Spin and charge excitations in artificial hole- and electron-doped infinite layer cuprate superconductors

The asymmetry between electron and hole doping in high critical-temperature superconducting (HTS) cuprates is key information for the understanding of Cooper pair formation mechanisms. Despite intensive studies on different cuprates, a comprehensive description of related magnetic and charge excitations is still fragmentary. In the present work, artificial cuprates were used to cover the entire phase diagram within the same HTS family. In particular, Cu $L_3$-edge resonant inelastic x-ray scattering (RIXS) measurements were performed on artificial $n$- and $p$-type infinite layer (IL) epitaxial films. Beside several similarities, RIXS spectra show noticeable differences in the evolution, with doping level, of magnetic and charge intensity and damping. Compatible trends can be found in spectra measured on bulk cuprates, as well as in theoretical calculations of the spin dynamical structure factor $S(\mathbf{q},\omega )$. The findings give a deeper insight into the evolution of collective excitations across the cuprate phase diagram, and on underlying general features, only connected to the doping type. Moreover, they pave the way to the exploration of general properties of HTS physics over a broad range of conditions, by means of artificial compounds not constrained by the thermodynamic limitations governing the chemical stability of bulk materials.

Figure 1

(a) Experimental setup layout and (b) reciprocal space region spanned inside the first Brillouin zone.

Figure 2

$dd$ excitation spectra of (a) (${\mathrm{CCO})}_3$/(${\mathrm{STO})}_2$ SLs: undoped (black squares) and optimally doped (red circles); and (b) undoped SCO (black squares) and optimally doped (red circles). The spectra have been measured with ${\mathbf{q}}_{\parallel }=(0.37,0)$ and $\pi$ polarization. The spectra have been normalized to the spectral weight in the energy range $[1,3.5]$ eV equal to 100.

Figure 3

(a)–(c) Cu $L_3$-edge RIXS raw spectra waterfall plots of momentum dependence as a function of doping type, measured with $\pi$ incident polarization along the $(0,0)-(\pi ,0)$ direction. The in-plane transferred momentum is defined as ${\mathbf{q}}_{\parallel }=(h,0)$ with $h$ expressed in r.l.u. SLCO spectra are denoted with blue lines, while (${\mathrm{CCO})}_n$/(${\mathrm{STO})}_m$ spectra are defined with red lines. Green ticks indicate the (para)magnon position as estimated by fitting procedure. Thick orange lines give the fast dispersing charge peak. (a) Optimally e-doped doped sample: SLCO with $x=0.1$ and $T_c=28$ K. Thin gray lines represent the residual RIXS intensity after subtraction of the elastic and paramagnon peak, revealing the presence of the fast dispersing mode. (b) Insulating AFM parent compounds: SCO (blue solid lines) and not superconducting (${\mathrm{CCO})}_3$/(${\mathrm{STO})}_2$ (red solid lines). (c) Hole-doped best superconducting sample: (${\mathrm{CCO})}_3$/(${\mathrm{STO})}_2$ with $T_c=25$ K.

Figure 4

Examples of spectra decomposition in the low energy region, at $q_{\parallel }=0.14$ r.l.u. and $\pi$ incident polarization, for (a) undoped ${\mathrm{SrCuO}}_2$ and (b) optimally e-doped SLCO. The data are plotted with circles, while lines are used to plot the Gaussian components: elastic peak (purple), magnon (green), charge mode (orange), tail of $dd$ excitations and $q_{\parallel }$-independent continuum background (black dashed line); the thin red line represents the sum of all the components. The shadowed region in (a) is the residual intensity attributed to multimagnon or charge continuum and to the tail of $dd$ excitations. The same approach is used for undoped and h-doped SLs.

Figure 5

(a) Cu $L_3$-edge RIXS raw spectra of nonsuperconducting SCO (black), best superconducting (${\mathrm{CCO})}_3$/(${\mathrm{STO})}_2$ (red), and optimally doped SLCO (blue), at $q_{\parallel }=0.37$ r.l.u. and $T=20$ K, measured with $\pi$ incident polarization. Intensities are normalized to have the same height on the (para)magnon peak. A horizontal solid line represents the FWHM of the (non-)resolution-limited Gaussian used to decompose the data. Vertical arrows indicate the intensity in the energy range $[0.8,1.5]$ eV, where continuum excitations appear upon doping. Plotting undoped SL instead of SCO would lead to the same conclusions. (b) (Para)magnon dispersion [black circle: undoped SLCO, black cross: undoped SL, red open diamonds: (${\mathrm{CCO})}_3$/(${\mathrm{STO})}_2$, blue filled diamonds: SLCO $x=0.1]$ and fast dispersing charge mode (pink hexagons) as deduced from RIXS spectra compared to $S(\mathbf{q},\omega )$ theoretical calculations in a single band Hubbard model (black line: no doping, red line: hole doping, blue line: electron doping) with nearest hopping parameter $t=500$ meV. Experimental error bars correspond to three times the standard deviation associated with the fitting parameter.

Figure 6

Filling dependence at fixed transferred momentum: comparison between raw RIXS spectra and dynamic spin structure factor $S(\mathbf{q},\omega )$ in a single band Hubbard model. (a) Raw RIXS spectra of SLCO are denoted with blue lines, SLs (${\mathrm{CCO})}_3$/(${\mathrm{STO})}_m$ are defined with red lines, while nonhomogeneously doped $n=7,13$ SLs are reported with gray lines. Green arrows are a guide for the eyes and indicate the (para)magnon position as estimated by fitting procedure. (b) DQMC simulations of the dynamic spin structure factor $S(\mathbf{q},\omega )$ at $(3/4\pi ,0)$ in the single band Hubbard model as a function of $N$. (c) Schematic picture of the first Brillouin zone with dashed lines denoting the AFM ZB. The green solid line highlights the entire RIXS accessible region of the reciprocal space, while the green dot indicates the ${\mathbf{q}}_{\parallel }$ selected in (a) and (b).