Higher-order exchange interactions leading to metamagnetism in FeRh

Abstract

The origin of the metamagnetic antiferromagnetic-ferromagnetic phase transition of FeRh is a subject of much debate. Competing explanations invoke magnetovolume effects and purely thermodynamic transitions within the spin system. It is experimentally difficult to observe the changes in the magnetic system and the lattice simultaneously, leading to differing conclusions over which mechanism is responsible for the phase transition. A non-collinear electronic structure study by Mryasov [O.N. Mryasov, Phase Transitions 78, 197 (2005)] showed that non-linear behavior of the Rh moment leads to higher order exchange terms in FeRh. Using atomistic spin dynamics (ASD) we demonstrate that the phase transition can occur due to the competition between bilinear and the higher order four spin exchange terms in an effective spin Hamiltonian. The phase transition we see is of first order and shows thermal hysteresis in agreement with experimental observations. Simulating sub-picosecond laser heating we show an agreement with pump-probe experiments with a ferromagnetic response on a picosecond timescale. Below the transition temperature, FeRh exists as an antiferromagnet where the Fe site has moment |m Fe | 3.15µ B and the Rh site has no net magnetic moment. Above the transition temperature the Fe moments realign ferromagnetically and the Rh site forms a moment of |m Rh | 1.00µ B while the Fe moment is largely unchanged. There is also a 1% expansion of the unit cell volume in the FM phase. Debate exists about the driving force behind the phase transition. The contention concerns whether the expansion of the unit cell through the phase transition alters the magnetic state, or whether a thermodynamic phase transition in the magnetic state drives the lattice expansion. As yet neither experiments nor theory have been conclusive on this matter. Non-collinear electronic structure studies have shown a non-linear dependence of the direction and magnitude of the Rh moment on the Weiss field from the surrounding Fe moments [8]. This unusual behavior allows one to write an effective spin Hamiltonian which contains only the Fe degrees of freedom where the non-linear induced Rh moment leads to higher order effective exchange contributions of biquadratic and four spin order. It has been suggested that the competition between exchange interactions of different orders around the transition temperature could drive the phase transition, with the volume expansion occurring as a subsidiary effect, thus explaining observations of sub-picosecond laser heating where the reponse of the magnetic system was demonstrated to respond faster than that of the lattice [9].In this Letter we demonstrate that it is the thermally driven competition between the bilinear and four spin contributions to the effective Fe-Rh-Fe exchange which lead to the AFM-FM phase transition. Specifically, it will be shown that the transition is a direct result of the differential thermal scaling of the two terms. Using a minimal set of interaction parameters we are able to reproduce...

Impact of lattice dynamics on the phase stability of metamagnetic FeRh: Bulk and thin films

“…The paper concluded that a quadratic exchange term is needed to produce the transition and that both volume and magnetic fluctuations are equally important [49]. Barker and Chantrell extended Mryasov's model by fully expanding the quadratic spin interactions into four spin exchange terms, which were parameterized from experimental data [50]. Solving the Landau-Lifshitz-Gilbert equation using atomistic spin dynamics yields T M in good agreement with experiment.…”

Modeling the thickness dependence of the magnetic phase transition temperature in thin FeRh films

“…As was shown in Ref. [6], the four-spin term has a different temperature scaling from the bilinear term which gives rise to a competition between ferromagnetic (bilinear) and antiferromagnetic (four-spin) order. The dynamics of each spin in the system S i are calculated by integrating the stochastic Landau-Lifshitz-Gilbert (LLG) [32][33][34] …”

“…The present approach allows for the simultaneous description of both the FM and the AFM phases using a single set of parameters, based on the atomistic spin dynamics formalism [30]. This second-principles model is based on a Heisenberg Hamiltonian as presented by Barker and Chantrell [6]. They showed that it is possible to reproduce the phase transition through the contribution of exchange terms, which implies a magnetic origin of the phase transition [3].…”

“…In the Hamiltonian (1) an adiabatic approximation is made such that the rhodium moment is assumed to appear due to the Weiss field from iron on a much faster time scale than the precession of the magnetic moments. To that end, the Hamiltonian is written in terms of the Fe degrees of freedom only [6]. The four-spin term in the Hamiltonian that arises due to electron hopping among four sites must be calculated taking into account all of the 32 (nearest-neighbor quartets) [35].…”

“…At that same point the lattice also undergoes a volume expansion [4]. There has been much debate as to whether this phase transition is driven by structural effects, such as lattice expansion, or purely magnetic interactions [6], such as magnetovolume effects or a superposition of the two [7]. In Ref.…”