Mn-induced Fermi-surface reconstruction in the SmFeAsO parent compound

The electronic ground state of iron-based materials is unusually sensitive to electronic correlations. Among others, its delicate balance is profoundly affected by the insertion of magnetic impurities in the FeAs layers. Here, we address the effects of Fe-to-Mn substitution in the non-superconducting Sm-1111 pnictide parent compound via a comparative study of SmFe\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{1-x}$$\end{document}1-xMn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{x}$$\end{document}xAsO samples with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x(\text{Mn})=$$\end{document}x(Mn)= 0.05 and 0.10. Magnetization, Hall effect, and muon-spin spectroscopy data provide a coherent picture, indicating a weakening of the commensurate Fe spin-density-wave (SDW) order, as shown by the lowering of the SDW transition temperature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_\text{SDW}$$\end{document}TSDW with increasing Mn content, and the unexpected appearance of another magnetic order, occurring at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T^{*} \approx 10$$\end{document}T∗≈10 and 20 K for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$x=0.05$$\end{document}x=0.05 and 0.10, respectively. We attribute the new magnetic transition at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T^{*}$$\end{document}T∗, occurring well inside the SDW phase, to a reorganization of the Fermi surface due to Fe-to-Mn substitutions. These give rise to enhanced magnetic fluctuations along the incommensurate wavevector \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{Q}_2 =(\pi \pm \delta ,\pi \pm \delta )$$\end{document}Q2=(π±δ,π±δ), further increased by the RKKY interactions among Mn impurities.

132.36(5) 0. 10 3.9478(4) 8.550 (1) 133.25 (5) preliminary XRPD analysis of the x = 0.05 sample carried out at the high-resolution, high-intensity ID22 beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) above (15 K) and below (8 K) the critical temperature T * . Remarkably, incommensurate satellite peaks are observed at both temperatures (see inset), indicating a structural modulation characterizing the low-T orthorhombic crystal structure. Similar satellite peaks were also observed in the analogous La(Fe,Mn)AsO system [3] and ascribed to the presence of a charge-density-wave instability. Superposition of the synchrotron XRPD data collected above and below T * . To enhance the low-intensity peaks, the intensities are reported in a logarithmic scale. The upper part shows the difference curve, where changes are only associated to thermal expansion and/or peak-intensity variation (i.e., no new peaks at lower T ). The inset shows the magnified pattern collected at 8 K, where the incommensurate satellite peaks are highlighted in blue (the same peaks are also observed at 15 K).

TRANSPORT PROPERTIES
Electrical resistivity vs temperature Figure SI-4 shows the normalized resistivity ρ(T )/ρ(300 K) of the two doped samples (x = 0.05 and 0.10). For comparison we report also the resistivity dataset taken on the undoped compound (x = 0). As expected, the normalized resistivity of the x = 0 sample (black curve in Fig. SI-4) decreases upon cooling, exhibiting a clear anomaly at the spin density wave (SDW) transition temperature T SDW 150 K [4,5]. Below T SDW , ρ(T ) decreases much faster, reaching 1.8 mΩcm at 2 K. Upon Mn doping, T SDW is progressively reduced, while ρ(T ) increases upon cooling and shows only minor anomalies. The latter are more evident if one plots the derivative dρ(T )/dT vs. temperature (see inset in Fig. SI-4). Thus, in the x = 0.05 case, we observe a broad peak centred at about 80 K. The shape of such anomaly suggests that it represents T SDW , the magnetic ordering temperature of the FeAs layers [4]. In the x = 0.10 case, a small change in slope at ca. 25 K suggests again the occurrence of a magnetic transition. The prominent increase in resistivity with decreasing temperature, most likely reflects theweak localization effects occurring in the Mn-substituted samples. In particular, the residual resistivity at 2 K is about 15.2 mΩcm for x = 0.05  Table II. Figure SI-5 shows the transverse resistivity ρ x y for the x = 0.05 (a) and x = 0.10 (b) samples as a function of the magnetic field B up to 9 T, applied perpendicular to the electric current direction for selected temperatures in the range 2-160 K. In order to remove spurious magnetoresistance components (ρ x x ), generally due to contact misalignments, ρ x y (B) was determined by extracting the antisymmetric component of the field-reversed transverse voltage V x y :

