Magnetoelastic effects in doped Fe${}_2$P

We use combined high resolution neutron diffraction (HRPD) with density functional theory (DFT) to investigate the exchange striction at the Curie temperature ($T_C$) of Fe${}_2$P and to examine the effect of boron and carbon doping on the P site. We find a significant contraction of the basal plane on heating through $T_C$ with a simultaneous increase of the $c$ axis that results in a small overall volume change of $\sim 0.01\%$. At the magnetic transition the Fe${}_I$-Fe${}_I$ distance drops significantly and becomes shorter than Fe${}_I$-Fe${}_{II}$. The shortest metal-metalloid (Fe${}_I$-P${}_I$) distance also decreases sharply. Our DFT model reveals the importance of the latter as this structural change causes a redistribution of the Fe${}_I$ moment along the $c$ axis (Fe-P chain). We are able to understand the site preference of the dopants, the effect of which can be linked to the increased moment on the Fe${}_I$ site, brought about by strong magnetoelasticity and changes in the electronic band structure.

Figure 1

The effect of boron, silicon, and arsenic doping in Fe${}_2$P${}_{1-x}$Z${}_x$ on the magnetic ordering temperature $T_C$ (top) and the room temperature lattice parameters (bottom).[6, 7, 8]

Figure 2

Atomic arrangement of the Fe${}_2$P in the basal plane. Fe atoms occupy two nonequivalent threefold symmetry sites, 3f (Fe${}_I$) and 3g (Fe${}_{II}$), and the phosphorus atoms sit on a singlefold 1b (P${}_I$) and twofold position, 2c (P${}_{II}$) in the hexagonal crystal lattice. Fe${}_I$ ($x{}_I$, 0, 0) atoms share the same plane with P${}_I$ (1/3, 2/3, 0) and Fe${}_{II}$ atoms ($x{}_{II}$, 0, 1/2) with P${}_{II}$ (0,0, 1/2), respectively.

Figure 3

Thermomagnetic curves of the parent Fe${}_2$P alloy with the C and B doped counterparts (top, left axis) in the field of ${\mu }_{0}M=0.01$ T. Derivatives ($\frac{dM}{dH}$) are linked to the right axis (top). Bottom figure shows the change of the lattice parameters ($a,c$) for comparison, obtained using HRPD.

Figure 4

Temperature evolution of the lattice parameters of the parent Fe${}_2$P compound together with that of the C- and B-doped samples. The strong magnetoelastic response is especially apparent around the magnetic ordering temperature ($\sim$215 K).

Figure 5

The shortest Fe${}_I$-2Fe${}_I$ and Fe${}_I$-2Fe${}_{II}$ distances as a function of temperature for all investigated samples. Inset depicts the temperature region of the crossover.

Figure 6

The shortest metal-metalloid distances, Fe${}_I$-2P${}_I$ and Fe${}_I$-2P${}_{II}$, as a function of temperature in Fe${}_2$P together with the doped counterparts. Both distances relate to the metamagnetic 3f (Fe${}_I$) site.

Figure 7

Total magnetic moment/formula unit as a function of lattice parameter of Fe${}_2$P. The magnetic moment is strongly linked to the change in $a$-lattice parameter. The red and black dots indicate the high and low magnetization states (see text).

Figure 8

A comparison of the spin density of the low magnetization state (left) and high magnetization state (right) and of Fe${}_2$P. The large magnetic moment around the Fe${}_{II}$ site is only decreased in amplitude above the transition, when strong delocalization of the Fe${}_I$ magnetization occurs simultaneously.

Figure 9

Comparison of the density of states of a high magnetization state (red) and a low magnetization state (black) in Fe${}_2$P.

Figure 10

Site preference of the $p$-block dopants as established from DFT. Negative total energy differences represent preference for the singlefold position. Positive total energy differences suggest tendency for twofold site occupancy.

Figure 11

Equilibrium lattice parameters for NM and FM states as a result of DFT calculations as a function of dopants in Fe${}_2$P${}_{2/3}$Z${}_{1/3}$, where $\text{Z}=\text{C}$, B, Si, or As, respectively.

Figure 12

Total and site-projected magnetic moments in Fe${}_2$P${}_{2/3}$Z${}_{1/3}$, for $\text{Z}=\text{C}$, B, Si, and As, respectively.