Robust magnetism and crystal structure in Dirac semimetal EuMnBi2 under high pressure

Dirac materials offer exciting opportunities to explore low-energy carrier dynamics and novel physical phenomena, especially their interaction with magnetism. In this context, this work focuses on studies of pressure control on the magnetic state of EuMnBi2, a representative magnetic Dirac semimetal, through time-domain synchrotron Mössbauer spectroscopy in 151Eu. Contrary to the previous report that the antiferromagnetic order is suppressed by pressure above 4 GPa, we have observed robust magnetic order up to 33.1 GPa. Synchrotron-based x-ray diffraction experiment on a pure EuMnBi2 sample shows that the tetragonal crystal lattice remains stable up to at least 31.7 GPa.

Among the AMnX 2 materials, the initial focus turned toward SrMnBi 2 [6][7][8] for its manifestation of spin-degenerate quasi-2D Dirac bands observable along the Γ-M line [22].In SrMnBi 2 , the antiferromagnetic (AFM) order within the Mn layer seems to exert minimal impact on the Dirac fermion, while in EuMnBi 2 , with the substitution of nonmagnetic Sr by magnetic Eu, high-field transport measurements indicate a robust influence of the AFM order from the Eu layers [23], on quantum transport and the Dirac band due to strong exchange interactions [4].
EuMnBi 2 crystallizes in a tetragonal structure (space group I4/mmm) consisting of a MnBi layer with edge-sharing MnBi 4 tetrahedrons and a Bi square net layer sandwiched by Eu atoms [13,24].The Eu layers demonstrate AFM ordering below the Néel temperature, T N = 22 K, characterized by a ferromagnetic arrangement of Eu moments within the ab plane and a sequential alignment along the c-axis as up-up-down-down [13,14,24].EuMnBi 2 stands out as a distinctive system within the AMnBi 2 family, where the transport characteristics and the Fermi surface are significantly impacted by the magnetism from the Eu sublattice.It was found that the interlayer conductivity, along with the extent of spin splitting, significantly relies on the magnetic arrangement of the Eu layers and this arrangement can be regulated using an external magnetic field [4].The Quantum Hall effect was detected in the system with the fieldinduced reorientation of the Eu moment [14].This reorientation led to a decrease in the interlayer coupling, effectively constraining the Dirac fermions within the individual 2D Bi layer.Additionally, the Fermi energy in EuMnBi 2 can be regulated through the partial substitution of Gd 3+ for Eu 2+ within the block layer [5].These studies demonstrate the strong tunability of this system.
These findings motivate us to use pressure as a control parameter and investigate the impact on the magnetic state, which provides the foundation for the magnetic control of electronic structure.Earlier electronic transport study indicates that the application of pressure initially enhances the T N of Eu ions up to 4 GPa, beyond which the magnetic order is suppressed [25].Under further compression to 6 GPa, another low-temperature transition of a different nature was observed.It was proposed that this transition is linked to temperature-induced valence transition from Eu 2+ towards Eu 3+ .Furthermore, x-ray absorption spectroscopy (XAS) studies up to 28 GPa provide evidence for divalent toward trivalent transition above 7 GPa without structural transformation.The valence transition is concurrent with Fermi surface modification suggested by Hall measurements.However, the sample used in this study contains a significant amount of Bi metal and an unidentified impurity phase.This necessitates further careful investigation into the magnetic and electronic states of this important material.
In this work, we have carefully analyzed the magnetism of Eu sublattice and crystal structure using a pure EuMnBi 2 sample under quasihydrostatic pressure using timedomain synchrotron Mössbauer spectroscopy (SMS) in 151 Eu and synchrotron x-ray diffraction (XRD) techniques up to 33.1 GPa and 31.7 GPa, respectively.Our experiments show that the magnetic ordering temperature (T o ) rises monotonically with increasing pressure and the magnetic order survives up to 33.1 GPa, contrary to the previous findings [25].In addition, the tetragonal crystal lattice remains stable under compression up to at least 31.7 GPa.

