Realization of interlayer ferromagnetic interaction in MnSb₂Te₄ toward the magnetic Weyl semimetal state

Abstract

Magnetic properties of MnSb₂Te₄ were examined through magnetic susceptibility, specific-heat, and neutron-diffraction measurements. As opposed to isostructural MnBi₂Te₄ with the antiferromagnetic ground state, MnSb₂Te₄ develops a spontaneous magnetization below 25 K. From our first-principles calculations on the material in a ferromagnetic state, the state could be interpreted as a type-II Weyl semimetal state with broken time-reversal symmetry. Detailed structural refinements using x-ray-diffraction and neutron-diffraction data reveal the presence of site mixing between Mn and Sb sites, leading to the ferrimagnetic ground state. With theoretical calculations, we found that the presence of site mixing plays an important role for the interlayer Mn-Mn ferromagnetic interactions.

I. INTRODUCTION

Topological semimetals (TSMs), characterized by crossings of valence and conduction bands in the momentum space, have brought exciting opportunities to explore properties that are unattainable in conventional semimetals or metals [1–5]. Dirac semimetal is the first experimentally confirmed TSM, where a fourfold degenerate Fermi point is topologically protected by time-reversal symmetry (TRS) as well as space-inversion symmetry (SIS). This type of material has been experimentally verified in systems including Cd₃As₂ and Na₃Bi [6–9]. The degeneracy at the Dirac point can be lifted by breaking of either symmetry, leading to the Weyl semimetal state. The resultant twofold degenerated Weyl points have a distinct chirality, resulting in an open arc surface state and chiral anomaly at high magnetic fields [9–11]. Weyl semimetals have been found in materials without SIS (e.g., NbP and TaAs) [12–14] or TRS (e.g., Mn₃Sn and Co₃Sn₂S₂) [15,16].

A new class of TSMs called “type-II TSMs” has recently been proposed from theoretical perspectives [17]. Unlike conventional type-I TSMs, Dirac cones in type-II TSMs are largely tilted along certain momentum directions, violating the Lorentz invariance [17]. The distinct band topology leads to extremely anisotropic magnetoresistance [17,18]. After the prediction of the type-II Weyl semimetal state in WTe₂, several compounds were shown as type-II Weyl semimetal without SIS, including MoTe₂, LaAlGe, and TaIrTe₄ [19–25]. On the other hand, the experimental study of TRS-broken type-II Weyl semimetal is rather scarce. A rare example is the layered bismuthide YbMnBi₂, where the canting of the Yb moment from the c axis was initially proposed to break the TRS, resulting in the type-II Weyl semimetal state [26]. Subsequent optical conductivity measurements in YbMnBi₂, however, failed to confirm the canted Yb moments [27]. More recently, LnAlGe (Ln = Ce, Pr) have been predicted as a TRS broken TSM with both type-I and type-II crossings [28].

Ternary tellurides MPn₂Te₄ (M = Ge, Sn, Pb, Mn and Pn = As, Sb, Bi) have a layered structure as shown in Fig. 1(a) [29–31]. MnBi₂Te₄ with magnetic ions was theoretically proposed to have an antiferromagnetic topological insulating state [32–36], which was later confirmed from experimental studies [35–37]. It was also predicted that this material becomes TRS broken type-II Weyl semimetal if Mn moments are aligned ferromagnetically [34], a situation that has not been observed experimentally. In this paper, we synthesized isostructural MnSb₂Te₄ and conducted magnetic susceptibility, specific-heat, and neutron-diffraction measurements. Unlike the previous theory on MnSb₂Te₄ showing the A-type antiferromagnetic state [38], a ferromagnetic component develops in MnSb₂Te₄ below 25 K. Density functional theory calculations suggest that MnSb₂Te₄ in a ferromagnetic state can be expected to be a TRS broken type-II Weyl semimetal. Structural refinements using x-ray-diffraction (XRD) and neutron-diffraction data, however, reveal the presence of site mixing between Mn and Sb sites, leading to the ferrimagnetic ground state. The effect of site mixing is investigated through first-principles calculations.

FIG. 1.

(a) Crystal structure of MnSb₂Te₄. Pink, orange, and dark blue spheres represent Mn, Sb, and Te, respectively. Note that there are several antisite disorders between Sb and Mn sites. (b) Observed and calculated XRD patterns of MnSb₂Te₄. Red crosses and green and blue lines represent observed, calculated, and difference profiles. Green ticks are used to show the positions of the Bragg peaks.

