One of the most intriguing aspects of condensed matter physics is its diversity. Numerous materials with various physical properties have been discovered. They are often classified according to symmetry breaking in the electron system. For example, ferroelectricity is related to the breaking of spatial-inversion symmetry and ferromagnetism is related to the breaking of time-reversal symmetry.

Utilizing the symmetry breakings, various cross correlations and transport phenomena have been discovered. In this regard, electronic multipoles have been introduced as the symmetry-adapted complete basis set to describe any internal electronic degrees of freedom in solids, such as charge, spin, and orbital degrees of freedom, in a unified manner. The complete basis set includes four types of multipole bases, including electric, magnetic, electric toroidal, and magnetic toroidal multipoles.

In a new study published in Journal of the Physical Society of Japan, physicists reviewed the recent developments in the research of multipole representations and their applications to different kinds of materials. According to their review, multipole representation offers several advantages, including systematic identification and classification of electronic order parameters, predictability of overlooked physical phenomena under various electronic orderings, and the exploration of cross correlations and transport properties.

These advantages provide a comprehensive understanding of various physical phenomena observed in solids beyond the symmetry argument and can lead to bottom-up engineering of desired functionalities based on microscopic electronic degrees of freedom.

Lastly, the study also presented methods to identify active multipoles and expected physical phenomena in real materials using various examples. Thus, it serves as the foundation for studying unknown electronic phases and their related physical phenomena, pushing condensed matter physics onto the next stage.

]]>First-principles calculations based on electronic theory are powerful method for quantitatively representing the individuality of materials without the need for adjustable parameters. However, most industrial materials are far from perfect crystals and exhibit many defects such as vacancies, grain boundaries, and strains. Currently, it is difficult to describe the properties of these practical materials solely via first-principles calculations, and coarse graining based on the stiffness or characteristic length of order parameters is required. In such scale regions, the equations, such as the Landau-Lifshitz-Gilbert (LLG) equation for magnetism, are effective. This equation enables visualization of the macroscopic behavior of the order parameters (magnetization) in complex environments. Based on this perspective, the role of the first-principles calculations is to provide the parameters (magnetic constants) constituting the LLG equation.

The magnetic constants that constitute the LLG equation include the exchange stiffness constant (𝐴), magnetic anisotropy constant (*K*), and Gilbert damping constant (α). The issue arises because the interest in material properties predominantly focuses on room temperature or higher temperature regimes. Hence, the challenge involves determining the magnetic constants at finite temperatures from a microscopic standpoint. With respect to general metallic ferromagnets, functional integral methods have been powerful prescriptions for the finite temperature magnetism.

In this study, we focus on the first-principles calculations of the exchange stiffness constant 𝐴 at finite temperatures based on the functional integral method. The exchange stiffness constant is a measure of the rigidity (or hardness) of regular spin arrangements (such as ferromagnetic alignments) arising from the exchange interaction between spins. To evaluate 𝐴(𝑇), a spiral magnetic structure characterized by wavevector **𝑞** is generated in the presence of spin fluctuations. Subsequently, we can obtain 𝐴(𝑇) from the increase in free energy.

Specifically, we calculate 𝐴(𝑇) of Permalloy (Fe_{0.2}Ni_{0.8}) and L10-type FePt. For Fe_{0.2}Ni_{0.8}, the calculated magnetic moment is approximately 1 Bohr magneton (*µ*_{B}) at 𝑇 = 300 K, closely reproducing the measured values. The Curie temperature is approximately 550 K, slightly lower than the measured value (670 K). The obtained 𝐴(𝑇) falls within the range of values empirically used in the LLG equation (several meV/Å to 10 meV/Å), and 𝐴(𝑇) at room temperature appears to match well with the measured values. Additionally, 𝐴(𝑇) of FePt shows similar temperature dependence, aligning well with room temperature measurements. The results highlight the structure’s anisotropy, with significant directional dependence in 𝐴(𝑇).