Experimental methods
Single crystals of EuMnBi 2 were grown by the Bi self-flux method.Reactants included elemental Eu pieces (Alfa Aesar, sublimed dendritic, 99.9%), Mn pieces (Alfa Aesar, 99.9%), and Bi chunks (Alfa Aesar, 99.99%).The three metals were mixed in the ratio of Eu/Mn/Bi = 1:1:15, placed in an alumina crucible, and subsequently sealed in an evacuated silica tube (<10 −5 torr) with a sample mass of ∼3 g.The sample was heated up to 1050 • C at a rate of 60 • C h −1 and kept at 1050 • C for 10 hours.Then the sample was cooled to 850 • C at a rate of 100 • C h −1 , and finally, slowly cooled to 400 • C at a rate of 3 • C h −1 .The samples were then centrifuged to remove the excess Bi flux.Plate-like single crystals with a typical size of ∼3 × 3 × 1 mm 3 were obtained.The crystal structure was determined using an XtaLAB Synergy-S single crystal x-ray diffractometer, equipped with Mo K α radiation (λ = 0.710 73 Å) with an ω of 2.0 • per scan and an exposure time of 10 s per frame.A SHELXTL package with the direct methods and full-matrix least-squares on the F 2 model was used to determine the crystal structure [26,27].
The magnetic state of EuMnBi 2 was probed under high pressure using 151 Eu SMS.Mössbauer spectroscopy under high-pressure sample environment is more feasible at the third-generation synchrotron sources compared to the conventional method using radioactive sources, due to the enhanced brilliance and compact size of the x-ray beams.Therefore, SMS is frequently employed in high-pressure magnetic research [28][29][30][31][32].In conventional Mössbauer spectroscopy using a radioactive source, the Doppler effect modulates the source energy for energy-dependent absorption, whereas in time-domain SMS experiments, synchrotron radiation with an energy linewidth of ∼1 meV is used to coherently excite nuclear transitions and probe the hyperfine interactions from the reemitted radiation in time domain.Particularly, the 7/2 → 5/2 M1 nuclear transition at 21.54 keV in 151 Eu with half life of 9.5 ns is well suited for synchrotron radiation studies [33].The substantial 48% natural abundance of the 151 Eu isotope allows for the use of samples with natural isotope abundance.The experiments were conducted at the Beamline 3ID of the Advanced Photon Source (APS), Argonne National Laboratory (ANL).The time-domain data was collected using 24-bunch timing mode with 153 ns intervals between the consecutive electron bunches.A miniature diamond anvil cell (DAC) and a compatible helium flow cryostat were utilized to achieve high pressure and low temperature [34].A single crystal sample was loaded in the DAC.Pressures were determined in situ based on the shift of the ruby R1 fluorescence line [35].Neon gas served as a quasihydrostatic pressure-transmitting medium.CONUSS program was used to analyze the SMS data and derive hyperfine parameters such as magnetic hyperfine field (B hf ) and electric quadrupole interaction (∆) [36].
To investigate the crystal structure under high pressures, angle-dispersive synchrotron XRD experiments were carried out at room temperature at the 13BM-C beamline (PX 2 ) of the APS, ANL [37].X-rays with a wavelength of 0.434 Å were employed.To generate pressures up to 32 GPa, a BX-90 DAC equipped with Boehler-Almax anvils of 400 µm diameter culet size was used.A Re gasket, preindented to 76 µm with a 210 µm hole drilled using electrical discharge machining, was positioned between the anvils to create a sample chamber.A powder sample was loaded in the chamber with two ruby balls serving as an in situ pressure marker [35].Neon gas was used as a pressure-transmitting medium.The two-dimensional diffraction images were integrated using the DIOPTAS software [38].High-pressure XRD data were fitted using Le Bail method in GSAS-II [39].

