Magnetic structure of the topological semimetal Co3Sn2S2

Co3Sn2S2 has recently been predicted to be a Weyl semimetal in which magnetic order is key to its behavior as a topological material. Here, we report unpolarized neutron diffraction and spherical neutron polarimetry measurements, supported by magnetization and transport data, which probe the magnetic order in Co3Sn2S2 below TC = 177 K. The results are fully consistent with ferromagnetic order in which the spins on the Co atoms point along the crystal c axis, although we cannot rule out some canting of the spins. We find no evidence for a type of long-ranged (k = 0) in-plane 120?? antiferromagnetic order which had previously been considered as a secondary phase present at temperatures between -90 K and TC. A discontinuous change in bulk properties and neutron polarization observed at T = 125 K when samples are cooled in a field and measured on warming is found to be due to a sudden reduction in ferromagnetic domain size. Our results lend support to the theoretical predictions that Co3Sn2S2 is a magnetic Weyl semimetal.

Magnetic properties of surface-adsorbed single rare earth atoms, molecules, and atomic scale clusters

Aparajita Singha

This thesis presents combined experimental and theoretical investigations of nanoscale, surface-supported magnets based on rare earths (RE) to understand and control the magnetic properties down to the scale of single atoms. We present the effects of adatom-substrate interaction on the magnetic properties of isolated single RE atoms using x-ray absorption spectroscopy (XAS), x-ray magnetic circular dichroism (XMCD), and multiplet analysis. Our systematic investigations of Dy, Ho, Er, and Tm adatoms adsorbed on Pt(111), Cu(111), Ag(100), and Ag(111), reveal that the REs can possess two types of 4f occupations, namely divalent 4f^n and trivalent 4f^(n-1). The trivalent state is realized in presence of low promotion energy of the RE and strong hybridization of their external spd shell with the surrounding environment. Notably, none of the REs exhibit magnetic hysteresis, suggesting that magnetic relaxation is faster than about 10 seconds. We also report on the effect of adatom-adatom interaction by studying the size-dependent magnetic properties of Er clusters adsorbed on Cu(111). Combining XMCD, scanning tunneling microscopy (STM), and mean-field nucleation theory we reveal that the adatom-adatom interaction dominates over the adatom-substrate interaction in Er clusters starting from the size of three atoms. Consequently the easy axis of Er changes from in-plane for the single atoms and dimers to out-of-plane for trimers and bigger clusters. In addition, the out-of-plane magnetic anisotropy of 2.9 meV/atom results in magnetic hysteresis at 2.5 K in all clusters starting from trimers. With a magnetic lifetime of approximately 2 minutes at 0.1 T, the Er trimers are one of the smallest metal-supported ferromagnetic clusters observed so far. The investigation of adatom-adatom interaction is further extended by studying 4f-3d heterodimers namely, Ho-Co adsorbed on thin insulating layers of MgO. Their magnetic easy axis is oriented out-of-plane. Using spin-polarized STM we have detected spin-excitations in these heterodimers at ±20 and ±8 meV. We have identified the origin behind these spin-excitations using an effective spin Hamiltonian model, which indicates that, given a ferromagnetic exchange interaction between Ho and Co, the most intense feature at ±20 meV corresponds to a transition in which the spin moment of Co is strongly diminished. This is further accompanied by an overall change of the total magnetic moment of the heterodimer, i.e., ¿J=-1. In contrast, the weaker transition at ±8 meV occurs following a change in the out-of-plane moment of Ho while the total moment of the heterodimer remains intact i.e., ¿J=0. Notably, we observe an effective g factor of 3.1 for the ±20 meV transition, which significantly exceeds the free electron value of 2. In addition, the ferromagnetic coupling between Ho and Co is very unusual compared to the ferrimagnetic exchange interaction known for the bulk 4f-3d compounds, especially those derived from the late lanthanides. Nonetheless, this marks the first evidence of spin-excitations in the smallest 4f containing cluster. The knowledge gained on the fundamental aspects of magnetism in surface-supported REs combined with the continued parallel search for magnetic stability down to single atoms, enabled us to achieve magnetic remanence in single adatoms with lifetimes of the order of 1000 s at 2.5 K. In addition we have achieved significantly enhanced hysteresis and magnetic lifetime in TbPc2.

