Initial experiments

The control of micro-/nanoscale magnetic domains has been extensively studied during the past decade. Several geometries, including thin films,^{Reference Wu, Bur, Hockel, Wong, Chung and Carman21–Reference Chung, Wang, Chen, Lin, Chu, Lin and Hung24} bars,^{Reference Chung, Keller and Carman25} ellipses,^{Reference Buzzi, Chopdekar, Hockel, Bur, Wu, Pilet, Warnicke, Carman, Heyderman and Nolting26–Reference D’Souza, Fashami, Bandyopadhyay and Atulasimha30} and rings^{Reference Hockel, Bur, Wu, Wetzlar and Carman31,Reference Sohn, Nowakowski, Liang, Hockel, Wetzlar, Keller, McLellan, Marcus, Doran, Young, Kläui, Carman, Bokor and Candler32} have been investigated. Figure 1a schematically shows an experimental thin-film setup. A magnetoelastic film is deposited on a piezoelectric substrate. Applying a voltage to the substrate strains both materials, thereby controlling the magnetization. This control method is inherently different from conventional approaches that drive currents through small wires to create a magnetic field. Applying a voltage to a piezoelectric material (i.e., dielectric capacitor) dissipates significantly less energy than driving a large current through a metal by mitigating ohmic losses and relying on strong intrinsic piezoelectric and magnetoelastic coupling.

Figure 1.

(a) Depositing a magnetoelastic film on a piezoelectric substrate enables voltage control of magnetism through strain-mediated magnetoelectric (ME) coupling. Magnetic force microscope (MFM) imaging has recorded ME control of domains in (b) thin-film, (c) single domain rod, and (d) ring geometries. In the MFM images (b–d) light regions are magnetized up and dark regions down (i.e., into and out of plane, respectively). In (b), enclosed green regions show domain walls curving, bending, branching, and elongating, respectively. The ME response in (c) (left to right) shows out-of-plane single domain rotation, and (d) (left to right) shows 90° rotation of an “onion-state” domain. Reprinted with permission from References Reference Chung, Carman and Mohanchandra23, Reference Chung, Keller and Carman25, and Reference Hockel, Bur, Wu, Wetzlar and Carman31. © 2008, 2009, and 2010 AIP Publishing. Note: ε_x and ε_y, in plane strain; H, magnetic field; K _ε, induced magnetoelastic anisotropy; V, applied voltage.

Controlling magnetism in small structures is integral to the workings of several technologies (e.g., magnetic memory), and numerous nano-/microscale studies have demonstrated the usefulness of strain-mediated ME approaches. Figure 1b shows an early observation of strain-mediated ME domain wall control.^{Reference Chung, Carman and Mohanchandra23} Magnetic force microscopy (MFM) was used to observe the evolution of magnetic stripe domains in a nickel film on a PZT substrate. Figure 1c–d shows MFM images before (left) and after (right) applying voltage for (c) a single domain rod^{Reference Chung, Keller and Carman25} and (d) ring geometry with a so-called “onion state” domain pattern.^{Reference Hockel, Bur, Wu, Wetzlar and Carman31} Voltage rotated the ring magnetization 90°, providing early evidence that strain-mediated coupling could switch between multiple states. Additionally, the size scale of these figures reveals strain-mediated control works in nanometer-sized regions. Modeling the coupled physics observed in these small elements has helped establish the key effects governing strain-mediated ME coupling, and led to strategies accurately controlling magnetic domains.

Modeling and control strategies

Micromagnetic simulations describe the evolution of magnetic domains in response to various stimuli. The dominant energies include the Zeeman (${U_{\rm{Z}}}$), magnetocrystalline (${U_{{\rm{MCA}}}}$), exchange (${U_{{\rm{Ex}}}}$), demagnetization (${U_{{\rm{Demag}}}}$), and magnetoelastic (${U_{\rm{\varepsilon }}}$) anisotropy.^{Reference Chikazumi33–Reference Liang, Keller, Sepulveda, Sun, Cui, Lynch and Carman36} The total magnetic energy density is:

