The specific heat of Mn3−xFexSi was measured over a wide temperature range. Aside from the lattice and electronic specific heat components, another component had a significant contribution to the specific heat at low temperatures in the case of x = 0.2; however, its contribution decreased when x = 1.0. It is observed that the net component was retained at temperatures significantly higher than TN for both x. The XAFS spectra of the Mn K-edge for x = 0 not only indicated a smooth structure near the edge, but also an unusually small amplitude in the extended high energy region; however, these features disappeared with Fe doping. The specific heat and XAFS data were discussed in terms of the charge degree of freedom or electronic inhomogeneity.
The Heusler intermetallic compound Mn3Si [MnI(MnII)2Si] is an itinerant antiferromagnetic material, which exhibits an incommensurate spin-density-wave (SDW) order below TN = 21 K with two types of magnetic moments: μI ∼ 1.7μB and μII ∼ 0.2μB at the 4b (I site) and 8c (II site) sites, respectively, as presented in the notation.1 The most remarkable features of Mn3Si include its field insensitive bulk properties in specific heat, resistivity, and magnetic susceptibility, even though its TN 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 TN 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 TN.
To better understand its peculiarities, in this study, we analyzed the specific heat of Mn3Si using Fe substitution across a wide temperature range for TN. 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 TN.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.
II. EXPERIMENTAL PROCEDURES
Polycrystalline samples of Mn3−xFexSi 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.
A. Specific heat measurements
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 TN = 21.3 (45.3) K for x = 0.2 (1.0). The contribution from the lattice and electronic components (Cl+e) was determined based on the data for high temperatures above 150 K using the equation: Cl+e(T) = γHT + 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 Cl+e using γH = 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 Cl+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 EF in the paramagnetic state of Mn3Si (∼8 states/eV);4 this value is almost in agreement with γH, 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 − Cl+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) = γLT + βT3 for T → 0, we obtained γL = 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 γH and γL, where γL for Mn3Si3 and Fe3Si10 were also included. Large γL, i.e., the heavy effective mass of electrons for x = 0 and 0.2, drastically changed to normal mass owing to Fe doping.
B. XAFS measurement
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 Rint 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 Å2 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 MnII site in this x range6,8 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 MnII 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 MnII compared with in MnI at low temperatures.
IV. DISCUSSION AND CONCLUSIONS
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 TN 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 TN and it successively transformed to a charge-density-wave (CDW) gap below TN. 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 MnII atoms and/or local structural distortion around the MnII atoms. We speculate that the large disorder of MnII ions induced inhomogeneity in the positive charge distribution and enhanced the inhomogeneous electronic states of the itinerant electrons that originated from the MnII 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 (∝γL) 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).