Drastic enhancement of magnetic critical temperature and amorphization in topological magnet EuSn2P2 under pressure

High pressure is an effective tool to induce exotic quantum phenomena in magnetic topological insulators by controlling the interplay of magnetic order and topological state. This work presents a comprehensive high-pressure study of the crystal structure and magnetic ground state up to 62 GPa in an intrinsic topological magnet EuSn2P2. With a combination of high resolution X-ray diffraction, 151Eu synchrotron Mössbauer spectroscopy, X-ray absorption spectroscopy, molecular orbital calculations, and electronic band structure calculations, it has been revealed that pressure drives EuSn2P2 from a rhombohedral crystal to an amorphous phase at 36 GPa accompanied by a fourfold enhancement of magnetic ordering temperature. In the pressure-induced amorphous phase, Eu ions take an intermediate valence state. The drastic enhancement of magnetic ordering temperature from 30 K at ambient pressure to 130 K at 41.2 GPa resulting from Ruderman–Kittel–Kasuya–Yosida (RKKY) interactions likely attributes to the stronger Eu–Sn interaction at high pressure. These rich results demonstrate that EuSn2P2 is an ideal platform to study the correlation of the enhanced RKKY interactions, disordered lattice, intermediate valence, and topological state.


INTRODUCTION
Topological materials have recently emerged as a frontier of condensed matter physics and materials research due to their rich quantum phases and potential applications in future dissipationless topological electronics and quantum computations (for reviews see refs. 1,2 ). Among them, intrinsic magnetic topological systems are particularly interesting due to the potential applications in spintronic devices. Compared to dilute magnetic topological insulators, intrinsic magnetic materials are stoichiometric magnetic compounds that provide an easily synthesized, tunable, and clean platform to study magnetic topological materials with new intriguing quantum states. Such intrinsic magnetic topological materials are generally narrow-gap semiconductors that combine nontrivial band topology and intrinsic magnetic order 3 . The intriguing interplay between magnetic ordering and topological states can generate exotic topological quantum phenomena, such as the quantum Hall effect [4][5][6] , axion electrodynamics 7-10 , and Majorana states 11 . Efforts in the study of emergent phenomena in intrinsic magnetic topological systems are mostly focused on MnBi 2 Te 4 6,9,12-14 due to the very few available candidate materials. Very recently, a series of Eu-based compounds have been demonstrated experimentally, or proposed theoretically, to be intrinsic topological semimetals 5,[15][16][17][18] . Among them, EuSn 2 P 2 has been shown to be a magnetic topological system with type-A antiferromagnetic (AFM) order below 30 K 15 . EuSn 2 P 2 crystallizes in a layered rhombohedral structure with space group of R3m, similar to the A 2 B 3 family of topological insulators 19 . It is comprised of strongly magnetic Eu layers sandwiched between Sn-P layers. Traditionally, Eu-based intermetallic materials have achieved considerable interest for their rich properties including magnetic phases from the strong local moment, valence transition, superconductivity, heavy-Fermion states, and Kondo physics 20 . Despite of the rich quantum phenomena, much work is needed to understand the intriguing properties. In this work pressure is employed to control the crystal structure, magnetic, and valence states. Pressure has been proven to be a clean and effective way to tune the atomic distances and therefore electronic interactions to induce interesting quantum phenomena in materials, such as superconductivity, magnetism, or electronic topological transitions. For example, pressureinduced suppression of Néel temperature and the emergence of superconductivity have been observed in magnetic compounds including heavy Fermions and iron-based superconductors 21,22 .
Here we report the systematic high-pressure investigation in EuSn 2 P 2 using a combined experimental approach including angular-dispersive X-ray diffraction (XRD), time-domain synchrotron Mössbauer spectroscopy (SMS), partial fluorescence-yield Xray absorption spectroscopy (PFY-XAS), and molecular orbital and electronic band structure calculations. In EuSn 2 P 2 the rhombohedral crystal structure remains stable up to 33 GPa before transforming to an amorphous phase. Surprisingly, an impressive over fourfold enhancement in magnetic ordering temperature (T o ) from 30 K at ambient pressure to 130 K at 41.2 GPa has been observed, despite of an increased mean valence above 20 GPa. The enhancement of magnetic exchange interaction is likely attributed to the stronger Eu-Sn interaction under pressure. This comprehensive study presents intriguing interplay of crystal structure, magnetic ground state, and the associated valence state tuned by high pressure.