(1)$$U = {U_{\rm{Z}}}\left( {{\bf{m}},{\bf{H}}} \right) + {U_{{\rm{MCA}}}}\left( {\bf{m}} \right) + {U_{{\rm{Ex}}}}\left( {\nabla {\bf{m}}} \right) + {U_{{\rm{Demag}}}}\left( {\bf{m}} \right) + {U_{\rm{\varepsilon }}}\left( {{\bf{m}},\,{\bf{\varepsilon }}} \right),$$

where ${\bf{M}}$ is the magnetization, m the magnetic unit vector, H the magnetic field, ${\bf{\varepsilon }}$ the elastic strain, and the material is assumed to be locally saturated (i.e., ${\bf{M}} = {M_s}{\bf{m}}$ and $\left| {\bf{M}} \right| = {M_s}$). The magnetoelastic anisotropy term provides the key coupling term for strain-mediated ME composites, where the strain is applied by a piezoelectric material.^{Reference Liang, Keller, Sepulveda, Bur, Sun, Wetzlar and Carman35–Reference Bur, Wu, Hockel, Hsu, Kim, Chung, Wong, Wang and Carman38} Equation 2 calculates the magnetoelastic energy density for a cubic material:

(2)$$\eqalign{ & {U_{\rm{\varepsilon }}} = {B_1}\left( {{{\rm{\varepsilon }}_{xx}}\left( {m_x^2 - {1 \over 3}} \right) + {{\rm{\varepsilon }}_{yy}}\left( {m_y^2 - {1 \over 3}} \right) + {{\rm{\varepsilon }}_{zz}}\left( {m_z^2 - {1 \over 3}} \right)} \right) + \ldots \cr & 2{B_2}({{\rm{\varepsilon }}_{xy}}{m_x}{m_y} + {{\rm{\varepsilon }}_{xz}}{m_x}{m_z} + {{\rm{\varepsilon }}_{yz}}{m_y}{m_z})\,, \cr}$$

where ${B_1}$ and ${B_2}$ are the magnetoelastic anisotropy coefficients, ${m_i}$ are the components of the magnetization unit vector, and ${{\rm{\varepsilon }}_{ij}}$ are the components of the strain tensor ($i,j = \{ x,y,z\}$).

Figure 2a–e sequentially shows the effects of several energy terms in a two-dimensional thin-film ellipse and the resulting equilibrium orientations.^{Reference Liang, Keller, Sepulveda, Sun, Cui, Lynch and Carman36} The highlighted energies are the (b) demagnetization, (c) Zeeman, and (d–e) magnetoelastic anisotropy. A key point to highlight is that the energy landscape can have more than the two energy minima shown in this simple example. The energy minima are locations where the magnetization exists in equilibrium with the surrounding fields. For example, these critical points provide the nonvolatile equilibrium states for a magnetic memory bit (i.e., the 0 and 1 states). Applying strain deforms the energy landscape and allows the magnetization to switch states.

Figure 2.

(a–e) The effects of multiple energies in a thin-film ellipse with the resulting equilibrium configurations (energy minima) highlighted by black arrows. The magnetic field and strain control local and global equilibrium orientations. Methods of applying biaxial strain include (f–g) using 011 cut Pb(Mg_1/3Nb_2/3)O₃–PbTiO₃ (PMN-PT) or (h) patterning local electrodes around magnetic elements. (f) Shows the strain along perpendicular x and y directions for electric field applied through the thickness of a PMN-PT plate. Bipolar means the electric field flips the ferroelectric polarization direction. Unipolar means the electric field never exceeds the polarization switching field. The unipolar y strain shows significant hysteresis, and insets show remanent polarization states with both in- and out-of-plane orientations existing (i.e., two stable equilibrium strain states at an electric field E = 0). (f) Rhombohedral structure of the (011) PMN-PT measured in (g), with relevant directions indicated. (h) Two pairs of electrodes (A and B) create biaxial strain ε_AA-ε_BB. The magnitude and orientation of ε_AA-ε_BB are controlled by the applied voltage. Reprinted with permission from References Reference Liang, Keller, Sepulveda, Sun, Cui, Lynch and Carman36 and Reference Wu, Zhao, Bao, Bur, Hockel, Wong, Mohanchandra, Lynch and Carman40. © 2014 and 2011 AIP Publishing. Note: ε, strain; H, magnetic field; M, magnetization; U _Demag, demagnetization energy; U _Zeeman, Zeeman energy; ${U_{\rm{\varepsilon }}}$, magnetoelastic energy; P _xy, XY polarization ; P _z, Z polarization.

