Erratum: Electric Control of Spin Helicity in a Magnetic Ferroelectric [Phys. Rev. Lett.98, 147204 (2007)]

Abstract

Magnetic ferroelectrics or multiferroics, which are currently extensively explored, may provide a good arena to realize a novel magnetoelectric function. Here we demonstrate the genuine electric control of the spiral magnetic structure in one of such magnetic ferroelectrics, TbMnO3. A spinpolarized neutron scattering experiment clearly shows that the spin helicity, clockwise or counterclockwise, is controlled by the direction of spontaneous polarization and hence by the polarity of the small cooling electric field.Electric control of magnetic spins or their ordering structure has long been a big challenge in condensed matter physics. Furthermore, manipulating the magnetization by electric field may provide a low energy-consuming way in spin-electronics and a higher data density in information storages [1,2]. There are a number of magnetoelectric materials whose magnetization can be changed, though minutely, with an external electric field, yet only a very few are known whose magnetic structure itself can be controlled by an electric field [1,3,4,5]. The use of ferroelectricity is perhaps indispensable to enhance the electric field action on the magnetic spins. [2] One of the robust mechanisms to produce the ferroelectricicty of magnetic origin has been recently proposed by Katsura, Nagaosa, and Balatsky (KNB) [6]. The overlap of the electronic wave function between the two atomic sites (i and i + 1) with mutually canted spins (S i and S i+1 ) can generate electric polarization,, where e i,i+1 denotes the unit vector connecting the two sites and A is a constant determined by the spin exchange interaction and the spin-orbit interaction. (Note that the similar theoretical results have been obtained independently also in refs. [7,8]). In case the transverse-spiral (cycloidal) spin order is realized ( Fig. 1(b)), the uniform spontaneous polarization is expected to emerge as the sum of the local polarization p i in the direction perpendicular to the spiral propagation vector and the vector chirality,). This spin-driven ferroelectricity has recently been found in several transversespiral magnets such as TbMnO 3 (ref.[9]), Ni 3 V 2 O 8 (ref.[10]), MnWO 4 (ref.[11]), and also in a transverse conespiral magnet CoCr 2 O 4 (ref.[12]). We report here the quantitative elucidation of such magnetically induced ferroelectricity in terms of the spin ellipticity as the order parameter and show the successful electric control between the clockwise (CW) and counter-clockwise (CCW) spin helixes.A family of perovskite manganites, RMnO 3 with R being Tb, Dy, and their solid solution, have recently been demonstrated to undergo a ferroelectric transition at the Curie temperature T C of 20 − 30 K (see the example shown in Fig. 1(c)) [13,14]. Below T N ∼ 40 K, the compounds undergo a long-range spin ordering with the modulation vector Q s = (0, ±q, 1) with q = 1/2 − 1/4 (in P bnm orthorhombic setting) [9,15]. This has been ascribed to the spin frustration effect caused by the combination of GdFeO 3 -type distortion and staggered orbital or...

Polarized neutron diffraction

“…The ferroelectricity in this compound is also of magnetic origin and emerges from a cycloidal spin order, just as in the case of Ni 3 V 2 O 8 . The same questions, that is to know whether the spin helicity was connected to the direction of the spontaneous polarization, and if it was possible to control this sense by an electric field was answered by a slightly different polarized neutron experiment [33]. The authors have investigated this helicity in a simpler setup, using incoming polarized neutrons without subsequent polarization analysis (often called half-polarized experiment in the literature), in a geometry where P i Q.…”

Spin-orbit qubit on a multiferroic insulator in a superconducting resonator

“…1(a)] due to the magnetoelectric coupling. 33 The strength of the exchange coupling J (we assume J > 0) between the electron spin and the magnetic moments, depending on their distance and the specific hosts, is weak and assumed to be of the order of 1-10 µeV. 20,23 Due to the spiral geometry of the magnetic order, the macroscopic magnetism of the multiferroic insulator is zero, while the exchange coupling still breaks the time-reversal symmetry locally and causes an inhomogeneous Zeeman-like interaction on the quantum-dot spin.…”

“…Different from previous studies, 15,[19][20][21][22][23][24][25] our proposal relies on the inhomogeneous exchange field arising from the multiferroic insulators with a cycloidal spiral magnetic order. [31][32][33][34][35][36] These multiferroic insulators provide a unique opportunity for the design of functional devices owing to the cycloidal spiral magnetic order as well as the magnetoelectric coupling. [36][37][38] In our setup for the spin-orbit qubit, as illustrated in Fig.…”

Helical multiferroics for electric field controlled quantum information processing

“…The underlying physics is governed by competing exchange and Dzyaloshiskii-Moriya (DM) [33] interactions: The spin-orbital coupling associated with d(p) orbitals of magnetic (oxygen) ions triggers the FE polarization [34,35] P ∝ê ij × (S i × S j ); e ij is a unit vector connecting the sites i and j at which the effective spins S i/j reside (e.g., along the [110] direction for TbMnO 3 ). P is thus linked with the spin order chirality κ = (S i × S j ), offering thus a tool for electrical control of κ because, as shown experimentally [36], P can be steered with an external electric field E (with |E| ∼ 1 kV/cm). Indeed, effects of magnetoelectric coupling (ME) are evident in the dynamical response to moderate E [37][38][39][40][41][42], i.e., phenomena rooted in ME can be driven, and possibly controlled, by moderate external fields.…”