Colloquium: Atomic spin chains on surfaces

Magnetism at low dimensions is a thriving field of research with exciting opportunities in technology. This Colloquium focuses on the properties of 1D magnetic systems on solid surfaces. From the emulation of 1D quantum phases to the potential realization of Majorana edge states, spin chains are unique systems to study. The advent of scanning tunneling microscope (STM) based techniques has permitted us to engineer spin chains in an atom-by-atom fashion via atom manipulation and to access their spin states on the ultimate atomic scale. Here the current state of research on spin correlations and dynamics of atomic spin chains as studied by the STM is presented. After a brief review of the main properties of spin chains on solid surfaces, spin chains are classified according to the coupling of their magnetic moments with the holding substrate. This classification scheme takes into account that the nature and lifetimes of the spin-chain excitations intrinsically depend on the holding substrate. Interest is shown of using insulating layers on metals, which generally results in an increase in the spin state’s lifetimes such that their quantized nature gets evident and they are individually accessible. Next shown is the use of semiconductor substrates promising additional control through the tunable electron density via doping. When the coupling to the substrate is increased for spin chains on metals, the substrate conduction electron mediated interactions can lead to emergent exotic phases of the coupled spin chain-substrate conduction electron system. A particularly interesting example is furnished by superconductors. Magnetic impurities induce states in the superconducting gap. Because of the extended nature of the spin chain, the in-gap states develop into bands that can lead to the emergence of 1D topological superconductivity and consequently to the appearance of Majorana edge states. Finally, an outlook is given on the use of spin chains in spintronics, quantum communication, quantum computing, quantum simulations, and quantum sensors.

Figure 1

The effect of different perturbations on the electronic states of a ${\mathrm{Co}}^{2+}$ ion on MgO is shown incrementally. First the axial field due to the presence of the surface plane is included, shifting the ten low-energy spherical levels (one eightfold and one twofold degenerate), and second the crystal field of the four neighboring ${\mathrm{Mg}}^{2+}$ ions is considered. Next the spin-orbit coupling is adiabatically switched on. And finally a magnetic field is included. The lowest-energy transitions induced by tunneling electrons from an STM are depicted by arrows. From [159].

Figure 2

(a) Two-spinon continuum corresponding to single spin-flip excitations of an inifinite Heisenberg antiferromagnetic chain of atoms with $S=1/2$ (spin $1/2$ chain). The continuum is bounded by spin-wave excitations as the low-energy branch, Eq. (8), and the higher branch, Eq. (9). (b) Scheme of a spin $1/2$ chain showing the propagation of a two-spinon becoming two domain-wall excitations for an Ising antiferromagnetic chain.

Figure 3

A ${\mathrm{Fe}}_6$ chain is initially in state 1 of the two classical Néel states of this antiferromagnetic spin chain. In the presence of decoherence, the population of state 1 (${\rho }_{11}$) is exponentially reduced to 0.5, populating both states, (1), while the coherences become zero (${\rho }_{12}={\rho }_{21}\to 0$). Here a measurement at $\sim 0.02\mathrm{s}$ is assumed to find the system in state 1, and then the population is suddenly 100% for state 1. Afterward the exponential decay leads to 50% populations. In the absence of decoherence, the population is given by Rabi oscillations of very fast frequency for the ${\mathrm{Fe}}_6$ chain on ${\mathrm{Cu}}_2\mathrm{N}$. From [63].

Figure 4

(a) Current vs voltage spectrum with an additional tunnel channel at a threshold voltage $|V_{\mathrm{exc}}|$ due to an inelastic excitation. (b) Inelastic excitations are typically studied measuring the differential conductance and then appear as symmetric steps at $-V_{\mathrm{exc}}$ and $V_{\mathrm{exc}}$ around the Fermi energy.