II. EXPERIMENTAL AND CALCULATION DETAILS

A polycrystalline sample of MnSb₂Te₄ was synthesized via the solid-state reaction. Mn, Sb, and Te (99.99%, Kojundo Chemical) were weighed in a stoichiometric ratio, mixed, and pelletized in a nitrogen filled dry box. A pellet was sealed in an evacuated silica tube and heated up to 600 °C and kept for 10 h. Powder x-ray-diffraction experiments were performed using Bruker AXS D8 ADVANCE with Cu-Kα radiation.

Dc magnetic susceptibility was measured by a commercial superconducting quantum interference device magnetometer (Quantum Design, MPMS) in the temperature range of 2–350 K under the magnetic field of 0–7 T. Specific heat C_total was measured by the relaxation method using a physical property measurement system (Quantum Design) down to 2 K. To estimate the lattice contribution C_L, we obtained the thermal variation of the Debye temperature θ_D(T) for the isostructural nonmagnetic analog GeSb₂Te₄ using the Debye equation. θ_D(T) of MnSb₂Te₄ was then estimated by multiplying a scaling factor according to θ_D ∝ M₀^−1/2V₀^−1/3, where M₀ and V₀ are the molar ratio mass and volume, respectively. C_L was obtained by converting the scaled θ_D(T) into specific heat. Detail of the analysis is provided in the Supplemental Material [39]. Electronic structure calculations were performed within the generalized gradient approximation using the Vienna ab initio simulation package [40,41].

Powder neutron-diffraction (PND) data were collected at 50 and 5 K using the high-resolution powder diffractometer BT-1 (λ = 2.08 Å) at the NIST Center for Neutron Research, USA. The obtained diffraction data were structurally refined using the JANA2006 [42] and FullProf Suite [43]. We employed group theoretical analysis to identify magnetic structures that are allowed by symmetry.

III. RESULTS AND DISCUSSIONS

Figure 1(b) shows the room-temperature XRD profile of the target compound. All the observed Bragg peaks can be indexed based on the rhombohedral unit cell. The lattice parameters of a = 4.2385(3) Å and c = 40.8497(3) Å are slightly smaller than those of MnBi₂Te₄ (a = 4.334 Å and c = 40.910 Å) [31], which is reasonable given the smaller ionic radius of Sb than that of Bi. Figure 1(a) displays the structure of MnSb₂Te₄ (space group R3m), with NaCl-type MnTe layers and tetradymite-type Sb₂Te₃ layers stacking alternatively along the c axis. The edge-shared MnTe₆ octahedral layer forms a regular triangular lattice. Since the formal valence is given by (Mn²⁺)(Sb³⁺)₂(Te²⁻)₄ and Mn²⁺ in a high-spin configuration has quenched the orbital degree of freedom, one can expect Heisenberg-type magnetic behavior in this material.

Eremeev et al. predicted that MnSb₂Te₄ has the A-type antiferromagnetic ground state, where the ferromagnetic Mn layers are stacked antiferromagnetically [38]. However, as shown in Fig. 2(a), the magnetic susceptibility of MnSb₂Te₄ in an applied field of 0.1 T rapidly increases below around 30 K, suggesting a transition to a ferromagnetic state (which, however, will be corrected later). From the Arrott plot [Fig. 2(c)], the transition temperature, T_C, is estimated to be 25 K, close to the Néel temperature of 24.2 K observed in MnBi₂Te₄ [35–37,44]. The isotherm magnetization curve at 5 K up to 7 T [Fig. 2(b)] shows a small but finite ferromagnetic hysteresis loop. Such a small hysteresis has been sometimes reported in ferro- or ferrimagnets such as yttrium iron garnet [45]. The Curie-Weiss fitting yields the effective magnetic moment of p_eff = 5.842(7) μ_B, in good accordance with the value expected from the high-spin state of Mn²⁺ (5.92 μ_B). Figure S1 in the Supplemental Material [39] shows a difference in neutron data between T = 5 and 50 K. This clearly shows the increase of several nuclear reflections (e.g., 101 and 104) below T_C, which is consistent with the ferromagnetic order with the magnetic wave vector q_m = (0, 0, 0).

FIG. 2.

