Magnetism and site exchange in CuFeAs and CuFeSb: A microscopic and theoretical investigation

We have investigated the magnetic ground state of CuFeAs and CuFeSb by means of ${}^{57}\mathrm{Fe}$-Mössbauer spectroscopy, muon spin rotation/relaxation $\left(\mu \mathrm{SR}\right)$, neutron diffraction, and electronic structure calculations. Both materials share the 111-LiFeAs crystal structure and are closely related to the class of iron-based superconductors. In both materials there is a considerable occupancy of the Cu site by Fe, which leads to ferromagnetic moments, which are magnetically strongly coupled to the regular Fe site magnetism. Our study shows that CuFeAs is close to an antiferromagnetic instability, whereas a ferromagnetic ground state is observed in CuFeSb, supporting theoretical models of anion height driven magnetism.

Figure 1

Neutron powder diffraction pattern collected at 20 K (Bragg R-factor 10.26%, RF-factor 12.6%, ${\chi }^2=1.22)$.

Figure 2

Results of Mössbauer spectroscopy on the CuFeAs $\mu \mathrm{SR}$ sample. The left inset shows the two component model at 2 K with CuFeAs (solid) and ferrocene (dashed, providing experimental linewidth). The increase of magnetic field $B_{\mathrm{tot}}$ below 11 K is accompanied by a drop of spectral area (right inset), indicating that $\approx 10\%$ of the Fe nuclei sense much higher fields than quantified by $B_{\mathrm{tot}}$. The transition temperature shifts upon the application of a 0.5 T longitudinal field (LF) revealing the ferromagnetic character of the magnetic order. Only at the lowest temperatures does a static superposition of zero field (ZF) $B_{\mathrm{hyp}}$ and applied field $B_{ex}$ as described by $B_{\mathrm{tot},\mathrm{theo}}$ [Eq. (1)] apply. In that case dominant AFM order is present.

Figure 3

High statistics Mössbauer spectra of the neutron sample, fit with a four fraction model (parameters in Table 3).

Figure 4

CuFeAs Mössbauer spectrum of the neutron sample at 2 K in 6.3 T applied transverse field.

Figure 5

Asymmetry of the muon spin polarization at zero field. The fast relaxation for low temperatures indicates static magnetic order.

Figure 6

Relaxation rates of the muon spin polarization functions.

Figure 7

Magnetic volume fraction in CuFeAs derived from ZF and TF $\mu \mathrm{SR}$ experiments. The solid line is a phenomenological fit using two error functions $\left(erf\right)$ quantifying the magnetic inhomogeneity. The discrepancy between ZF and TF data probably shows that for $T<10$ K internal fields are partly smaller than 5 mT. On the other hand the applied field induces ferromagnetism at $\approx 20$ K.

Figure 8

Asymmetry of the muon spin polarization for a transverse field. The oscillating signal is due to paramagnetic and weak magnetically ordered volume fractions, whereas the dashed component with partial tail $(f_{\mathrm{tail}}$, inset) corresponds to static magnetic order.

Figure 9

Neutron powder diffraction pattern of CuFeAs collected at 2.5 and 20 K (orange squares and blue circles, respectively) $\left(\lambda =2.44\AA \right)$. Bottom plot indicates the difference in diffraction intensities collected at 2.5 K and 20 K. Peaks at $2\theta \approx 63.2^{\circ }$ and $\approx 74.4^{\circ }$ are from the Al sample holder.

Figure 10

${\mathrm{Cu}}_{1+\mathrm{\Delta }{x}_{Cu}}{\mathrm{Fe}}_{1+\mathrm{\Delta }{x}_{Fe}}\mathrm{As}$ elemental deviations for $\mu \mathrm{SR}$ and neutron samples, probed by WDX. It suggests that the Cu sites have some limited occupation by Fe.

Figure 11

Calculated nonmagnetic total and site-resolved density of states for stoichiometric CuFeAs. The states close to the Fermi energy $\left(E_F\right)$ consist mainly of Fe-$3d$ contributions. The Cu-$3d$ states are essentially fully occupied. The contribution of the copper $3d$ states to the Fermi surface is very small.

Figure 12

Dependence of the arsenic height $h_{As}$ (green) and the magnetic moment (black) on the formal Cu occupancy $y$ for experimental and relaxed atom positions of ${\mathrm{Cu}}_y\mathrm{FeAs}$. Experimental atomic positions are obtained from neutron powder diffraction data.

Figure 13

Upper panel: Calculated atom-resolved density of states for ${\mathrm{Cu}}_{0.75}{\mathrm{Fe}}_{1.25}\mathrm{As}$. The additional Fe atom, replacing Cu [Fe(4) on the Wyckoff position 1b, see inset], yields a strong increase in the density of states near the Fermi level $E_F$. The next nearest Fe atom [Fe(5)] also shows an increased $\mathrm{DOS}(E_F)$ due to sizable hybridization, while the distant Fe layer [Fe(6)] gives a small contribution, only. Inset: Comparison of total density of states near Fermi level of stoichiometric CuFeAs (CFA) and the substituted CuFeAs (sCFA). The $\mathrm{DOS}(E_F)$ increases from 1.8 to 7.0 states/eV/f.u. Lower panel: Display of the dominant $3d$ orbitals (in-plane vs out-of-plane) for Fe(4) and Fe(5). Inset: Model of the calculated Fe substituted ${\mathrm{Cu}}_{0.75}{\mathrm{Fe}}_{1.25}\mathrm{As}$ (space group $P4mm)$, the different Fe sites are colored corresponding to the DOS graphs.

Figure 14

CuFeSb Mössbauer spectra show magnetic splitting with a saturation field of 16.08(2) T. Approximately 10% of the intensity is assigned to a second sextet identified as a secondary iron at the Cu position. Spectra at temperatures between 50 K and 100 K are dominated by the magnetic phase transition of ${\mathrm{Fe}}_{\mathrm{x}}\mathrm{Sb}$, which give an impurity signal of $\approx 20\%$.

Figure 15

CuFeSb magnetic order parameter $B_{\mathrm{hyp}}$, modeled by $B\left(T\right)=B_0{(1-{(T/T_C)}^{{\beta }_1})}^{{\beta }_2}$, assuming $T_C=375$ K [24]. The individual critical exponents do not differ significantly and were set equal. A single critical exponent fit for $T>200$ K (dashed) approaches an exponent of 0.17.

Figure 16

CuFeSb applied transverse field Mössbauer spectra at 2.1 K, fit by a distribution of internal hyperfine fields (Fig. 17).

Figure 17

CuFeSb hyperfine field distribution [extracted using maximum entropy method (MEM)] as a function of applied transverse field (TF). The asymmetry of the distribution of internal fields above 4 T describes the anomaly in the left peak (negative velocity) of the spectrum (Fig. 16).