix [1,2]. The iron langasite spin lattice is built of triangles formed by antiferromagnetically coupled Fe³⁺-ions (S = 5/2). The orientation of three co-planar spins added into the zero total spin is described by three Euler angles. This amazing material is both chiral and magnetically frustrated. It shows a non-collinear 120^o spin ordering at the scale of one unit cell, a spiral with a period of 7 lattice constants and complex spin superstructures at the scale of 1000 Å. Lifshitz invariants allowed by the lack of inversion symmetry give rise to interesting modulated magnetic phases and stabilize particle-like topological defects previously discussed in very different physical contexts, e.g. nuclear physics and superfluid ³He.

References:

[1] J. D. Reim, E. Rosén, O. Zaharko, M. Mostovoy, J. Robert, M. Valldor, and W. Schweika, Phys. Rev. B 97, 144402 (2018).

[2] M. Ramakrishnan et al., npj Quantum Materials 4, 60 (2019).

Topological semimetals have high carrier mobility in the form of quasiparticles resembling relativistic fermions. Experimental realisations of magnetic topological semimetals are relatively thin on the ground. Here we probe both the magnetic structure and interactions of the topological semimetal candidate YbMnSb₂ using neutron scattering.

YbMnSb₂ belongs to the P4/nmm space group and shows evidence of a magnetic ordering transition involving the Mn moments at ~350 K [1]. This is a relatively high Néel temperature among the family of materials AMnSb₂ (A = Ca, Sr, Ba, Yb, Eu), which has demonstrated characteristics of the topological semimetals. The quasi-2D plane formed by the Sb ‘square’ may host Weyl or Dirac fermions [1-3]. YbMnSb₂ has previously been studied via quantum oscillations, magnetometry, optical spectroscopy, ab initio band structure calculations, and angle-resolved photon emission spectroscopy [1, 4, 5]. Interestingly, these studies reached different conclusions as to the magnetic structure of YbMnSb₂, and hence its semimetal nature: the jury is out on whether it is a Dirac [4], nodal-line [5], or Weyl semimetal [1].

In this presentation I shall report the magnetic structure of YbMnSb₂ found by neutron diffraction, which is different to any previously proposed structures: C-type antiferromagnetism with the spins pointing along the c axis. This magnetic structure is shared by YbMnBi₂ [6]. Dirac physics is also seen in such AMnBi₂ materials; however, Bi rather than Sb layersresults in stronger spin-orbit coupling. This widens the band gap at any nodes and makes the resulting quasiparticles more massive [1]. We have also measured the spin wave spectrum of YbMnSb₂ and the results of this measurement will be described and compared with the spin dynamics in related materials. The implications for the topology of the electrons will be discussed.

Magnetic topological insulators (MTIs) are a hot topic of materials science, promising future availability of spintronics with low energy consumption, quantum computing and phenomena like the Quantized Anomalous Hall Effect (QAHE) [1-2]. MTIs are chemically and structurally akin to the original non-magnetic topological insulators. Of those, the tetradymites Bi₂Te₃ and Sb₂Te₃ have recently proven to allow the introduction of a third magnetic element resulting in magnetically active, topologically non-trivial compounds. A magnetic element can be incorporated either via substitution on the Bi/Sb position in (Bi, Sb)₂Te₃, or by adding a third element which introduces a new crystallographic site, resulting for example in MnBi₂Te₄. (Bi, Sb)₂Te₃ itself and all members of its family exhibit the rhombohedral Rm1 space group (No. 166) [2]. Therein interchanging sheets of Mn, (Bi, Sb) and Te build septuple layers with the central sheet being Mn (Wyckoff position 3a). Situated between the respective layers is a van der Waals gap (Fig. 1).

Our group was the first to successfully grow single crystals, and conduct an in depth study of the physical properties of MnBi₂Te₄ [4-5]. Single crystal diffraction experiments reported in that study showed intermixing of Mn and Bi and since then several studies have reported intermixing of the two elements (MnBi_2.14Te_3.96 [6], Mn_1.01Bi_1.99Te₄ and Mn_0.98Bi_2.05Te₄ [7]). While a lot of attention has been given to MnBi₂Te₄, MnSb₂Te₄ proved to be synthetically achievable too. Similar to MnBi₂Te₄, MnSb₂Te₄ features intermixing of Mn and Sb (Mn_0.852Sb_2.296Te₄ [8]). For MnSb₂Te₄, a recent study by Murakami et al. uncovers the impact of finding a certain amount of the magnetic Mn on the position of the non-magnetic Sb [9]. According to their discoveries, this changes the magnetic order from antiferromagnetic to ferrimagnetic.