Experimental details on the Hall-effect measurements
where t is the thickness of the samples (t ∼1.5 mm) and I the applied current. The Hall coefficient R H was subsequently derived as the slope of the linear fits to ρ x y (B). In the x = 0.05 case we performed a linear fit of ρ x y (B) up to 9 T, with ρ x y being linear across the entire temperatureand field range. In the x = 0.10 case, instead, we limited the fits to 3.5 T, above which ρ x y is not anymore linear in field (see inset in Fig. SI-5b).

ZERO-FIELD µSR
The analysis of the ZF-µSR time-dependent asymmetry data was performed by using the following fitting function: Here B i µ is the magnetic field at the i-th implanted muon site and γ µ = 2π × 135.53 MHz/T is the muon gyromagnetic ratio; a T i and a L i refer to muons probing local fields in the transverse (T) or longitudinal (L) directions with respect to the initial muon-spin polarization. The coherent precession of muons is taken into account by the f (γ µ B i µ t) function, whereas D T i (t) and D L i (t) functions represent the precession damping: D T i (t) reflects the static distribution of local magnetic fields (T) and D L i (t) represents the effects of dynamical relaxation processes (L). Finally, the sum over i takes into account the two inequivalent muon implantation sites in 1111 iron pnictides. Of these, the most populated one (i = 1) is located near the FeAs layers, whereas the least populated one (i = 2) is near the SmO layers [6].
In the high-temperature paramagnetic regime the two samples exhibit different behaviors. A comparison is shown in Fig. SI-6, where the muon-spin polarization P(t) (i.e., the normalised asymmetry) is plotted at selected temperatures. In the x = 0.05 case, for temperatures above 80 K, P(t) is best described by an exponential relaxation function D L (t) = e −λ L t , which suggests the presence of fast fluctuating electronic magnetic moments. The longitudinal relaxation rate is about 0.10 µs −1 , in agreement with existing data for Sm-1111 pnictides [7][8][9]. Below 80 K a strong depolarization due to fluctuating Sm 3+ moments (see below) is expected [7][8][9]. However, the concomitant onset of the Fe 2+related SDW order at the same temperature makes it difficult to disentangle the two effects. The scenario in the x = 0.10 case is a bit more complicated. As expected, muon spins undergo a strong depolarization below 80 K (see Fig. SI-6), likely unrelated to the Fe 2+ SDW order, here occurring well below 50 K. Incidentally, as the temperature decreases, the depolarization rate becomes higher than that observed in the x = 0.05 case or in F-doped Sm-1111 samples [7]. In fact, by using the same fit model as in the x = 0.05 case, at low temperatures the slow relaxing component acquires too high values to be realistic (generally in the range up to 0.5 µs −1 [7][8][9]). This is probably the reason why the best P(t) fits could be obtained with a stretched exponential model [7], generally valid for disordered magnetic moments, most notably for diluted spin glasses [10].
For T < T SDW , in the x = 0.05 case the best fits were obtained by assuming the transverse components to be f 1 2 represent the field distribution widths at sites i = 1, 2. It is worth noting that a cosine-like oscillating term suggests the presence of a commensurate magnetically ordered phase. No significant changes of this term were detected below and above T * , likely due to not adequate statistics at such temperatures. The relative amplitudes of these two terms resulted very similar, contrary to the usual distinction between the majority (FeAs layers) and the minority (SmO layers) muon implantation sites [9,11,12]. The longitudinal relaxation, instead, was modeled with two Lorentzian terms D L i (t) = e −λ i t , corresponding to a fast and a slow decay. The "slow" relaxation (with λ L1 0.1 µs −1 ) accounts for the longitudinal relaxation of muons implanted in FeAs layers. The "fast" relaxation (with λ L2 0.1-4 µs −1 ), arises from muons implanted in SmO layers and, therefore, is strongly affected by Sm 3+ fluctuating moments. Differently from the undoped case, this last term becomes visible only below 30 K. Here, too, the x = 0.10 case presents some differences. Firstly, its transverse component had to be fitted by the sum of a Gaussian-damped zeroth order Bessel function ) and a fast Gaussian relaxation term ( f 2 (γ µ B 2 µ t)D T 2 (t) = e −σ 2 2 t 2 /2 ) whose amplitude ratio was kept fixed at all temperatures. The longitudinal fast-and slow relaxing components, instead, were merged into a single term, well modelled by a stretched exponential function D L (t) = e −(λ L t) β , as already mentioned above.
In Fig. 2a-b we show the fits of the time-dependent asymmetry at short times for both samples at selected tempera-tures, whereas the resulting fit parameters are reported in Fig. 2c-d and discussed in the main article. Figure SI-7a summarizes the best-fit parameters of the longitudinal-decay components of asymmetry for the x = 0.05 case. Below 100 K, the slow relaxation rate, λ 1 (upper panel) increases progressively, to show a broad peak at T SDW = 83 K. Upon further lowering the temperature λ 1 saturates (noisily) at about 0.2 µs −1 . The fast relaxation rate, λ 2 (bottom panel), becomes detectable only below 30 K and rises up to 5.4 µs −1 at the lowest temperature. Figure SI-7b shows the longitudinal relaxation and the β parameter as a function of temperature for the x = 0.10 case. λ st (upper panel) starts increasing as T decreases below 50 K (the onset of the magnetic transition) and peaks at T * = 20 K and ∼ 5 K. Unfortunately, the lack of finely spaced data does not allow us to better clarify these features. Interestingly, the stretching coefficient β is ca. 1 (Lorentzian relaxation) at high temperature. Then it decreases almost linearly with temperature down to β = 0.5, to finally show a broad peak with an onset at about 20 K.

