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Understanding the Superior Stability of Single‐Molecule Magnets on an Oxide Film

Abstract The stability of magnetic information stored in surface adsorbed single‐molecule magnets is of critical interest for applications in nanoscale data storage or quantum computing. The present study combines X‐ray magnetic circular dichroism, density functional theory and magnetization dynamics calculations to gain deep insight into the substrate dependent relevant magnetization relaxation mechanisms. X‐ray magnetic circular dichroism reveals the opening of a butterfly‐shaped magnetic hysteresis of DyPc2 molecules on magnesium oxide and a closed loop on the bare silver substrate, while density functional theory shows that the molecules are only weakly adsorbed in both cases of magnesium oxide and silver. The enhanced magnetic stability of DyPc2 on the oxide film, in conjunction with previous experiments on the TbPc2 analogue, points to a general validity of the magnesium oxide induced stabilization effect. Magnetization dynamics calculations reveal that the enhanced magnetic stability of DyPc2 and TbPc2 on the oxide film is due to the suppression of two‐phonon Raman relaxation processes. The results suggest that substrates with low phonon density of states are beneficial for the design of spintronics devices based on single‐molecule magnets.


Details of DFT calculations
We performed total energy calculations using density functional theory (DFT) [1] within the Kohn-Sham formalism [2] using the QuickStep module [3] in the CP2K code (http://www.CP2K.org/). The rB86-vdW-DF2 approximation [4] to the exchange-correlation functional was applied. We used DZVP-MOLOPT-SR-GTH basis sets and a cut-off energy of 1300 Ry and the relative cut-off energy 70 Ry to expand the Kohn-Sham orbitals and the augmented electron density, respectively. The pseudo potentials were of the type Goedecker-Teter-Hutter. [5] 2 × 2 points were used in the calculations due to the relatively large dimensions, together with the Fermi-Dirac broadening of the occupation numbers with a width of 25.8 meV. The molecule was inserted in the experimental super-cell of MgO/Ag(100), which contains 25 atoms per layer. Five layers of MgO were employed. The experimental lattice constant of Ag of 4.09 Å was used in the calculations. [6] Six layers of Ag atoms in the Ag(100) support were included, and three top layers of the metal were relaxed both in the calculations of YPc2/MgO/Ag(100) and YPc2/Ag(100), with all the atoms relaxed in the MgO (when present) and the adsorbate. Figure S1. Charge transfer between YPc2 and surfaces. Differences of electronic density Δn(z) = nYPc2/Ag -nYPc2 -nAg (red curve) and Δn(z) = nYPc2/MgO/Ag -nYPc2 -nMgO/Ag (black curve) as explained in the text of the SI. The z direction denotes the surface normal, and the plotted densities were averaged in the surface (x,y) plane. The green dashed curve has been offset horizontally to match the position of the Y(III) ions. The red curve has been offset vertically for clarity.
In order to evaluate the transfer of charge between LnPc2 molecules and the substrate we have calculated the differences of electronic density Δn(r) = nYPc2/MgO/Ag -nYPc2 -nMgO/Ag and Δn(r) = nYPc2/Ag -nYPc2 -nAg . Here, nYPc2/MgO/Ag is the electron density of the full system, i.e., YPc2 adsorbed on 5 MLs of MgO/Ag(100), and nYPc2 and nMgO/Ag are the densities of the molecule and the substrate, calculated separately with the coordinates of the full system. Table S1. Adsorption energies of YPc2 on the Ag(100) hollow site and on the MgO(5 ML)/Ag(100) oxygen-on-top and magnesium-on-top sites.
In Figure S1 one-dimensional plots of Δn(z) along the surface normal direction z averaged in the (x,y) plane are shown. The green, shifted, curved is aligned so that the yttrium(III) ion is at the same value of z, to clarify the differences between the two curves around the molecule at the right of the plot. The brown circle is the yttrium(III) ion, the cyan and the blue circles are the two phthalocyanine molecules. The red curve has been offset vertically for clarity.
The results plotted in Figure S1 indicate that there are significant movements of charges toward the YPc2 molecules in both cases of Ag(100) and MgO/Ag(100). Interestingly, in both cases there is a depletion, i.e., a dip, at the Ag(100) surface and there are peaks just below both phthalocyanine ligands. The pattern looks similar for both substrates in the vicinity of the molecules. Since in the case of TbPc2/Ag(111) a charge transfer between molecules and surface was found leading to the absence of the ligand hole (radical spin), [7,8] we interpret these results in that the ligand hole is absent in YPc2/MgO(5 ML)/Ag(100), too.
2. X-ray linear dichroism (full energy range of spectra in Figure 2). Figure S2. Full scale X-ray linear dichroism spectra of DyPc2. X-ray absorption spectra recorded with linear vertical (σv) and horizontal (σh) X-ray polarization (top panels) and corresponding XLD (bottom panels) at the Dy M4,5 edges of DyPc2 (sub-ML) on (a) MgO(4 ML)/Ag(100) and on (b) Ag(100). The spectra were recorded at grazing X-rays incidence 60 o to sample normal, at T = 2.5 ± 0.5 K and at 50 mT of applied external magnetic field.

Relaxation rate of the Orbach process for DyPc 2 and TbPc 2 on MgO/Ag and Ag surfaces
In the Orbach process one phonon is absorbed promoting the Ln(III) ion to an excited state, and subsequently another phonon is emitted, with the energy difference of the phonons equal to the Zeeman energy. The rate is given by the Arrhenius-type law: [9] where o −1 is the attempt frequency and ∆ denotes the effective energy barrier for magnetization reversal. To establish the relaxation rate of the Orbach process we used values from Reference [9], i.e., Δ = 3.84 meV, τo = 3.3•10 -6 s for DyPc2 and Δ = 0.032 eV, τo = 2•10 -8 s for TbPc2. This leads to the Orbach process relaxation rates of 1.6•10 -57 s -1 for TbPc2 at 2.5 K, 5.5•10 -3 s -1 for DyPc2 at 2.5 K. These relaxation rates insignificantly contribute to the magnetization dynamics of studied molecules, nevertheless, they are taken into account in the simulation. The Orbach process rates are not plotted in Figure 5 in the main text for clarity.
6. Simulation of magnetization dynamics in the TbPc 2 /MgO system including field dependence of Raman relaxation rate ~C|H| l with l = 1, 2, 3, 4 In the main text we explain that the theoretical value of the l exponent in the magnetic field dependence of Raman relaxation rate ~|H| l, remains unknown and differs between various literature reports. We have tested how well the simulation matches the experimental data for integer values of l , 0 ≤ l ≤ 4. The case of l = 0, i.e., field-independent Raman relaxation yields the best fit and is presented in the main text. We find that, in addition, when including 20% of fast relaxing molecules, as described in the main text, only l = 1 and 2 provide reasonable fits to the experimental data ( Figure S5). Further increasing the l parameter yields a strong deviation of the fit in the lowfield range. Therefore, our model implies that the relaxation rate ascribed to the Raman process in the studied systems is still consistent with a field dependence ~H l with 0 ≤ l ≤ 2. 7. Changes of TbPc 2 magnetic hysteresis when switching from MgO to Ag surface upon varying QTM and direct spin-phonon (S-P) relaxation rates. a b Figure S6. Magnetization dynamics modeling of TbPc2 on Ag(100). Changes to the magnetic hysteresis of TbPc2/Ag as induced by increasing (a) 10 5 times the QTM rate or (b) 10 5 times the spin-phonon direct relaxation rate while keeping the other relaxation rates equal to the ones found for TbPc2/MgO/Ag(100) as listed in Table 1 of the main text.