Pressure-induced crystalline to amorphous transition
The evolution of structural properties of EuSn 2 P 2 under hydrostatic pressure has been investigated by high resolution XRD experiments. The XRD data reveal that the ambient rhombohedral structure is maintained under pressure up to 33 GPa. At higher pressure the sample loses the long range crystalline order and becomes amorphous at 36 GPa, evidenced by the loss of sharp crystalline diffraction peaks (see Fig. 1). With further compression the amorphous phase persists up to 62 GPa, the highest pressure measured in this study. The observed pressure-induced amorphization (PIA) contrasts with the rhombohedral-to-monoclinic transition reported in EuSn 2 As 2 23 . The lattice parameters, interatomic distances, and unit cell volume of EuSn 2 P 2 in the crystalline phase obtained from the Rietveld refinements from both XRD runs are plotted as a function of pressure (Fig. 2). Parameters from run 1 with helium as hydrostatic pressure medium and run 2 with neon as quasihydrostatic pressure medium agree reasonably well. Using the third-order Birch-Murnaghan equation 24 a fit to the volume versus pressure data gives bulk modulus B 0 = 58 (2) GPa, its pressure derivative B ′ 0 = 3.6 (1) and volume at zero pressure V 0 = 375.1 (9) Å 3 .

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. The PIA may be related to structural instability violating Born stability criteria 28 or related to density/entropy-driven liquid phase 25,31 . However, the operative mechanism remains an open question in many cases. Additional experimental and computational investigation of variables (charge, orbital, elastic stability) could potentially help to gain a comprehensive understanding of the driving mechanism of PIA in EuSn 2 P 2 .
Drastic enhancement of T o Typical SMS spectra at selected pressures across T o are presented in Fig. 3. The SMS spectra were analyzed using CONUSS 32   modeling the data with two sets of hyperfine parameters, magnetic hyperfine field (H hf ) and quadrupole splitting along with sample thickness. In the presence of magnetic ordering, quantum oscillations emerge in the time-domain SMS spectrum due to nuclear Zeeman splitting. The analysis shows that the direction of magnetic hyperfine field is perpendicular to the X-ray propagation direction and lies in the ab-plane at ambient pressure, consistent with the results from neutron diffraction experiments at ambient pressure 15 . And this direction remains up to 42.7 GPa, the highest pressure reached, indicating Eu spins remain in-plane. When EuSn 2 P 2 is warmed above T o , H hf drops to zero. The periodic oscillations in the data at 16.4 GPa and 96 K indicate a minor oxide impurity phase present in the sample used in run 2, which shows absence of magnetic hyperfine field and can be modeled with two paramagnetic sites with different isomer shift values, one from the sample and another from the impurity phase. In the magnetic phase a small quadrupole splitting of 1-5 mm/s has been included to fit the spectra. The temperature dependence of the extracted magnetic hyperfine field at various pressures is shown in Fig. 4 Table 1). Caution needs to be taken when interpreting the change of isomer shift as change in valence state by simply assuming the contribution solely originating from the change in 4f electrons. For example, in pure Eu metal significant change in isomer shift was observed without obvious change in 4f electron occupancy 33 .
To probe the valence state directly, PFY-XAS experiments at Eu's L 3 edge (2p 3/2 → 5d transition) were carried out up to 47 GPa. The normalized high-pressure PFY-XAS data are shown in Fig. 6. Eu ions in EuSn 2 P 2 remain mostly divalent up to 19.8 GPa, indicating that the change in isomer shift at lower pressure is largely due to compression effect without involving the 4f electrons. At 19.8 GPa a second absorption peak emerges at ∼8 eV higher in energy and grows with increasing pressure, indicating a transition toward Eu 3+ . The 8 eV shift corresponds to the excitation energy difference for Eu 3+ (4f 6 5d 1 ) and for Eu 2+ (4f 7 5d 0 ). Due to the

