Magnetic properties of single rare-earth atoms on graphene/Ir(111)

We employed x-ray absorption spectroscopy and x-ray magnetic circular dichroism to study the magnetic properties of single rare-earth (RE) atoms (Nd, Tb, Dy, Ho, and Er) adsorbed on the graphene/Ir(111) surface. The interaction of RE atoms with graphene results for Tb in a trivalent state with $4f^{n-1}$ occupancy, and in a divalent state with $4f^n$ occupancy for all other studied RE atoms ($n$ corresponds to the $4f$ occupancy of free atoms). Among the studied RE on graphene/Ir(111), Dy is the only one that shows magnetic hysteresis and remanence at 2.5 K. By comparing measured spectra and magnetization curves with multiplet calculations, we determine the energy diagram of the magnetic states and show for each element the magnetization reversal process that determines the timescale of its magnetic bistability.

Figure 1

Measured and simulated (a) XAS, (b) XMCD, and (c) XMLD spectra of 0.004 ML Dy on graphene/Ir(111) ($B=6.8\mathrm{T}, T=2.5\mathrm{K}$). In (a) and (b), A marks the peak at 1289.3 eV, and B marks the one at 1291.8 eV. (d) Magnetization curves obtained by acquiring the XMCD signal at 1289.3 eV as a function of the external field $B$ ($T=2.5\mathrm{K}, \varphi =5{\varphi }_0$ and $\dot{B}=33\mathrm{mT}{\mathrm{s}}^{-1}$). (e) Energy diagram of the Dy lowest multiplet ($J=8$) resulting from multiplet calculations. Each color identifies $J_z$ states that belong to one of the six classes of eigenstates defined by the $C_{6v}$ symmetry. Dashed lines connect doublets with quenched $J_z$. Grey arrows indicate the relaxation mechanism at $B=0\mathrm{T}$ via thermal excitation to $J_z=\pm 6$ doublet. (f) Planar representation of the point charge CF scheme employed in multiplet calculations; red marks positive, and blue negative charge. The size of each circle reflects the amount of charge. Table 2 reports spatial coordinates and value of each charge, Table 7 the parameters describing the CF splitting in the Stevens operator representation.

Figure 2

(a) Coverage dependence of Dy XAS at the $M_5$ edge acquired at $\theta =0^{\circ }$ and $B=0.05\mathrm{T}$. All spectra were normalized to the intensity at the peak at or near 1289.3 eV, and were subsequently offset for clarity. Dashed lines mark the peak energy associated with divalent Dy atoms at 1289.3 eV (grey) and trivalent Dy clusters at 1291.8 eV (black). STM images for coverages close to the ones employed in XAS measurements: (b) 0.005 ML, (c) 0.010 ML, (d) 0.014 ML, and (e) 0.019 ML. The scale bar applies to all images [(b)–(d): $V_{\text{t}}=-0.5\mathrm{V}, I_{\text{t}}=20\mathrm{pA}$, (e): $V_{\text{t}}=-0.2\mathrm{V}, I_{\text{t}}=100\mathrm{pA}$; $T_{\mathrm{dep}}=10\mathrm{K}, T=5\mathrm{K}$]. (f) Coverage dependence of Dy average cluster size deducted from STM measurements. Grey line serves as guide to the eye.

Figure 3

Exposure time dependence of the XAS for 0.01 ML Dy on graphene/Ir(111) at the $M_5$ edge. All spectra were acquired at $\theta =0^{\circ }$ and $B=6.8\mathrm{T}$. Dashed lines mark the peak positions associated with divalent Dy atoms at 1289.3 eV (grey) and trivalent Dy objects at 1291.8 eV (black). Spectra are vertically offset for clarity.

Figure 4

Magnetization curves of Dy on graphene/Ir(111) acquired with two combinations of x-ray flux and acquisition speeds ($T=2.5\mathrm{K}, \theta =0^{\circ }$; blue, $\varphi =5{\varphi }_0$ and $\dot{B}=33\mathrm{mT}{\mathrm{s}}^{-1}$; red, $\varphi =9{\varphi }_0$, and $\dot{B}=12\mathrm{mT}{\mathrm{s}}^{-1}$).