These compounds are known to react sensitively to synthesis procedure and tempering history. Hence, our studies aim at understanding the greater connection between synthesis aspects and the resulting structural and physical properties. More precisely we studied MnBi₂Te₄ and MnSb₂Te₄ containing various amounts of Mn and other analogues of these systems. In these studies we uncovered, that the magnetism in MnSb₂Te₄ is even more sensitive to annealing procedures than previously expected.

[1] Y. Ando, Journal of the Physical Society of Japan, (2013), 82, 102001

[2] I. I. Klimovskikh, M. M. Otrokov, D. Estyunin, et al., Quantum Materials, (2020), 54.

[3] Y. Feutelais, B. Legendre, N. Rodier, V. Agafonov, Materials Research Bulletin, (1993), 28, 591-596

[4] A. Zeugner, F. Nietschke, A. U. B. Wolter, et al., Chemistry of Materials, (2019), 31, 2795-2806.

[5] M. M. Otrokov, I. I. Klimovskikh, H. Bentmann, et al., Nature, (2019), 576, 416-422.

[6] H. Li, S. Liu, C. Liu, et al., Physical Chemistry Chemical Physics, (2020), 22, 556-563.

[7] M.-H. Du, J. Yan, V. R. Cooper, M. Eisenbach, Advanced Functional Materials, (2020), 2006516.

[8] L. Zhou, Z. Tan, D. Yan, et al., Physical Review B, (2020), 102, 85114.

[9] T. Murakami, Y. Nambu, T. Koretsune, et al., Physical Review B, (2019), 100, 195103.

Eudialyte-group minerals (EGMs) are of a scientific and industrial interest as important concentrators of rare and strategic elements (mainly, Zr and REE) in agpaitic alkaline rocks. The general crystal chemical formula of EGMs is [N(1)₃N(2)₃N(3)₃N(4)₃N(5)₃]{M(1)₆M(2)₃M(3)M(4)Z₃(Si₉O_27-3x(OH)_3x)₂(Si₃O₉)₂Ø_0–6}X(1)X(2) where M(1) = ^VICa, ^VIMn²⁺, ^VIREE, ^VINa, ^VIFe²⁺; M(2) = ^IV,VFe²⁺, ^V,VIFe³⁺, ^V,VIMn²⁺, ^V,VINa, ^IV,VZr; M(3) and M(4) = ^IVSi, ^VINb, ^VITi, ^VIW⁶⁺; Z = ^VIZr, ^VITi; Ø = O, OH; N(1)–N(5) are extra-framework cations (Na, Н₃О⁺, K, Sr, REE, Ba, Mn²⁺, Ca) or H₂O; X(1) and X(2) are extra-framework water molecules, halide (Cl^–, F^–) and chalcogenide (S^2–) anions, and anionic groups (CO₃^2–, SO₄^2–); x = 0–1 (Rastsvetaeva & Chukanov, 2012).

The crystal structure of EGMs is based on a heteropolyhedral framework (Chukanov et al., 2004) which makes these minerals similar to zeolite-like materials and molecular sieves. The first topological analysis of the eudialyte-type structures (eudialyte, kentbrooksite, oneillite, and khomyakovite) was performed using the approach of coordination sequences {N_k} (k = 1–12), using the representation of crystal structure as a finite ‘reduced’ graph (Ilyushin & Blatov, 2002). As an invariant of the eudialyte-type structure and its derivatives the MT-layer [Zr₃Si₂₄O₇₂]_∞∞ (PBU: primary building unit, an elementary component of an MT-framework) was chosen.

