M A T E R I A L S F O R T O M O R R O W ' S I N N O V A T I V E A N D S U S T A I N A B L E I N D U S T R Y

S C I E N T I F I C H I G H L I G H T S

8 2 H I G H L I G H T S 2 0 2 3 I

Discovery of long-lived high-energy spin waves in a metallic host

Spin waves, i.e., collective excitations of the ordered lattice of spins in magnets, usually decay very rapidly if the magnet is a metal. Using resonant inelastic X-ray scattering to excite spin waves and then study their decay rate, the possibility of very long-lived spin waves in special types of metallic magnets was demonstrated.

The elementary excitations of the spin lattice in magnetically ordered systems are called spin waves, a wave of oscillating spins emerging from the excited magnetic site. Propagating spin waves is an attractive way of transporting information in materials as it does not require the physical transport of charge carriers, and thus holds potential for low-power information processing at very high frequencies, often referred to as spintronics. In real materials, the propagation distances and lifetimes of spin waves are limited by the rate at which they interact in scattering processes. Spin-wave scattering can occur at crystalline defects, magnetic impurities or magnetic domain walls. In metallic magnets, a further scattering mechanism called Landau damping typically dominates. In metals, typically both empty spin-up and spin-down states are present close to the Fermi level. In such an environment, spin waves easily decay into a low-energy spin-flip (Stoner) excitation and their decay rate can become comparable or even larger than their excitation energy, in which case the spin waves decay before they can propagate. The strong increase in spin- wave scattering in metals can be readily observed as a reduction of the lifetime of the excited spin wave. Therefore, energy-loss spectroscopies with sufficiently high energy resolution like resonant inelastic X-ray scattering (RIXS) can investigate the decay rate of spin-

wave excitations through the natural line width of the excitation, which is inversely proportional to its lifetime (Figure 62).

RIXS at beamline ID32 was used to investigate the spin wave spectrum, i.e., the energies and lifetimes of spin-wave excitations, in the metallic antiferromagnet CeCo2P2. The high energy resolution, 28 meV at the Co L3 edge, was crucial to demonstrate the presence of very sharp spin-wave excitations up to frequencies in excess of 50 THz, or 200 meV (Figure 63, top). Such properties would be expected and are observed in magnetic insulators, like undoped cuprates [1] and other TM oxides, but not in metals due to the strong Landau damping (Figure 63, bottom). This is, for instance, why the sharp magnon excitations in the cuprate parent compounds become immediately very broad as soon as the system transitions into the metallic state upon doping [2].

With the help of theoretical calculations, it was shown that the unexpectedly long lifetimes of the spin waves in this material is due to a special configuration of the electronic structure. The Co 3d states that host the ordered magnetic moments show an electronic structure practically identical to an insulating system, with a gap at the Fermi level that is wide enough to suppress the spin- wave scattering due to Stoner excitations to the highest probed spin-wave frequencies of 50+ THz. By contrast, the electronic states not involved in the magnetism show the electronic structure of a metal, with a sizeable electronic density of states across the Fermi energy, which is responsible for the electric conductivity of the material. By gradually raising the temperature from 20 K to 300 K and repeating the RIXS measurements, it was shown that the lifetime of the spin-wave excitations does not notably decrease, even at room temperature, which is important for potential technological applications.

Fig. 62: Excitation and characterisation of spin waves in magnets with RIXS. The energy loss experienced by

the X-rays in the scattering process corresponds to the energy (frequency) of the excited spin wave, Esw.

The natural linewidth of the excitation is inversely proportional to the decay rate of the excited spin waves.