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X-ray free-electron laser observation of giant and anisotropic magnetostriction in $β$-O$_{2}$ at 110 Tesla

Akihiko Ikeda, Yuya Kubota, Yuto Ishii, Xuguang Zhou, Shiyue Peng, Hiroaki Hayashi, Yasuhiro H. Matsuda, Kosuke Noda, Tomoya Tanaka, Kotomi Shimbori, Kenta Seki, Hideaki Kobayashi, Dilip Bhoi, Masaki Gen, Kamini Gautam, Mitsuru Akaki, Shiro Kawachi, Shusuke Kasamatsu, Toshihiro Nomura, Yuichi Inubushi, Makina Yabashi

TL;DR

This work addresses the challenge of observing magnetostriction in materials under ultrahigh fields ($\gtrsim100$ T) with microscopic detail, using a portable 100 T generator (PINK-02) integrated with single-shot X-ray diffraction from an XFEL to study $\beta$-O$_2$. The authors observe giant, anisotropic magnetostriction of up to about $1\%$ at $110$ T, with $\Delta a/a \approx 0.95\%$ and $\Delta c/c \approx -0.62\%$ (and $\Delta c/c = -1.16\%$ at 28 K), corresponding to a $\Delta V/V \approx 1.28\%$ and a distortion $\Delta D/D \approx -1.57\%$. They interpret the effect as exchange-striction within a two-dimensional triangular spin lattice, supported by first-principles calculations showing a $\sim11.8\%$ reduction in $J_1$ under 110 T and a smaller change in $J_2$, indicating strong spin-lattice coupling and cooperative softness between spin and lattice degrees of freedom. The study demonstrates the feasibility of microscopic high-field XRD measurements beyond $100$ T and highlights the potential to explore spin-lattice phenomena, including transitions toward the high-field phase $ heta$-O$_2$, using portable high-field sources.

Abstract

In strong magnetic fields beyond 100 T, the significant Zeeman energy competes with the lattice interactions, where a considerable magnetostriction is expected. However, the microscopic observation of the magnetostriction above 100 T has been hindered due to the short pulse duration of $μ$-seconds and the coil's destruction. Here, we report the observation of the giant and anisotropic magnetostriction of $\sim 1$ % at 110 T in the spin-controlled crystal, $β$-O$_{2}$, by combining the single-shot diffraction of x-ray free-electron laser (XFEL) and the newly developed portable 100 T generator (PINK-02). The very soft and anisotropic response of $β$-O$_{2}$ should originate in the competing van der Waals force and exchange interaction, and also the frustration of spin and lattice on the triangular network. The XFEL experiment above 100 T using PINK-02 enables microscopic investigations on materials' properties at high magnetic fields, providing insights into how spins contribute to the stability of crystal structures.

X-ray free-electron laser observation of giant and anisotropic magnetostriction in $β$-O$_{2}$ at 110 Tesla

TL;DR

This work addresses the challenge of observing magnetostriction in materials under ultrahigh fields ( T) with microscopic detail, using a portable 100 T generator (PINK-02) integrated with single-shot X-ray diffraction from an XFEL to study -O. The authors observe giant, anisotropic magnetostriction of up to about at T, with and (and at 28 K), corresponding to a and a distortion . They interpret the effect as exchange-striction within a two-dimensional triangular spin lattice, supported by first-principles calculations showing a reduction in under 110 T and a smaller change in , indicating strong spin-lattice coupling and cooperative softness between spin and lattice degrees of freedom. The study demonstrates the feasibility of microscopic high-field XRD measurements beyond T and highlights the potential to explore spin-lattice phenomena, including transitions toward the high-field phase -O, using portable high-field sources.

Abstract

In strong magnetic fields beyond 100 T, the significant Zeeman energy competes with the lattice interactions, where a considerable magnetostriction is expected. However, the microscopic observation of the magnetostriction above 100 T has been hindered due to the short pulse duration of -seconds and the coil's destruction. Here, we report the observation of the giant and anisotropic magnetostriction of % at 110 T in the spin-controlled crystal, -O, by combining the single-shot diffraction of x-ray free-electron laser (XFEL) and the newly developed portable 100 T generator (PINK-02). The very soft and anisotropic response of -O should originate in the competing van der Waals force and exchange interaction, and also the frustration of spin and lattice on the triangular network. The XFEL experiment above 100 T using PINK-02 enables microscopic investigations on materials' properties at high magnetic fields, providing insights into how spins contribute to the stability of crystal structures.

Paper Structure

This paper contains 12 sections, 5 figures.

