The huge effect of Mn substitution on the structural and magnetic properties of LaFeAsO: the La(Fe,Mn)AsO system

As revealed by NPD analysis, at 150 K all samples crystallize in the tetragonal system, but undergo a P4/nmm  →  Cmme structural transition on cooling at T_s, evidenced by selective peak splitting. As a matter of fact, split peaks can be only observed in the high-resolution D2B data, whereas in the high-intensity D20 data they are convoluted in a single peak; as a result only selective peak broadening is detected. Figure 1 shows the thermal evolution of the tetragonal 220 and 322 Bragg peaks that split into the orthorhombic 040  +  400 062 and 152  +  512 doublets, marking the symmetry breaking (high-resolution D2B data). In particular, Rietveld refinements reveal that the tetragonal and the orthorhombic polymorphs coexist in a rather extended thermal range in the inspected samples, indicating that the character of the structural transition is 1st order, as in pure LaFeAsO.

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Table 1 lists the structural parameters at 10 K as obtained by Rietveld refinement, whereas figure 2 depicts the corresponding crystal structure; figure 3 shows the Rietveld refinement plot for the sample La(Fe_0.96Mn_0.04)AsO, selected as representative (data collected at 10 K). Chemical substitution in LnFeAsO compounds has previously been found to lead to a contraction of the lattice constant c; this is observed for F-substitution in the SmFeAs(O,F) system [26, 27] as well as for Y-, Ru- and Co-substitution in LaFeAsO and SmFeAs(O_0.85F_0.15) [9, 11, 14, 28]. Conversely, Mn-substitution in LaFeAsO produces a peculiar increase of this parameter (table 1); in particular, this behaviour is related to the decrease of the As–Fe–As bond angle (As atoms at the same xy plane) with the increase of the Mn content (from ~113.9° down to ~113.0° moving from x  =  0.01 to 0.08; see table 1), opposite to what observed in Ru-doped samples [11]. Figure 4 shows the effect of Mn substitution on the crystal structure of LaFeAsO: a notable expansion along the c-axis in the tetrahedral Fe–As layer is observed, yielding a significant compression of the La–O layer.

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As afore-mentioned the tetragonal and orthorhombic phases are found to coexist within a significant thermal range; figure 5 shows a selected Q-region of the diffraction pattern where several diffraction lines split on account of the structural transformation (sample with x  =  0.04, selected as representative). It is evident that the structural model foreseeing the coexistence of both polymorphs perfectly fits the experimental data collected at 80 K.

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The evolution of the lattice microstrain with Mn-content is displayed in figure 6, where the Williamson–Hall plots for selected samples are superposed. It is evident that the highest strain is measured along [0 0 l] in all the inspected samples, consistently with the structural distortion displayed in figure 4, and hence it can be largely ascribed to the expansion of the tetrahedral FeAs layer along the c-axis. Noteworthy, the lattice strain tends to decrease with the increase of the Mn content.

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Figure 7 shows the thermal evolution of the tetragonal 322 Bragg peaks into the orthorhombic 152  +  512 doublets for the samples with x  ⩽  0.04; as already mentioned, the peak splitting cannot be directly resolved with the D20 data, but a selective broadening is observed. These peaks have been fitted in the whole inspected thermal range and the corresponding Lorentzian isotropic strain values (a measure of their width) are plotted in figure 8 (normalized values). It is evident that the structural transition not only decreases in temperature, but also completes within thermal ranges that increase with the Mn content.

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Accordingly with previous analyses on both pure and substituted samples [13, 14, 26], the lattice microstrain in the tetragonal phase remains constant along the main crystallographic directions as T_s is approached, but increases significantly along [h h 0] (figure 9), that is along the direction of the nesting wave-vector between the electron and hole pocket. This behaviour clearly evidences the progressive destabilization of the tetragonal structure; in particular, lattice microstrain in the tetragonal phase reveals a local breaking of this symmetry along $\left\langle h\ h\ 0 \right\rangle$, thus producing the orthorhombic distortion on cooling [26].