Figure 5

Experimentally acquired and simulated (a) XAS, (b) XMCD, and (c) XMLD spectra of 0.002 ML Nd on graphene/Ir(111) ($B=6.8\mathrm{T}, T=2.5\mathrm{K}$). (d) Magnetization curves obtained by acquiring the XMCD signal at 996.7 eV ($T=2.5\mathrm{K}, \varphi =9{\varphi }_0$ and $\dot{B}=12\mathrm{mT}{\mathrm{s}}^{-1}$), together with simulated ones. (e) Energy diagram of the lowest multiplet ($J=4$) resulting from multiplet calculations. Each color identifies $J_z$ states that belong to one of the six classes of eigenstates defined by the $C_{6v}$ symmetry. Dashed lines connect $J_z=\pm 3$ doublet with quenched $\langle J_z\rangle$. Grey arrows indicate relaxation mechanism at $B=0\mathrm{T}$ via thermal excitation to $J_z=\pm 3$ doublet. (f) Planar representation of the point charge CF scheme employed in multiplet calculations; blue marks negative charge. Table 3 reports spatial coordinates and value of each charge, Table 7 the parameters describing the CF splitting in the Stevens operator representation.

Figure 6

Experimentally acquired and simulated (a) XAS, (b) XMCD, and (c) XMLD spectra of 0.003 ML Ho on graphene/Ir(111) ($B=6.8\mathrm{T}, T=2.5\mathrm{K}$). (d) Magnetization curves obtained by acquiring the XMCD signal at 1346.6 eV ($T=2.5\mathrm{K}, \varphi =9{\varphi }_0$ and $\dot{B}=12\mathrm{mT}{\mathrm{s}}^{-1}$), together with simulated ones. (e) Energy diagram of the Ho lowest multiplet ($J={}^{15}{/}_2$), resulting from multiplet calculations. Each color identifies $J_z$ states that belong to one of the six classes of eigenstates defined by the $C_{6v}$ symmetry. Grey arrows indicate the relaxation mechanism at $B=0\mathrm{T}$ via thermal excitation to $\langle J_z\rangle =\pm 5.4$. (f) Planar representation of the point charge CF scheme employed in multiplet calculations; red marks positive and blue negative charge. The size of each circle reflects the amount of charge. Table 4 reports spatial coordinates and value of each charge, Table 7 the parameters describing the CF splitting in the Stevens operator representation.

Figure 7

Experimentally acquired and simulated (a) XAS, (b) XMCD, and (c) XMLD spectra of 0.004 ML Er on graphene/Ir(111) ($B=6.8\mathrm{T}, T=2.5\mathrm{K}$). (d) Planar representation of the point charge CF scheme employed in multiplet calculations; red marks positive and blue negative charge. The size of each circle reflects the amount of charge. Table 5 reports spatial coordinates and value of each charge, Table 7 the parameters describing the CF splitting in the Stevens operator representation. (e) Energy diagram of the Er lowest multiplet ($J=6$). Each color identifies $J_z$ states that belong to one of the six classes of eigenstates defined by the $C_{6v}$ symmetry. Dashed lines connect doublets with quenched $\langle J_z\rangle$. Grey and black arrows indicate two relaxation mechanisms at $B=0\mathrm{T}$.

Figure 8

Experimentally acquired and simulated (a) XAS, (b) XMCD, and (c) XMLD spectra of 0.003 ML Tb on graphene/Ir(111) ($B=6.8\mathrm{T}, T=2.5\mathrm{K}$). (d) Magnetization curves obtained by acquiring the XMCD signal at 1236.9 eV ($T=2.5\mathrm{K}, \varphi =9{\varphi }_0$ and $\dot{B}=12\mathrm{mT}{\mathrm{s}}^{-1}$), together with simulated ones. (e) Energy diagram of the Tb lowest multiplet ($J=6$) resulting from multiplet calculations. The splitting at $J_z=0$ is emphasized for better clarity. Each color identifies $J_z$ states that belong to one of the six classes of eigenstates defined by the $C_{6v}$ symmetry. Dashed lines connect doublets with quenched $\langle J_z\rangle$. (f) Planar representation of the point charge CF scheme employed in multiplet calculations; red marks positive and blue negative charge. The size of each circle reflects the amount of charge. Table 6 reports spatial coordinates and value of each charge, Table 7 the parameters describing the CF splitting in the Stevens operator representation.