Physical properties of FeRh alloys: The antiferromagnetic to ferromagnetic transition

The electronic, magnetic, thermodynamical, and transport properties of FeRh alloys are studied from first principles. We present a unified approach to the phase stability, an estimate of exchange interactions in various magnetic phases, and transport properties including the effect of temperature which are all based on the same electronic-structure model. Emphasis is put on the transition between the ferromagnetic (FM) and antiferromagnetic (AFM) phases. Such a study is motivated by a recent suggestion of FeRh as a room-temperature antiferromagnetic memory resistor. The theory predicts the order-disorder transformation from the hypothetical disordered bcc phase into ordered B2 phase. Comparison of exchange interactions in the magnetically ordered FM and AFM phases with corresponding spin-disordered counterparts allows us to identify relevant interactions which are precursors of magnetically ordered phases. The most important result is the explanation of a dramatic decrease of the resistivity accompanying the AFM to FM phase transition which is due to the spin disorder present in the system. The study of the anisotropic magnetoresistance in the AFM phase found recently experimentally is extended also to finite temperatures.

Figure 1

The total and local densities of states for various phases: (a) the nonmagnetic B2-FeRh; (b) the FM B2-FeRh; (c) the DLM FeRh in the AFMII lattice; and (d) the ordered AFMII FeRh lattice. The DOS are resolved into the majority (maj) and minority (min) contributions while $E_{\mathrm{F}}$ denotes the Fermi energy. The majority and minority contributions are shown for one spin-orientation for the AFMII and DLM FeRh phases, for the other spin orientation the role of the majority and minority spins is interchanged. Note that the AFMII and CsCl lattices have different formula units containing, respectively, four and two atoms which are reflected in the area under the total DOS's, while the local DOS are normalized equally irrespective of the formula unit.

Figure 2

The constrained noncollinear calculations assuming variation of the canting angle $\theta$ between magnetizations of Fe and Rh sublattices in the AFMII phase. The Rh moment (filled circles) points in the direction of the $z$ axis, while the sublattice Fe moments (empty circles) are canted by an angle $\pm \theta$. The dotted line shows results of non-self-consistent calculations assuming a simple cosine form, namely, $m^{\mathrm{Rh}}\left(\theta \right)$= $m^{\mathrm{Rh}}\left(\theta =0\right) \cos \left(\theta \right)$. The values $\theta =0$ and $\pi /2$ correspond to the collinear FM and AFMII phases, respectively.

Figure 3

(a) Effective pair interactions $V_{ij}$ in the disordered nonmagnetic bcc-$\left({\mathrm{Fe}}_{0.5},{\mathrm{Rh}}_{0.5}\right)$ alloy as a function of the interatomic distance $d$ in units of the lattice constant $a$, and (b) its corresponding lattice Fourier transform $V\left(\mathbf{q}\right)$. The minimum of $V\left(\mathbf{q}\right)$ at the ordering vector ${\mathbf{q}}_{\mathrm{ord}}=H$ indicates ordering to the B2 phase (the CsCl lattice type).

Figure 4

The exchange interactions $J^{Q,Q^{\prime }},Q,Q^{\prime }=$ Fe, Rh, as functions of the interatomic distance $d$ (in units of the lattice parameter $a$) calculated in the disordered FM bcc-$\left({\mathrm{Fe}}_{0.5},{\mathrm{Rh}}_{0.5}\right)$ alloy (a) and the ordered FM B2-FeRh alloy (b).

Figure 5

The exchange interactions $J^{\mathrm{Fe},\mathrm{Fe}}$ as a function of the interatomic distance $d$ calculated using different reference states: (i) the B2 DLM state (stars), and (ii) the ordered AFMII FeRh alloy. In the latter case, we distinguish between interactions among spins on the same Fe sublattice (filled circles, labeled as “same”) and interactions between different magnetic Fe sublattices with opposite spin orientations (empty circles, labeled as “diff”), respectively. All interatomic distances are given in units of the AFMII lattice parameter $a$.

Figure 6

The exchange interactions $J^{\mathrm{Fe},\mathrm{Fe}}$ calculated for the AFMII reference state and for different lattice constants expressed in terms of corresponding Wigner-Seitz (WS) radii: (i) WS = 2.63 a.u., (ii) WS = 2.77 a.u. (experiment), and (iii) WS = 2.91 a.u. The full (empty) symbols correspond to interactions between the same (full symbols) and different (empty symbols) Fe sublattices.

Figure 7

The transport properties of the $\left({\mathrm{Fe}}_{1-x},{\mathrm{Rh}}_x\right)\mathrm{Rh}$ alloys in the AFMII and hypothetical FM phases both neglecting the temperature effect ($T=0$ K): (a) the AMR ratios $r^{\mathrm{AMR}}$, and (b) the residual resistivities.