Monolayer CrCl_{3} as an Ideal Test Bed for the Universality Classes of 2D Magnetism.

The monolayer halides CrX_{3} (X=Cl, Br, I) attract significant attention for realizing 2D magnets with genuine long-range order (LRO), challenging the Mermin-Wagner theorem. Here, we show that monolayer CrCl_{3} has the unique benefit of exhibiting tunable magnetic anisotropy upon applying a compressive strain. This opens the possibility to use CrCl_{3} for producing and studying both ferromagnetic and antiferromagnetic 2D Ising-type LRO as well as the Berezinskii-Kosterlitz-Thouless (BKT) regime of 2D magnetism with quasi-LRO. Using state-of-the-art density functional theory, we explain how realistic compressive strain could be used to tune the monolayer's magnetic properties so that it could exhibit any of these phases. Building on large-scale quantum Monte Carlo simulations, we compute the phase diagram of strained CrCl_{3}, as well as the magnon spectrum with spin-wave theory. Our results highlight the eminent suitability of monolayer CrCl_{3} to achieve very high BKT transition temperatures, around 50 K, due to their singular dependence on the weak easy-plane anisotropy of the material.

Band Filling Control of the Dzyaloshinskii-Moriya Interaction in Weakly Ferromagnetic Insulators.

We observe and explain theoretically a dramatic evolution of the Dzyaloshinskii-Moriya interaction (DMI) in the series of isostructural weak ferromagnets, MnCO_{3}, FeBO_{3}, CoCO_{3}, and NiCO_{3}. The sign of the interaction is encoded in the phase of the x-ray magnetic diffraction amplitude, observed through interference with resonant quadrupole scattering. We find very good quantitative agreement with first-principles electronic structure calculations, reproducing both sign and magnitude through the series, and propose a simplified "toy model" to explain the change in sign with 3d shell filling. The model gives insight into the evolution of the DMI in Mott and charge transfer insulators.

Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.

By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.

X-ray magnetic circular dichroism measurements in Ni up to 200 GPa: resistant ferromagnetism.

The structural stability of fcc Ni over a very large pressure range offers a unique opportunity to experimentally investigate how magnetism is modified by simple compression. K-edge x-ray magnetic circular dichroism (XMCD) shows that fcc Ni is ferromagnetic up to 200 GPa, contradicting recent predictions of an abrupt transition to a paramagnetic state at 160 GPa. Density functional theory calculations point out that the pressure evolution of the K-edge XMCD closely follows that of the p projected orbital moment rather than that of the total spin moment. The disappearance of magnetism in Ni is predicted to occur above 400 GPa.

Perpendicular and in-plane hole asymmetry in a strained NiFe2O4film.

Strained materials can exhibit drastically modified physical properties in comparison to their fully relaxed analogues. We report on the x-ray absorption spectra (XAS) and magnetic circular dichroism (XMCD) of a strained NiFe2O4inverse spinel film grown on a symmetry matched single crystal MgGa2O4substrate. The Ni XAS spectra exhibit a sizable difference in the white line intensity for measurements with the x-ray electric field parallel to the film plane (normal incidence) vs when the electric field is at an angle (off-normal). A considerable difference is also observed in the FeL2,3XMCD spectrum. Modeling of the XAS and XMCD spectra indicate that the modified energy ordering of the cation 3dstates in the strained film leads to a preferential filling of 3dstates with out-of-plane character. In addition, the results point to the utility of x-ray spectroscopy in identifying orbital populations even with elliptically polarized x-rays.

First-principles Dzyaloshinskii-Moriya interaction in a non-collinear framework.

We have derived an expression of the Dzyaloshinskii-Moriya interaction (DMI), where all the three components of the DMI vector can be calculated independently, for a general, non-collinear magnetic configuration. The formalism is implemented in a real space-linear muffin-tin orbital-atomic sphere approximation (RS-LMTO-ASA) method. We have chosen the Cr triangular trimer on Au(111) and Mn triangular trimers on Ag(111) and Au(111) surfaces as numerical examples. The results show that the DMI (module and direction) is drastically different between collinear and non-collinear states. Based on the relation between the spin and charge currents flowing in the system and their coupling to the non-collinear magnetic configuration of the triangular trimer, we demonstrate that the DMI interaction can be significant, even in the absence of spin-orbit coupling. This is shown to emanate from the non-collinear magnetic structure, that can induce significant spin and charge currents even with spin-orbit coupling is ignored.

The Bethe-Slater curve revisited; new insights from electronic structure theory.

The Bethe-Slater (BS) curve describes the relation between the exchange coupling and interatomic distance. Based on a simple argument of orbital overlaps, it successfully predicts the transition from antiferromagnetism to ferromagnetism, when traversing the 3d series. In a previous article [Phys. Rev. Lett. 116, 217202 (2016)] we reported that the dominant nearestneighbour (NN) interaction for 3d metals in the bcc structure indeed follows the BS curve, but the trends through the series showed a richer underlying physics than was initially assumed. The orbital decomposition of the inter-site exchange couplings revealed that various orbitals contribute to the exchange interactions in a highly non-trivial and sometimes competitive way. In this communication we perform a deeper analysis by comparing 3d metals in the bcc and fcc structures. We find that there is no coupling between the E g orbitals of one atom and T 2g orbitals of its NNs, for both cubic phases. We demonstrate that these couplings are forbidden by symmetry and formulate a general rule allowing to predict when a similar situation is going to happen. In γ-Fe, as in α-Fe, we find a strong competition in the symmetry-resolved orbital contributions and analyse the differences between the high-spin and low-spin solutions.

Erratum: The Bethe-Slater curve revisited; new insights from electronic structure theory.

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