$4f$-spin dynamics in ${\mathrm{La}}_{2-x-y}{\mathrm{Sr}}_x{\mathrm{Nd}}_y{\mathrm{CuO}}_4$

We have performed inelastic magnetic neutron scattering experiments on ${\mathrm{La}}_{2-x-y}{\mathrm{Sr}}_x{\mathrm{Nd}}_y{\mathrm{CuO}}_4\hspace{0.5em}(0\mathrm{}<~x<~0.2$ and $0.1<~y<~0.6)$ in order to study the Nd $4f$-spin dynamics at low energies $(ħ\omega \lesssim 1\hspace{0.5em}\mathrm{meV}).\mathrm{}$ In all samples we find at high temperatures a quasielastic line (Lorentzian) with a linewidth which decreases on lowering the temperature. The temperature dependence of the quasielastic linewidth $\Gamma /2\mathrm{}\left(T\right)\mathrm{}$ can be explained with an Orbach process, i.e., a relaxation via the coupling between crystal field excitations and phonons. At low temperatures the $\mathrm{Nd}-4f$ magnetic response $S(\mathbf{Q},\omega )$ correlates with the electronic properties of the ${\mathrm{CuO}}_2$ layers. In the insulator ${\mathrm{La}}_{2-y}{\mathrm{Nd}}_y{\mathrm{CuO}}_4\hspace{0.5em}\mathrm{}(y=0.1,0.3\mathrm{})\mathrm{}$ the quasielastic line vanishes below 80 K and an inelastic excitation occurs. This directly indicates the splitting of the ${\mathrm{Nd}}^{3+}$ ground state Kramers doublet due to the static antiferromagnetic order of the Cu moments. In ${\mathrm{La}}_{1.7-x}{\mathrm{Sr}}_x{\mathrm{Nd}}_{0.3}{\mathrm{CuO}}_4$ with $x=0.12,0.15\mathrm{}$ and ${\mathrm{La}}_{1.4-x}{\mathrm{Sr}}_x{\mathrm{Nd}}_{0.6}{\mathrm{CuO}}_4$ with $x=0.1,0.12,0.15,0.18\mathrm{}$ superconductivity is strongly suppressed. In these compounds we observe a temperature independent broad quasielastic line of Gaussian shape below $T\approx 30\hspace{0.5em}\mathrm{K}.$ This suggests a distribution of various internal fields on different Nd sites and is interpreted in the frame of the stripe model. In ${\mathrm{La}}_{1.8-y}{\mathrm{Sr}}_{0.2}{\mathrm{Nd}}_y{\mathrm{CuO}}_4\hspace{0.5em}\mathrm{}(y=0.3,0.6\mathrm{})\mathrm{}$ such a quasielastic broadening is not observed even at lowest temperature.