The interplay of magnetic order with the electronic scattering and crystal-field effects in a metallic ferromagnet

TL;DR

This study investigates how magnetic order, charge dynamics, and crystal-field effects interact in the metallic ferromagnet PrSi using time-domain terahertz spectroscopy. The THz conductivity is predominantly non-Drude and is described by a Drude-Smith framework across temperatures, while a classical Kondo lattice model accounts for itinerant electron scattering off localized 4$f$ moments at higher temperatures. At lower temperatures, crystal-field excitations emerge as dominant features, notably sharp peaks at $f=$ $0.6$ THz and $1.54$ THz, with the latter showing a dynamic correlation with the onset of ferromagnetic order. The two-CEF peak analysis reveals temperature-dependent occupation, particularly a peak in CEF3 near the Curie temperature $T_{ m C}=52$ K, indicating a strong spin–CEF coupling and suggesting extensions of CKLM to include low-temperature quantum fluctuations for a broader class of rare-earth intermetallics and related compounds.

Abstract

The interplay between magnetic order, charge dynamics, and crystal field excitations underpins the emergent ground states of rare-earth intermetallics. Using time-domain terahertz spectroscopy, we probe this coupling in PrSi, a metallic ferromagnet. The optical response exhibits pronounced Drude-Smith behavior over a broad temperature range, indicating persistent carrier scattering. A classical Kondo-lattice model (CKLM) attributes this non-Drude conductivity to scattering of itinerant electrons by localized magnetic moments, persisting down to temperatures well below the magnetic ordering scale. At lower temperatures, beyond the scope of CKLM, our experiment reveals that the response is dominated by crystal-field excitations, with sharp transitions at 0.6 THz and 1.54 THz. The mode at 1.54 THz shows a dynamic correlation with the onset of ferromagnetic order, marking the onset of a crystal-field-governed low temperature regime.

Figures (4)

• Figure 1: (a) A schematic of the orthorhombic crystal structure of PrSi. (b) A schematic showing the splitting of the $J = 4$ level of the central ion Pr$^{3+}$ into $2J+1 = 9$ sub-levels of distinct energy values, all in the THz range. The incident THz pulse interacts with the lowest four CEF multiplets. (c) THz transients reflected from the reference Pt-mirror and the PrSi sample at different temperatures. (Inset) The incident THz spectra. (d) The spectral amplitude corresponding to the sample at the corresponding temperatures shown in (c), obtained from the Fourier transform of the time transients. The zero-level corresponding to each spectra is marked. The red-dashed lines refer to the Lorentzian fitting of the respective spectra. The arrow indicates the peak shift as we lower the temperature. (e) The temperature-dependent peak frequency corresponding to (d), which shows a blue shift as we enter in the ferromagnetic phase of the material. Here, the error bars are the standard errors from the modeling of the spectra. The vertical dashed line indicates the Curie temperature, $T_{\rm C} = 52$ K.
• Figure 2: (a) Temperature-dependent magnetization and its derivative, showing the $T_{\rm C}$ of the material at 52 K. The real part of the THz conductivity as a function of frequency for (b) 2 K, (c) 50 K and (d) 100 K, respectively. The solid-red lines represent the Drude-Smith (DS) model. The colored areas represent the fitting using the double-Lorentz (DL) oscillator model.
• Figure 3: (a) Temperature-dependent real part of the THz conductivity obtained from our experiments. The solid lines represent the fitting using Drude-Smith (DS) model. (b) A schematic representation of the CKLM, where the localized 4$f$-moments (red arrows, $S_i$) are coupled to the itinerant electrons (green arrows, $\sigma_i$) at every lattice site. (Inset) The localized and itinerant electrons are coupled with a coupling strength $J_k$ and $t$ being the nearest-neighbor hopping parameter. (c) Temperature-dependent real part of the THz conductivity obtained from our theoretical CKLM. The solid lines represents fitting using Drude-Smith model. (d) The scattering time $\tau_{\rm DS}$ obtained by fitting the Drude-Smith models corresponding to the experimental and theoretical conductivity spectra. The yellow and green-shaded regions show the paramagnetic and the ferromagnetic phases, respectively. The vertical black-dashed line marks the $T_{\rm C}$ of the material. The vertical cyan-dashed line marks the temperature below which the conductivity obtained from CKLM deviates from the experimental observations. Here, the error bars represent the standard errors from the DS-modeling of the experimental and theoretical conductivity data.
• Figure 4: (a) Real part of the THz conductivity at different temperatures. The solid lines represents fitting using the double-Lorentz (DL) model. (b) The plasma frequency corresponding to both oscillators, plotted as a function of temperature. (c) The ratio of the plasma frequencies in (b). The yellow- and green-shaded regions show the paramagnetic and the ferromagnetic phase, respectively, while the vertical dashed-line marks the Curie temperature of the system. Here, the error bars are the standard errors from the modeling of the experimental conductivity data.