Modeling magnetism of hexagonal Fe monolayers on 4d substrates

Abstract

Mapping the total energies obtained from first principles calculations to model Hamiltonians is a powerful technique to explore the magnetic ground state of a system. We analyze the applicability of this approach in the presence of highly polarizable substrates, e.g. for an ultrathin Fe layer on Pd(111), Rh(111), Ru(0001), or Tc(0001). We find that the traditionally accepted model Hamiltonians (Heisenberg plus nearest neighbor higher-order spin Hamiltonians) are not sufficient to capture the magnetic interactions in these systems and examine new terms that can be included to improve the description. Challenges for this technique are exemplified by the double-rowwise antiferromagnetic (AFM) ground state predicted for Fe/Rh(111). Usually, magnetic structures are explained within classical spin models like the Heisenberg model, H ¼ Àð1=2ÞTheir foundation results primarily from quantum mechanical exchange interactions of different orders and between different neighbors, and is expressed by spin operators, Ŝ. Typically, the operator is then replaced by the expectation value, S, and quantum fluctuations are neglected. The change from FM to AFM order of the Fe monolayers deposited on Ag(001) or W(001)

Effective magnetic Hamiltonians from first principles

“…The higher order terms in Hamiltonian, such as quartic ones, (4), are usually small. If one adopts the approximation of the spiral spin density wave (6) for the Hamiltonian with higher order terms, all higher order terms can be mapped onto J i j 's as observed in [7]. The net effect of higher order terms is then reduced to a renormalization of J i j 's.…”

Complex trend of magnetic order in Fe clusters on4dtransition-metal surfaces. II. First-principles calculations

“…Since the energy difference between the FM and the AFM state is small for these two systems, exchange beyond nearest-neighbors and higher-order interactions become important and may lead to complex magnetic ground states. For Fe/Ru(0001), a 120 • Néel state has been theoretically predicted and for Fe/Rh(111) a double row-wise antiferromagnetic structure also denoted as the uudd state has been proposed [20,21]. In particular, the uudd state is very intriguing since it cannot be understood based on mapping the total energies from a DFT calculation to a Heisenberg model but is closely linked to the large induced magnetic moments in the Rh substrate [21].…”

“…For Fe/Ru(0001), a 120 • Néel state has been theoretically predicted and for Fe/Rh(111) a double row-wise antiferromagnetic structure also denoted as the uudd state has been proposed [20,21]. In particular, the uudd state is very intriguing since it cannot be understood based on mapping the total energies from a DFT calculation to a Heisenberg model but is closely linked to the large induced magnetic moments in the Rh substrate [21]. Up to now, however, these predictions still lack experimental verification.…”

Complex trend of magnetic order in Fe clusters on4dtransition-metal surfaces. I. Experimental evidence and Monte Carlo simulations

“…Based on first-principles calculations, it has been predicted that the nearest-neighbor (NN) exchange coupling changes from antiferromagnetic (AFM) to ferromagnetic (FM) for Fe monolayers on Ru(0001) and Rh(111), respectively [15]. Since its magnitude is small, interactions beyond NNs as well as higher-order terms beyond the pairwise Heisenberg exchange, such as the four-spin and biquadratic interactions, can play a decisive role for the magnetic order [15,16]. Magnetic configurations that are surprising for Fe have been predicted for those substrates, namely, a Néel state with angles of 120 • between adjacent spins for Fe monolayers on Ru(0001), and a collinear double row-wise AFM uudd state on Rh(111).…”