Current-induced magnetic superstructures in exchange-spring devices

A. M. Kadigrobov, R. I. Shekhter, and M. Jonson

Phys. Rev. B 86, 014436 – Published 30 July 2012

Abstract

We investigate the potential to use a magnetothermoelectric instability that may be induced in a mesoscopic magnetic multilayer (F/f/F) to create and control magnetic superstructures. In the studied multilayer two strongly ferromagnetic layers (F) are coupled through a weakly ferromagnetic spacer (f) by an “exchange spring” with a temperature-dependent “spring constant” that can be varied by Joule heating caused by an electrical dc current. We show that in the current-in-plane configuration a distribution of the magnetization, which is homogeneous in the direction of the current flow, is unstable in the presence of an external magnetic field if the length $L$ of the sample in this direction exceeds some critical value $L_{c} \sim 10$ $μ$ m. This spatial instability results in the spontaneous formation of a moving domain of magnetization directions, the length of which can be controlled by the bias voltage in the limit $L ≫ L_{c}$ . Furthermore, we show that in such a situation the current-voltage characteristic has a plateau with hysteresis loops at its ends and demonstrate that if biased in the plateau region the studied device functions as an exponentially precise current stabilizer.

Received 14 May 2012

DOI:https://doi.org/10.1103/PhysRevB.86.014436

Authors & Affiliations

A. M. Kadigrobov^1,2, R. I. Shekhter¹, and M. Jonson^1,3,4

¹Department of Physics, University of Gothenburg, SE-412 96 Gothenburg, Sweden
²Theoretische Physik III, Ruhr-Universität Bochum, D-44801 Bochum, Germany
³SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, Scotland, UK
⁴Department of Physics, Division of Quantum Phases and Devices, Konkuk University, Seoul 143-701, Republic of Korea

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 86, Iss. 1 — 1 July 2012

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Orientation of the magnetic moments in the stack of three ferromagnetic layers discussed in the text. The magnetic moments in layers 0, 1, and 2 (whose relative magnitudes are indicated by the thickness of the short arrows) are coupled by the exchange interaction thus forming an exchange spring trilayer. An external magnetic field $H$ is directed antiparallel to the magnetization in layer 0 and a current $J$ flows in the plane of the layers (along the $x$ axis). In panel A the stack temperature $T$ is lower than the critical temperature $T_{c}^{(or)}$ for the orientational phase transition in layer 1 and hence all the magnetic moments in the stack are parallel. In panel B, where $T_{c}^{(1)} > T > T_{c}^{(or)}$ , the magnetic moments of layers 1 and 2 tilt towards the direction of the magnetic field; the angle $Θ$ between the magnetization directions in layers 0 and 2 increases with an increase of the stack temperature $T$ , approaching $Θ = π$ as $T \to T_{c}^{(1)}$ .Reuse & Permissions
Figure 2
Normalized temperature dependence of the magnetic stack resistance, $R = R [Θ (T)]$ , as determined by the $T$ dependence according to Eq. (2) of the angle $Θ (T)$ between the magnetization directions in layers 0 and 2 of Fig. 1. The calculations were made for $R_{-} / R_{+} = 0.2$ , $D_{0} = 0.2$ ; $R_{\pm} = R (π) \pm R (0)$ and $T_{c}^{(1)}$ is the Curie temperature of the spacer layer 1 between layers 0 and 2.Reuse & Permissions
Figure 3
Current-voltage characteristics (CVCs) of the magnetic stack of Fig. 1 in which the magnetization directions in the layers are homogeneously distributed along the $x$ direction (along the stack). They were calculated for $R (Θ) = R_{+} - R_{-} \cos Θ$ , $R_{-} / R_{+} = 0.2$ , $D_{0} = 0.2$ ; $J_{c} = V_{c} / R (π)$ ; $V_{c} = \sqrt{R (π) Q (T_{c}^{(1)}) / Ω_{st}}$ . The branches $0 - a$ and $b - b^{'}$ of the CVCs correspond to parallel and antiparallel orientations of the stack magnetization, respectively (the parts $a - a^{'}$ and $0 - b$ are unstable); the branch $a - b$ corresponds to $0 ⩽ Θ [T (V)] ⩽ π$ .Reuse & Permissions
Figure 4
Plots of the function $χ (T) = Q (T) / R [Θ (T)]$ and the “potential” energy $W (T, J)$ calculated for $R (Θ) = R_{+} - R_{-} \cos Θ$ , $R_{-} / R_{+} = 0.2$ , $D_{0} = 0.2$ , and $J / J_{c} = 1.03$ ; $J_{c} = V_{c} / R (π)$ ; $t_{1, 2, 3} = T_{1, 2, 3} / T_{c}^{(1)}$ .Reuse & Permissions
Figure 5
Current-voltage characteristics (CVCs) of the magnetic stack of Fig. 1 for $L ≫ L_{c}$ , i.e., when the stack contains a magnetothermoelectric domain. The CVCs were calculated for $R (Θ) = R_{+} - R_{-} \cos Θ$ , $R_{-} / R_{+} = 0.2$ , $D_{0} = 0.2$ ; $J_{c} = V_{c} / R (π)$ ; $V_{c} = \sqrt{R (π) Q (T_{c}^{(1)}) / Ω_{st}}$ . The branches $a^{'} - a$ and $b - b^{'}$ of the CVCs correspond to parallel and antiparallel orientations of the stack magnetization, respectively, while the solid branch $a - b$ corresponds to a stable magnetothermoelectric domain (MTED) spontaneously formed inside the stack. The dashed lines indicate sections where the CVCs are unstable. The red vertical arrows indicate the hysteresis loop in the CVCs caused by the disappearance and emergence of the MTED as the bias voltage is changed. The thin horizontal line shows the stabilization current $J_{0}$ .Reuse & Permissions
Figure 6
Coordinate dependence of the temperature, $T (x)$ , and the magnetization-misorientation angle, $Θ (x)$ , in a magnetic stack containing a magnetothermoelectric domain, calculated for $R (Θ) = R_{+} - R_{-} \cos Θ$ , $R_{-} / R_{+} = 0.2$ , $D_{0} = 0.2$ ; $J / J_{c} = 1.0265$ , $J_{c} = V_{c} / R (π)$ , $V_{c} = \sqrt{R (π) Q (T_{c}^{(1)}) / Ω_{st}}$ , $L_{0} = {[j_{c}^{2} ρ (π) / κ T_{c}^{(1)}]}^{(1 / 2)} \sim L_{c}$ .Reuse & Permissions

Physical Review B

covering condensed matter and materials physics