Written by A. Sakuma

]]>In 2023, the discovery of the superconductivity of La_{3}Ni_{2}O_{7} with a transition temperature (*T*_{c}) of ~80 K under pressure led to nickelates joining the family of high-*T*_{c} superconductors. La_{3}Ni_{2}O_{7} has a two-layered perovskite structure resembling cuprates, which are well-known high-*T*_{c} superconductors. However, it actually possesses different characteristics from those of cuprates, anticipating a new superconducting mechanism.

One of the major mysteries of La_{3}Ni_{2}O_{7} is what kind of electronic orders and/or fluctuations exist and how they lead to the superconducting phase from the non-superconducting phase at ambient pressure. In addition, La_{3}Ni_{2}O_{7} belongs to the Ruddlesden–Popper (RP) phase La_{n+1}Ni* _{n}*O

We investigated the electronic states of (La_{3}Ni_{2}O_{7}) (*n=2*) and La_{4}Ni_{3}O_{10} (*n=3*) at ambient pressure using nuclear magnetic resonance (NMR) experiments, which can be used to microscopically observe the orders and/or fluctuations of charge and spin. The NMR spectra at high temperatures exhibited multiple distinct peaks, which allowed us to identify two crystallographically inequivalent sites. At temperatures below 150 K for La_{3}Ni_{2}O_{7} and 130 K for La_{4}Ni_{3}O_{10}, significant broadening of their spectra, particularly in the satellite peaks, was observed. This suggests the existence of a density-wave transition accompanied by a spatial charge distribution. We also measured the nuclear spin relaxation rate (*1/T _{1}*), showing that, in addition to the sharp drop in

The fact that these characteristics are commonly observed in La_{3}Ni_{2}O_{7} and La_{4}Ni_{3}O_{10} provides important insights. These observations are likely associated with the different features of the multiple bands composed of the *d*_{x2-y2} and *d*_{3z2-r2} orbitals, which are common to these compounds. Recently, superconductivity with a of ~25 K under pressure was also discovered in La_{4}Ni_{3}O_{10}. This finding suggests a connection between the multiband nature, density wave phase, and emergence of the superconducting phase under high pressure. The possibility of spin order coexisting with charge order remains debatable, and further investigations are required to understand how the charge and spin degrees of freedom evolve toward the superconducting phase under high pressure.

Written by M. Kakoi and H. Mukuda on behalf of all authors.

]]>Since the discovery of high critical temperature (high-*T*_{c}) superconductivity in cuprates in 1986, numerous experimental and theoretical research have been conducted to elucidate this mechanism. However, the reason for an extremely high *T*_{c} has not yet been completely understood. One approach to understanding the high-*T*_{c}
mechanism is to investigate the physical properties of the material with the highest *T*_{c} and determine the essential parameters for realizing a high *T*_{c}. Among high-*T*_{c} cuprates, Hg-based cuprates with three CuO_{2} layers, HgBa_{2}Ca_{2}Cu_{3}O_{8+}_{d} (Hg-1223), have the highest *T*_{c} above 130 K at ambient pressure.

However, at present, information on the physical properties of Hg-1223 is insufficient because of the lack of high-quality large single crystals of Hg-1223. One reason for this lack may be the nature of Hg; that is, it is poisonous and has high vapor pressure. Moreover, because Hg-1223 is chemically unstable at high temperatures and difficult to obtain the phase, the range of chemical compositions and temperatures at which single crystals can be grown is extremely narrow, causing difficulty in growing Hg-1223 single crystals with good reproducibility.

Accordingly, we carefully examined earlier studies on the single crystal growth of Hg-1223 and determined the key factors for obtaining large single crystals reproducibly and safely. We employed an explosion-proof stainless-steel container to control the high pressure of the Hg vapor at high temperatures to ensure safe crystal growth.

