# Fileset
[Supplemental_Materials_final_3.pdf](https://mdr.nims.go.jp/filesets/b7942258-864f-4372-b7e4-83c331426c81/download)
## Creator
[Hiroaki Hayashi](https://orcid.org/0000-0001-7787-9082), Moyu Kato, [Taichi Terashima](https://orcid.org/0000-0001-9239-0621), [Naoki Kikugawa](https://orcid.org/0000-0003-3975-4478), [Hiroya Sakurai](https://orcid.org/0000-0003-1964-6023), Hiroyuki K. Yoshida, [Kazunari Yamaura](https://orcid.org/0000-0003-0390-8244)
## Rights
©2024 The Physical Society of Japan[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)
## Other metadata
[Exploring the Magnetic Phase Diagram and Hall Resistivity Suppression in Centrosymmetric GdOs2Si2 Single Crystal](https://mdr.nims.go.jp/datasets/50732d10-5a9f-4071-8ad1-39f5cebfbb71)
## Fulltext
S1 Supplemental Materials Exploring the magnetic phase diagram and Hall resistivity suppression in centrosymmetric GdOs2Si2 single crystal Hiroaki Hayashi,1,2,* Moyu Kato,3 Taichi Terashima,1 Naoki Kikugawa,4 Hiroya Sakurai,1 Hiroyuki K. Yoshida,3 Kazunari Yamaura 1,2 1 Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan 2 Graduate School of Chemical Sciences and Engineering, Hokkaido University, North 10 West 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan 3 Department of Physics, Hokkaido University, North 10 West 8, Kita-ku, Sapporo, Hokkaido 060-0810, Japan 4 Research Center for Energy and Environmental Materials, National Institute for Materials Science, 3-13 Sakura, Tsukuba, Ibaraki 305-0003, Japan *E-mail: hhayashi@issp.u-tokyo.ac.jp Magnetic susceptibility over a wide temperature range: Additional data for magnetic susceptibility over a wide temperature range is presented in Fig. S1, depicting the χ-T curves for μ0H = 1 T with H//[100], [110], and [001]. Each curve displays Curie-Weiss behavior at higher temperatures, and a distinctive peak at T1 = 26.6 K signifies the antiferromagnetic ordering of the Gd3+ moments. The Curie constant (C) and Weiss temperature (Θw) were determined by analyzing the linear temperature dependence of the inverse magnetic susceptibility above 100 K. For H//[100] and H//[110], C was calculated to be 8.39(1) emu K mol-1 with Θw of +24.9(1) K, while for H//[001], C was found to be 8.20(1) emu K mol-1 with Θw of +25.4(5) K. The calculated effective magnetic moment derived from the Curie constant was 8.19(1) μB for H//[100] and [110], and 8.01(1) μB for H//[001]. These values slightly exceed the theoretical value of μeff = 7.94 μB for Gd3+ ions, suggesting a well-localized nature of the 4f electrons of Gd3+ ions, with the itinerant 5d electrons of Os ions contributing to the spin moment [43]. Despite the antiferromagnetic ordering, analogous to GdRu2Si2 [26,27], the dominant interaction between Gd3+ moments is considered to be ferromagnetic due to the positive Weiss temperature. Moreover, while the paramagnetic state is nearly isotropic, the magnetic susceptibility below T1 is highly anisotropic, notably with the susceptibility for H//[001] significantly lower than that for H//[100] or [110]. This observation suggests that the Gd3+ moments are ordered along the c-axis, in line with the magnetic structure of GdRu2Si2 [24]. S2 Fig. S1: Temperature dependence of magnetic susceptibility under a magnetic field of 1 T along [100], [110], and [001]. The solid black line represents the Curie-Weiss fitting. The inset shows the crystal structure of GdOs2Si2 [35]. The inset is a photograph of the centrosymmetric GdOs2Si2 single crystal. All measurements were carried out using the single crystal shown in this photograph. S3 Supplemental Hall conductivity data: Additional data for Hall conductivity are determined using the equation σyx = –ρyx / (ρxx2 +ρyx2) as presented in Fig. S2. The σyx increases linearly up to H1, whereas the hump-like enhancement is identified in phase II. This enhancement is completely suppressed in phase II’, leading to broad peak in phase III. Fig. S2: Magnetic field dependence of σyx at 5 K for H//[001]. The gray and yellow regions correspond to the phases II and II’, respectively. S4 Supplemental Hall resistivity analysis: We fitted the magnetic field dependence of Hall resistivity data (ρyx) along with magnetization (M) and longitudinal resistivity (ρxx) curves, as shown in Fig. S3. The calculated anomalous Hall component, ρyxA , assuming intrinsic (∝ Mρxx2 ) and extrinsic (∝ Mρxx) mechanisms, is plotted in the bottom panel of Fig. S3. As mentioned in the main text, adequate fitting could not be achieved; this analysis considers scattering of conduction electrons by relatively larger single skyrmions, whereas a short-period skyrmion lattice with smaller diameters is predicted in GdOs2Si2. The band folding resulting from the periodicity of the skyrmion lattice may contribute to increased resistivity. Therefore, a more appropriate approach is needed for analyzing the topological Hall effect. Fig. S3: Magnetic field dependence of magnetization (M), longitudinal resistivity (ρxx), and Hall resistivity (ρyx). The red and blue dots represent the anomalous Hall term calculated assuming intrinsic (ρyxA ∝ Mρxx2 ) and extrinsic (ρyxA ∝ Mρxx) mechanisms, respectively. S5 Supplemental electrical resistivity data: Additional data for electrical resistivity are presented in Fig. S3. The ρxx vs T curves exhibit anomalies at characteristic temperatures of T1, T2, and T3, which correspond to the temperatures determined in the magnetization measurements. At μ0H = 0 and 1 T, ρxx decreases as the temperature is lowered below T1. However, at μ0H ≥ 2 T, a significant change in the temperature dependence of ρxx is observed. Specifically, at μ0H = 2 T, ρxx experiences an abrupt increase near T2 during cooling, followed by a subsequent decrease with further cooling. For μ0H ≥ 2.4 T, ρxx shows a weak kink at T1 and a subsequent slight increase, followed by a further increase below T2. Interestingly, as shown in the inset of Fig. S3, a negative magnetoresistance is observed not only below T1 but also at high temperatures, specifically below 40 K. This finding suggests the presence of the magnetic precursor effect, a phenomenon observed in isostructural Gd-based compounds [40,41]. Fig. S4: Temperature dependence of the ρxx under different magnetic fields. Dotted, solid, and dashed lines denote the characteristic temperatures T1, T2 and T3, respectively, determined from χ-T measurements. The data have been shifted for clarity. The inset presents ρxx-T curves at μ0H = 0 T (black) and 4 T (red) without any offset. S6 Supplemental Cp data: Fig. S5: Temperature dependence of Cp below 40 K under various magnetic fields. The magnetic transition temperatures at T1, T2, and T3 determined from χ-T measurements are indicated by dotted, solid, and dashed lines, respectively. The data have been shifted for clarity. S7 Phase diagram obtained from an alternate crystal: Fig. S6: Phase diagram obtained from an alternate crystal of GdOs2Si2 for H//[001]. Circles and triangles represent the characteristic points observed in M-H and χ-T measurements, respectively.