Table of Contents

  1. Data Availability
  2. Endmatter
  3. Micro-cryostat
  4. Preparation of solid O$_{2}$
  5. X-ray detectors
  6. Estimation of exchange interaction using calculations
  7. Qualitative comparison of the lattice change with a previous XRD report
  8. Cooperative softness of the lattice and spin system in $\beta$-O$_{2}$
  9. Analysis of the XRD peak profile
  10. Comparison with other giant magnetostriction systems
  11. Software
  12. Video of destructive generation of 110 T using a portable 100 T generator PINK-02

Figures (5)

  • Figure 1: (a) The molecular orbital of O$_{2}$ with $S=1$. (b) The competing interactions in solid O$_{2}$. (c) A phase diagram of solid O$_{2}$ on a temperature-magnetic field plane reproduced from Ref. NomuraPRB2017. (d) The crystal structure of $\beta$-O$_{2}$ whose space group is $R\bar{3}m$. Layers of a triangular lattice are stacked vertically in the ABC-ABC manner. (e) The schematic of spin configuration on the triangular lattice of $\beta$-O$_{2}$. Due to an intense frustration from the lattice symmetry, the spin shows a short-range order with a 140$^{\circ}$ structure DunstetterJMMM1988. (f) The crystal structure of $\alpha$-O$_{2}$ whose space group is $C2/m$. It is a deformed structure of $\beta$-O$_{2}$. In the layer, the triangle lattice is deformed so that the spin frustration is relaxed. (g) The schematics for the arrangement of the Néel order of spins on the deformed triangular lattice in $\alpha$-O$_{2}$, which results in the non-equivalent exchange constant in $a$ and $b$ direction. (h) The temperature dependence of lattice parameters and volume in solid O$_{2}$. The data are extracted from Ref. FreimanPhysRep2004. (i) The temperature dependence of magnetization of solid O$_{2}$ . The data is extracted from Ref. MeierJPC1982. (j) The magnetization of solid O$_{2}$ at 32 K up to 124 T. The data is adopted from Ref. NomuraPRB2015. Magnetic field induced phase transition from $\beta$-O$_{2}$ to $\theta$-O$_{2}$ occur above 120 T. In the present study, we generated up to 110 T, where we obtained XRD of the strained $\beta$-O$_{2}$ by magnetostriction.
  • Figure 2: (a) A schematic view of PINK-02 and the arrangement for the x-ray diffraction in combination with the XFEL installed in SACLA. (b) A magnification at the single-turn coil (STC) and x-ray beam incident on the sample, with diffracted beams propagating to the 2D x-ray detectors. (c) A schematic drawing of the electric circuit of PINK-02 and a single-turn coil. (d) A photo of a single-turn coil of $\phi4$ mm before the shot. (e) A photo of the single-turn coil during the magnetic field generation. (f) A photo of a single-turn coil after the shot. (g) X-ray photodiode (PD) signal intensity as a function of time. (h) Representative waveforms of pulsed magnetic field generated using PINK-02 with single-turn coils of $\phi4$ and 5 mm diameter, and charging voltages of 20 and 30 kV. (i) Representative waveforms of the current injected into the single-turn coil. There are two switches connected in parallel.
  • Figure 3: (a) Powder XDR data from $\beta$-O$_{2}$ recorded using two-dimensional x-ray detectors at 0 T and (b) at 110 T. (c) Integrated powder XDR data from $\beta$-O$_{2}$ at 0 T and at 110 T. The inset shows the schematic drawing of the experimental set up at the sample position. (d) The magnified powder XRD data at the 003 reflection of $\beta$-O$_{2}$ at 35 and 28 K, showing -0.62 and -1.16 % shrinkage of the inter-plane separation at 110 T, respectively. (e) The magnified data of powder XRD at the 101 reflection of $\beta$-O$_{2}$ at 35 K, showing +0.73 % elongation of the inter-plane separation at 110 T. (f) The magnified data of powder XRD at the 012 reflection of $\beta$-O$_{2}$ at 35 K, showing +0.737 % elongation of the inter-plane separation at 110 T. (g) The schematic drawing of the crystal structure of $\beta$-O$_{2}$ with the indication of the shrinkage in the $c$ axis and elongation in the $ab$ plane. The diffraction planes are also depicted. (h) The schematic drawing of the crystal structure and spin configuration in $\beta$-O$_{2}$ at 0 T, where the O$_{2}$ molecules form the triangular lattice with the short-range order due to the antiferromagnetic coupling and geometrical frustration. (i) The schematic drawing of the crystal structure and spin configuration in $\beta$-O$_{2}$ at 110 T, where the spins are more aligned to the external magnetic field, losing the antiferromagnetic short-range order. This results in the expansion of the lattice parameter in $ab$ plane to relax the antiferromagnetic exchange coupling between spins.
  • Figure 4: (a) Intermolecular potential of the dimer (O$_{2}$)$_{2}$ calculated as a function of the inter-molecular distance $R$ in H geometry with a variation of the total spin $S_{(\rm{O}_{2})_{2}} = 0$, 1, and 2 BusseryPRB1993. (b) A magnification of (a). (c) Exchange constant $J_1$ of between molecular spins as a function of $R$ deduced from the high-pressure experiment SantoroPRB2001. (d) A magnification of (c).
  • Figure 5: (a) A schematic of the micro-cryostat, 3D printed vacuum chamber, and the single-turn coil setup. (b) A photo of the micro-cryostat, the single-turn coil, and the 3D printed vacuum chamber. (c) Detailed cross-sectional view of the micro-cryostat, 3D printed vacuum chamber, and the single-turn coil.