We attempted crystal growth more than 100 times and established a method for growing Re-doped Hg-1223 ((Hg,Re)1223) single crystals using the self-flux method by optimizing the growth conditions. Under the optimal conditions, large single crystals with sizes up to 1 × 1 × 0.04 mm^{3}
were obtained, and crystals with sizes of approximately 0.8 × 0.8 mm^{2}
in the *ab*-plane area were obtained with good reproducibility. We expect that further research using Hg-1223 single crystals will provide clues to understand the high-*T*_{c} mechanism in cuprates.

Written by Shigeyuki Ishida on behalf of all authors.

]]>Stochastic differential equations are differential equations where stochastic terms are introduced. Stochastic differential equations were originally introduced by Einstein in research on Brownian motion and are now used not only in mathematics and physics, but also in various fields such as financial engineering. In many cases, solving stochastic differential equations analytically is extremely difficult compared to solving ordinary differential equations, and solving stochastic differential equations numerically also incurs a much higher cost than solving ordinary differential equations.

Our research attempts to obtain analytical solutions for stochastic differential equations. Geometric Brownian motion is one of the most famous stochastic differential equations for which analytical solutions have been obtained. Geometric Brownian motion is used in financial engineering option pricing models. Geometric Brownian motion can be regarded as an ordinary first-order linear homogeneous differential equation, in which the coefficients are replaced by stochastic noise. The exact solution of the geometric Brownian motion can be easily obtained in the same manner as an ordinary first-order homogeneous linear differential equation can be easily solved.

What happens when we consider multivariable geometric Brownian motion? In the case of ordinary differential equations, multivariable first-order homogeneous linear differential equations can be solved by diagonalizing the matrices. However, for multivariable geometric Brownian motion, this problem becomes extremely difficult, and when there is more than one stochastic noise, multivariable geometric Brownian motion cannot be solved by diagonalization. In other words, it has been believed that it is impossible to obtain an exact solution for multivariable geometric Brownian motion.

Under these circumstances, we considered a 2x2 matrix-valued geometric Brownian motion to be the simplest and most nontrivial multivariable geometric Brownian motion. As explained above, it is difficult to solve the 2x2 matrix-valued geometric Brownian motion using the conventional method. Instead, we applied the replica method developed in the spin-glass theory of statistical physics (which is closely related to the Nobel Prize in Physics awarded to Parisi in 2021). The replica method analyzes a model with randomness by mapping it onto an effective model without randomness.

Using the replica method, we found that the time-evolution operator of the matrix-valued geometric Brownian motion can be mapped to the partition function of a mean-field quantum spin system called the Lipkin-Meshkov-Glick model, which was originally proposed in nuclear physics. Furthermore, by analyzing the partition function of the Lipkin-Meshkov-Glick model, we succeeded in obtaining analytical solutions for various quantities of matrix-valued geometrical Brownian motion.

In summary, by analyzing a mean-field quantum spin system, we obtained exact solutions for various quantities of matrix-valued geometric Brownian motion that was previously thought to be unsolvable. Our results imply that there is a close connection between matrix-valued geometric Brownian motion and a mean-field quantum spin system, which, at first glance, have nothing to do with each other.

Written by Manaka Okuyama on behalf of all authors

]]>UTe_{2} is among the most intriguing materials in condensed matter physics owing to its unusual superconducting properties. The significant features of UTe_{2} include its immense field-reentrant superconductivity and the observation of multiple superconducting phases that have been highlighted in the study of superconducting phenomena. These experimental findings align with the spin-triplet superconductivity scenario, in which the superconducting upper critical field surpasses the limit of the critical field for conventional superconductivity. Moreover, spin and orbital degrees of freedom may contribute to the emergence of multiple superconducting phases.

