X-ray diffraction of single-crystal EuMnBi2 at 300 K. XRD pattern shows sharp (0,0,L) peaks. The left inset is a photograph of single-crystal samples of EuMnBi2, showing a typical size of ∼5 mm with a thickness of ∼1.5 mm (grid width is 1 mm) and clear rectangular natural edge; the right inset is an X-Ray Laue pattern of the (H,K,0) reciprocal plane, and a 4-fold symmetry can be clearly seen.

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... crystalline quality and structure were checked by XRD and x-ray Laue (Fig. 1). EuMnBi 2 shares the same structure as SrMnBi 2 with space group I4/mmm (no. 139). The lattice parameter c = 22.614(5) Å at room temperature extracted from XRD (in Fig. 1) is quite consistent with the previous results [39]. It is worth noting that the small peak around 2θ = 27 • in Fig. 1 is due to the residual bismuth flux on the ...

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... crystalline quality and structure were checked by XRD and x-ray Laue (Fig. 1). EuMnBi 2 shares the same structure as SrMnBi 2 with space group I4/mmm (no. 139). The lattice parameter c = 22.614(5) Å at room temperature extracted from XRD (in Fig. 1) is quite consistent with the previous results [39]. It is worth noting that the small peak around 2θ = 27 • in Fig. 1 is due to the residual bismuth flux on the ...

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... quality and structure were checked by XRD and x-ray Laue (Fig. 1). EuMnBi 2 shares the same structure as SrMnBi 2 with space group I4/mmm (no. 139). The lattice parameter c = 22.614(5) Å at room temperature extracted from XRD (in Fig. 1) is quite consistent with the previous results [39]. It is worth noting that the small peak around 2θ = 27 • in Fig. 1 is due to the residual bismuth flux on the ...

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... 2J − K u + K e can be easily extracted from the fitting of the field-dependence curves of the reflections (1,0,2) and (1,1,1); subsequently, the critical tilting angle θ of the Eu moments at the spin-flop phase transition can also be determined, as shown in Fig. 7(b), which is about 76.8 • . Furthermore, both the fitted results for the reflections (1,0,2) and (1,1,1) show the saturated magnetic field H s () at around 23 T, which is quite consistent with the previously reported magnetization in Ref. [6] as well as the theoretical calculation in Ref. [68] that also successfully reproduced the half-integer quantum Hall effect. ...

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... 2J − K u + K e can be easily extracted from the fitting of the field-dependence curves of the reflections (1,0,2) and (1,1,1); subsequently, the critical tilting angle θ of the Eu moments at the spin-flop phase transition can also be determined, as shown in Fig. 7(b), which is about 76.8 • . Furthermore, both the fitted results for the reflections (1,0,2) and (1,1,1) show the saturated magnetic field H s () at around 23 T, which is quite consistent with the previously reported magnetization in Ref. [6] as well as the theoretical calculation in Ref. [68] that also successfully reproduced the half-integer quantum Hall effect. ...

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... reveal possible interplay between Eu and Mn magnetism, we now turn to the temperature and field dependence of two representative magnetic reflections (1,0,1) and (1,0,2), which are attributed to the AFM ordering of Mn and Eu respectively. Detailed field dependence experiments of magnetic reflection (1,0,1) at 1.5 and 25 K were performed. ...

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... similar zero-field temperature-dependence experiment was also performed with polarized neutrons by using another EuMnBi 2 sample at DNS. As shown in Fig. 10(a), a small but finite increase of the intensity of the Mn magnetic refection (1,0,1) can clearly be observed at T Eu N ≈ 22 K. Such an increase is also visible from a comparison of the rocking curve scans at 4 and 30 K, as shown in Fig. 10(b). With a large 043100-9 Q-range mapping in the x spin-flip channel, the difference diffraction ...

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... experiment was also performed with polarized neutrons by using another EuMnBi 2 sample at DNS. As shown in Fig. 10(a), a small but finite increase of the intensity of the Mn magnetic refection (1,0,1) can clearly be observed at T Eu N ≈ 22 K. Such an increase is also visible from a comparison of the rocking curve scans at 4 and 30 K, as shown in Fig. 10(b). With a large 043100-9 Q-range mapping in the x spin-flip channel, the difference diffraction pattern in the (H,0,L) plane between 4 and 30 K is shown in Fig. 10(c), from which all the magnetic intensity enhancement can be easily seen. Except for the Eu magnetic reflections (−1, 0, ±2), there are some extra intensities on (−1, 0, ±1) ...

