Manipulating surface magnetic order in iron telluride

Manipulation of the surface composition of a strongly correlated electron material enables control of the magnetic order.


This PDF file includes:
Section S1. DFT calculation of magnetic contrast Section S2. SP-STM study of the magnetic structure of Fe 1.06 Te Section S3. Incommensurate order in Fe 1.16 Te Section S4. Manipulating the surface excess Fe concentration Section S5. Alternative method to determine sample spin polarization Section S6. Model for the magnetic structure at x = 0.12 Section S7. Model for the magnetic structure at x = 0.2 Fig. S1. Spin-polarized imaging at low excess iron concentrations x < 0.12.  Table S1. Crystal structure of Fe 1+x Te at different excess iron concentrations x.

S1 DFT calculation of magnetic contrast
The calculations were performed using the density functional theory in the generalized gradient approximation (32), as implemented in the QUANTUM ESPRESSO package (33). To describe the bicollinear magnetic order of FeTe, a 2×1×1 supercell is considered, with details of the crystal structure and atomic positions taken from experiment (34). The magnetic moment changes upon structural relaxation (20%), however the STM images remain essentially the same when using the experimental structure or the optimized structure. We used optimized norm-conserving Vanderbilt pseudopotentials (35) with semi-core states included for both Fe and Te and we counter-checked our results using projector-augmented plane wave pseudopotentials (36). A kinetic energy cutoff of 100 Ry was chosen for the wavefunctions. The electronic Brillouin zone of the magnetic supercell was sampled using 12×24×12 points. To simulate STM maps, a vacuum region of 10Å was added to 2 FeTe layers. Including more FeTe layers did not have any effects on our results.
The tunneling current in an STM experiment at small bias voltages can be approximated by (37) where E F is the Fermi energy of the sample, E j the energy of the electron wavefunction ψ j (r) of the sample at the tip position r and the arrows indicate the two different spin polarizations.
The plus and minus signs in this expression are for spin-unpolarized and spin-polarized calculations, respectively, corresponding to STM measurements using a non-magnetic tip and maps of the spin-polarization obtained by subtracting two SP-STM images obtained with oppositely polarized tips from each other. Simulated (SP-)STM images are calculated for an average tipsample distance of 5Å and bias voltage of 0.1V.

Fe Te
Here we summarize SP-STM measurements carried out on multiple samples of Fe 1+x Te with low excess Fe concentration x. On each sample that we have measured only single q magnetic order with a wave vector q = (0.5, 0) was ever observed. To determine the magnetic structure we have measured the surface spin polarization on multiple samples using ferromagnetic STM  scattering. (2) The quality and magnetic properties of STM tips after manipulation have been judged from atomic resolution images and spin-polarized STM images taken in different magnetic fields.
All results presented in this work have been confirmed with different micro tips (i.e. tips with a different apex).
To study the effect of the interstitial Fe atoms on the magnetic order of Fe 1+x Te we have used the STM tip to remove them from the surface. This was done in two ways: (1) the surface can be cleaned by using aggressive tunneling parameters while scanning the STM tip and (2) the Fe atoms can be more gently removed to study how the removal of the Fe atoms affects the magnetic order and how the tip collects the Fe. For the first method, the tip sample tunneling parameters are typically set to I t = 6nA and V t = 500mV and the tip is quickly scanned across the surface with a minimal feedback response time. This allows for the complete removal of almost all of the surface Fe atoms as can be seen in fig. S3. The cleaned areas on the high excess Fe samples that were studied in the main text were selected from larger areas that had been cleaned by this method. Secondly it is possible to see exactly how the excess Fe is removed by the tip. This is done by employing slightly less aggressive tunneling parameters than those used to completely remove all of the surface interstitial Fe. Typically bias voltages in the range of 30mV to 150mV are used with a tunneling current between 1 and 2nA. The surface is then repeatedly scanned with these parameters which allow for the observation of how the Fe atoms are removed. It can be seen from the sequential images shown in ig. S4(a) to (c) that the Fe atoms are dislodged from the surface and group together to form clusters, it is then these clusters that are collected by the tip. By repeatedly scanning an area on a sample with a 12% excess Fe concentration it is then possible to see how the magnetic order changes as the Fe is Section S4. Manipulating the surface excess Fe concentration f dislodged from its position and removed. Figure S4(d) and (e) show the same area imaged before and after manipulation of the Fe atoms. As the Fe is dislodged and moved between (d) and (e) it is possible to see the spread of the bicollinear magnetic order to areas that previously had weak magnetic ordering and a high excess Fe concentration. Figure S5 shows the same data as in Fig. 3 of the main manuscript, showing the Fourier transformations of the regions marked by a blue and green box, as well as a line cut through the peak due to the magnetic order, highlighting that excess iron rich regions show dominantly an incommensurate wave vector of the magnetic order, whereas regions where the excess iron has been removed exhibit the bicollinear order with a commensurate wave vector. We note that even in the excess iron rich region, a weak component of the magnetic order is seen at the commensurate wave vector, which we attribute to areas with locally lower excess iron concentration.

