Exploring the phase diagram of the two-impurity Kondo problem

Abstract

A system of two exchange-coupled Kondo impurities in a magnetic field gives rise to a rich phase space hosting a multitude of correlated phenomena. Magnetic atoms on surfaces probed through scanning tunnelling microscopy provide an excellent platform to investigate coupled impurities, but typical high Kondo temperatures prevent field-dependent studies from being performed, rendering large parts of the phase space inaccessible. We present a study of pairs of Co atoms on insulating Cu2N/Cu(100), which each have a Kondo temperature of only 2.6 K. The pairs are designed to have interaction strengths similar to the Kondo temperature. By applying a sufficiently strong magnetic field, we are able to access a new phase in which the two coupled impurities are simultaneously screened. Comparison of differential conductance spectra taken on the atoms to simulated curves, calculated using a third-order transport model, allows us to independently determine the degree of Kondo screening in each phase.

Electronic properties of transition metal atoms onCu2N/Cu(100)

“…For that matter we propose a zero bandwidth multi-orbital Anderson model in which many-body states that mixes configurations with two charge states in the d shell are considered. Importantly, even if the charge is not well defined in the d shell, these multi-electron wave functions have a well defined total spin S. We find that the states with a quantized charge in the d shell are adiabatically connected with the actual many-body states that mix configurations d n p 12 and d n+1 p 11 in the sense that both have the same total spin S and there is no mixing with higher energy multiplets as the additional energy is varied numerically. We thus conclude that quantized spin S of the model actually refers to the spin of these many-body states that include both the d electrons and the ligand electrons.…”

“…In the following we shall show results for the case of Fe on Cu 2 N. Given the small size of the single-particle basis (five d orbitals and six p orbitals ) and the fact that we restrict the Hilbert space to the configurations d n p 12 and d n+1 p 11 , with n = 6 for Fe, with a total of 1650 multi-electron states, the zero bandwidth multi-orbital Anderson model can be solved by exact numerical diagonalization.…”

“…Importantly, both the spin excitation spectra of individual atoms [2,3,14] and multi-atom structures [1,4,[7][8][9][11][12][13], as well as their spin relaxation dynamics have been successfully described using model Hamiltonians [18][19][20][21][22][23][24][25][26] where quantized spins interact with each other via Heisenberg coupling [1,11,18,20], and are Kondo coupled both to the tunneling electrons [18,19] and to the substrate [9,[22][23][24]. Treating Kondo coupling up to second order in perturbation theory accounts for spin relaxation [22,23] and magnetic anisotropy renormalization [9,24].…”

“…The Cu(100) surface coated with a Cu 2 N monolayer has turned out to be a remarkable system [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] to probe and engineer the electronic properties of individual transition metal atoms using scanning tunneling microscopy (STM) and inelastic electron tunneling spectroscopy (IETS). A variety of breakthroughs have been reported on this system, such as the first measurement of the magnetic anisotropy of an individual quantized spin by means of IETS [2], the demonstration of single atom spin torque [5], the fabrication of nano-engineered chains both with antiferromagnetic [7] and ferromagnetic [11] broken symmetry ground states, probed by means of spin-polarized STM, the measurement of spin excitations in spin chains with strong quantum fluctuations that prevent spin symmetry breaking [1,8], the measurement of single spin relaxation time by means of the voltage pulse pump-probe technique [6], the observation of renormalization of magnetic anisotropy due to Kondo exchange interactions [9], and the imaging of spin wave modes with atomic scale resolution [11].…”

Scaling of Tripartite Entanglement at Impurity Quantum Phase Transitions

“…The 2IKM and the 2CKM are the best examples of non-Fermi-liquid behavior generated by criticality [32][33][34]. There are also several experimental realizations for both the 2IKM [35][36][37] and the 2CKM [38][39][40][41].…”