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... of the Mn magnetic refection (1,0,1) can clearly be observed at T Eu N ≈ 22 K. Such an increase is also visible from a comparison of the rocking curve scans at 4 and 30 K, as shown in Fig. 10(b). With a large 043100-9 Q-range mapping in the x spin-flip channel, the difference diffraction pattern in the (H,0,L) plane between 4 and 30 K is shown in Fig. 10(c), from which all the magnetic intensity enhancement can be easily seen. Except for the Eu magnetic reflections (−1, 0, ±2), there are some extra intensities on (−1, 0, ±1) as shown in the enlarged plot in Fig. 10(d) and in the corresponding line cut [ Fig. 10(e)]. Therefore, both field dependence and temperature dependence of magnetic ...

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... Q-range mapping in the x spin-flip channel, the difference diffraction pattern in the (H,0,L) plane between 4 and 30 K is shown in Fig. 10(c), from which all the magnetic intensity enhancement can be easily seen. Except for the Eu magnetic reflections (−1, 0, ±2), there are some extra intensities on (−1, 0, ±1) as shown in the enlarged plot in Fig. 10(d) and in the corresponding line cut [ Fig. 10(e)]. Therefore, both field dependence and temperature dependence of magnetic reflections suggest a strong interplay between the two magnetic sublattices in EuMnBi 2 . ...

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... the difference diffraction pattern in the (H,0,L) plane between 4 and 30 K is shown in Fig. 10(c), from which all the magnetic intensity enhancement can be easily seen. Except for the Eu magnetic reflections (−1, 0, ±2), there are some extra intensities on (−1, 0, ±1) as shown in the enlarged plot in Fig. 10(d) and in the corresponding line cut [ Fig. 10(e)]. Therefore, both field dependence and temperature dependence of magnetic reflections suggest a strong interplay between the two magnetic sublattices in EuMnBi 2 . ...

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... in the spin flip channel. Hence, we summarize the possible magnetization components responsible for the scattering intensity in Table II for x, y, and z polarization in the spin-and non-spin-flip channels. The background and the incoherent scattering are not included here. As a supplement to Fig. 5, the z-polarization data are shown in Fig. ...

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... the absorption cross section of Eu is about 4530 b, which is by far larger than that of Mn and Bi, we only corrected the absorption of Eu. As shown in Fig. 12(a), the sample we measured is flake-like with irregular shape. Therefore, the dimension parameters were measured and a 3D model [ Fig. 12(b)] was established for the absorption calculation. According to Beer-Lambert's law, we have where n s is the density of scattering units in the sample, σ abs is the absorption cross section, and L is ...

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... the absorption cross section of Eu is about 4530 b, which is by far larger than that of Mn and Bi, we only corrected the absorption of Eu. As shown in Fig. 12(a), the sample we measured is flake-like with irregular shape. Therefore, the dimension parameters were measured and a 3D model [ Fig. 12(b)] was established for the absorption calculation. According to Beer-Lambert's law, we have where n s is the density of scattering units in the sample, σ abs is the absorption cross section, and L is the length of the neutron absorption path inside the sample. In order to simplify the calculation, a representation of isolated points were ...

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... law, we have where n s is the density of scattering units in the sample, σ abs is the absorption cross section, and L is the length of the neutron absorption path inside the sample. In order to simplify the calculation, a representation of isolated points were selected and treated as scattering positions inside the sample, as shown in Fig. 12(b). Assuming the neutron beam flux is uniform and time independent, then for a certain scattering condition as shown in Fig. 12(c), the scattering intensity will be as ...

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... L is the length of the neutron absorption path inside the sample. In order to simplify the calculation, a representation of isolated points were selected and treated as scattering positions inside the sample, as shown in Fig. 12(b). Assuming the neutron beam flux is uniform and time independent, then for a certain scattering condition as shown in Fig. 12(c), the scattering intensity will be as ...

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... Fig. 12(d), for some selected reflections, the absorption factors quickly start to get saturated as N increases. In this paper, we use N = 3500 to make sure that all the absorption factors are convergent and in considerable credibility. Raw integrated intensities and corrected intensities of some selected strong reflections are plotted in Fig. ...

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... Fig. 12(d), for some selected reflections, the absorption factors quickly start to get saturated as N increases. In this paper, we use N = 3500 to make sure that all the absorption factors are convergent and in considerable credibility. Raw integrated intensities and corrected intensities of some selected strong reflections are plotted in Fig. 12(e), and the variance becomes significantly better for equivalent reflections after proper correction. In addition, we noticed that there is new and much more efficient software, Mag2pol [76], made by Qureshi, which can also do the neutron absorption correction, and gives similar correction results as our method, shown in Fig. ...

