Magnetic Biasing of a Ferroelectric Hysteresis Loop in a Multiferroic Orthoferrite

Y. Tokunaga, Y. Taguchi, T. Arima, and Y. Tokura

Phys. Rev. Lett. 112, 037203 – Published 23 January 2014

Abstract

In a multiferroic orthoferrite ${Dy}_{0.7} {Tb}_{0.3} {FeO}_{3}$ , which shows electric-field-( $E$ -)driven magnetization ( $M$ ) reversal due to a tight clamping between polarization ( $P$ ) and $M$ , a gigantic effect of magnetic-field ( $H$ ) biasing on $P − E$ hysteresis loops is observed in the case of rapid $E$ sweeping. The magnitude of the bias $E$ field can be controlled by varying the magnitude of $H$ , and its sign can be reversed by changing the sign of $H$ or the relative clamping direction between $P$ and $M$ . The origin of this unconventional biasing effect is ascribed to the difference in the Zeeman energy between the $+ P$ and $- P$ states coupled with the $M$ states with opposite sign.

Received 6 October 2013

DOI:https://doi.org/10.1103/PhysRevLett.112.037203

Authors & Affiliations

Y. Tokunaga¹, Y. Taguchi¹, T. Arima^1,2,3, and Y. Tokura^1,4

¹RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
²Department of Advanced Materials Science, University of Tokyo, Kashiwa 277-8561, Japan
³RIKEN SPring-8 Center, Hyogo 679-5148, Japan
⁴Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Tokyo 113-8656, Japan

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Vol. 112, Iss. 3 — 24 January 2014

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Figure 1
(a) Relation among energetically stable domain states and domain walls that can be driven by the $E$ field is displayed in the $P − M − M^{'}$ order-parameter phase space of ${D y}_{0.7} {Tb}_{0.3} {FeO}_{3}$ for $H = 0$ . Each corner of cube corresponds to the $+$ or $-$ state of the corresponding order parameter. Only four states out of eight (as presented with closed circles) are stable due to the trilinear-type interaction energy among $P$ , $M$ , and $M^{'}$ (see text). FEDW and MFDW denote ferroelectric and multiferroic domain walls, respectively. Green (red) arrow indicates the $P$ -reversal process for a slow (rapid) $E$ scan whose frequency is larger (smaller) than those indicated with yellow in panel (b). (b) Electric-pulse width dependence of $M$ and the $M$ -reversal ratio in ${D y}_{0.7} {Tb}_{0.3} {FeO}_{3}$ at 2.5 K. ( $P +$ , $M +$ , $M^{'} +$ ) initial state is prepared, and a triangle-shaped single $E$ pulse with the peak height of $E_{peak} = - 69.4 kV / cm$ and temporal width of $τ$ was applied. After the application of the pulse, magnetization was measured (reproduced from Ref [8]).
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Figure 2
(a) $P − E$ loops measured at $f = 0.1 Hz$ (slow scan) at 2.5 K. Dotted (solid) line corresponds to the loop measured in $H = + 500 Oe$ (0 Oe). $P − E$ loops measured at $f = 100 Hz$ (rapid scan) in (b) $H = - 500$ , (c) $H = 0$ , and (d) $H = + 500 Oe$ , respectively. Vertical dashed lines indicate the center of the hysteresis loop, which corresponds to the bias field $Δ E$ . (e) Schematic of $P$ -reversal paths for slow $E$ scan ( $f = 0.1 Hz$ ) in the presence of $H (> 0)$ . Filled (open) circles represent states with lower (higher) energy due to Zeeman energy induced by $H (> 0)$ along the $c$ axis. $P$ reversal occurs through the nucleation and propagation of FEDW without changing the sign of $M$ . (f),(g) Schematic paths of $P$ reversal for rapid $E$ scan ( $f = 100 Hz$ ) in a (f) negative and (g) positive $H$ field. $P$ reversal occurs through the MFDW without changing the sign of $M^{'}$ . Filled (open) circles represent states with lower (higher) energy by an amount of $2 U_{c} \equiv 2 M H$ due to the Zeeman energy. Free energy with double minimum show asymmetric deformation that depends on this Zeeman energy at $E = 0$ (blue solid curves). The energy difference $2 U_{c}$ is totally compensated when $E = Δ E$ is applied (red dashed curves).
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Figure 3
(a)–(d) $P − E$ loops measured in $H = 0$ , +1, +2, and +3 kOe, respectively, at $T = 2 K$ and at $f = 100 Hz$ (rapid scan). Each loop was measured after preparing an initial state of ( $P +$ , $M +$ , $M^{'} +$ ) by an ME poling. Dotted lines indicate center of the hysteresis loop, corresponding to bias field $Δ E$ . (e) $M − H$ loop measured after zero-field cooling at 2 (blue line) and 2.5 K (red line). Dotted lines correspond to initial curves. (f) Comparison between $| P Δ E |$ and $M H$ obtained from $P − E$ loops and $M − H$ curves (filled symbols). $Δ E$ , $P$ , $M$ values are the bias $E$ field at $H$ , saturation value of polarization, and weak-ferromagnetic moment at each temperature. The dotted line represents the relation that $| P Δ E | = M H$ .
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Figure 4
(a)–(e) Isothermal electric switching of the sign of bias field under a fixed $H (= + 500 Oe)$ at 2.5 K. An initial state ( $P +$ , $M +$ , $M^{'} +$ ) is prepared by an ME poling, and (a) a full $P − E$ loop is driven at 100 Hz. Then, (b) half a loop is driven at 0.1 Hz. Next, (c) a full $P − E$ loop is driven at 100 Hz. Then, (d) half a loop is driven at 0.1 Hz again. After this, (e) a $P − E$ loop is driven again at 100 Hz. In (a)–(e), open circles indicate starting points of each $P − E$ loop. (f) $P$ -reversal paths in $P − M − M^{'}$ phase space at 100 and 0.1 Hz in a positive $H$ . I–V correspond to each process appearing in (a)–(e). Closed (open) circles indicate states with lower (higher) energy.
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