Strain-gradient-induced magnetic anisotropy in straight-stripe mixed-phase bismuth ferrites: Insight into flexomagnetism

Jin Hong Lee, Kwang-Eun Kim, Byung-Kweon Jang, Ahmet A. Ünal, Sergio Valencia, Florian Kronast, Kyung-Tae Ko, Stefan Kowarik, Jan Seidel, and Chan-Ho Yang

Phys. Rev. B 96, 064402 – Published 1 August 2017

Abstract

Implementation of antiferromagnetic compounds as active elements in spintronics has been hindered by their insensitive nature against external perturbations which causes difficulties in switching among different antiferromagnetic spin configurations. Electrically controllable strain gradient can become a key parameter to tune the antiferromagnetic states of multiferroic materials. We have discovered a correlation between an electrically written straight-stripe mixed-phase boundary and an in-plane antiferromagnetic spin axis in highly elongated La-5%-doped $BiFe O_{3}$ thin films by performing polarization-dependent photoemission electron microscopy in conjunction with cluster model calculations. A model Hamiltonian calculation for the single-ion anisotropy including the spin-orbit interaction has been performed to figure out the physical origin of the link between the strain gradient present in the mixed-phase area and its antiferromagnetic spin axis. Our findings enable estimation of the strain-gradient-induced magnetic anisotropy energy per Fe ion at around $5 \times 10^{- 12} eV m$ , and provide a pathway toward an electric-field-induced 90° rotation of antiferromagnetic spin axis at room temperature by flexomagnetism.

Received 7 April 2017
Revised 18 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.064402

Physics Subject Headings (PhySH)

Antiferromagnetism Ferroelectricity Magnetoelastic effect Magnetoelectric effect

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Jin Hong Lee^1,*, Kwang-Eun Kim¹, Byung-Kweon Jang¹, Ahmet A. Ünal², Sergio Valencia², Florian Kronast², Kyung-Tae Ko³, Stefan Kowarik⁴, Jan Seidel⁵, and Chan-Ho Yang^1,6,†

¹Department of Physics, KAIST, Yuseong-gu, Daejeon 34141, Republic of Korea
²Helmholtz-Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, D-12489 Berlin, Germany
³Max Planck–POSTECH Center for Complex Phase Materials & Department of Physics, POSTECH, Pohang, Gyeongbuk 37673, Republic of Korea
⁴Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, D-12489 Berlin, Germany
⁵School of Materials Science and Engineering, University of New South Wales, Sydney, New South Wales 2052, Australia
⁶KAIST Institute for the NanoCentury, KAIST, Yuseong-gu, Daejeon 34141, Republic of Korea

^*rifle@kaist.ac.kr
^†chyang@kaist.ac.kr

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 96, Iss. 6 — 1 August 2017

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) Reciprocal space map around the (002) diffraction. The reciprocal lattice unit is defined as $2 π / 3.789 Å^{- 1}$ . (b) Out-of-plane PFM image of a double-box-poled region (white dashed boxes). The dc-bias voltages and two slow-scan axes during the double-box poling are provided. (c) Atomic force microscope image of the same region. Four well-aligned MPB regions are classified by four colored polygons and lines. Each MPB elongation axis has a 12°-offset from [100] or [010] crystalline axis. The scale bars indicate 2 μm.
Reuse & Permissions
Figure 2
(a) Area-averaged Fe L-edge XAS spectra from the four electrically aligned MBP regions with a σ-polarized x-ray beam where its electric-field axis is parallel to the green MPB elongation axis. On the right side, a zoomed-in graph is shown near the $L_{2}$ edge. (b) Four XLD-PEEM images at the double-box-poled region. On the top left of each image, a relation between an incident electric-field axis and the four MPB elongation axes is displayed. Here, the definition of the image contrast is $I_{XLD − PEEM} = (I_{B} - I_{A}) / (I_{B} + I_{A})$ .
Reuse & Permissions
Figure 3
Cluster model calculations on a T-phase unit cell showing (a) XNLD and (b) XNLD+XMLD. (c,d) Experimental XLD spectra when the electric-field axis (purple-colored double arrow) of the incident x-ray beam is parallel to [100] or [010]. The experimental XLD signals are the difference between the XAS spectra of the two MPB regions. The color names (Black, Red, Green, and Blue) correspond to the four MPB regions. The zero of the vertical scale is set to the orange solid line and the other solid lines are shifted with a constant offset. (e) Schematic diagram showing the correlation between the MPB elongation axis and the AFM spin axis.
Reuse & Permissions
Figure 4
(a) Our structural model with a possible flexoelectric cation shift by −δ at MPB. (b) Calculated magnetic anisotropy as a function of δ. (c) Schematic diagram of the magnetic easy axis at and near the MPB. Local AFM spin axis at MPB (expressed by green double-headed arrows) is compelled toward the axis of strain gradient due to the asymmetry in the environment of the Fe ion thereby inducing a nonquenched orbital angular momentum. Spins in the neighboring T and S phase (blue double-headed arrows) are also aligned to the same axis through the intersite spin-spin interaction because the spins in the regions have less anisotropy within the $x y$ plane at $δ \sim 0$ .
Reuse & Permissions
Figure 5
Three orbital angular momentum components ( $〈 L_{i} 〉$ where $i = {x, y, z}$ ) as a function of the displacement δ along the $y$ axis when spins are enforced to align along (a) $\hat{α} = \hat{x}$ , (b) $\hat{α} = \hat{y}$ , and (c) $\hat{α} = \hat{z}$ . The color label for each line is defined in (a). There exists the inversion of two energy levels between $d_{3 z^{2} - r^{2}}$ -orbital-dominant level and $d_{x y}$ -orbital-dominant level at $δ \sim 0.3$ Å, making the evolution pattern of the orbital angular momentum components complex. (d) The spin component parallel to $\hat{α}$ as a function of δ under the three different directions of $\hat{α}$ . The other spin components are almost suppressed due to the large molecular exchange field. $n_{ν}^{α}$ is the occupation number of the $ν$ th eigenstate for the given molecular field direction (see the Appendix).
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics