Microscopic Theory of Magnetic Detwinning in Iron-Based Superconductors with Large-Spin Rare Earths

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Microscopic Theory of Magnetic Detwinning in Iron-Based Superconductors with Large-Spin Rare Earths

Jannis Maiwald, I. I. Mazin, and Philipp Gegenwart

Phys. Rev. X 8, 011011 – Published 23 January 2018

Abstract

Detwinning of magnetic (nematic) domains in Fe-based superconductors has so far only been obtained through mechanical straining, which considerably perturbs the ground state of these materials. The recently discovered nonmechanical detwinning in ${EuFe}_{2} {As}_{2}$ by ultralow magnetic fields offers an entirely different, nonperturbing way to achieve the same goal. However, this way seemed risky due to the lack of a microscopic understanding of the magnetically driven detwinning. Specifically, the following issues remained unexplained: (i) ultralow value of the first detwinning field of approximately 0.1 T, two orders of magnitude below that of ${BaFe}_{2} {As}_{2}$ , and (ii) reversal of the preferential domain orientation at approximately 1 T and restoration of the low-field orientation above 10–15 T. In this paper, we present, using published as well as newly measured data, a full theory that quantitatively explains all the observations. The key ingredient of this theory is a biquadratic coupling between Fe and Eu spins, analogous to the Fe-Fe biquadratic coupling that drives the nematic transition in this family of materials.

Received 10 June 2017
Revised 8 December 2017

DOI:https://doi.org/10.1103/PhysRevX.8.011011

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Magnetic interactions Magnetism Superconductivity Superconductors

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jannis Maiwald¹, I. I. Mazin², and Philipp Gegenwart¹

¹Experimentalphysik VI, Universität Augsburg, Universitätstraße 1, 86135 Augsburg, Germany
²Code 6393, Naval Research Laboratory, Washington, DC 20375, USA

Popular Summary

In the last 10 years, iron-based high-temperature superconductors (FeBS) have gained considerable attention. To study the intriguing interplay between magnetism and superconductivity in many FeBS, researchers need to eliminate one of the two kinds of magnetic domains in the crystal, a process called detwinning. This is usually done by applying an external stress, a complicated and poorly controlled process, or by a very high external magnetic field. However, in one compound, ${EuFe}_{2} {As}_{2}$ (Eu122), the necessary field is 2 orders of magnitude weaker than for similar compounds, and as the magnetic field increases, the domains spontaneously rotate by 90°, not once but twice. We develop a theoretical model that explains all the observations and reveals the underlying physics.

One of the puzzling aspects of the Eu122 paradox is that, while the Eu ion carries a magnetic moment, it does not couple with the crystal lattice, so it should be able to rotate freely in an external magnetic field without triggering any crystallographic change. We resolve this discrepancy by introducing a minuscule biquadratic coupling between the magnetic moments of Eu and Fe, which tries to make the two as parallel as possible. This model fully explains all reorientation transitions, despite the fact that the interaction in question has energy equivalent to 0.1 K, nearly vanishing by all electronic measures.

Our results open new avenues for exploring the physics of not just Eu-based iron superconductors but for a range of similar compounds as well.

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Vol. 8, Iss. 1 — January - March 2018

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Images

Figure 1
Low-temperature kinetic detwinning process of ${EuFe}_{2} {As}_{2}$ for an increasing (from left to right) external magnetic field $H ∥ [110]_{T}$ (gray arrows). Fe atoms and spins are shown in blue. Open circles indicate Eu atoms and spins (red) in the next layer. (a) Definition of the spin angles. (b) Initial twin population (a b-twin domain in green, an a-twin one in purple) at $H = 0$ . (c) The b-twin domains grow with increasing field until (d) the system is completely detwinned, and only b-twin domains ( $b ∥ H$ ) are present. (e) Above $H_{0}$ , the first reorientation sets in, and the population of the a-twin domains starts to grow. (f) At $H_{1}$ the two populations are equal. (g) At a higher field, the system becomes again fully detwinned ( $a ∥ H$ , no more b-twin domains). (h) At an even higher field, another reorientation starts, and at $H_{2}$ , the populations of the two domain types are equal again (at even higher fields, eventually the b-twin domains will dominate).
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Figure 2
Magnetization at ( $T = 5 K$ ) as a function of decreasing magnetic field applied along the $[110]_{T}$ direction (blue symbols) remeasured from Zapf et al. [9]. The solid line (red) represents our theoretical prediction using the determined coupling constants. The short dashed line depicts the a-twin domain population $n$ derived from a fit to the corresponding magnetoresistance data, similar to Fig. 5, yielding $Δ = 0.004 meV$ , $n_{i} = 0.12$ , and $d n = 0.81$ (see Supplemental Material [18]). The long dashed line depicts the extrapolation of $H_{b}^{sat}$ , as discussed in the text.
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Figure 3
Calculated domain energy difference $d E$ as a function of $M H / J_{⊥}$ for a characteristic ratio of $K / J_{⊥} = 0.05$ . For better visibility, values above $H_{2}$ (vertical dashed line) are rescaled by a factor of 10. Positive values and negative values correspond to the b-twin and a-twin domain, respectively. The horizontal dashed line indicates $d E = 0$ .
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Figure 4
Phase diagram $K / J_{⊥}$ vs $M H / J_{⊥}$ in thermodynamic equilibrium. The four phases shown correspond to the b-twin domains (green) with canted ${Eu}^{2 +}$ spins, a-twin domains with saturated (purple) or unsaturated (blue) Eu magnetization, respectively, followed by the b-twin domains (gray) induced by the canting of Fe spins. Finally, another hypothetical phase of a-twin domains, induced by further canting of the Fe spins, is shown (light blue). More details, also on the significance of the dotted line, indicating $12 K / J_{⊥} = 1$ , can be found in the Supplemental Material [18].
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Figure 5
Twin domain population derived from magnetostriction data at ( $T = 5 K$ ) from Ref. [9] as a function of (increasing) magnetic field applied along the $[110]_{T}$ direction (blue line) as discussed in the main text. The solid line (red) represents the theoretical prediction using the constants’ values derived in the main text and the Supplemental Material [18] (see Table SII, #2). The dashed line (gray) depicts the theoretically derived domain energy difference $d E$ , similar to Fig. 3. The a-twin domain population is reduced, because of the pressure of the dilatometer, which favors the b-twin domain in this orientation.
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