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The inset of figure 9 shows the tensor isosurface representing the microstrain broadening observed as the structural transition is approached. A large microstrain is observed along the c-axis, produced by the lattice distortion described in figure 4, increased by the thermal compression on cooling; more interestingly, an in-plane 4-fold tensor surface is observed, that is fully consistent with the microstrain expected for a 4/mmm  →  mmm structural transition [29].

The thermal expansion behaviour of the La(Fe,Mn)AsO samples was investigated by fitting the thermal dependence of the cell volume using a Grüneisen second-order approximation for the zero-pressure equation of state [30]:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle V\left( T \right)=\frac{{{V}_{0}}U}{Q-bU}+{{V}_{0}}\nonumber \end{align} \tag{ 1 }$$

where $Q={{V}_{0}}{{K}_{0}}/{{\gamma }^{\prime }}$ and $b=\left( K_{0}^{\prime }-1 \right)/2$; ${{\gamma }^{\prime }}$ is a dimensionless Grüneisen parameter of the order of unity; ${{K}_{0}}$ is the compressibility and $K_{0}^{\prime }$ its derivative with respect to applied pressure; ${{V}_{0}}$ is the zero temperature limit of the unit cell volume; $U$ is the internal energy calculated by the Debye approximation:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle U\left( T \right)=9N{{k}_{{\rm B}}}T{{\left( \frac{T}{{{\Theta }_{{\rm D}}}} \right)}^{3}}\int_{0}^{\frac{T}{{{\Theta }_{{\rm D}}}}}{\frac{{{x}^{3}}{\rm d}x}{{{e}^{x}}-1}}\nonumber \end{align} \tag{ 2 }$$

where N is the number of atoms in the unit cell; ${{k}_{{\rm B}}}$ is the Boltzmann's constant; ${{\Theta }_{{\rm D}}}$ is the Debye temperature. The fitting was carried out assuming ${{K}_{0}}$  =  1.03 · 10¹¹ Pa, which is the experimental bulk modulus value extracted from high pressure synchrotron x-ray powder diffraction measurements on SmFeAs(O_0.93F_0.07) [31], consistent with the theoretically calculated value for LaFeAsO (K₀ ~ 9.8 · 10¹⁰ GPa) [32]; ${{\gamma }^{\prime }}$, ${{\Theta }_{{\rm D}}}$ and $K_{0}^{\prime }$ are free parameters. ${{\Theta }_{{\rm D}}}$ values turn out to be in the range 250 K–305 K in all cases, in agreement with the value calculated in pure LaFeAsO (${{\Theta }_{{\rm D}}}$  =  282 K) from heat capacity data [33]. Figure 10 shows the resulting fitting curve for the La(Fe_0.97Mn_0.03)AsO sample, selected as representative; the Grüneisen law well accounts for the observed temperature dependence of the volume in the whole inspected temperature range; no departure is detected at low temperature, in agreement with the results obtained for the La(Fe_1−xRu_x)AsO system [14].

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The lattice distortion solely induced by the structural transition (i.e. neglecting thermal expansion) is defined as spontaneous strain ${{e}_{{\rm s}}}$; the strain behaviour has thus been studied using the high resolution D2B data by applying the general equations for calculating the components of ${{e}_{{\rm s}}}$ [34, 35]. At this scope, cell parameters for the tetragonal phase have been extrapolated at low temperature in the orthorhombic field, by fitting the experimental tetragonal cell edge a above the structural transition with modified equations (1) and (2). Hence in this case ${{\Theta }_{{\rm D}}}$ was fixed to 282 K, γ and K₀ being the values obtained from the cell volume fitting and ${{a}_{0}}$ was a free parameter. The proper symmetry-breaking component of the spontaneous strain ${{e}_{{\rm s}}}$ for the P4/nmm  →  Cmme structural transition is ${{e}_{6}}$ [4, 35], that in its general formulation corresponds to:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{e}_{6}}=\left( \frac{{{a}_{{\rm ortho}}}\cdot {\rm cos}\gamma }{{{a}_{0}}\cdot {\rm sin}{{\gamma }_{0}}}-\frac{{{b}_{{\rm ortho}}}\cdot {\rm cos}{{\gamma }_{0}}}{{{b}_{0}}\cdot {\rm sin}{{\gamma }_{0}}} \right).\nonumber \end{align} \tag{ 3 }$$

