The double exchange model describing interactions of itinerant electrons with localized spins is usually used to explain ferromagnetism in metals. We show that for a variety of crystal lattices of different dimensionalities and for a wide range of model parameters the ferromagnetic state is unstable against a non-collinear spiral magnetic order. We revisit the phase diagram of the double exchange model on a triangular lattice and show in a large part of the diagram the incommensurate spiral state has a lower energy than the previously discussed commensurate states. These results indicate that double exchange systems are inherently frustrated and can host unconventional spin orders. Introduction: Non-collinear spin orders are inextricably related to inversion symmetry breaking in crystals and give rise to unconventional physical phenomena, such as magnetically-induced ferroelectricity and electric excitation of magnons in spiral magnets [1,2]. Non-coplanar spin structures of skyrmions induce effective electromagnetic fields resulting in topological electron and magnon Hall effects [3]. Skyrmion dynamics induced by applied electric currents can be used in high-density magnetic memory devices [4]. Non-collinear magnetic orders are, however, relatively rare and it is of great interest to find new materials showing such states.There are several well-understood microscopic mechanisms for non-collinear spin ordering. One of them is the relativistic Dzyaloshinskii-Moriya interaction which stabilizes spiral and skyrmion crystal states in chiral magnets [5,6]. Non-collinear magnetism in Mott insulators is often a result of competing ferromagnetic (FM) and antiferromagnetic (AFM) Heisenberg interactions between spins, while in magnets with both itinerant and localized electrons it can originate from the RKKY interaction [7][8][9] closely related to Fermi surface instability.Here we focus on the double exchange (DE), which was originally invoked to explain ferromagnetism in doped manganites [10,11]. The DE model, also known as the ferromagnetic Kondo lattice model, describes a lattice of classical spins interacting with the conduction electrons through the Hund's rule coupling which aligns the spins of the conduction and localized electrons occupying the same lattice site. If the spins on neighboring sites are not parallel, the effective electron hopping amplitude decreases, which increases kinetic energy of the conduction electrons. In this way conduction electrons provide an effective FM interaction between the lattice spins.This argument, however, cannot hold for all values of the model parameters, which is clear already from the fact that in the limit of small Hund's rule coupling constant, J, the model yields the RKKY interactions that can be FM or AFM, depending on the distance between

In polar magnets, such as GaV4S8, GaV4Se8 and VOSe2O5, modulated magnetic phases namely the cycloidal and the Néel-type skyrmion lattice states were identified over extended temperature ranges, even down to zero Kelvin. Our combined small-angle neutron scattering and magnetization study shows the robustness of the Néel-type magnetic modulations also against magnetic fields up to 2 T in the polar GaMo4S8. In addition to the large upper critical field, enhanced spin-orbit coupling stabilize cycloidal, Néel skyrmion lattice phases with sub-10 nm periodicity and a peculiar distribution of the magnetic modulation vectors. Moreover, we detected an additional single-q state not observed in any other polar magnets. Thus, our work demonstrates that non-centrosymmetric magnets with 4d and 5d electron systems may give rise to various highly compressed modulated states.

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We study the high-temperature phase diagram of the chiral magnetic insulator Cu 2 OSeO 3 by measuring the spin-Hall magnetoresistance (SMR) in a thin Pt electrode. We find distinct changes in the phase and amplitude of the SMR signal at critical lines separating different magnetic phases of bulk Cu 2 OSeO 3 . The skyrmion lattice state appears as a strong dip in the SMR phase. A strong enhancement of the SMR amplitude is observed in the conical spiral state, which we explain by an additional symmetry-allowed contribution to the SMR present in noncollinear magnets. We demonstrate that the SMR can be used as an all-electrical probe of chiral surface twists and skyrmions in magnetic insulators.

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