One key point emerging from thin-film models and experiments is that the magnetoelastic energy predominantly relies on the biaxial strain ${{\rm{\varepsilon }}_{\rm{b}}} = {{\rm{\varepsilon }}_1} - {{\rm{\varepsilon }}_2}$, where ${{\rm{\varepsilon }}_1}$ and ${{\rm{\varepsilon }}_2}$ are the in-plane principal strains.^{Reference Bur, Wu, Hockel, Hsu, Kim, Chung, Wong, Wang and Carman38,Reference Lo Conte, Xiao, Chen, Stan, Gorchon, El-Ghazaly, Nowakowski, Sohn, Pattabi, Scholl, Tamura, Sepulveda, Carman, Candler and Bokor39} This means strategies to locally control the magnetic moment focus on controlling the biaxial strain state (e.g., applying tension in one direction and compression perpendicularly). Two primary methods of applying biaxial strains are illustrated in Figure 2f–h.

Figure 2f–g illustrates the biaxial strain generated by an 011 cut Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PMN-PT) substrate and relevant crystalline orientation. Wu et al. found giant anisotropic strain hysteresis, biaxial strains of ${\rm{\varepsilon }}_{\rm{b}} \approx 2000\,{\rm{\mu }}\varepsilon $, and multiple tunable metastable remanent strains by properly reversing the electric polarization.^{Reference Wu, Bur, Zhao, Mohanchandra, Wong, Wang, Lynch and Carman16,Reference Hsu, Hockel and Carman22,Reference Wu, Zhao, Bao, Bur, Hockel, Wong, Mohanchandra, Lynch and Carman40–Reference Wu, Bur, Wong, Zhao, Lynch, Amiri, Wang and Carman42} This approach needs only two electrodes to apply uniform biaxial strain over a large region. Several tunable ME devices have been demonstrated using this approach, such as magnetic random-access memory (MRAM),^{Reference Wu, Bur, Wong, Zhao, Lynch, Amiri, Wang and Carman42} low-power ME microwave devices,^{Reference Wu and Carman43} and tunable ME spin wave busses.^{Reference Bao, Zhu, Wong, Hockel, Lewis, Zhao, Wu, Amiri and Wang44,Reference Cherepov, Amiri, Alzate, Wong, Lewis, Upadhyaya, Nath, Bao, Bur, Wu, Carman, Khitun and Wang45}

Figure 2h illustrates the second main approach to generating biaxial strain.^{Reference Cui, Hockel, Nordeen, Pisani, Liang, Carman and Lynch46} Multiple electrodes are patterned around a magnetoelastic element, and activating one or more electrodes controls the strain state. In the figure, electrode pair A–A is activated, while pair B–B has no voltage applied. This generates a biaxial strain ${{\rm{\varepsilon }}_{{\rm{AA}}}} - {{\rm{\varepsilon }}_{{\rm{BB}}}}$ between the electrodes. In contrast to the first approach, multiple electrodes allow the biaxial strain to change directions.^{Reference Liang, Sepulveda, Hoff, Keller and Carman37} A rotating strain state allowed recent multielectrode experiments to deterministically control 180° rotations where other methods only reached 90°.^{Reference Cui, Liang, Paisley, Sepulveda, Ihlefeld, Carman and Lynch47,Reference Sohn, Liang, Nowakowski, Hwang, Han, Bokor, Carman and Candler48} This approach excels at localized control of small regions and can be used with numerous piezoelectric substrates (i.e., not constrained to using 011 PMN-PT).

