Using density functional theory to describe slowly varying fluctuations at finite temperatures: local magnetic moments in Gd and the ‘not so local’ moments of Ni

Abstract

We briefly describe the density functional theory (DFT)-based 'disordered local moment' (DLM) picture for magnetism at finite temperatures. It shows how relatively slowly fluctuating local moments can emerge from the interacting electrons of many materials. Such entities have rigid magnitudes and fluctuate their orientations from atomic site to atomic site on a timescale long compared to other electronic times. We illustrate this theory with calculations of the magnetocaloric effect in Gd where we find excellent agreement with experiments. Fluctuating moments do not appear to establish naturally over such small regions for some other materials. We show how the DFT-DLM theory can be extended to these materials with the use of the Korringa-Kohn-Rostoker nonlocal coherent potential approximation (KKR-NLCPA) to allow for more extensive, slow magnetic fluctuations. We present the first application of this approach by revisiting the description of the magnetic fluctuations prevalent in the paramagnetic state of nickel. We find that local moments can emerge above Tc and that these form coherently over small clumps of atomic sites (4-8 sites).

Improvement of magnetic hardness at finite temperatures:Ab initiodisordered local-moment approach forYCo5

“…Indeed we will see below some inherent underestimate near the Curie point in our calculations which might indicate some fragile nature of the local moments in YCo 5 . This problem can be cured by extending the calculation to that based on the non-local CPA 37,38 . For now we are mostly concerned with the lowest temperature properties and the middle-temperature range of T < ∼ 600 [K] which is well below the Curie temperature at T Curie = 920 [K] 26 .…”

“…Up to 600 [K] therefore the DLM theory as applied is adequate and we can examine the effects of transverse fluctuations on the MAE that it describes. For higher temperatures however, the effects of shortranged correlations among theê orientation (via the use of the non-local CPA for example 37,38 ) and longitudinal fluctuations 40 need to be addressed for a more complete picture. Comprehensive analyses on bcc-Fe, where the robustness of the local moments are established, can be found in a recent work 41 .…”

Complex Magnetism of Lanthanide Intermetallics and the Role of their Valence Electrons:Ab InitioTheory and Experiment

“…The orientations of these moments fluctuate slowly compared to the dynamics of the valence electron glue surrounding them. By labeling these transverse modes by local spin polarization axes fixed to each lanthanide atom i,ê i , and using a generalization of SDFT [14](þSIC [15,16]) for prescribed orientational arrangements, fê i g, we can determine the ab initio energy for each configuration, Ωfê i g [16][17][18][19]24], so that the configuration's probability at a temperature T can be found. The magnetic state of the system is set by an average over all such configurations, appropriately weighted, and specifies the magnetic order parameters, fm i ¼ hê i ig, where the magnitudes m i ¼ jm i j range from 0 for the high-temperature paramagnetic (PM) (fully disordered) state to 1 when the magnetic order is complete at T ¼ 0 K. A distribution where the order parameters are the same on every site, fm i ¼ m fẑ g, say, describes a ferromagnetically ordered…”

Exchange interactions from a nonorthogonal basis set: From bulk ferromagnets to the magnetism in low-dimensional graphene systems

“…The meanfield approximation is known to overestimate the exact transition temperatures, which might explain the higher values of T MFA C as compared with the experimental T C in case of Fe and Co. The considerably lower mean-field estimates for the Curie temperature with respect to the experimental value in case of Ni is most possibly the consequence of the highly itinerant nature of the magnetism of bulk Ni [36,37].…”