To thoroughly investigate this fascinating material, precise experiments conducted under extreme conditions using high-quality single crystals are essential. This paper introduces a novel approach known as molten salt flux liquid transport (MSFLT) method for growing high-quality single crystals of UTe_{2}. This technique is a hybrid of the molten salt flux (MSF) and chemical vapor transport (CVT) methods . Large, high-quality single crystals were obtained by gradually synthesizing UTe_{2} single crystals at relatively low temperatures that were maintained throughout the process. These single crystals were buried in the NaCl/KCl salt, akin to fish in a salt crust.

The quality of the single crystals was validated by resistivity and specific heat measurements. The superconducting transition temperature reached 2.1 K for the highest-quality sample, and the residual density of states in the superconducting state approached zero, indicating an ideal superconducting transition. The observation of quantum oscillations, known as the de Haas–van Alphen effect, under extreme conditions (low temperature and high field) clearly suggested that the high-field condition was satisfied for the cyclotron motion of the conduction electrons.

The MSFLT method, also known as the liquid transport method or horizontal flux method, holds promise for broader applications beyond UTe_{2}. This technique can be extended to many other materials for which high-quality single crystals are scarce, opening new avenues for the discovery of exotic superconductors.

Written by D. Aoki

Much like inorganic metals, organic compounds can exhibit superconductivity at low temperatures where electrons move through the material without any resistance. However, unlike conventional inorganic metals, the superconductivity is due to strong electron-electron interactions.

To reveal the electronic states responsible for the material’s superconducting behavior, a review published in Journal of the Physical Society of Japan summarizes the electronic states inherent in a BEDT-TTF or bis(ethylenedithio)tetrathiafulvalene type of organic superconductor.

*κ*-type BEDT-TTF compounds have a layered structure composed of anion layers and BEDT-TTF layers. These molecules form a distinctive triangular lattice, resulting in a hole-like Fermi surface at half-filling, where strong electron correlations hold electrons at the lattice sites, leading to a Mott insulating state.

The review highlights that, under pressure, the compound with a half-filled electronic configuration undergoes a metal-insulator transition due to a shift in the occupancy of electronic states. This is accompanied by the Mottness transition which is the tendency or degree of prohibited double occupation. However, when additional charge carriers are introduced into the material through doping, the excess electrons or holes make the material conductive even under the prohibition of double occupancy.

In such cases, two distinct metallic states are formed: a conventional Fermi liquid at high pressures and a non-Fermi liquid state at low pressures. The high-pressure state exhibits typical Bardeen-Cooper-Schrieffer superconductivity due to Cooper pairing of conventional Fermi particles. As the material passes through the Mottness transition at low pressures, it behaves as a quantum spin liquid, exhibiting Bose-Einstein Condensate-like superconductivity.

These findings underscore the significance of pressure and cooling in effectively managing electron interactions, that lead to the formation of a superconducting state.

The insights gained may contribute to understanding similar phenomena in complex electron systems and hold potential value in the information industry, where efficient electron control is essential for energy conservation.

]]>Spin-rotation coupling, which refers to the coupling between mechanical rotations and electron spins, leads to various phenomena, such as the Einstein-de Haas effect and the Barnett effect, in which the mechanical rotation of a crystal acts on the electron spins as an effective magnetic field. Recently, surface acoustic waves and chiral phonons involving the rotational motion of atoms have attracted considerable attention in spintronics. Surface acoustic waves refer to classical surface waves in continuous elastic media, whereas chiral phonons represent the microscopic local rotation of atoms with a phonon angular momentum.

Previous studies have indicated a phenomenon involving the conversion of phonon angular momentum into electron spins and charges in nonmagnetic materials and shown that chiral phonons behave as an effective magnetic field. Chiral phonons accompanying atomic rotations modulate electron hopping and spin-orbital coupling because the distance between atoms periodically changes with time. In the case of magnets, spin-spin interactions, such as exchange interactions and Dzyaloshinskii-Moriya interaction, always exist. These spin-spin interactions govern the collective propagation of precessions of electron spins, which are known as magnons. However, the interplay between atomic rotation and magnons in magnets is not fully understood.

