58 Physical Science Research Frontiers 2022 Near-room-temperature superconductors are certainly among the most attention-grabbing compounds in materials science. Theoretically, compressed hydrogen should be the best high-temperature superconductor, but it is hard to squeeze it above 450 GPa to turn hydrogen into a metal [1]. Thus instead, scientists are exploring compounds that contain additional elements, besides lots of hydrogen. In that way, some critical temperature ( T C ) is sacrificed to reduce the pressures needed to stabilize the superconducting material to 100 – 200 GPa and into the realm of what is technologically possible. At this moment, lanthanum superhydride LaH 10 with a well- reproducible critical temperature ( T C ) of 250 K is the best- known superconductor [2]. This is very impressive, but to attain even higher critical temperatures, we first had to understand how superconductivity in this material works. There are multiple microscopic mechanisms of superconductivity. The one best understood is called conventional phonon-mediated superconductivity [3]. The well-established theory of conventional superconductivity can be applied to improve the properties of LaH 10 , perhaps by introducing some crucial third element to create a novel ternary compound. The problem was, up until now, that no general models of ternary superconducting systems existed determine how much we can improve the properties of polyhydrides by introducing a third element into the system. In this work, we have cleared the way by eliminating this uncertainty. We investigated the La– Nd–H system under pressure and found that the doping of polyhydrides obeys Anderson’s theorem proposed for conventional superconductors back in 1959 [4]. Anderson’s theorem [4] states that nonmagnetic impurities do not affect the order parameter in the conventional Bardeen–Cooper–Schrieffer (BCS) theory [3], whereas scattering on magnetic centers (e.g., Nd, Eu, Fe, Gd, etc.) is very efficient in destroying electron-electron pairing. Nonmagnetic and magnetic impurities are equally detrimental to the critical temperature T C of unconventional superconducting states [5]. Therefore, the introduction of such impurities can provide important information on the mechanism of pairing in LaH 10 under pressure. The first step in our work [6] was the laser-assisted synthesis of La–Nd polyhydrides in diamond anvil cells (DACs). X-ray diffraction experiments (XRD) at high pressures were performed at SPring-8 BL10XU . The analysis of the XRD showed that we successfully synthesized ternary polyhydride (La, Nd)H 10 containing about 9 at% of Nd atoms, randomly distributed in a LaH 10 - like metal sublattice (Fig. 1). Transport measurements demonstrated that the addition of magnetic Nd leads to a significant suppression of superconductivity in LaH 10 : each atomic % of Nd causes a decrease in T C by 10–11 K (Fig. 2(b)). Superconductivity in the (La, Nd)H 10 hydrides disappears at a critical concentration of Nd of about 15– 20 at%. The pronounced suppression of superconductivity in LaH 10 by magnetic Nd atoms and the robustness of T C with respect to nonmagnetic impurities (such as B and N from ammonia borane, C and CH 4 from diamond anvils, Y [7], Al [8], etc.) within Anderson’s theorem indicate the isotropic character of electron–phonon pairing in LaH 10 . The applicability of Anderson’s theorem is limited by the following two conditions: 1. Introduced 3 rd element does not change the lattice symmetry of the parent polyhydride and nor lead to the appearance of new phase transitions. 2. Concentration of the doping element remains low (5–15 at% ). For many metal alloys, these conditions are not met. However, they are satisfied in Nb–Ti alloys and T C almost does not depend on Ti concentration ( x ) at x < 0.3 (Fig. 2(a)) [8]. Surprisingly, La–Y, La–Ce, and La–Nd polyhydrides are one of the best examples of the experimental realization of Anderson’s theorem due to the similarity of the physical and chemical properties of La, Y, Ce, and Nd atoms. From the obtained results, we can draw important conclusions concerning all ternary polyhydrides. As we can see, nonmagnetic impurities do not affect T C so much. This leads to good reproducibility of the superconducting properties of polyhydrides synthesized in many laboratories around the world. The absence of the effects of C, B and N impurities from NH 3 BH 3 also casts doubt on attempts to explain the supposedly huge increase in T C in experiments with