Related papers: Thermodynamic formulation of the spin magnetic oct…
Magnetic multipoles have been recognized as order parameters characterizing magnetic structure in solids. Recently, magnetic octupoles have been proposed as the order parameters of time-reversal-symmetry breaking centrosymmetric…
Magnetic multipole moments beyond dipoles have emerged as key descriptors of unconventional electromagnetic responses in crystalline solids. However, a gauge-invariant bulk expression for orbital magnetic multipole moments has remained…
Antiferromagnets with vanishing net magnetization are naturally expected to host higher-order magnetic multipole moments. Understanding and utilizing the multipole degrees of freedom are imperative for novel conceptual designs and…
We establish a quantitative relation between the altermagnetic spin-splitting and different higher order multipoles of the charge and magnetization density around the magnetic atoms. Magnetic multipoles such as octupoles or triakontadipoles…
Altermagnets host an array of magnetic multipoles, which are often visualized and studied in the reciprocal space. In the real space, the relative phase of the multipoles of the spin-density around atoms determines whether a system is an…
Altermagnetism has been recently experimentally verified by photoemission mapping of the spin order in momentum space in MnTe and CrSb, which feature two anisotropic sublattices with antiparallel magnetic dipole moments. In this work, we…
Multipole moments serve as order parameters for characterizing higher-order magnetic effects in momentum space, providing a framework to describe diverse magnetic responses by extending the concept of magnetism. In this letter, we introduce…
Out-of-plane spin polarization {\sigma}_z has attracted increasing interests of researchers recently, due to its potential in high-density and low-power spintronic devices. Noncollinear antiferromagnet (AFM), which has unique 120{\deg}…
Altermagnets have recently emerged as promising materials for next-generation spintronic devices. For their device applications, realizing a single-domain configuration is essential but remains challenging. We theoretically consider…
Cluster magnetic multipoles are order parameters that describe the symmetry of spin arrangements in magnetic materials. High-order multipoles are particularly important in non-collinear antiferromagnets, where they determine key physical…
We revisit a quantum-mechanical formula of the spin magnetic quadrupole moment (MQM) in periodic crystals. Two previous attempts were inconsistent with each other; one is gauge dependent, and the other is gauge invariant. Here we define the…
Unconventional magnetism represents a class of metallic states whose Fermi surfaces exhibit spin-dependent splittings under the non-trivial representations of the rotation group. The $d$-wave $\alpha$-phase unconventional magnetic state,…
Beyond conventional ferromagnetism and antiferromagnetism, altermagnetism is a recently discovered unconventional magnetic phase characterized by time-reversal symmetry breaking and spin-split band structures in materials with zero net…
Efficient transport of spin and orbital moments, and their electrical detection, are among the main challenges in spintronics and orbitronics. In magnetic insulators, these currents are mediated by magnons. In addition to carrying spin and…
d-wave altermagnets have the magnetic octupole as their primary order parameter. A recent study [Han et al. arXiv 2409.14423 (2024)] demonstrated that magnetic octupole current can induce N\'eel vector dynamics. Therefore, identifying…
Order parameters not only characterize symmetry-broken equilibrium phases but also govern transport phenomena in the nonequilibrium regime. Altermagnets, a class of magnetic systems integrating ferromagnetic and antiferromagnetic features,…
We show that time-reversal symmetry broken, centrosymmetric antiferromagnets with nonrelativistic spin-splitting are conveniently described in terms of the ferroic ordering of magnetic octupoles. The magnetic octupoles are the lowest-order…
A method proposed for measuring the electric dipole moment (EDM) of a charged fundamental particle such as the proton, is to measure the spin precession caused by a radial electric bend field $E_r$, acting on the EDMs of frozen spin…
Motivated by experimental and theoretical interest in realizing multipolar orders in $d$-orbital materials, we discuss the quantum magnetism of $J\!=\!2$ ions which can be realized in spin-orbit coupled oxides with $5d^2$ transition metal…
Altermagnets break time-reversal symmetry and their spin-orbit coupling (SOC) allow for an anomalous Hall effect (AHE) that depends on the direction of the N\'eel ordering vector. The AHE and the ferromagnetic spin moment share the same…