Caloric effects around phase transitions in magnetic materials described by ab initio theory : the electronic glue and fluctuating local moments

We describe magneto-, baro-, and elastocaloric effects (MCEs, BCEs, and eCEs) in materials, which possess both discontinuous (first-order) and continuous (second-order) magnetic phase transitions. Our ab initio theory of the interacting electrons of materials in terms of disordered local moments has produced explicit mechanisms for the drivers of these transitions, and here, we study associated caloric effects in three case studies where both types of transition are evident. Our earlier work had described FeRh’s magnetic phase diagram and large MCE. Here, we present calculations of its substantial BCE and eCE. We describe the MCE of dysprosium and find very good agreement with experimental values for isothermal entropy ((ΔSiso) and adiabatic temperature (ΔTad) changes over a large temperature span and different applied magnetic field values. We examine the conditions for optimal values of both ΔSiso and ΔTad that comply with a Clausius–Clapeyron analysis, which we use to propose a promising elastocaloric cooling cycle arising from the unusual dependence of the entropy on temperature and biaxial strain found in our third case study—the Mn3GaN antiperovskite. We explain how both ΔSiso and ΔTad can be kept large by exploiting the complex tensile strain–temperature magnetic phase diagram, which we had earlier predicted for this material and also propose that hysteresis effects will be absent from half of the caloric cycle. This rich and complex behavior stems from the frustrated nature of the interactions among the Mn local moments

First-order ferromagnetic transitions of lanthanide local moments in divalent compounds: An itinerant electron positive feedback mechanism and Fermi surface topological change

Around discontinuous (first-order) magnetic phase transitions the strong caloric response of materials to the application of small fields is widely studied for the development of solid-state refrigeration. Typically strong magnetostructural coupling drives such transitions and the attendant substantial hysteresis dramatically reduces the cooling performance. In this context we describe a purely electronic mechanism which pilots a first-order paramagnetic-ferromagnetic transition in divalent lanthanide compounds and which explains the giant non-hysteretic magnetocaloric effect recently discovered in a Eu$_2$In compound. There is positive feedback between the magnetism of itinerant valence electrons and the ferromagnetic ordering of local $f$-electron moments, which appears as a topological change to the Fermi surface. The origin of this electronic mechanism stems directly from Eu's divalency, which explains the absence of a similar discontinuous transition in Gd$_2$In.Comment: 8 pages, 7 figure

Theory of magnetic ordering in the heavy rare earths : ab initio electronic origin of pair- and four-spin interactions

We describe a disordered local moment theory for long-period magnetic phases and investigate the temperature and magnetic field dependence of the magnetic states in the heavy rare earth elements (HREs), namely, paramagnetic, conical and helical antiferromagnetic (HAFM), fan, and ferromagnetic (FM) states. We obtain a generic HRE magnetic phase diagram which is consequent on the response of the common HRE valence electronic structure to f-electron magnetic moment ordering. The theory directly links the first-order HAFM-FM transition to the loss of Fermi surface nesting, induced by this magnetic ordering, as well as provides a template for analyzing the other phases and exposing where f-electron correlation effects are particularly intricate. Gadolinium, for a range of hexagonal, close-packed lattice constants c and a, is the prototype, described ab initio, and applications to other HREs are made straightforwardly by scaling the effective pair and quartic local moment interactions that emerge naturally from the theory with de Gennes factors and choosing appropriate lanthanide-contracted c and a values

Ab-initio theory of magnetic ordering : electronic origin of pair- and multi- spin interactions

We present an ab initio theory to describe magnetic ordering and magnetic phase transitions at finite temperatures from pairwise and multi-spin interactions. Our formalism is designed to model thermal fluctuations of disordered local moments associated with atomic sites and adequately describes how these emerge from the glue of many interacting electrons. The key ingredient is to assume a time-scale separation between the evolution of the local moment orientations and a rapidly responsive electronic background setting them. This is the Disordered Local Moment picture grounding the framework of our theory. The method uses Density Functional Theory calculations constrained to specific local moment configurations to model the electronic structure and exploits Green's functions within a Multiple Scattering Theory to solve the Kohn-Sham equations. Two central objects are calculated as functions of magnetic ordering: internal magnetic fields sustaining the local moments and the lattice Fourier transform of the interactions in the paramagnetic state. We develop a methodology to extract the pairwise and multi-spin constants from the first and use the second to study the magnetic interactions in the reciprocal space and gain information of the type and extent of most stable magnetic order. These quantities are directly related to the first and second derivatives of the free energy of a magnetic material, respectively. Hence, our approach is able to provide thermodynamic quantities of interest, such as temperature and entropy changes for the evaluation of caloric effects, and magnetic phase diagrams for temperature, magnetic field, and lattice spacing studies can be constructed. Transition temperatures and their order, as well as tricritical points, are obtainable. We apply the theory to carry out major investigations on long-period magnetic phases in the heavy rare earth elements (HREs) and magnetic frustration in the Mn-based antiperovskite nitride Mn₃GaN. The mixing of both pairwise and four-site magnetic interactions have been found to have profound consequences on the magnetism of both systems. We have obtained a generic HRE magnetic phase diagram which is consequent on the response of the common valence electronic structure to the f-electron magnetic moment ordering. We also present a modelling based on the lanthanide contraction to describe ferromagnetic, helical antiferromagnetic, and fan phases in Gd, Tb, Dy, and Ho, in excellent agreement with experiment. Our study of Mn₃GaN shows that its first-order paramagnetic-antiferromagnetic triangular transition originates from the fourth order terms and that the effect of biaxial strain to distort the compensated antiferromagnetic interactions has a large impact on the frustrated magnetism. As a consequence, new collinear magnetic phases stable at high temperatures are predicted and a very rich temperature-strain phase diagram is obtained. We also show how to get the best refrigerating performance and design a novel elastocaloric cooling cycle from the features of the diagram

