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An approach to account for the effect of thermal lattice vibrations when calculating exchange coupling parameters is presented on the basis of the KKR (Korringa-Kohn-Rostoker) Green function method making use of the alloy analogy model. Using several representative systems, it is shown that depending on the material the effect of thermal lattice vibrations can have a significant impact on the isotropic exchange as well as anisotropic Dzyaloshinskii-Moriya interactions (DMI). This should lead in turn to an additional contribution to the temperature dependence of the magnetic properties of solids, which cannot be neglected in the general case. As an example, we discuss such an influence on the critical temperature of various magnetic phase transitions. In particular, in the case of skyrmion hosting materials, a strong impact of lattice vibrations on the DMI is an additional source for temperature dependent skyrmion stability which should be taken into consideration.
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For epitaxial trilayers of the magnetic rare-earth metals Gd and Tb, exchange coupled through a non-magnetic Y spacer layer, element-specific hysteresis loops were recorded by the x-ray magneto-optical Kerr effect at the rare-earth $M_5$ thresholds. This allowed us to quantitatively determine the strength of interlayer exchange coupling (IEC). In addition to the expected oscillatory behavior as a function of spacer-layer thickness $d_Y$, a temperature-induced sign reversal of IEC was observed for constant $d_Y$, arising from magnetization-dependent electron reflectivities at the magnetic interfaces.
We work out the method for evaluating the QCD coupling constant at finite temperature ($T$) by making use of the finite $T$ renormalization group equation up to the one-loop order on the basis of the background field method with the imaginary time formalism. The background field method, which maintains the explicit gauge invariance, provides notorious simplifications since one has to calculate only the renormalization constant of the background field gluon propagator. The results for the evolution of the QCD coupling constant at finite $T$ reproduce partially the ones obtained in the literature. We discuss, in particular, the origin of the discrepancies between different calculations, such as the choice of gauge, the break-down of Lorentz invariance, imaginary versus real time formalism and the applicability of the Ward identities at finite $T$.
We demonstrate that magnetic skyrmions with a mean diameter around 60 nm can be stabilized at room temperature and zero external magnetic field in an exchange-biased Pt/Co/NiFe/IrMn multilayer stack. This is achieved through an advanced optimization of the multilayer stack composition in order to balance the different magnetic energies controlling the skyrmion size and stability. Magnetic imaging is performed both with magnetic force microscopy and scanning Nitrogen-Vacancy magnetometry, the latter providing unambiguous measurements at zero external magnetic field. In such samples, we show that exchange bias provides an immunity of the skyrmion spin texture to moderate external magnetic field, in the tens of mT range, which is an important feature for applications as memory devices. These results establish exchange-biased multilayer stacks as a promising platform towards the effective realization of memory and logic devices based on magnetic skyrmions.
Mn$_2$Au is an important antiferromagnetic (AF) material for spintronics applications. Due to its very high Neel temperature of about 1500 K, some of the basic properties are difficult to explore, such as the AF susceptibility and the exchange constants. Experimental determination of these properties is further complicated in thin films by unavoidable presence of uncompensated and quasiloose spins on antisites and at interfaces. Using x-ray magnetic circular dichroism (XMCD), we have measured the spin and orbital contribution to the susceptibility in the direction perpendicular to the in-plane magnetic moments of a Mn$_2$Au(001) film and in fields up to 8 T. By performing these measurements at a low temperature of 7 K and at room temperature, we were able to separate the loose spin contribution from the susceptibility of AF coupled spins. The value of the AF exchange constant obtained with this method for a 10 nm thick Mn$_2$Au(001) film equals to (24 $pm$ 5) meV.
We consider the mapping of tight-binding electronic structure theory to a local spin Hamiltonian, based on the adiabatic approximation for spin degrees of freedom in itinerant-electron systems. Local spin Hamiltonians are introduced in order to describe the energy landscape of small magnetic fluctuations, locally around a given spin configuration. They are designed for linear response near a given magnetic state and in general insufficient to capture arbitrarily strong deviations of spin configurations from the equilibrium. In order to achieve this mapping, we include a linear term in the local spin Hamiltonian that, together with the usual bilinear exchange tensor, produces an improved accuracy of effective magnetic Weiss fields for non-collinear states. We also provide examples from tight-binding electronic structure theory, where our implementation of the calculation of exchange constants is based on constraining fields that stabilize an out-of-equilibrium spin configuration. We check our formalism by means of numerical calculations for iron dimers and chains.
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