tion
The equation that represents spin polarized tunneling in an STM setup is given by I = I 0 (1 + P tip P sample cos θ), where I 0 is the tunneling current that would be measured with a non magnetic tip, P tip is the spin polarization of the tip and P sample is the spin polarization of the sample. A model that reproduces the SP-STM results for the magnetic structure of Fe 1.12 Te is given by where S a , S b and S c are the components of the local magnetization along the a, b and c lattice directions respectively. X and Y are the position across the sample surface, X being along the a direction and Y being along the b direction.

S7 Model for the magnetic structure at
To determine the magnetic structure underlying the double-q order, we have created simulated STM images for different models of the magnetic order. The order that we find most closely reproduces the SP-STM data is comprised of two spin spirals that propagate through the crystal along the Fe-Fe [110] direction. The spirals alternate between being right handed and left handed corkscrews on alternate rows of Fe atoms. (See Fig. 6 in main text). Mathematically this order is described by Ta le S1 Crystal structure of Fe 1+x Te at different excess iron concentrations x. Values for Ψ shown as grey background in g. 6(e) for different excess Fe concentrations x obtained using the lattice parameters in Ref.
x > 0.12 Te sample imaged successively with moderate tunneling parameters (I = 1nA and V = 100mV) and a slow feedback response time, leading to removal of excess iron. The Fe atoms in the top right corner can be seen to be dislodged from their original positions to form iron clusters, it is then these clusters that are removed by the tip. (d) and (e) the same location on a sample of Fe 1.12 Te at different stages of the cleaning process through scanning with a tunneling current close to 2nA and a bias voltage of 150mV, with (d) having been imaged before (e). Both images were taken at intervals during the cleaning process (V = 150mV, I = 50pA). Highlighted the same hole like defects for reference. The excess Fe atoms in the bottom section of the image can be seen to have been dislodged from their original locations and the overall concentration of Fe atoms has been reduced indicating the success of the manipulating process.  (c), highlighting that the commensurate wave vector is dominant in the blue region, where excess iron has been removed at the surface, and that the magnetic order is dominant at an incommensurate wave vector in the excess iron-rich region. .
. . (a) Images (green box) corresponding to an in-plane rotation of the tip spin through 30 • steps from being parallel to the b axis at φ = −90 • to being parallel to the a axis at φ = 0 • (color scale between -1 and 1). (b) Images (pink box) corresponding to an out-of-plane rotation of the tip spin from being parallel to the b axis at θ = 0 • to being parallel to the c axis at θ = 90 • . (c) Intensities of the magnetic peaks from the Fourier transform of the simulated SP-STM images I(q a ) (red) and I(q b ) (blue) as a function of in-plane angle φ of the tip magnetization. (d) Intensities of the magnetic peaks I(q a ) (red) and I(q b ) (blue) as a function of out-of-plane angle θ of the tip magnetization.