Results and discussion
The substantial difference in isomer shift values between the Eu 2+ and Eu 3+ valence states renders it a valuable parameter for providing information on the valence state of Eu ions [29,40].The isomer shift (δ) of 151 Eu in EuMnBi 2 at 0.6 GPa and room temperature was determined from the SMS spectrum taken together with a trivalent EuF 3 (δ:0 mm s −1 ) as a reference sample.Figure 1 shows the time-domain spectrum as well as the simulated Mössbauer spectrum in the energy domain based on the parameters obtained from fitting the experimental data.δ is derived to be −11.3mm s −1 , a typical value for Eu 2+ .This value is also comparable to the reported −11.4 mm s −1 (relative to the 151 SmF 3 source) in a sister compound EuMnSb 2 [41].
Representative SMS spectra in 151 Eu from EuMnBi 2 at different temperatures and pressures are displayed in figure 2. B hf and ∆, along with the effective sample thickness, served as fitting variables.For 4f 7 ions, the magnetic hyperfine field arises due to contributions from core electron polarization, conduction electron polarization by ions, and neighboring atoms [28,42].In the presence of magnetic order, Zeeman splitting of nuclear levels leads to quantum oscillations in the SMS spectrum, with additional beating frequency from quadrupole interaction.At constant pressure, the oscillation frequency decreases as the temperature rises due to a reduction in the B hf strength.The oscillations disappear when the sample is warmed up to the paramagnetic phase.At 1.6 GPa and 13.2 K B hf is 25.98(3) T, consistent with the magnetic hyperfine field observed in other divalent Eu-based compounds [41,43,44].At 1.6 GPa T o lies between 23 K and 37 K. Above T o no sizable quadrupole interaction is resolved.At pressure higher than 8.6 GPa, T o increases to a temperature above 35 K.At the lowest temperature (∼13 K), the oscillation frequency increases as pressure is raised from 1.6 GPa to 33.1 GPa, attributed to increasing B hf which leads to nuclear Zeeman splitting in larger energy range.This is also demonstrated in the simulated energy-domain spectra (see figure 2(b)) based on the fitting parameters to the experiment data.The B hf values at various temperatures and pressures are summarized in figure 3.At around 13 K, B hf increases monotonically with pressure.
Table 1 tabulates the derived hyperfine parameters.The main determinant of ∆ is the electric field gradient (EFG) at the nucleus, which arises from lattice charge distribution and incompletely filled electronic shells.In the case of Eu 2+ , the half-filled 4f shell conforms to Hund's rule, rendering the isotropic electronic ground state ( 8 S 7/2 ) and yielding no electronic contribution to ∆ due to zero total angular momentum [45].Consequently, ∆ values predominantly mirror the EFG originating from the lattice effects.Note that in the magnetic phase, a small ∆ value is needed to fit the SMS data.
The tetragonal crystal structure (I4/mmm) of EuMnBi 2 was confirmed at ambient conditions from single crystal XRD with Mo radiation (λ = 0.71073 Å).The lattice parameters agree well with the reported values in [13].The atomic occupancies were checked carefully and no vacancies were observed from the XRD data.The detailed crystal structure information is tabulated in table 2.
The crystal structure of EuMnBi 2 was investigated under pressures up to 31.7 GPa using synchrotron XRD.As shown in figure 4(a), the XRD data can be indexed with the tetragonal space group I4/mmm up to at least 31.7 GPa, indicating the stable tetragonal lattice in this pressure range.The XRD data also confirms the purity of the sample.The lattice parameters and volume under pressure are displayed in figures (b)-(e).Analyzing the pressure-volume data with the third-order Birch-Murnaghan equation of state yields the bulk modulus B 0 = 36.7(3)GPa, its pressure derivative B ′ 0 = 4.32 (5), and zero-pressure volume V 0 = 457.87(6)Å 3 .The B 0 value is slightly lower than the reported value of 41.8 GPa [25].This small discrepancy may originate from the less hydrostatic pressure medium used in the earlier study.
Our high-pressure SMS measurements show that the magnetic ordering temperature in EuMnBi 2 lies above 25 K at 3 GPa, in agreement with the earlier report that T N increases continuously to 31 K at 3.9 GPa.This initial increase may be attributed to the enhanced Ruderman-Kittel-Kasuya-Yosida exchange interaction, primarily the intralayer exchange coupling due to the smaller Eu-Eu distance within the ab-plane than along the c-axis.At higher pressure, our SMS data show that at 20.5 GPa the T o lies higher than 35 K and the magnetic order persists up to 33.1 GPa, contrary to the report from Susilo et al that T N is suppressed above 4 GPa based on electrical resistivity measurements [25].It is noted that   Mössbauer effect is a sensitive probe for detecting magnetic transition, while in resistivity measurements other phenomena may obscure the signature of magnetic order and it becomes challenging to interpret the data on magnetic state with full confidence.
In Eu-based magnetic intermetallic compounds, pressure typically has the effect of reducing the magnetic transition temperature and/or magnetic moment [46].This is because a valence transition from magnetic Eu 2+ (J = 7/2) to nonmagnetic Eu 3+ (J = 0) is anticipated under high pressure, given that the ionic radius of Eu 3+ is smaller than that of Eu 2+ .This valence transition has been observed in many compounds such as parent and doped EuFe 2 As 2 [43,47], Eu(Fe 1−x Ni x )As 2 [29], and EuRh 2 Si 2 [48].Similarly, in EuMnBi 2 high-pressure XAS measurements at Eu L 3 edge indicate a large increase in Eu mean valence by ∼0.4 at 27 GPa [25].It is surprising to maintain the magnetic order up to 33.1 GPa with such a significant valence increase.To understand the robust magnetism in this important material, further theoretical investigations are desired.

