Magnetic Field Induced Orbital Polarization in Cubic ${\mathrm{YbInNi}}_4$: Determining the Quartet Ground State Using X-Ray Linear Dichroism

We have been able to induce a linear dichroic signal in the Yb $M_5$ x-ray absorption white line of cubic ${\mathrm{YbInNi}}_4$ by the application of a magnetic field. The nonzero integrated intensity of the magnetic field induced dichroic spectrum indicates a net noncubic $4f$ orbital polarization. A quantitative analysis of the temperature and field strength dependence establishes that the crystal-field ground state is a ${\Gamma }_8$ quartet. The results demonstrate the potential of magnetic field induced linear dichroism as a new powerful approach for the investigation of the degeneracy and orbital degrees of freedom of cubic heavy-fermion and Kondo systems.

Figure 1

Crystal-field schemes as published in 23, 24, 25, 26.

Figure 2

Angular hole distributions and their corresponding polarization dependent $M_5$ XAS spectra of the $4f_{7/2}^{13}$ wave functions in cubic symmetry. The upper panels show the distributions and spectra in the absence of an external field. The lower panels display the decomposition of the $|{\Gamma }_8⟩$ distribution in the presence of magnetic field into the $|{\tilde{\Gamma }}_6⟩$ and $|{\tilde{\Gamma }}_7⟩$ [see Eq. (1)], together with their corresponding spectra. The orientation of the applied magnetic field and electric field vector $\mathbf{E}$ of the linearly polarized light relative to the [001] crystallographic axis is also depicted.

Figure 3

Experimental x-ray absorption spectrum of ${\mathrm{YbInNi}}_4$ at the Yb $M_5$ edge for linearly polarized light coming in with the electric field vector $\mathbf{E}$ parallel [light (red) lines] and perpendicular [dark (blue) lines] to the magnetic field oriented close to the [001] crystallographic axis.

Figure 4

Magnetic field induced linear dichroism (MILD) as a function of magnetic field calculated using the CF scheme of Severing et al. [23] (blue line), Sarrao et al. [24] (orange line), Pagliuso et al. [25] (green dotted line), and Aviani et al. [26] (red dashed line), at 0 K (top panel) and for the temperature range between 6 and 7 K ($6.5\pm 0.5\mathrm{K}$) (bottom panel). The open and full circles in the bottom panel correspond to the measurements of two different ${\mathrm{YbInNi}}_4$ crystals.