DETAILS OF THE THEORETICAL MODEL
In the normal state, the electronic Hamiltonian near the Γ -point has the following form: where Ψ Γ = c yz,↑ , −c xz,↑ , c yz,↓ , −c xz,↓ T is the four-component spinor, while the h Γ (k) operator consists of two parts, h Γ (k) = h Γ ,0 (k) + h Γ ,SOC (k), modeling the electronic dispersion and the effects of spin-orbit coupling, respectively. The first term is given by while the spin-orbit coupling can be expressed as Here σ i and τ i are the Pauli matrices in the spin-and the orbital space, respectively. For the electron pockets near the X and Y point of the one-iron BZ, which are hybridized by the spin-orbit coupling in the folded two-iron BZ, the Hamiltonian has the form (SI-6) Here, the spinors read Ψ Y = c xz,↑ , c x y Y ,↑ , c xz,↓ , c x y Y ,↓ T and Ψ X = c yz,↑ , c x y X ,↑ , c yz,↓ , c x y X ,↓ T , while the dispersion is where v Y /X = v(±k x + k y ) + p 1 (±k 3 x + k 3 y ) + p 2 k x k y (k x ± k y ). The spin-orbit coupling term is as follows As for the resulting mean-field Hamiltonian, which includes both the commensurate and the incommensurate SDW orders, it reads: is the combined normal state Hamiltonian and It is worth noting that the dimension of Ψ(k) is 12 × 12, reflecting the three 4 × 4 matrices for each symmetry point of the Brillouin zone (Γ , X , and Y ). The commensurate magnetic order, M X ,c at Q X = (π, 0) is contained in Ψ(k) as off-diagonal matrix elements connecting the Γ -and the X points of the Brillouin zone, respectively. With the inclusion of the incommensurate momentum, Ψ(k) becomes 24 × 24. The M x,c and M y,c values are determined by the Hubbard-Hund interactions (M x ∝ U + J ) in the parent system and can be computed unambiguously by solving the mean-field equations. However, in the Mn-doped case, the situation is more tricky due to an additional Mn-Mn RKKY type interaction and the interaction of Mn impurities with the multiorbital host system. Therefore, the calculations become more involved. In the present manuscript we treat M y,ic as a parameter which minimizes the total free energy of the system by gapping the residual Fermi surface of the orthorhombic AF state. The detailed microscopic calculations are planned to be published elsewhere.