Figure 5

Simplified diagram of the electronic pump-probe technique. (a) First, the pump pulse excites the spin states of the adsorbed magnetic atom and second, the probe pulse at certain time delay ($\mathrm{\Delta }{t}_1$) detects the status of the spin by spin-polarized tunneling. By varying the time delay ($\mathrm{\Delta }t$) and sending repeated sets of pump-probe pulses, (b) the conductance as a function of time is obtained, which gives information of the spin relaxation time ($T_1$). In the present example the initial number of collected electrons is $-20$ and the relaxation time is 120 ns. Adapted from [122].

Figure 6

Constant current images (a) of the created ${\mathrm{Mn}}_n$ chains with $n=2,\dots ,9$ on ${\mathrm{Cu}}_2\mathrm{N}/\mathrm{Cu}(100)$. (b) Atomic scheme where the Mn atoms are depicted by blue (dark gray) balls, N atoms are represented by small circles, and Cu atoms by large circles. (c) Differential conductance over atomically manipulated ${\mathrm{Mn}}_n$ chains with $n=1,\dots ,10$ (b). Depending on the number of Mn atoms, the behavior is different. For odd number, it shows a small bias feature with the spin changing excitation energy steps while for even number, it gives only the spin excitation energy steps. The lowest spin changing excitations are marked by blue arrows. Adapted from [83].

Figure 7

Detection of spin waves in a ferromagnetic chain. (a) STM topography of a ferromagnetic six-atom Fe chain on ${\mathrm{Cu}}_2\mathrm{N}/\mathrm{Cu}(100)$. (b) Telegraph noise measured using spin-polarized STM on the first three atoms of the chain. Switching is observed between two metastable states. The switching rate decreases as the tip is moved toward the center of the chain. (c) Left: IETS spectra taken on each of the atoms in the chain. Spin-wave states are observed with recognizable nodal structure at $\sim 3.5$, $\sim 4.0$, and $\sim 5.5\mathrm{mV}$. Right: Corresponding theory obtained from diagonalization of the spin Hamiltonian. Adapted from [183].

Figure 8

Using an atomic spin chain for quantum simulation. (a) IETS spectrum taken on a single Co atom on ${\mathrm{Cu}}_2\mathrm{N}/\mathrm{Cu}(100)$, indicating a split between the $\pm 1/2$ and $\pm 3/2$ doublets. (b) Atomic design of an $XXZ$ Heisenberg chain in transverse field using Co atoms. (c) Top: IETS performed on the first atom of chains up to length 6 for transverse magnetic fields up to 9 T. Transitions in the ground state are observed leading up to the critical point near 6 T, which coincide with theoretically predicted ground state changes (bottom). Adapted from [197].

Figure 9

Heterogeneous ${\mathrm{FeMn}}_n$ spin chains ($n=1–9$), on ${\mathrm{Cu}}_2\mathrm{N}/\mathrm{Cu}(100)$. (a) Density difference between spin-up (blue, dark gray) and spin-down (red, light gray) states over a ${\mathrm{Mn}}_9\mathrm{Fe}$ chain. Copper atoms (yellow, light gray) and nitrogen atoms (cyan, dark gray). (b) Differential conductance ($dI/dV$) map along the ${\mathrm{Mn}}_9\mathrm{Fe}$ chain. $dI/dV$ signals plotted as a function of sample bias (V) and displacement (nm). Mn (green, dark gray) and Fe (red, light gray) atoms are visualized to show where they sit. (c) Half width at half maximum (HWHM) (meV) of the zero-bias anomaly for the MnFe dimer plotted as a function of temperature. The black line is a fit to the Kondo peak as a function of temperature. (d) The differential conductance as a function of applied bias for two different magnetic fields in the MnFe dimer. The green (upper) curve corresponds to no magnetic field and the blue one to a $B=5\mathrm{T}$ field applied perpendicular to the surface. The measuring temperature is 0.5 K. The green line (upper line) is vertically shifted by 5 nS for clarity. Adapted from [31].