Conclusion
In this study, we investigated the magnetic properties and crystal structure of EuMnBi 2 under quasihydrostatic pressure conditions.Using time-domain SMS in 151 Eu, we have found that the magnetic order of Eu sublattice persists up to 33.1 GPa with T o higher than 35 K at 20.5 GPa.These results are in sharp contrast to the previous claim of suppression of magnetic order above 4 GPa based on electrical resistivity studies.Our synchrotron XRD experiment on a high-quality EuMnBi 2 sample shows that the ambient tetragonal structure remains stable up to pressure as high as 31.7 GPa.Our findings highlight that high pressure serves as an effective approach to enhance the magnetic exchange interaction.The experimental data provide foundation for further experimental as well as theoretical studies.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers.The data that support the findings of this study are available upon reasonable request from the authors.

Figure 1 .
Figure 1.(a) Time-domain 151 Eu SMS spectrum in EuMnBi 2 at 0.6 GPa along with EuF 3 as a reference at ambient conditions.(b) The corresponding simulated energy-domain spectrum.Shaded blue line represents the resonant absorption from EuMnBi 2 and shaded brown line is from the reference sample EuF 3 .

Figure 2 .
Figure 2. (a) Time-domain 151 Eu SMS spectra in EuMnBi 2 .The black solid circles represent the experimental data and red lines correspond to the fits from the CONUSS program.(b) Simulated Mössbauer spectra in energy domain corresponding to the fits for the time-domain data in (a) at the lowest temperature (∼13 (K) achieved at each pressures.

Figure 3 .
Figure 3. Magnetic hyperfine field of 151 Eu in EuMnBi 2 as a function of temperature at various pressures.Error bars are smaller than the symbol size.The dashed lines serve as a guide to the eye.The plot of B hf as a function of pressure around 13 K is shown in inset.

Figure 4 .
Figure 4. (a) XRD spectra of EuMnBi 2 under pressure up to 31.7 GPa.In this pressure range, the Bragg peaks can be indexed with the I4/mmm space group.(b)-(e) Lattice parameters and unit cell volume under pressure.Error bars are smaller than the symbol size.The inset in (b) shows the crystal structure of EuMnBi 2 .

Table 1 .
List of magnetic hyperfine field (B hf ) and electric quadrupole interaction (∆) of 151 Eu in EuMnBi 2 at high pressures and various temperatures.The error bars are generated from the fitting uncertainties in CONUSS.

Table 2 .
Single crystal XRD refinement and atomic coordinates and equivalent isotropic displacement parameters for EuMnBi 2 at ambient conditions.Ueq is defined as one-third of the trace of the orthogonalized U ij tensor (Å 2 ).