Topological analysis of the heteropolyhedral MT-framework in the eudialyte-type structure and its derivatives was performed based on a natural tiling (Blatov et al., 2007) (partition of the crystal space by the smallest cage-like units) analysis of the 3D cation nets using the ToposPro software (Blatov et al., 2014). According to the modern topological classification, it is necessary to use the standard representation to determine the topological type of the net. For the topological analysis carried out in this work, atomic nets for each of the 12 structure types were simplified and the corresponding underlying nets, which characterize the connectivity of the primary structural units as well as their point symbols, were obtained. The 0-1-2-free representation was used for topological analysis of cages within the tiling approach because it represented the cages in more detail. To analyze the migration paths of sodium cations in these structures, the Voronoi method was used.

The parental eudialyte-type MT-framework is formed by isolated ZO₆ octahedra, six-membered [M(1)₆O₂₄] ring of edge-shared M(1)O₆ octahedra, and two types of rings of tretrahedra, [Si₃O₉] and [Si₉O₂₇]. Different occupancies of additional M(2), M(3), and M(4) sites with variable coordination numbers by Q, T*, and M* cations, respectively, result in 12 types of the MT-framework. Corresponding point symbols for the cationic 3D-nets of the MT-frameworks as well as tiles’ sequences have been calculated.

Based on the results of natural tilings calculations as well as theoretical analysis of migration paths, it was found that Na⁺ ions can migrate through six- and seven-membered rings, while all other rings are too small. In eight types of the MT-frameworks, Na⁺-ion migration and diffusion is possible at standard temperature and pressure, while in four other types cages are connected by narrow gaps and, as a result, the Na⁺ diffusion in them is complicated at ambient conditions but may be possible either at higher temperatures or under mild geological conditions during long times. This conclusion is in a good agreement with numerous examples of the transformation of initial EGMs into their hydrated Na-deficient counterparts as a result of natural processes of sodium leaching and hydrolysis under hydrothermal conditions.

The relationships between heteropolyhedral substitutions and topological features of the derivative framework structures have been also discussed for alluaudite supergroup (Aksenov et al., 2021) minerals and related synthetic compounds. However, in the case of eudialyte-type structures such relationships look more complicated because of multiple variants of their derivative structures. Moreover, in the case of so-called “megaeudialytes” (Rastsvetaeva et al., 2012), i.e. EGMs which are characterized by modular structures and doubling of the c parameter (c ~ 60 Å), different modules regularly alternating in the structure can represent different types of the framework, which increases the amount of topological variations. Similar influence of modularity on the topological features of zirconium silicates have been described for the lovozerite-type structures (Pekov et al., 2009), where different ways of stacking of the lovozerite modules define the unit cell parameters, symmetry, and topology of the derivative structures (Krivovichev, 2015).

This work was financially supported by the Russian Science Foundation, project No. 20-77-10065, Ministry of Education and Science of the Russian Federation for financial support within grant No. 0778-2020-0005 , and state task, state registration number ААAА-А19-119092390076-7.

References:

Aksenov, S. M., Yamnova, N. A., Kabanova, N. A., Volkov, A. S., Gurbanova, O. A., Deyneko, D. V., Dimitrova, O. V. & Krivovichev, S. V. (2021). Crystals. 11, 237.

Blatov, V. A., Delgado-Friedrichs, O., O’Keeffe, M. & Proserpio, D. M. (2007). Acta Crystallogr. Sect. A Found. Crystallogr. 63, 418–425.

Blatov, V. A., Shevchenko, A. P. & Proserpio, D. M. (2014). Cryst. Growth Des. 14, 3576–3586.

Chukanov, N. V, Pekov, I. V & Rastsvetaeva, R. K. (2004). Russ. Chem. Rev. 73, 205–223.

Ilyushin, G. D. & Blatov, V. A. (2002). Acta Crystallogr. Sect. B Struct. Sci. 58, 198–218.

Krivovichev, S. V. (2015). Proc. Steklov Inst. Math. 288, 105–116.

Pekov, I. V., Krivovichev, S. V., Zolotarev, A. A., Yakovenchuk, V. N., Armbruster, T. & Pakhomovsky, Y. A. (2009). Eur. J. Mineral. 21, 1061–1071.

Rastsvetaeva, R. K. & Chukanov, N. V. (2012). Geol. Ore Depos. 54, 487–497.

Rastsvetaeva, R. K., Chukanov, N. V. & Aksenov, S. M. (2012). Minerals of Eudialyte Group: Crystal Chemistry, Properties, Genesis Nizhniy Novgorod: University of Nizhni Novgorod.