Magnetoelectric effects in single crystals of the cubic ferrimagnetic helimagnet Cu2OSeO3

Abstract

We present magnetodielectric measurements in single crystals of the cubic spin-1/2 compound Cu2OSeO3. A magnetic field-induced electric polarization (P) and a finite magnetocapacitance (MC) is observed at the onset of the magnetically ordered state (Tc = 59 K). Both P and MC are explored in considerable detail as a function of temperature (T), applied field Ha, and relative field orientations with respect to the crystallographic axes. The magnetodielectric data show a number of anomalies which signal magnetic phase transitions, and allow to map out the phase diagram of the system in the Ha-T plane. Below the 3up-1down collinear ferrimagnetic phase, we find two additional magnetic phases. We demonstrate that these are related to the field-driven evolution of a long-period helical phase, which is stabilized by the chiral Dzyalozinskii-Moriya term D M·(∇×M) that is present in this non-centrosymmetric compound. We also present a phenomenological LandauGinzburg theory for the MEH effect, which is in excellent agreement with experimental data, and shows three novel features: (i) the polarization P has a uniform as well as a long-wavelength spatial component that is given by the pitch of the magnetic helices, (ii) the uniform component of P points along the vector (, and (iii) its strength is proportional to η 2 − η 2 ⊥ /2, where η is the longitudinal and η ⊥ is the transverse (and spiraling) component of the magnetic ordering. Hence, the field dependence of P provides a clear signature of the evolution of a conical helix under a magnetic field. A similar phenomenological theory is discussed for the MC.

The quantum nature of skyrmions and half-skyrmions in Cu2OSeO3

“…In the following, we cast the theory in terms of the total magnetization per volume M(r) ¼ M sat (0)F, where M sat (0) is the magnetization density in the field-aligned, ferrimagnetic (1/2 plateau) state at T ¼ 0. At the atomic level, M sat (0) ¼ 4gm B /a 3 , where g is the electronic spectroscopic factor of the Cu 2 þ ions, while experimentally 16 , the corresponding magnetization is 0.531m B per Cu atom, which amounts to M sat (0) ¼ 111.348 kA m À 1 .…”

“…One source of K 1 comes from the magnetoelectric effect but, as shown in the Supplementary Methods (Sec. 3) based on the experimental magnetoelectric data 16 , this contribution is too small to account for the experimental data. Here, the numerical value of K 1 ( Table 4) has been adjusted to reproduce the field H c2 in the (100) field direction.…”

“…3 16 . This behaviour can be qualitatively understood by noting that the effect of K 1 sets in when the magnetization tends towards saturation, and if the exchange anisotropy A 0 is relatively much smaller (the latter has been checked independently by ab initio calculations at the atomic level).…”

“…That the value of K 1 is sizeable can be also seen by the remarkably high fields H c1 B0.02-0.035 T (ref. 16), corresponding to the helix reorientation transition from the helicoidal states or a multi-domain helix state into the conical helix state, that is, the flopping of the helix in field direction. As the ratio H c2 /H c1 is not small, also the ratio between anisotropy and DM-coupling is expected to be sizeable.…”

“…Cu 2 OSeO 3 is actually the first example of an insulating material displaying the chiral helimagnetism that is desired for skyrmion formation while sharing the non-centrosymmetric cubic space group P2 1 3 of the metallic B20 phases, but with a unit cell that is much more complex, containing 16 Cu atoms. Due to the presence of a magnetoelectric coupling 15,16 , its skyrmions can be manipulated by an electric field [17][18][19] , which is in principle very energy efficient as this avoids losses due to joule heating.…”