Note that the unit cell of the low-temperature orthorhombic phase is rotated by 45° in the xy plane with respect to that of the high-temperature tetragonal one; as a consequence, ${{a}_{{\rm ortho}}}$ does not represent the cell edge of the orthorhombic structure, but is an interplanar distance roughly parallel to the pristine tetragonal [1 0 0] direction. In our specific case ${{e}_{6}}$ simplifies to:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle {{e}_{6}}=\left( \frac{{{a}_{{\rm ortho}}}\cdot {\rm cos}\gamma }{{{a}_{0}}} \right).\nonumber \end{align} \tag{ 4 }$$

The ${{e}_{6}}$ component has the same symmetry of the order parameter of the structural transition η_s (${{e}_{6}}$ $\propto$ η_s). Figure 11 shows the dependence of η_s (obtained by normalizing the values of the symmetry breaking strain component ${{e}_{6}}$) for La(Fe_0.96Mn_0.04)AsO, selected as representative, consistent with a 1st order nature of the structural transition.

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Among the other components, ${{e}_{3}}$ is not-symmetry breaking, whereas ${{e}_{1}}$ and ${{e}_{2}}$ are both constituted by a symmetry breaking component plus a non-symmetry breaking one. The symmetry breaking components ${{e}_{2.{\rm sb}}}$  =  $-{{e}_{1.{\rm sb}}}$ (not shown) exhibit similar thermal dependences, but they do not vary linearly with ${{e}_{6}}$ (figure 12), implying a different strength of coupling between these components and η_s. A closer analysis reveals that:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \frac{{{e}_{6}}}{{{e}_{2.{\rm sb}}}}=\frac{2a_{{\rm ortho}}^{2}\cdot {\rm cos}\gamma }{a_{0}^{2}\cdot \left( {\rm sin}\gamma -1 \right)}.\nonumber \end{align} \tag{ 5 }$$

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The observed behaviour plotted in figure 12 is consistent with the shrinking and expansion experienced by the tetragonal basal plane with the symmetry breaking, since that $a{\rm cos}\gamma$ and $a{\rm sin}\gamma$ are parallel to the orthorhombic x and y axes, respectively.

The magnetic moment characterizing LnFeAsO compounds is generally very low, never exceeding 1 μ_B [3]; for this reason magnetic scattering can be appreciated only in the high-intensity data. Using the NPD data collected at D20, the magnetic transition taking place at T_m was studied in samples with x  =  0.01, 0.02, 0.03 and 0.04. Figure 13 shows thermodiffractograms displaying the thermal evolution of the magnetic peaks; comparing the plots one can see that the magnetic transition lowers in temperature with the increase of Mn content and that the peak intensity progressively decreases as well.

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The spin ordering is the same as observed in pure LaFeAsO, with a magnetic propagation wave-vector q  =  [1,0,1/2] and moments aligned along the a axis (figure 2). In all cases, the magnetic transition is continuous (2nd order) and the magnetic moment grows smoothly from zero below T_m (figure 14). The refined values for the magnetic moments are consistent with those reported by Qureshi et al [36] for pure LaFeAsO, ranging between 0.3 μ_B and 0.6 μ_B.

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To our knowledge, the critical exponent β has never been estimated for the magnetic transition taking place in REFeAsO compounds; nonetheless, β  =  0.21 is obtained after fitting the data obtained by muon spin spectroscopy for pure LaFeAsO reported by Amato et al [37]. This value is in fair agreement with that obtained for BaFe₂As₂ (β  =  0.206) [38]; remarkably, in this case it was found that the calculated value β resulted almost constant by fitting the full data set or, otherwise, within a reduced temperature range Δt ~ 0.9–1.0.