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... are plotted in Fig. 12(e), and the variance becomes significantly better for equivalent reflections after proper correction. In addition, we noticed that there is new and much more efficient software, Mag2pol [76], made by Qureshi, which can also do the neutron absorption correction, and gives similar correction results as our method, shown in Fig. ...

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... crystalline quality and structure were checked by XRD and X-Ray Laue (Fig.1). EuMnBi 2 shares the same structure as SrMnBi 2 with space group I4/mmm (No. 139). ...

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... 2 shares the same structure as SrMnBi 2 with space group I4/mmm (No. 139). The lattice parameter c = 22.614(5) ˚ A at room temperature extracted from XRD (in Fig.1) is quite consistent with the previous results [39]. It is worth noting that the small peak around 2θ ∼ 27 • in Fig.1 is due to the residual bismuth flux on the surface. ...

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... lattice parameter c = 22.614(5) ˚ A at room temperature extracted from XRD (in Fig.1) is quite consistent with the previous results [39]. It is worth noting that the small peak around 2θ ∼ 27 • in Fig.1 is due to the residual bismuth flux on the surface. ...

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... similar zero field temperature dependence experiment was also performed with polarized neutrons by using another EuMnBi 2 sample at DNS. As shown in Fig.10(a), a small but finite increase of the intensity of the Mn magnetic refection (1,0,1) can clearly be observed at T Eu N =∼22 K. ...

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... shown in Fig.10(a), a small but finite increase of the intensity of the Mn magnetic refection (1,0,1) can clearly be observed at T Eu N =∼22 K. Such an increase is also visible from a comparison of the rocking curve scans at 4 K and 30 K, as shown in Fig.10(b). With a large Q-range mapping in the x spin flip channel, the difference diffraction pattern in the (H,0,L) plane between 4 K and 30 K is shown in Fig.10(c), from which all the magnetic intensity enhancement can be easily seen. ...

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... an increase is also visible from a comparison of the rocking curve scans at 4 K and 30 K, as shown in Fig.10(b). With a large Q-range mapping in the x spin flip channel, the difference diffraction pattern in the (H,0,L) plane between 4 K and 30 K is shown in Fig.10(c), from which all the magnetic intensity enhancement can be easily seen. ...

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... a large Q-range mapping in the x spin flip channel, the difference diffraction pattern in the (H,0,L) plane between 4 K and 30 K is shown in Fig.10(c), from which all the magnetic intensity enhancement can be easily seen. Except the Eu magnetic reflections (-1,0,±2), there are some extra intensities on (-1,0,±1) as shown in the zoom-in plot in Fig.10(d), and in the corresponding line cut (Fig.10(e)). ...

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... a large Q-range mapping in the x spin flip channel, the difference diffraction pattern in the (H,0,L) plane between 4 K and 30 K is shown in Fig.10(c), from which all the magnetic intensity enhancement can be easily seen. Except the Eu magnetic reflections (-1,0,±2), there are some extra intensities on (-1,0,±1) as shown in the zoom-in plot in Fig.10(d), and in the corresponding line cut (Fig.10(e)). Therefore, both field dependence and temperature dependence of magnetic reflections suggest a strong interplay between the two magnetic sublattices in EuMnBi 2 . ...

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... were selected and treated as scattering positions inside the sample, as shown in Fig.11(b). Assuming the neutron beam flux is uniform and time independent, then for a certain scattering condition as shown in Fig.11(c), the scattering intensity will be as following: ...

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... were selected and treated as scattering positions inside the sample, as shown in Fig.11(b). Assuming the neutron beam flux is uniform and time independent, then for a certain scattering condition as shown in Fig.11(c), the scattering intensity will be as following: ...

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... the calculated f abs will converge to a certain value using a reasonable limited number of scattering points N . In Fig.11(d), for some selected reflections, the absorption factors quickly start to get saturated as N increases. ...

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... this paper, we use N = 3500 to make sure that all the absorption factors are convergent and in considerable credibility. Raw integrated intensities and corrected intensities of some selected strong reflections are plotted in Fig.11(e), the variance becomes significantly better for equivalent reflections after proper correction. ...

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... integrated intensities and corrected intensities of some selected strong reflections are plotted in Fig.11(e), the variance becomes significantly better for equivalent reflections after proper correction. In addition, we noticed that there is a new and much more efficient software Mag2pol [52] made by Navid Qureshi, which can also do the neutron absorption correction correction, and gives similar correction results as our method, shown in Fig.11(e). ...