doped H 3 S and LaH 10 . If the leading Effect of impurities on superconductivity in LaH 10 Fig. 1. (a) XRD patterns of (La, Nd)H 10 , obtained from La 0.91 Nd 0.09 alloy, recorded during decompression from 202 to 143 GPa. Asterisks mark the XRD peaks of an impurity phase. (b) Migration (indicated by arrows) of Nd atoms in the LaH 10 lattice. The values given with the arrows are the formation energy differences D H in m eV/atom between the corresponding P 1-La 9 NdH 100 modifications. For simplicity, hydrogen is not shown. Such low barriers between structures indicate that Nd atoms are randomly distributed in the La sublattice of LaH 10. (a) 2 (deg) (0.413 Å) θ θ (b) Intensity (arb. units) 6 8 10 12 14 16 18 (La, Nd)H 10 202 GPa 197 190 184 178 172 167 159 148 143 * ** * – 19.0 μ μ eV +8.8 +4.2 +35.8 +29.6 – 4.7 – 7.4 – 15.5 – 42.8 +11.0 La Nd 59 Research Frontiers 2022 mechanism in compressed polyhydrides is the electron– phonon interaction, as most results of experimental and theoretical studies suggest, then it is impossible to expect a significant effect of a small additive, such as carbon or methane in H 3 S. The partial replacement of La atoms by magnetic Nd atoms results in a decrease in not only T C but also the upper critical field m 0 H C2 (0), which makes the upper critical field H C2 (0) attainable for existing pulse magnets. Using strong pulsed magnetic fields up to 68 T, we constructed the magnetic phase diagram of the (La,Nd)H 10 superhydride; the magnetic phase diagram appears to be surprisingly linear with H C2 ∝ ⎥ T – T C ⎥ . This discovery motivated us to look at the behavior of other hydride superconductors as well. Figure 3 shows that several known superhydrides have a linear H C2 (T), and the coefficient a = – dH C2 / dT varies in a quite narrow range, a = 0.9 ± 0.3. This leads to the interesting conclusion that the upper critical field in many compressed polyhydrides can be expressed as a linear dependence, H C2 (0) = a T C . Fig. 3. Magnetic phase diagrams of superhydrides. The legend on the right shows the proposed chemical formula and the research group (city) that investigated the compound. Dmitrii Semenok Center for High Pressure Science and Technology Advanced Research (HPSTAR), China Email: dmitrii.semenok@hpstar.ac.cn References [1] L. Monacelli et al. : Nat. Phys . 17 (2021) 63. [2] A. Drozdov et al. : Nature 569 (2019) 528. [3] J. Bardeen et al. : Phys. Rev. 108 (1957) 1175. [4] P. Anderson et al. : J. Phys. Chem. Solids 11 (1959) 26. [5] J. Bobroff et al. : Phys. Rev. Lett. 83 (1999) 4381. [6] D. Semenok, I. Troyan, A. Sadakov, D. Zhou, M. Galasso, A. Kvashnin, I. Kruglov, A. Bykov, K. Terent’ev, A. Cherepahin, O. Sobolevskiy, K. Pervakov, A. Seregin, T. Helm, T. Förster, A. Grockowiak, S. Tozer, Y. Nakamoto, K. Shimizu, V. Pudalov, I. Lyubutin, A. Oganov: Adv. Mater. 34 (2022) 2204038. [7] D. Semenok et al. : Mater. Today 48 (2021) 18. [8] S. Chen et al. : Natl. Sci. Rev. (2023) nwad107. [9] R. P. Reed and A. F. Clark: Advances in Cryogenic Engineering Materials, Plenum Press, NY (1980). E3 (a) x = Ti/(Ti + Nb) Nd/La+Nd (b) 0.0 0.0 LaH 10 0 50 100 150 200 E4 E2 experiment LDA calculations E0, E1 250 300 0.1 0.2 0.3 0.4 0.5 0.6 0 2 4 6 8 10 0.1 0.2 0.3 0.4 0.5 Nb–Ti alloys, 0 GPa 0.6 0.7 Critical Temperature T C (K) Critical Temperature T C (K) T C (K) d H C 2 /d T C ~ 0.427 – 1.125 H C 2 (T) 0 0 10 20 SnH 4 ThH 9 CeH 9 CeH 10 ( (La La, , N Nd d) )H H 10 10 Y YH H 6 6 L La aH H 10 10 H H 3 3 S S 30 40 50 60 70 80 90 25 50 75 100 125 150 175 200 225 250 1.07 0.653 0.525 0.427 0.847 0.845 0.61 0.99 0.88 0.88 0.684 1.12 0.85 0.856 0.758 0.98 LaH 10 (Mainz) YH 9 (Mainz) YH 9 (Moscow) YH 6 (Moscow) H 3 S (Mainz) H 2 S (Mainz) LaH x (130 GPa, Bristol) H 3 S (155 GPa, Mainz) H 3 S (160 GPa, Mainz) ThH 10 (170 GPa, Moscow) ThH 9 (170 GPa, Moscow) CeD 9 (120 GPa, JLU) CeH9 (100 GPa, JLU) CeH9 (88 GPa, JLU) CeH10 (104 GPa, JLU) CeH 9 (139 GPa, JLU) CeH9 (115 GPa, Hefei) CeH10 (115 GPa, Dresden) ThH 9 (180 GPa) SnH 4 (180 GPa) YH 4 (180 GPa, Bristol) (La,Nd)H 10 (La,Nd)H 10 CaNdZrH x (Moscow) 136 GPa LaH 10 120 GPa LaH 10 Fig. 2. (a) Transition temperature of Nb–Ti alloys vs their composition at 0 GPa [9]. Data points are the midpoints of transitions. (b) Experimental and calculated (using the local density approximation) dependences of T C on the concentration of Nd in (La, Nd)H 10 at 170–180 GPa. Inset: DAC for electrical measurements in pulsed magnetic fields.
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