This Colloquium reviews the 25~year quest to understand the continuous (second-order), mean-field-like phase transition occurring at 17.5~K in URu2Si2. About ten years ago, the term ``hidden order'' (HO) was coined and has since been utilized to describe the unknown ordered state, whose origin cannot be disclosed by conventional solid-state probes, such as x~rays, neutrons, or muons. The HO is able to support superconductivity at lower temperatures (Tc$\approx${}1.5\,\,K), and when magnetism is developed with increasing pressure both the HO and the superconductivity are destroyed. Other ways of probing the HO are via Rh~doping and large magnetic fields. During the last few years a variety of advanced techniques have been tested to probe the HO state and these attempts will be summarized. A digest of recent theoretical developments is also included. It is the objective of this Colloquium to shed additional light on the HO state and its associated phases in other materials.

The generation of spin and orbital currents is of crucial importance in the field of spin-orbitronics. In this work, using relativistic density functional theory and the Kubo linear-response formalism, we systematically investigate the spin Hall and orbital Hall effects for 40 monoatomic metals. The spin Hall conductivity and orbital Hall conductivity (OHC) are computed as a function of the electrochemical potential and the influence of the spin-orbit interaction strength is also investigated. Our calculations predict a rather small OHC in $sp$ metals, but a much larger OHC in $d$-band metals, with maximum values $[\sim 8000(\hslash /e){\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}]$ near the middle of the $d$ series. Using the Mott formula, we evaluate the thermal counterparts of the spin and orbital Hall effects, the spin Nernst effect (SNE), and the orbital Nernst effect (ONE). We find that the as-yet unobserved ONE is significantly larger $(\sim 10\times )$ than the SNE and has maximum values for group 10 elements (Ni, Pd, and Pt). Our work provides a broad overview of electrically and thermally induced spin and orbital transport in monoatomic metals.

The orbital Hall effect has been theoretically predicted but its direct observation is a challenge. Here, we report the magneto-optical detection of current-induced orbital accumulation at the surface of a light $3d$ transition metal, Cr. The orbital polarization is in-plane, transverse to the current direction, and scales linearly with current density, consistent with the orbital Hall effect. Comparing the thickness-dependent magneto-optical measurements with ab initio calculations, we estimate an orbital diffusion length in Cr of $6.6\pm 0.6\mathrm{nm}$.

High-harmonic spectroscopies reveal that fast energy transfer within 20 fs triggers ultrafast magnetic phase transition in Ni.

Efficient manipulation of magnetic order with electric current pulses is desirable for achieving fast spintronic devices. The Rashba-Edelstein effect, wherein spin polarization is electrically induced in noncentrosymmetric systems, provides a mean to achieve staggered spin-orbit torques. Initially predicted for spin, its orbital counterpart has been disregarded up to now. Here we report a generalized Rashba-Edelstein effect, which generates not only spin polarization but also orbital polarization, which we find to be far from being negligible. We show that the orbital Rashba-Edelstein effect does not require spin-orbit coupling to exist. We present first-principles calculations of the frequency-dependent spin and orbital Rashba-Edelstein tensors for the noncentrosymmetric antiferromagnets CuMnAs and Mn $${}_{2}$$2 Au. We show that the electrically induced local magnetization can exhibit Rashba-like or Dresselhaus-like symmetries, depending on the magnetic configuration. We compute sizable induced magnetizations at optical frequencies, which suggest that electric-field driven switching could be achieved at much higher frequencies.

Ultrafast heating of a ferrimagnet’s crystal lattice leads to a new state of matter with hot spins yet unchanged magnetization.