Strongly anisotropic antiferromagnetic coupling in ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ revealed by stress detwinning

Of all parent compounds of iron-based high-temperature superconductors, ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ exhibits by far the largest magnetostructural coupling due to the sizable biquadratic interaction between Eu and Fe moments. While the coupling between Eu antiferromagnetic (AFM) order and Fe structural/AFM domains enables rapid field detwinning, this prevents simple magnetometry measurements from extracting the critical fields of the Eu metamagnetic transition. Here, we measure these critical fields by combining x-ray magnetic circular dichroism spectroscopy with in situ tunable uniaxial stress and applied magnetic field. The combination of two tuning knobs allows us to separate the stress detwinning of structural domains from the field-induced reorientation of Eu moments. Intriguingly, we find a spin-flip transition which can only result from a strongly anisotropic interaction between Eu planes. We argue that this anisotropic exchange is a consequence of the strong anisotropy in the magnetically ordered Fe layer, which presents a form of higher-order coupling between Eu and Fe magnetism.

Figure 1

(a) ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ unit cell at $T=7$ K and zero applied magnetic field. Both Fe and Eu antiferromagnetic orders are stabilized with easy axes aligned with the longer $a$ lattice constant of the orthorhombic unit cell. (b) Uniaxial stress is applied along the $\widehat{x}$ direction aligned with the orthorhombic $a/b$ orthorhombic unit cell lattice directions such that tension (compression) detwins the sample to the A (B) domain (orange/blue outline). Resistivity measurements along the stress axis measure ${\rho }_a$ (${\rho }_b$) aligned with the $a\left(b\right)$ lattice constant of the A (B) domain. A magnetic field is applied perpendicular to the strain axis at ${10}^{\circ }$ above parallel from the $a/b$ plane, causing a reorientation of Eu moments to align along the field direction. XMCD is proportional to the Eu magnetization along the applied field direction. For simplicity, we collapse the 4 Eu atoms and 8 Fe atoms of the doubled orthogonal unit cell into 2 Eu (blue arrows) and 4 Fe (red arrows) effective moments.

Figure 2

$T=30\mathrm{K}$ single pass applied magnetic field sweep for the detwinned A and B domains [XMCD data were not collected for B domain 0.8–1 T]. XMCD above the Eu antiferromagnetic (AFM) ordering temperature shows a nearly isotropic response to field. ${\rho }_{xx}$ vs applied magnetic field reveals a minimal magnetoresistance. (Inset, left) ${\rho }_{xx}$ vs temperature for the detwinned A and B monodomains reveal no additional anisotropy induced at the Eu AFM ordering temperature $T_{N,\mathrm{Eu}}=19.1\mathrm{K}$. (Inset, right) The resistivity anisotropy $\eta =\frac{{\rho }_b-{\rho }_a}{{\rho }_b+{\rho }_a}$ (black).

Figure 3

Field sweep at $T=7$ K in the fully magnetically ordered phase presented in Fig. 1. Applied field ramped from 0 to 1, −1, and 0 T in each detwinned (a) A and (b) B monodomain states. Inset to bottom panel of (a) shows the small magnetoresistance hysteresis visible ∼0.5 T in the A domain.

Figure 4

(a) Data from Figs. 3 and 3 replotted as the average value of positive and negative field sweeps of XMCD and the magnetoresistance against the absolute value of applied magnetic field for the detwinned A (orange) and B (blue) monodomains. Linear fits (black lines) to the XMCD magnitude for $|{\mu }_{0}H|=0.6\mathrm{T}$ to $1\mathrm{T}$ indicate both values coincide at $|{\mu }_0{H}_{\mathrm{A}}^{\mathrm{sat}}|\sim 1.17\mathrm{T}$. The magnetoresistance for positive and negative field are nearly identical and tightly overlap. (b) The difference in XMCD and ${\rho }_{xx}$ for increasing and decreasing fields yields $\mathrm{\Delta }\mathrm{XMCD}=\mathrm{XMCD}\left(H_{\mathrm{inc}}\right)-\mathrm{XMCD}\left(H_{\mathrm{dec}}\right)$ and $\mathrm{\Delta }{\rho }_{xx}={\rho }_{xx}\left(H_{\mathrm{inc}}\right)-{\rho }_{xx}\left(H_{\mathrm{dec}}\right)$. For the B domain, the peak values of $\mathrm{\Delta }\mathrm{XMCD}$ and $\mathrm{\Delta }{\rho }_{xx}$ coincide at ${\mu }_0{H}_{\mathrm{B}}^{\mathrm{flip}}=0.48\mathrm{T}$.

Figure 5

(a) XMCD data of Fig. 4 for the B domain normalized to the 1 T mean value. Black (magenta) line represents the $T=0$ K metamagnetic spin flip (spin flop) transition calculated using the anisotropic JKW (isotropic JK) model (see main text). (b) Octagon sample magnetization with field applied along the tetragonal ${\left[100\right]}_{\mathrm{T}}$ (blue) and ${\left[110\right]}_T$ (red) directions. Critical fields marked by dashed lines. Magnetization normalized by 1 T saturation value along ${\left[100\right]}_T$ (gray). Average of the two domain XMCD data of Fig. 4, normalized by the B domain saturated value at 1 T.