In this study, we investigate a new conversion of chiral phonons into magnons in both ferromagnets and antiferromagnets and show that chiral phonons modulate spin-spin interactions. Because the masses of atoms are much larger than those of electrons, the behavior of magnon dynamics in an adiabatic response to atomic rotations leads to a geometric effect. We demonstrate that this effect requires breaking the spin-rotation symmetry. Consequently, the geometric effect due to chiral phonons results in a nontrivial change in magnon excitations. Specifically, chiral phonons with clockwise and counterclockwise rotational modes induce a change in magnon numbers with opposite signs, which corresponds to increasing and decreasing spin magnetization due to the chiral nature of atomic rotations.

The proposed effect is universal for a wide range of magnets. Measurement in an antiferromagnet is easier than in a ferromagnet because the net spin magnetization becomes nonzero owing to the geometric effect induced by chiral phonons. Our theory can generally be applied to real materials and is expected to be experimentally realized in some candidate materials, such as antiferromagnets XPS3 (X =Fe, Mn, and Ni), with a strong magnetic anisotropy.

(Written by D. Yao and S. Murakami)

]]>In the muon spin relaxation (µSR) measurements, the distribution (described by linewidth D) of internal magnetic field *H*(*t*) and its temporal fluctuations (with mean fluctuation rate *n*) can be observed by implanting spin-polarized muons into a material. However, distinguishing whether the fluctuations are caused by the diffusive motion of the muon itself or the motion of the ions around it, is difficult. In this study, by reviewing the strong collision model, which is an assumption used to describe spin relaxation, we observed that the difference in the cause of the fluctuation appeared as a difference in the spin relaxation function. The new model reproduces well the spin relaxation owing to the local rotational motion of cation molecules observed in hybrid perovskites; this opens the way to distinguish the cause of fluctuations solely from the µSR data.

When a muon exhibits jump-diffusion in a nonmagnetic material, the configuration of the nuclear magnetic moments around the muon changes simultaneously before and after the site change. The fluctuation of *H*(*t*) owing to these jumps is well approximated by the strong collision model [where the autocorrelation of *H*(*t*) is given by equation *H*(*t*)*H*(0)~D^{2}exp(-*n**t*)], and the time evolution of the muon spin polarization, *G _{z}*(

Therefore, we performed Monte Carlo simulations for *G _{z}*(

Written by T. U. Ito and R. Kadono

]]>Spin current, the flow of spin angular momentum, is a central element in spintronics for future technological applications. Thus, elucidating various mechanisms to generate spin currents is an important topic. Since the discovery of the gyromagnetic effect more than 100 years ago by Einstein, de Haas, and Barnett, spin angular momentum has been known to be mutually converted with the mechanical angular momentum associated with rotational motion of materials. This suggests that spin currents can be generated mechanically. Present-day experiments have shown that spin currents are generated by shear flows in liquid metals and by surface acoustic waves in solids.

The electron spin also interacts with its orbital motion through relativistic effects, that is, the spin-orbit interaction (SOI). The SOI is responsible for various spin-current generation methods because it bends the electron orbits in spin-dependent directions. In particular, the Rashba SOI appears in systems with broken spatial inversion symmetries, such as at the surfaces and interfaces of materials. When generating spin currents using surface acoustic waves, the effects of Rashba SOI may be utilized.

In this study, we investigated spin-current generation from dynamic lattice distortions in systems with Rashba SOI. Unlike prior theoretical studies, we started from a multiorbital tight-binding model to derive a Rashba model perturbed by lattice distortions. This method enabled us to treat the lattice distortion effects microscopically through the modulation of hopping integrals and local rotation of the crystal axes. By calculating the linear response to the effective perturbations, we observed that surface acoustic waves can generate a variety of spin currents through the Rashba SOI, including unconventional spin currents, such as the quadrupolar spin current, perpendicular spin current, and helicity current.

Written by Y. Ogawa on behalf of all authors.

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