(a) Left: Temperature dependence of magnetic susceptibility under an applied field of 0.1 T with zero-field cooling (red) and field cooling (blue) process. Right: Temperature dependence of inverse susceptibility. (b) Isothermal magnetization curves at 5 K (red) and 100 K (blue). The inset shows a hysteresis loop. (c) M² vs H/M (Arrott plot) at various temperatures around T_C.

The magnetic transition is further probed by heat-capacity experiments. As shown in Fig. 3(a), the total specific heat C_total below 30 K is noticeably larger than that of the isostructural nonmagnetic GeSb₂Te₄, indicating the magnetic contribution to the specific heat. Its magnetic component C_mag is estimated by subtracting the lattice contribution from the data using GeSb₂Te₄ [Fig. 3(b), left axis]. Magnetic entropy, S_mag, calculated from the integration of C_mag/T [Fig. 3(b), right axis], shows saturating behavior toward 30 K, followed by a gradual increase upon further warming. S_mag reaches about 11 J/mol K² at 100 K, slightly smaller than the expected value of Rln6 for S = 5/2, where R is the gas constant. This observation implies that the short-range correlation persists well above T_C. A power-law behavior in C_mag ∝ T^α with α = 1.52(1) is observed at temperatures below 10 K [Fig. 3(c)]. If there is a long-range magnetic order, α follows the relation of α = d/υ, where d is the dimensionality of the magnon excitation and υ is related to the type of the magnetic order (υ = 1 and 2, respectively, stand for antiferromagnetic and ferromagnetic order). The observed T^3/2 dependence in MnSb₂Te₄ implies three-dimensional-like magnon excitations from a ferromagnetic state. However, the limited fitting range prevented us from further elucidation of the magnetic excitations.

FIG. 3.

(a) Temperature dependence of the specific heat divided by temperature. (b) Left: The magnetic part of the specific heat divided by temperature. Right: The magnetic entropy. The horizontal line indicates R ln 6. (c) The magnetic part of the specific heat in full logarithmic scale.

As shown above, MnSb₂Te₄ undergoes a magnetic transition with a spontaneous magnetization, in contrast to the antiferromagnetic structure in MnBi₂Te₄ [36,37,44,46]. To obtain more insight into the ground state in MnSb₂Te₄, we performed first-principles calculations assuming a ferromagnetic state with an out-of-plane easy axis. Without the spinorbit coupling (SOC), MnSb₂Te₄ is a semiconductor with a direct band gap of E_g ~ 0.09 eV [Fig. 4(a)]. When SOC is turned on [Fig. 4(b)], we found for the first time a clear band inversion around the Γ point, forming a pair of band crossings along the Γ-Z line. The resultant Weyl cones are tilted with respect to the Γ-Z line, a characteristic feature of type-II Weyl points. From the observed spontaneous magnetization, we deduce that MnSb₂Te₄ is a potential TRS broken type-II Weyl semimetal at zero magnetic field.

FIG. 4.

Calculated band structures for MnSb₂Te₄ (a) without and (b) with SOC. In (a), the red (blue) color represents up-spin (down-spin) bands.

It is noticed, however, that without SOC the antiferromagnetic (A-type) structure is more stable than the ferromagnetic one by 18.3 meV, similarly to the previous result [38], and inclusion of SOC hardly affects the relative energy difference (17.5 meV). The discrepancy from the ferromagnetic ground state is also inferred from the Curie-Weiss fitting for the susceptibility that yielded a negative Weiss temperature of Θ_W = −21.6(4) K) [Fig. 2(a)]. Furthermore, the saturation magnetization of about 1.8 μ_B/Mn at 5 K is somewhat smaller than that expected from high-spin Mn²⁺.

These contradictory observations led us to investigate the structural details of MnSb₂Te₄. A structural refinement was initially carried out assuming the ideal MnBi₂Te₄-type structure (R3m), which, however, resulted in rather poor reliability factors (e.g., R_wp ~ 11%) (Fig. S2 in the Supplemental Material [39]). Thus, site mixing among cations was considered in the analysis by allowing Sb (6c) to occupy the Mn (3a) site and vice versa, while the total occupancy factors were constrained to unity. This substantially improved the fitting [Goodness of fit (GOF) 1.77, R_wp = 4.51%, and R_p = 1.77%] and gave the chemical composition of (Mn_0.66Sb_0.34)(Sb_0.83Mn_0.17)₂Te₄. No site deficiency was found for the anionic sites. The full structural parameters are shown in Table I. Cation antisite disorder also occurs in other MPn₂Te₄-type compounds with a site mixing ranging from 15 to 35% [47,48].