Being the magnetic Bragg peak intensity I proportional to the square of the sub-lattice magnetization, its thermal dependence follows the power law:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle I\left( T \right)=A\cdot {{\left( \frac{{{T}_{{\rm m}}}-T}{{{T}_{{\rm m}}}} \right)}^{2\beta }}=A\cdot {{t}^{2\beta }}\nonumber \end{align} \tag{ 6 }$$

where I is the integrated intensity of the magnetic Bragg peak (the peak at Q ~ 1.55 Å⁻¹), A is a constant and β represents the critical exponent. In our case, we fitted data for t  ⩾  0.5 (figure 14). For samples with x  =  0.01–0.03 data fitting yields β ~ 0.22–0.26, quite consistent with the value obtained for pure LaFeAsO. For x  =  0.04 the paucity of the experimental data prevents any accurate analysis. The resulting fittings are displayed in figure 14.

Table 2 resumes the data relevant to the magnetic phase as obtained by the analysis of the data collected at the D20 diffractometer.

These results indicate that magnetic interactions are short-ranged [39] and that the nature of the magnetic interactions is not significantly affect by Mn-substitution, but their strength. It is worth noting that the substituting high-spin Mn²⁺ ion (3d⁵) is characterized by a strong Hund's coupling; on account of its extremely stable external electronic configuration, it may conjectured that Mn²⁺ opposes any variation to its electronic state and in this way affects its local environment, in particular the average exchange field produced by the neighbouring Fe ions. For this reason, the magnetic moments interactions are weakened on average and, as a consequence, the magnetic transition lowers in temperature and the value of the ordered magnetic moment decreases.

On the basis of the results obtained by investigating the thermal evolution of the crystal structure and of the spin ordering, a phase diagram for the La(Fe_1−xMn_x)AsO system can be tentatively drawn (figure 15). It becomes visible that the evolution of the structural (T_s) and the magnetic (T_m) transition temperatures with Mn-content is decoupled. At first, both temperatures decrease similarly with substitution, then, however, the magnetic ordering temperature decreases much faster than the structural transition temperature and starting from x ~ 0.6 magnetism is largely hindered down to its complete suppression. Moreover, one can now clearly state that magnetism sets only in after that the orthorhombic phase is well established, that is within the orthorhombic phase field. Conversely, the structural transition temperature almost homogenously decreases, but does not get suppressed within the inspected compositional range. This behaviour indicates that the structural transition is not originated by magnetic degrees of freedom. Charge and orbital degrees of freedom thus remain the most likely candidates driving the symmetry breaking. In a previous work, we detected the occurrence of satellite peaks in the orthorhombic polymorph of some La(Fe_1−xMn_x)AsO samples pertaining to this same series, evidencing the occurrence of a static charge density wave [21]; this result points to a charge density wave (CDW) instability playing a major role in the structural transition. In this context, it is worth to note that the very faint satellite peaks marking the incommensurate structure can be detected only by using high-resolution synchrotron x-ray powder diffraction; this is the reason why such diffraction lines are not observed in our NPD patterns.

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By comparing the phase diagrams of the La(Fe_1−xMn_x)AsO and La(Fe_1−xRu_x)AsO [14] systems, the huge effect of Mn-substitution on the structural transition temperature becomes evident. For example, the tetragonal phase is unstable above ~130 K in the La(Fe_1−xRu_x)AsO system for x  =  0.10, but the same result is obtained with x ~ 0.01 in the La(Fe_1−xMn_x)AsO. In the Ru-substituted systems properties are strongly affected by the disorder induced by Ru ions, which do not sustain any magnetic moment and act as nonmagnetic impurities [11]. The huge decrease of T_s observed in the Mn-substituted system clearly indicates that Mn does not induce only disorder; other effects are at play, especially the frustration of the electronic interactions surrounding the local environment of the dissolved Mn²⁺ ions.