Persistent Detwinning of Iron-Pnictide ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ Crystals by Small External Magnetic Fields

Our comprehensive study on ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ reveals a dramatic reduction of magnetic detwinning fields compared to other $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($A=\mathrm{Ba}$, Sr, Ca) iron pnictides by indirect magnetoelastic coupling of the ${\mathrm{Eu}}^{2+}$ ions. We find that only $\sim 0.1\mathrm{T}$ are sufficient for persistent detwinning below the local ${\mathrm{Eu}}^{2+}$ ordering; above $T_{\mathrm{Eu}}=19\mathrm{K}$, higher fields are necessary. Even after the field is switched off, a significant imbalance of twin domains remains constant up to the structural and electronic phase transition (190 K). This persistent detwinning provides the unique possibility to study the low temperature electronic in-plane anisotropy of iron pnictides without applying any symmetry-breaking external force.

Figure 1

(Magneto)resistance, thermal expansion and magnetostriction of ZFC ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ ($H\parallel [110{]}_{\mathrm{T}}$). (a),(b) Temperature-dependent resistivity ${\rho }_{\mathrm{FT}}(T)$ after field treatment (FT) with 4 T for currents parallel (red lines) and perpendicular (black lines) to $H$, normalized to ZFC ${\rho }_{\mathrm{ZFC}}(0\mathrm{T})$. For FT at (a) $T=4\mathrm{K}$ and (b) 30 K, the opposite behavior is observed. (c) Thermal expansion $\mathrm{\Delta }L(T)/L_0$ ($\mathrm{\Delta }L\parallel H$) after ZFC (black line) and FT with 2 T at 4 K (cyan line). (d),(e) Magnetoresistance ${\rho }_{\parallel }(H)/{\rho }_{\parallel }(0\mathrm{T})-1$ at (d) 5 K and (e) 30 K as well as (f) magnetostriction $\mathrm{\Delta }L(H)/L_0$ at 5 K for increasing (black and brown lines) and decreasing (green line) $H$. All measurements are consistent with a persistent detwinning induced by low magnetic fields that is achievable below or above $T_{\mathrm{Eu}}$ and robust against heating up to $T_{\mathrm{s},\mathrm{SDW}}$.

Figure 2

Frequency dependent reflectivity of ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ at (a–c) $T=15\hspace{0.17em}\hspace{0.17em}\text{K}$ and (d–f) 30 K, for (a,d) $H=0\mathrm{T}$ (ZFC), (b,e) 1 T, and (c,f) 0 T after FT ($H\parallel [110{]}_{\mathrm{T}}$). The magnetic field induces anisotropy between $R(E\parallel H)$ (red lines) and $R(E\perp H)$ (black lines) and also changes the Fe-As phonon mode at $\sim 260{\mathrm{cm}}^{-1}$, both corresponding to the magnetic detwinning.

Figure 3

${\mathrm{EuFe}}_2{\mathrm{As}}_2$. Field-dependent magnetization $M(H)$ (grey dots) and false color plot of the frequency and field-dependent FIR relative reflectivity $R(H)/R(0\mathrm{T})$ ($E\perp H$) at (a) $T=15\mathrm{K}$ and (b) 30 K ($H\parallel [110{]}_{\mathrm{T}}$). The detwinning fields $H_1$ and $H_2$ as well as the spin flip field $H_{\mathrm{SF}}$ of ${\mathrm{Eu}}^{2+}$ can be identified ($H_1<H_{\mathrm{SF}}<H_2$).

Figure 4

Sketch of twin distribution and spin configuration of ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ dependent on an (from left to right, increasing) external magnetic field $H\parallel [110{]}_{\mathrm{T}}$ at $T<T_{\mathrm{Eu}}$. Top and bottom rows show a detail of the ${\mathrm{EuFe}}_2{\mathrm{As}}_2$ crystal and magnetic structure [Eu atoms and spins (blue), Fe atoms (yellow) and spins (brown), and As atoms (green)] that correspond to the twin distribution sketched in the middle row. (a) For $H=0\mathrm{T}$, the ZFC crystal is twinned and the domains are equally distributed. The ${\mathrm{Eu}}^{2+}$ spins are ordered A-type antiferromagnetically with the spin direction along the $a$ axis. (b) With an external field, twin variant $B_{\parallel }$ (red, bottom) with $b\parallel H$ gets energetically favored and therefore grows at the expense of variant $A_{\parallel }$ (green, top) as soon as the energy difference exceeds the twin boundary pinning energy. (c) With a further increasing field, ${\mathrm{Eu}}^{2+}$ spins in the remaining type $A_{\parallel }$ twins flip along the field direction. Energetically, twin $B_{\parallel }$ is still more favorable. (d) At slightly higher fields, twin $A_{\parallel }$ is favored and the crystal is detwinned with $a\parallel H$. (e) Corresponding energy curves ($E_0$: ground state). While at low fields twin $B_{\parallel }$ is energetically favorable (red area), twin $A_{\parallel }$ becomes favorable at higher fields (green area). Detwinning takes place at $H_1$ and $H_2$, when the energy gain exceeds the pinning energy of the twin boundary.