Effects of Fe doping on anomalous specific heat and XAFS oscillation in antiferromagnetic metal Mn₃Si

The Heusler intermetallic compound Mn₃Si [Mn_I(Mn_II)₂Si] is an itinerant antiferromagnetic material, which exhibits an incommensurate spin-density-wave (SDW) order below T_N = 21 K with two types of magnetic moments: μ_I ∼ 1.7μ_B and μ_II ∼ 0.2μ_B at the 4b (I site) and 8c (II site) sites, respectively, as presented in the $Fm3¯m$ notation.¹ The most remarkable features of Mn₃Si include its field insensitive bulk properties in specific heat, resistivity, and magnetic susceptibility, even though its T_N is low.^2,3 Besides, it was observed that specific heat of Mn₃Si at low temperatures included a considerably large quantitative component aside from the lattice (∝T³) and electronic (∝T) specific heat components; the large component could not be explained using antiferromagnetic spin waves.³ 

Pfleiderer et al. noted that the Fermi-liquid theory would not be applicable to Mn₃Si, rather, its magnetic-field insensitivity could be explained by attributing a half-metallic behavior to it.³ In fact, the existence of a half-metallic band structure below T_N was supported by first-principle calculations performed in a later study.⁴ However, it is interesting to note that the insensitivity of Mn₃Si to magnetic fields was observed even in the paramagnetic state, wherein the half-metallic band structure of Mn₃Si should typically disappear. Recently, Steckel et al. studied the transport properties of Mn₃Si in detail and observed charge fluctuations persisting up to ∼200 K,⁵ indicating the presence of these charge fluctuations even at significantly higher temperatures than T_N.

To better understand its peculiarities, in this study, we analyzed the specific heat of Mn₃Si using Fe substitution across a wide temperature range for T_N. From the simple electronic band perspective, Fe doping increased the electron number in the 3d band, correspondingly transforming the SDW order through modified Fermi-surface nesting, thus increasing T_N.^6,7 In contrast, from the crystallographic perspective, the doped Fe selectively entered at the II site.⁷ However, thus far, almost no experimental studies have been reported on the relationship between Fe doping and local structure of Mn. Hence, we measured the X-ray absorption fine structure (XAFS) of the Mn K-edge to deduce any relationship that might exist between Fe doping and the local structure and/or local valence state of Mn.

Polycrystalline samples of Mn_3−xFe_xSi were synthesized via Ar arc melting;⁸ then, single crystals were grown from the melt of the polycrystalline samples using the vertical Bridgman method.¹ The X-ray powder diffraction patterns of these samples revealed that they contained a second phase; however, the quantity of this other phase was negligible.

The zero-field specific heat was measured using the obtained disk-shaped single crystals (∼4 mm² × 0.2 mm) of x = 0.2 and 1.0 by the relaxation method. The XAFS were measured on the beam line BL14B1 at SPring-8, Japan. The absorption spectra of the Mn K-edge were observed at 4 K using powder samples of x = 0, 0.6, 1.0, and 1.5, all of which were blended together with BN powder.

Figures 1(a) and 1(b) show the zero-field specific heat values over a wide temperature range for x = 0.2 and 1.0, respectively. The peak temperature corresponds to T_N = 21.3 (45.3) K for x = 0.2 (1.0). The contribution from the lattice and electronic components (C_l+e) was determined based on the data for high temperatures above 150 K using the equation: C_l+e(T) = γ_HT + 12RD(Θ/T), where γ, Θ, and D(x) are the coefficients for electronic specific heat, Debye temperature, and Debye function, respectively. (The subscript “H” for γ indicates that the value is determined at a high temperature.) The solid curve for x = 0.2 (1.0) shows the corresponding calculated values for C_l+e using γ_H = 22 (26) mJ K⁻² mol⁻¹ and Θ = 465 (490) K. As a result, it can be observed that the specific heat value starts to deviate from C_l+e at high temperatures (>100 K).

Based on the free electron model, γ ∼ 19 mJ K⁻² mol⁻¹ was evaluated using the density of states at E_F in the paramagnetic state of Mn₃Si (∼8 states/eV);⁴ this value is almost in agreement with γ_H, indicating normal metal properties at high temperatures for both x = 0.2 and 1.0.

In contrast, the specific heat trend at low temperatures was abnormal. Figure 1(c) shows C/T as a function of T² in the low temperature region. Similar to x = 0,⁹ a large net component (C/T − C_l+e/T) existed for the x = 0.2 case; however, on increasing x to 1.0, the net component considerably decreased. It is quantitatively difficult to attribute the net component only to the conventional magnetic specific heat from spin waves, as explained in Ref. 3.

By assuming C(T) = γ_LT + βT³ for T → 0, we obtained γ_L = 100 (10) mJ K⁻² mol⁻¹ and β = 1.0 (0.26) × 10⁻³ J K⁻⁴ mol⁻¹ for x = 0.2 (1.0). (The subscript “L” for γ indicates that the value is determined at a low temperature.) Figure 1(d) shows a semi-log plot for γ_H and γ_L, where γ_L for Mn₃Si³ and Fe₃Si¹⁰ were also included. Large γ_L, i.e., the heavy effective mass of electrons for x = 0 and 0.2, drastically changed to normal mass owing to Fe doping.