Table I.

Crystallographic data for MnSb₂Te₄ obtained from XRD at room temperature (upper) and PND at 50-K (lower) data. The assumed space group is R3m with a = 4.2385(3) Å and c = 40.8497(3) Å from XRD and a = 4.2219(2) Å and c = 40.606(3) Å from PND. g represents the occupancy factor of each site, and U_iso employs an overall Debye-Waller factor.

Atom	Site	gb	x	Y	z	Uiso/100 Å2
Mn1	3a	0.6645(3)	0	0	0	1.62(3)
		0.666(7)				0. 6(1)
Sb1	3a	0.3355(3)	0	0	0	1.62(3)
		0.333(7)				0.6(1)
Sb2	6c	0.8323(3)	0	0	0.42802(15)	1.62(3)
		0.833(4)			0.4254(2)	0.6(1)
Mn2	6c	0.1677(3)	0	0	0.424802(15)	1.62(3)
		0.167(4)			0.4254(2)	0.6(1)
Te1	6c	1	0	0	0.131456(12)	1.06(3)
					0.13160(11)	0.6(1)
Te2	6c	1	0	0	0.292259(14)	1.29(3)
					0.29175(13)	0.6(1)

We refined the PND data to clarify the effect of site mixing on the magnetism. Above T_C (at 50 K), the refined crystal structure is fully consistent with that obtained from the room-temperature XRD (Table I). At 5 K, we considered various magnetic structures including the ferromagnetic structure to account for the increased nuclear reflections. The best result with R_wp = 8.38% [Fig. 5(a)] was obtained for the ferrimagnetic structure, where the interexchanged Mn atoms at the 6c site align antiparallelly along the c axis with respect to Mn atoms at the original 3a site. Magnetic moments are 4.3(2) μ_B and 3.1(3) μ_B for 3a and 6c sites, respectively. The sublattice magnetic moment of Mn is 2.1 μ_B per unit cell, which is indeed in good accordance with the saturation magnetization value at 5 K [Fig. 2(b)].

FIG. 5.

PND patterns of MnSb₂Te₄ at (a) 5 K and (b) 50 K. Red crosses and green and blue lines represent observed, calculated, and difference profiles. Green ticks are used to show the positions of the Bragg peaks. (c) Proposed magnetic structure obtained from 5-K data.

The effect of site mixing between Mn and Sb sites was considered for theoretical calculations (see Fig. S3 in the Supplemental Material [39]). Here, we used two site-mixing patterns with a $\sqrt{3}\times \sqrt{3}\times 1$ supercell and calculated the ferromagnetic, ferrimagnetic, and antiferromagnetic spin configurations along the [001] direction. In all the cases, we found magnetic moments only at the Mn atoms. The calculated relative energies are summarized in Table S1 in the Supplemental Material. In the antiferromagnetic case, there are two choices for the magnetic moment of Mn atoms in the Sb layer so we considered their average. As opposed to the disorder-free configuration as described above, the ferrimagnetic structure was found to be most stable. This indicates that the site mixing alters the interlayer exchange coupling from antiferromagnetic to ferromagnetic. We note that the band structures of the ferrimagnetic structures have a band gap. Since these band structures highly depend on the site-mixing patterns, we speculate that a fully random antisite mixing, if achieved, will recover the original crystal structure symmetry and the Weyl-semimetal phase may appear.

IV. CONCLUSION

To summarize, we have synthesized a layered chalcogenide MnSb₂Te₄ and measured its fundamental physical properties. The observed spontaneous magnetization below 25 K, differing from the antiferromagnetic order in MnBi₂Te₄, can be explained in terms of the ferrimagnetic order where the interexchanged Mn moments are antiparallelly coupled with the original Mn moments. First-principles calculations show that the introduction of antisite disorder plays a key role for the ferromagnetic interaction between Mn layers, which we believe is an important step toward the TRS broken type-II Weyl semimetal state. It should be noted that the Sb sample used here is in a polycrystalline form, which may hamper the observation of the expected topological properties. For further analyses of the topological state in MnSb₂Te₄, growth of a single crystal is required, which is in progress. The known MPn₂Te₄ compounds have been predicted to have topological states including the topological insulator, antiferromagnetic topological insulator, and topological axion state [35–37]. We demonstrate here that MnSb₂Te₄ represents an example in this family possessing the interlayer ferromagnetic interaction, which warrants further development of topological physics.