Pressure-enhanced RKKY interaction
The magnetic order in EuSn 2 P 2 at ambient pressure is driven by indirect Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange coupling through spin-polarized conduction band. To provide insight to the enhanced T o , we have performed molecular orbital calculations to illustrate the chemical bonding evolution at high pressure. The generated molecular orbitals diagrams containing the degenerated highest occupied molecular orbitals (HOMOs) and the lowest unoccupied molecular orbitals (LUMOs) of EuSn 2 P 2 at ambient pressure and 23.3 GPa are shown in Fig. 7. The HOMOs and LUMOs diagrams reflect the orbital interactions just below and above Fermi level, respectively. The blue and red colors indicate the contrast of the orbital symmetry, i.e., antibonding interactions. At both ambient and high pressure, the antibonding characters from Eu-4f orbitals are dominant among intralayer Eu atoms in HOMOs. EuSn 2 P 2 can be viewed as Eu 2+ cation packed with (SnP) 2 2− anion along c-axis primarily by ionic bonding interactions from a charge balance view. Specifically, in chemistry Eu and P atoms are bonded ionically, Sn and P atoms are bonded covalently, and Eu and Sn atoms are bonded metallically. Near Fermi level the bonding interaction features can be observed between Eu-Sn and Eu-P at ambient pressure. When pressurized, EuSn 2 P 2 exhibits stronger metallic Eu-Sn bonding interaction and a weaker covalent Sn-Sn bonding feature. Moreover, the distance between Eu-P atoms decreases, likely due to the 3p electronic localization on P induced by pressure. It suggests that pressureenhanced Eu-Sn bonding interaction contributes to the increasing RKKY interaction and therefore enhanced T o . This is consistent with the monotonic decrease of distances of Eu-Sn and Eu-P shown in Fig. 2c. Due to the much shorter intralayer Eu-Eu distance than interlayer Eu-Eu distance which leads to stronger intralayer magnetic exchange interaction than interlayer interaction, it is expected that the enhanced intralayer exchange interaction play a more important role in the increase of T o , as concluded in the case of EuIn 2 As 2 30 . In addition, the pressureinduced weakening of the ionic and covalent bonding and enhancement of metallic properties in EuSn 2 P 2 may drive the crystal structure into amorphous phase, similar to amorphous magnets where the magnetic order is maintained in the amorphous phase 34 .

Band structure calculations
The surface states and spin texture of EuSn 2 P 2 from Eu termination were calculated using the Generalized Gradient approximation (GGA) plus correlation parameter (U = 6 eV) with spin-orbit coupling. According to the calculation, as the pressure is increased, the decreasing atomic distance along ab-plane may influence the topological properties if the in-plane magnetic spin orientation is maintained under pressure (Supplementary Fig. 1). On the other hand, slightly spin canting along c-axis from the Eu layers may change the topological properties completely, consistent with the recent experimental and computational study in EuSn 2 P 2 35 . Figure 8 presents the phase diagram constructed by combining the XRD, SMS, and PFY-XAS studies under pressure. The boundary between paramagnetic and magnetic phases is deduced from Fig. 4. T o shows a monotonic increase with pressure application with more than four times of the value at ambient pressure. Above 20 GPa a clear slope change in dT o /dP coincides with transition from Eu 2+ toward Eu 3+ in Eu's valence based on the PFY-XAS data. Strikingly, magnetic order is found to persist in the amorphous phase at 42.7 GPa. In another topological magnetic material, EuIn 2 As 2 , pressure-induced hexagonal-to-amorphous transition has been observed above 17 GPa with absence of magnetic order in the amorphous phase based on electrical resistivity measurements 30 . The PIA observed in both systems may suggest a similar origin of crystal structure instability. Furthermore, in the crystalline  show that both change in lattice parameter and change in magnetic configuration from in-plane to out-of-plane will impact the topological properties, with the latter playing a dominant role. The experimentally observed in-plane spin orientation of Eu ions in the measured pressure range suggests that the any possible change of topological properties will be attributed to the change in lattice parameters. Our work establishes that pressure is an effective tuning parameter to elevate the magnetic ordering temperature, a critical parameter to realize novel quantum phases. These rich results pave the way for further experimental and theoretical efforts to explore the pressure-tuning of magnetism, possible superconductivity, and their interplay with crystal structure and topological electronic states.

