Temperature Dependence of Magnetic Excitations: Terahertz Magnons above the Curie Temperature

When an ordered spin system of a given dimensionality undergoes a second order phase transition, the dependence of the order parameter, i.e., magnetization on temperature, can be well described by thermal excitations of elementary collective spin excitations (magnons). However, the behavior of magnons themselves, as a function of temperature and across the transition temperature $T_C$, is an unknown issue. Utilizing spin-polarized high resolution electron energy loss spectroscopy, we monitor the high-energy (terahertz) magnons, excited in an ultrathin ferromagnet, as a function of temperature. We show that the magnons’ energy and lifetime decrease with temperature. The temperature-induced renormalization of the magnons’ energy and lifetime depends on the wave vector. We provide quantitative results on the temperature-induced damping and discuss the possible mechanism, e.g., multimagnon scattering. A careful investigation of physical quantities determining the magnons’ propagation indicates that terahertz magnons sustain their propagating character even at temperatures far above $T_C$.

Figure 1

(a) The LEED pattern of the sample taken at a primary electron energy of 45 eV. (b) LMOKE hysteresis loops recorded at the temperatures of 13 and 380 K, labeled by red solid and blue open circles, respectively. (c) The Kerr ellipticity, open circles, and the SPEELS spin asymmetry $A$, field circles, as a function of temperature. (d) A schematic representation of the scattering geometry.

Figure 2

(a)–(d) SPEELS spectra recorded at $q=1.1{\AA }^{-1}$ on a two atomic-layer thick ${\mathrm{Fe}}_{50}{\mathrm{Pd}}_{50}$ film on Pd(001) at $T=13\mathrm{K}$ (a), 300 K (b), 350 K (c), and 400 K (d). The red ($I_{\downarrow }$) and blue ($I_{\uparrow }$) spectra represent the intensity of the scattered electrons for the spin polarization of the incident beam parallel and antiparallel to the sample magnetization, respectively. The difference ($I_{\downarrow }-I_{\uparrow }$) and total spectra ($I_{\downarrow }+I_{\uparrow }$) are represented by green and black solid symbols, respectively.

Figure 3

Magnon energy (solid circles) and lifetime (open squares) as a function of the reduced temperature at $q=0.6{\AA }^{-1}$ (a), $0.8{\AA }^{-1}$ (b), and $1.1{\AA }^{-1}$ (c). The insets represent the corresponding linewidth versus the reduced temperature. (d) The temperature dependence of the decay parameter ($\alpha =\mathrm{\Delta }E/E$). The field symbols denote the results of different wave vectors. The average is represented by open circles. The solid line indicates a linear fit to the data ($y=0.267+0.22x$).