EPFL2017

Magnetocrystalline anisotropy energy of Co and Fe adatoms on the (111) surfaces of Pd and Rh

Harald Brune, Markus Etzkorn, Pietro Gambardella, Anne Lehnert, Géraud Moulas, Stefano Rusponi

We performed a combined theoretical and experimental investigation of the orbital magnetism and magnetocrystalline anisotropy of isolated Co and Fe adatoms on Pd(111) and Rh(111). Theoretical calculations of the spin and orbital moments are based on ab initio spin-polarized density-functional theory (DFT) including a self-consistent treatment of spin-orbit coupling. The calculations use a slab model to represent the adsorbate/substrate complex and allow for a complete structural relaxation leading to a strong inward displacement of the adatom and modest vertical and lateral relaxations in the substrate atoms. Compared to an idealized geometry where the atoms are kept on bulk lattice positions up to the surface, relaxation leads to a much stronger adatom/ligand hybridization. This is also reflected in the results for orbital moments and magnetocrystalline anisotropy energy (MAE). The enhanced hybridization leads to strong quenching of the adatom orbital moments but also to the formation of large induced spin and orbital moments in the substrate. As a consequence, we find that the substrate contribution to the MAE is much more important than estimated before on the basis of studies using an idealized geometry. We also find the surprising result that the MAE strongly depends on the adsorption site. The magnitude and even the sign of the MAE change for adatoms on face-centered cubic with respect to the ones on hexagonal close-packed hollow sites on the (111) surface. The dependence of the MAE on the combination of adatom and substrate has been analyzed in terms of the electronic structure, leading to a sound physical picture of the origin of the MAE. A fundamental problem, however, is the correct prediction of the size of the orbital moments of the adatoms. We suggest that this problem can be solved only via post-DFT corrections introducing an orbital dependence of the exchange potential. The theoretical results are compared to site-averaged, element-specific x-ray magnetic circular dichroism (XMCD) measurements. Low-temperature XMCD spectra and magnetization curves reveal weak out-of-plane anisotropy for Fe adatoms on both substrates. Interestingly, Co adatoms on Rh(111) present in-plane anisotropy with MAE of about -0.6 meV, contrary to the known out-of-plane anisotropy of Co on Pd(111) and Pt(111). The orbital to spin magnetic-moment ratio measured by XMCD shows that the Co adatoms present much stronger orbital magnetization components compared to Fe. The connection between orbital moments and MAE is discussed at the theoretical level including the contribution of the induced substrate magnetization.

2010

Canted antiferromagnetic phases in the candidate layered Weyl material EuMnSb2

Xiao Wang

EuMnSb2 is a candidate topological material which can be tuned towards a Weyl semimetal, but there are differing reports for its antiferromagnetic (AFM) phases. The coupling of bands dominated by pure Sb layers hosting topological fermions to Mn and Eu magnetic states provides a potential path to tune the topological properties. Here we present single-crystal neutron diffraction, magnetization, and heat-capacity data as well as polycrystalline 151Eu M??ssbauer data which show that three AFM phases exist as a function of temperature, and we present a detailed analysis of the magnetic structure in each phase. The Mn magnetic sublattice orders into a C-type AFM structure below TNMn = 323(1) K with the ordered Mn magnetic moment ??Mn lying perpendicular to the layers. AFM ordering of the Eu sublattice occurs below TNEu1 = 23(1) K with the ordered Eu magnetic moment ??Eu canted away from the layer normal and ??Mn retaining its higher temperature order. ??Eu is ferromagnetically aligned within each Eu layer but exhibits a complicated AFM layer stacking. Both of these higher-temperature phases are described by magnetic space group (MSG) Pn'm'a' with the chemical and magnetic unit cells having the same dimensions. Cooling below TNEu2= 9(1) K reveals a third AFM phase where ??Mn remains unchanged but ??Eu develops an additional substantial in-plane canting. This phase a' . We also find some evidence of short-range magnetic correlations associated with the Eu between 12 K ??? T ??? 30 K. Using the determined magnetic structures, we postulate the signs of nearest-neighbor intralayer and interlayer exchange constants and the magnetic anisotropy within a general Heisenberg model. We then discuss implications of the various AFM states in EuMnSb2 and their potential for tuning topological properties.