The emergence of classical behaviour in magnetic adatoms

¹ International Iberian Nanotechnology Laboratory (INL) - Av. Mestre José Veiga, P-4715-310 Braga, Portugal
² Centro de Física de Materiales, CSIC- UPV/EHU - Paseo Manuel de Lardizabal 5, E-20018 San Sebastián, Spain
³ IKERBASQUE, Basque Foundation for Science - E-48013 Bilbao, Spain
⁴ Max Planck Institute for the Structure and Dynamics of Matter - Hamburg, Germany
⁵ Max Planck Institute for Solid State Research - Stuttgart, Germany
⁶ Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University Grudziadzka 5, PL-87-100 Torun, Poland

Received: 10 December 2014
Accepted: 18 February 2015

Abstract

A wide class of nanomagnets shows striking quantum behaviour, known as quantum spin tunnelling (QST): instead of two degenerate ground states with opposite magnetizations, a bonding-antibonding pair forms, resulting in a splitting of the ground-state doublet with wave functions linear combination of two classically opposite magnetic states, leading to the quenching of their magnetic moment. Here we study how QST is destroyed and classical behaviour emerges in the case of magnetic adatoms, where, contrary to larger nanomagnets, the QST splitting is in some instances bigger than temperature and broadening. We analyze two different mechanisms for the renormalization of the QST splitting: Heisenberg exchange between different atoms, and Kondo exchange interaction with the substrate electrons. Sufficiently strong spin-substrate and spin-spin coupling renormalize the QST splitting to zero allowing the environmental decoherence to eliminate superpositions between classical states, leading to the emergence of spontaneous magnetization. Importantly, we extract the strength of the Kondo exchange for various experiments on individual adatoms and construct a phase diagram for the classical to quantum transition.