METHODS XRD
Single crystals of EuSn 2 P 2 were grown by the Sn-flux method reported previously 15 . High-pressure XRD experiments were carried out at the 13BM-C (PX 2 ) Beamline at the Advanced Photon Source (APS), Argonne National Laboratory (ANL). Two runs of powder XRD experiments at high pressure and room temperature were conducted. X-rays with a wavelength of 0.434 Å were focused to 15 µm (v) × 15 µm (h) size. A piece of single crystalline sample was ground into powder and loaded in the diamond anvil cell. In run 1 a BX90 diamond anvil cell (DAC) equipped with one pair of Boehler-Almax anvils of 500 µm diameter culet to allow large diffraction angles was used 36 . Helium was used as the pressure-transmitting medium up to 23.3 GPa. Ruby was used to determine pressure 37 . In run 2 a symmetric cell was used up to 62 GPa with cubic boron nitride seats and anvils of 300 µm diameter culet. Neon pressure-transmitting medium was used. Initial pressure was determined from ruby during neon gas loading and subsequent pressures were determined in situ from the equation of state of Au 38 at the same position where XRD data was taken on the sample. In both runs rhenium (Re) gaskets were used to contain the samples between the diamond anvils. The 2-D diffraction images were integrated using DIOPTAS software 39 and Rietveld refinements on the XRD data were performed in GSAS-II 40 .

SMS under pressure
High-pressure 151 Eu SMS experiments were carried out at 3ID Beamline of the APS, ANL to investigate the evolution of the magnetism of EuSn 2 P 2 . SMS, also known as nuclear forward scattering, utilizes the pulsed synchrotron X-ray to probe the nuclear spin transition in time domain. SMS is a sensitive probe to study magnetic state down to the atomic level and is one of the few techniques compatible with extreme sample environments.   42 . High pressures were generated using a membrane-driven miniature panoramic DAC. Re gaskets were prepared and EDM-drilled to form the sample chamber. Three experimental runs were performed with different sample loadings, run 1 up to 10.4 GPa, run 2 up to 22.7 GPa, and run 3 up to 42.7 GPa. A single crystalline sample was loaded in each run such that the incident X-ray is along the c-axis of the crystal. In run 1 and 2 helium was used as pressure medium to ensure hydrostatic pressure environment at low temperatures. In run 3 a neon pressure medium was used. After gas loading at room temperature, all subsequent pressures were applied through gas membrane at low temperature between 100 and 150 K. Pressures were determined from ruby scale 37 . At each pressure the SMS spectra were collected at various temperatures across the magnetic order. Possible valence transition of Eu ions in the sample can be detected by the change of the isomer shift. The isomer shift values were obtained in situ by placing a reference sample with a known isomer shift value in the X-ray beam 33,[43][44][45] . For divalent Eu ions in EuSn 2 P 2 , a trivalent reference sample Eu 2 O 3 with an isomer shift of 1.024 mm/s (relative to EuF 3 ) was placed in the beam. SMS data together with the reference sample were collected in the paramagnetic phase of EuSn 2 P 2 which simplifies the spectra due to the absence of magnetic hyperfine field.

High-pressure PFY-XAS
PFY-XAS experiments were carried out at the 16ID-D Beamline to provide direct information on Eu's valent state and confirm any possible changes suggested by the isomer shift measurements, XAS experiment was carried out at Eu's L L 3 edge (6.97 keV) up to 47 GPa. A single crystal sample was loaded in a symmetric-type DAC with beryllium gasket and an insert from cubic boron nitride and epoxy. Pressures were measured in situ from ruby fluorescence. To avoid heavy absorption by diamond anvil at this energy, XAS was taken with the incident X-ray beam going through the Be gasket and absorption signal being taken in the fluorescence geometry using a Pilatus detector. The X-rays were focused to 5 µm (FWHM). The sample position at each pressure was carefully determined by scanning the sample position to minimize self-absorption. Ruby was used to determine the pressure in situ 37 .

DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.