Figure 10

Self-organized magnetic chains on metallic substrates. (a) Sketch of monatomic Co chains attached to the step edges of a Pt(997) single crystal as reported by [61]. (b) STM topography with atomic resolution of the ($5\times 1$)-Ir(001) surface and (c) top view ball model of this reconstructed surface and characteristic adsorption sites. (b), (c) From [134]. (d) Symmetry equivalent biatomic zigzag chains on the ($5\times 1$)-Ir(001) surface as realized by Co. From [46]. (e) SP-STM topography colorized with the simultaneously obtained differential conductance signal of biatomic Fe and Co chains grown on ($5\times 1$)-Ir(001); whereas the Fe chain on the left switches its magnetization frequently the magnetic spin spiral ground state of the right Fe chain (see sketch) is fixed by direct exchange coupling to the adjacent ferromagnetic Co chain. Adapted from [134].

Figure 11

STM-tip crafted magnetic chains on metallic substrates. (a), (b) Experimentally measured and DFT calculated (a) Heisenberg and (b) Dzyaloshinskii-Moriya components of the RKKY interaction between an Fe atom and an Fe-hydrogen complex on Pt(111) (see inset) as a function of their separation $d$. (c) DFT calculated in-plane component $D_{\perp }$ of the Dzyaloshinskii-Moriya vector which determines the indicated rotational sense of the magnetization in the pair. (a)–(c) Adapted from [101]. (d) Spin-resolved image of a chain of four antiferromagnetically RKKY-coupled Fe atoms on Cu(111) which are stabilized by the RKKY interaction to a magnetic Co island. Adapted from [104]. The color reflects the spin orientation of each atom in the chain, as indicated by the symbols. (e), (f) Spin-resolved images of a chain of 16 antiferromagnetically RKKY-coupled Fe atoms on Pt(111) which are stabilized by RKKY interaction to a magnetic Co layer. Adapted from [185]. (f) The magnetization of the Co layer is magnetized up (top) and down (bottom) resulting in the alignment of the spin of the first chain atom (up and down). (g) Sketch of the approximate spin orientations of the Fe chain atoms.

Figure 12

Parity effects in STM-tip assembled and self-organized spin chains on metallic substrates. (a), (b) Spin-resolved differential conductance images of several (a) odd- and (b) even-numbered artificially constructed Fe chains on Cu(111) in the indicated magnetic field. Adapted from [103]. The resulting Néel states (odd case) and the two states between which the chain fluctuates (even case) are given on the right side of each image. (c) Self-assembled biatomic Fe chains on ($5\times 1$)-Ir(001) as a function of the external out-of-plane magnetic field. (d) Results from micromagnetic simulations showing the chain-length dependent variation of the mean angle and the net magnetic moment. (c), (d) From [133].

Figure 13

YSR states in single Cr atoms on Pb(111) and Cr dimers on a $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$ superconductor. (a) Multiple YSR states are shown over a single Cr atom on Pb(111), originating from a hybridized orbital structure of Cr with nearest-neighbor Pb atoms. Differential conductance maps at the peak positions of the YSR states show the hybridized orbital features. From [32]. (b) Dependence of YSR states on the spacing of Cr atoms in dimers on $\beta \text{−}{\mathrm{Bi}}_2\mathrm{Pd}$. Separations from left to right: $\sqrt{5}$, 2, 1, and $\sqrt{2}$ by unit cell distances. All dimers were formed by STM-tip induced atomic manipulation. The top panels show the topographic images of the dimers, and the bottom panels show the corresponding differential conductances measured on one of the two atoms in the dimer (red lines) and on a single atom for comparison (gray lines). Adapted from [27].

Figure 14

STM-tip assembled chain of weakly coupled Fe atoms on $\mathrm{Ta}(100)\text{−}(3\times 3)\mathrm{O}$. (a) Assembled chain of subsurface interstitial Fe atoms. (b) Thirteen Fe atoms have been assembled on the surface along the subsurface atoms, such that each Fe atom is linked by a subsurface Fe atom. (c) The sixth atom from the top has been switched into a nonmagnetic state. (d) Comparison of differential conductance spectra taken with a superconducting tip on every Fe adatom and on the substrate, with all atoms in the magnetic state (solid lines) and the sixth atom in the nonmagnetic state (dashed lines). The dashed (dotted) vertical lines indicate the sample Fermi level (sample coherence peak). Adapted from [92].