Motivated by the recent observations of incommensurate magnetic order and electric polarization in YBaCuFeO 5 up to temperatures T N2 as high as 230 K [B. Kundys et al., Appl. Phys. Lett. 94, 072506 (2009); Y. Kawamura et al., J. Phys. Soc. Jpn 79, 073705 (2010)], we report here for the first time a model for the incommensurate magnetic structure of this material, which we complement with ab initio calculations of the magnetic exchange parameters. Using neutron powder diffraction, we show that the appearance of polarization below T N2 is accompanied by the replacement of the high-temperature collinear magnetic order by a circular inclined spiral with propagation vector k i = (1/2,1/2,1/2 ± q). Moreover, we find that the polarization approximately scales with the modulus of the magnetic modulation vector q down to the lowest temperature investigated (∼3 K). Further, we observe occupational Fe/Cu disorder in the FeO 5 -CuO 5 bipyramids, although a preferential occupation of such units by Fe-Cu pairs is supported by the observed magnetic order and by density functional calculations. We calculate exchange coupling constants for different Fe/Cu distributions and show that, for those containing Fe-Cu dimers, the resulting magnetic order is compatible with the experimentally observed collinear magnetic structure [k c = (1/2,1/2,1/2), T N2 > T > T N1 = 440 K]. Based on these results, we discuss possible origins for the incommensurate modulation and its coupling with ferroelectricity. M. MORIN et al. PHYSICAL REVIEW B 91, 064408 (2015) J ⊥ (meV) J (meV) J O (meV) J NNN (meV) (a) J 1,2 = 134.5 J 1,3 = 10.6 J 5,3 = −1.6 J 1,5 = −0.05 J 7,8 = 8.7 J 5,7 = 2.8 J 1+c,5 = −0.01 (b) J 1,2 = 129.9

We show that the magnetic anisotropy in spinel-structure CoCr2O4 thin films exhibits a strain dependence in which compressive strain induces an out-of-plane magnetic easy axis and tensile strain an in-plane easy axis, exactly opposite to the behavior reported for the related compound CoFe2O4. We use density functional theory calculations within the LSDA+U approximation to reproduce and explain the observed behavior. Using second-order perturbation theory, we analyse the anisotropy tensor of the Co 2+ ions in both octahedral and tetrahedral coordination, allowing us to extend our results to spinels with general arrangements of Co 2+ ions. PACS numbers: 75.70.Ak, 75.80.+q, 75.30.Gw, 71.15.Mb Thin films with out-of-plane spontaneous magnetization, showing so-called perpendicular magnetic anisotropy, are of great interest for applications such as high density magnetic memories with fast switching 1 . Perpendicular magnetic anisotropy is also needed for spintronic applications, for example in magnetic tunnel junctions, and for low energy current-driven domain wall motion 2-5 .In a system of finite size, magnetic anisotropy is determined by the balance of magnetocrystalline and shape anisotropy. The former is a bulk property originating from spin-orbit interaction, while the latter originates from magnetic dipole-dipole interaction and depends on the geometry of the sample. For the case of thin films, where shape anisotropy always favors in-plane magnetization, it is interesting to understand how the strain affects the magnetocrystalline part. Indeed, the way in which epitaxial strain can affect the magnetocrystalline anisotropy has been the subject of intensive investigations 6-13 . A prominent example of such investigations is the spinel compound CoFe 2 O 4 , which has a strong magnetostriction coefficient 7,10,11,14 . In CoFe 2 O 4 thin films, it was shown that changing the sign of the strain leads from cooperation to competition of shape and magnetocrystalline anisotropies 7 .Compounds with spinel (MgAl 2 O 4 -type) structure have chemical formula AB 2 X 4 where A and B are cations and X represents the ligand anion (usually O, S or Se). In this structure, the cations occupy either the tetrahedrally coordinated 15 (T) site or the octahedrally coordinated (O) site. There are twice as many O sites as T sites. In a normal spinel, A and B cations occupy T and O sites, respectively, while in an inverse spinel, half of the B cations occupy the T sites and the remaining half occupy the O sites together with the A cations. In general, spinels can be characterised by the degree of inversion (i.e. the concentration of B cations occupying T sites).The bulk structure (unstrained case) of the inverse spinel CoFe 2 O 4 , with a disordered Co 2+ /Fe 3+ occu-pancy on the octahedrally coordinated sites, has cubic symmetry (space group F d3m). This enforces the quadratic magnetization terms in the magnetocrystalline anisotropy to vanish, leaving as lowest order terms the quartic ones, which are typically of smaller size, although ...

We show that nonrelativistic exchange interactions and spin fluctuations can give rise to a linear magnetoelectric effect in collinear antiferromagnets at elevated temperatures that can exceed relativistic magnetoelectric responses by more than 1 order of magnitude. We show how symmetry arguments, ab initio methods, and Monte Carlo simulations can be combined to calculate temperature-dependent magnetoelectric susceptibilities entirely from first principles. Introduction.-Recent years have seen a resurgence of interest in materials with coupled electric and magnetic dipoles motivated by the prospect of controlling spins with applied voltages and charges with applied magnetic fields in novel multifunctional devices. The simplest form of such a control is the linear magnetoelectric (ME) coupling between electric polarization and an applied magnetic field or, conversely, between magnetization and an applied electric field. Although the linear ME effect was theoretically predicted and experimentally discovered more than 50 years ago [1], finding technologically useful materials displaying strong ME coupling at room temperature remains a challenging problem [2].Recent progress in the related field of multiferroic materials, in which ferroelectric polarizations are induced by noncentrosymmetric magnetic orderings, has led to a clarification of the microscopic origins for ME coupling [3]. In particular, two distinct coupling mechanisms have been identified. The first arises from relativistic effects linking electron spin and orbital momentum, resulting in the antisymmetric S 1 Â S 2 interaction between spins of different magnetic ions. The strength of this Dzyaloshinksii-Moriya interaction depends on polar displacements of ions, which can make magnets with noncollinear spiral orders becoming ferroelectric [4][5][6][7]. In the second mechanism, polar deformations of the lattice are induced by Heisenberg spin exchange interactions S 1 Á S 2 , originating from the Fermi statistics of electrons [8,9]. This nonrelativistic mechanism can give rise to stronger spin-lattice couplings than those resulting from relativistic effects, which tend to be relatively weak in 3D transition metal compounds. Indeed, in multiferroics, the electric polarizations induced by exchange interactions in Y 1Àx Lu x MnO 3 and GdFeO 3 exceed the largest polarizations observed in spiral multiferroics by 1 order of magnitude [10,11]. It was recently suggested that Heisenberg exchange can also give rise to a relatively strong linear ME effect [12] which, however, seemed to require rather special noncollinear spin orderings and crystal structures, making it difficult to find such materials in nature.