Fermi-surface origin of skyrmion lattices in centrosymmetric rare-earth intermetallics

We show from first-principles that barrel-shaped structures within the Fermi surface of the centrosymmetric intermetallic compounds GdRu$_2$Si$_2$ and Gd$_2$PdSi$_3$ give rise to Fermi surface nesting, which determines the strength and sign of quasi-two-dimensional Ruderman-Kittel-Kasuya-Yosida pairwise exchange interactions between the Gd moments. This is the principal mechanism leading to their helical single-$q$ spin-spiral ground states, providing transition temperatures and magnetic periods in good agreement with experiment. Using atomistic spin-dynamic simulations, we draw a direct line between the subtleties of the three-dimensional Fermi surface topology and the stabilization of a square skyrmion lattice in GdRu$_2$Si$_2$ at applied magnetic fields as observed in experiment

Frustrated magnetism and caloric effects in Mn-based antiperovskite Nitrides : Ab Initio theory

We model changes of magnetic ordering in Mn-antiperovskite nitrides driven by biaxial lattice strain at zero and at finite temperature. We employ a non-collinear spin-polarised density functional theory to compare the response of the geometrically frustrated exchange interactions to a tetragonal symmetry breaking (the so called piezomagnetic effect) across a range of Mn3AN (A = Rh, Pd, Ag, Co, Ni, Zn, Ga, In, Sn) at zero temperature. Building on the robustness of the effect we focus on Mn3GaN and extend our study to finite temperature using the disordered local moment (DLM) first-principles electronic structure theory to model the interplay between the ordering of Mn magnetic moments and itinerant electron states. We discover a rich temperature-strain magnetic phase diagram with two previously unreported phases stabilised by strains larger than 0.75\% and with transition temperatures strongly dependent on strain. We propose an elastocaloric cooling cycle crossing two of the available phase transitions to achieve simultaneously a large isothermal entropy change (due to the first order transition) and a large adiabatic temperature change (due to the second order transition)

Quantification of electronic and magnetoelastic mechanisms of first-order magnetic phase transitions from first principles : application to caloric effects in La(Fe x Si 1 − x ) 13

La(FexSi1−x)13 and derived quaternary compounds are well-known for their giant, tunable, magneto- and barocaloric responses around a first-order paramagnetic-ferromagnetic transition near room temperature with low hysteresis. Remarkably, such a transition shows a large spontaneous volume change together with itinerant electron metamagnetic features. While magnetovolume effects are well-established mechanisms driving first-order transitions, purely electronic sources have a long, subtle history and remain poorly understood. Here we apply a disordered local moment picture to quantify electronic and magnetoelastic effects at finite temperature in La(FexSi1−x)13 from first-principles. We obtain results in very good agreement with experiment and demonstrate that the magnetoelastic coupling, rather than purely electronic mechanisms, drives the first-order character and causes at the same time a huge electronic entropy contribution to the caloric response

Short period magnetization texture of B20-MnGe explained by thermally fluctuating local moments

B20-type compounds, such as MnSi and FeGe, host helimagnetic and skyrmion phases at the mesoscale, which are canonically explained by the combination of ferromagnetic isotropic interactions with weaker chiral Dzyaloshinskii-Moriya ones. Mysteriously, MnGe evades this paradigm as it displays a noncollinear magnetic state at a much shorter nanometer scale. Here we show that the length scale and volume-dependent magnetic properties of MnGe stem from purely isotropic exchange interactions, generally obtained in the paramagnetic state. Our approach is validated by comparing MnGe with the canonical B20-helimagnet FeGe. The free energy of MnGe is calculated, from which we show how triple-q magnetic states can stabilize by adding higher-order interactions