Figure 2(a) shows the raw data for the absorption spectra when x = 0 and 1.5 near the Mn K-edge at 4 K. In contrast to the normal oscillation size observed for x = 1.5, the oscillation amplitude in the case of x = 0 was unusually small. It is interesting to note that this unusual small amplitude behavior of x = 0 also appeared in the X-ray absorption spectra near the edge structure (XANES), as shown in Fig. 2(b). Figure 2(c) shows the derivative with respect to E. Four fine structures appeared at A–D for x = 1.5, whereas two of them (specifically, C and D) were not so clear in the case of x = 0. Note that the Mn K-edge shifts slightly to the high-energy side by Fe doping; it implies an increase in valence of Mn. This edge shift is probably caused by the larger electronegativity of Fe than that of Mn.

Figure 3(a) shows the x variation of the Fourier transform of k³χ(k), where χ(k) is the function for the extended XAFS (EXAFS) obtained from 3 ≤ k ≤ 11 Å⁻¹ and R is the distance from the Mn atoms. It can be clearly observed that the first peak at R ∼ 2.2 Å, which was composed of the nearest neighbor (NN) (∼2.48 Å) and next nearest neighbor (NNN) bonds (∼2.86 Å), developed as x increased. Because the number of coordinates around Mn atoms remained unchanged even after Fe doping, the significant change in peak height can be attributed to the Debye–Waller factor, σ².

In order to quantify σ², we conducted fitting for the first peak using five parameters: three σ² for the I–II, (I,II)–Si, and II–II bonds, and two inter-atomic distances R_int for the NN and NNN bonds. The resultant curve was in good agreement with the observed values, as is indicated by the solid lines in Fig. 3(a).

Figure 3(b) shows the determined σ² values for the I–II and (I,II)–Si bonds at 4 K. Considering the (I,II)–Si bonds, an increase in σ² is expected with an increase in x, because it is likely that the chemical substitution with Fe introduces disorder in the local structure. Thus, the dependence of σ² on x for the NN I–II bonds is quite unusual.

The relatively large σ² ∼ 0.02 Ų for x = 0 indicates that the structural distortion in terms of the I–II bond length was substantial in the case of Mn₃Si. Because the doped Fe selectively entered the Mn_II site in this x range^6,8 and EXAFS data at the Fe K-edge showed normal amplitude for oscillation (not shown in figure), the large σ² for the I–II bonds could be attributed to the disorder of Mn_II atoms along the bond axis. This observation is in agreement with the spin sector data for Mn₃Si obtained via NMR,¹¹ which indicates that a larger distribution in local magnetic fields at Mn_II compared with in Mn_I at low temperatures.

The net component of specific heat persisted up to more than 100 K [Figs. 1(a) and 1(b)]. This observation is consistent with significant fluctuations in the transport properties of Mn₃Si⁵ with a wider temperature range. This large energy scale of the net component, particularly for x = 0.2, could be explained using the inter-band excitations of itinerant electrons. Hence, the peak specific heat at T_N might manifest the energy gap opening through Fermi-surface nesting, rather than a conventional antiferromagnetic phase transition of localized spins.

It can be conjectured that a charge pseudo-gap opened at a significantly higher temperature than T_N and it successively transformed to a charge-density-wave (CDW) gap below T_N. In fact, an indication of CDW ordering was reported through neutron scattering.⁹ In this case, the specific heat at low temperatures is affected by the CDW gap, leading to its insensitivity to magnetic fields, which has been observed experimentally.^2,3 Because no exponential-type evolution was observed at low temperatures [Fig. 1(c)], the CDW gap could be gapless and relevant to the large β.

Thus far, we are not aware whether this CDW-relevant specific heat is related to the local valence state of Mn_II atoms and/or local structural distortion around the Mn_II atoms. We speculate that the large disorder of Mn_II ions induced inhomogeneity in the positive charge distribution and enhanced the inhomogeneous electronic states of the itinerant electrons that originated from the Mn_II orbital character. This electronic inhomogeneity could be attributed to the charge pseudo-gap formation in local, support the observed short-range and short-lifetime CDW, and promote deviation from the simple Fermi-liquid system. Because of the deterioration of potential periodicity and increase in the electron scattering rate, the effective electron mass (∝γ_L) was possibly enhanced in the case of small x and decreased when x increased [Fig. 1(d)], which corresponds to the dependence of σ² on x on the I–II bonds [Fig. 3(b)].

The authors are grateful to S. C. Che and Y. Yamaguchi for technical assistance with single crystal growth. The XAFS measurements were conducted under the Shared Use Program of JAEA Facilities: Proposal Nos. 2011B3618, 2012A3616, and 2012B3624. The study was performed at Tohoku University, KEK and Ibaraki University was supported by JSPS KAKENHI Grant numbers JP22340089 and JP25287081. The work at KAERI was financially supported by the project of Neutron Basic Research Scattering Instrument Optimization and Operation (No. 521210-18).