Storage: Energy-efficient magnetic memory

The large coupling strength and nonvolatility make strain-mediated ME control ideal for memory applications.^{Reference D’Souza, Fashami, Bandyopadhyay and Atulasimha30,Reference Sohn, Nowakowski, Liang, Hockel, Wetzlar, Keller, McLellan, Marcus, Doran, Young, Kläui, Carman, Bokor and Candler32,Reference Lo Conte, Xiao, Chen, Stan, Gorchon, El-Ghazaly, Nowakowski, Sohn, Pattabi, Scholl, Tamura, Sepulveda, Carman, Candler and Bokor39,Reference Sohn, Liang, Nowakowski, Hwang, Han, Bokor, Carman and Candler48–Reference Wang, Li, Liang, Barra, Domann, Lynch, Sepulveda and Carman51} Figure 3a,d shows a recently proposed ME memory device and model by Wang et al., indicating ME control combined with spin orbit torque enables deterministic control of MRAM with nanosecond switching times.^{Reference Wang, Domann, Yu, Barra, Wang and Carman52} Additionally, D’Souza et al. calculated the energy to flip a single bit to be approximately 1 aJ, multiple orders of magnitude better than commercial devices.^{Reference D’Souza, Fashami, Bandyopadhyay and Atulasimha30} D’Souza explained how this could enable a device with 10⁶ bits clocked at 1 GHz to dissipate as little as 100 μW.^{Reference D’Souza, Fashami, Bandyopadhyay and Atulasimha30} Such small power requirements can be met with modern energy harvesting^{Reference Chu, Annapureddy, PourhosseiniAsl, Palneedi, Ryu and Dong53,Reference Mori and Priya54} to provide a new paradigm in autonomous electronics systems (e.g., for the Internet of Things^{Reference Leung, Or, Ho and Lee55} or implantable technologies). At a large scale, memory this efficient can cut into the 70 billion kWhr of energy used by United States data centers every year (i.e., 1.8% of the total US energy expenditure).^{Reference Shehabi, Smith, Sartor, Brown, Herrlin, Koomey, Masanet, Horner, Azevedo and Lintner56}

Figure 3.

Examples of strain-mediated magnetoelectric (ME) coupling controlling the (a) storage, (b) transmission, and (c) processing of information. Each device has the potential for order of magnitude improvements in energy efficiency or size, over current state-of-the-art technologies. (a, d) Schematic and modeled response, respectively, of ME memory. (d) Blue line indicates voltage (strain) is applied, while red line indicates relaxation after the voltage is removed. Deterministic 180° rotation is predicted (i.e., flipping a 0 to a 1). (b) Schematic of a film bulk acoustic resonator (FBAR) ME antenna. (e) Radiation efficiency for acoustically driven magnetoelastic (Metglas) and piezoelectric (PZT) antennas. These effects are combined in a ME antenna. (c) Schematic of ME spin wave bus (cell) for constructing logic gates, and (f) measured S-parameters. (c, e, f) Reprinted with permission from References Reference Cherepov, Amiri, Alzate, Wong, Lewis, Upadhyaya, Nath, Bao, Bur, Wu, Carman, Khitun and Wang45 and Reference Domann and Carman57. © 2014 and 2017 AIP publishing. (b) Reprinted with permission from Reference Reference Yao, Wang, Keller and Carman58. © 2015 IEEE. Note: WL, word line; BL, bit line; PL, plate line; I, current; λ_acoustic, acoustic wavelength; ω, angular frequency; Ant., antenna; PZT, Pb(Zr_xTi_1–x)O₃; H, magnetic field; m _x, m _y, and m _z, magnetization unit vectors in x, y, and z directions, respectively; m, magnetization unit vector; t, time.

Transmission: Miniature antennas and radio frequency devices

Several authors have proposed ME antennas to transmit and receive information.^{Reference Domann and Carman57–Reference Keller, Sepulveda and Carman63} Figure 3b shows a proposed bulk acoustic wave antenna,^{Reference Yao, Wang, Keller and Carman58} and Figure 3e shows theoretical radiation efficiency predictions.^{Reference Domann and Carman57} In addition to antennas, numerous strain-mediated radio frequency (RF) components from tunable inductors^{Reference Wu and Carman43} to filters and phase shifters^{Reference Yang, Sun, Srinivasan, Priya and Sun64,Reference Lou, Liu, Reed, Ren and Sun65} have been developed. A primary motivation for ME RF devices is to reduce the size of modern components using the ∼5 order-of-magnitude wavelength reduction when an electromagnetic wave is converted into an acoustic wave. Strong ME coupling and low loss could enable revolutionary chip-scale antennas, RF gyrators, and isolators for full-duplex radios. The latter two devices rely on controlling nonreciprocal wave propagation, so waves (i.e., information signals) traveling in opposite directions can be effectively separated from one another. In addition to size advantages, magnetic antennas are better than electric antennas for transmitting in lossy environments due to a predominantly magnetic near-field.^{Reference Manteghi and Ibraheem66} If these technologies are successful, the size of our communications technology could be reduced by several orders of magnitude and allow for transmission from challenging locations (e.g., underground, under water, or to/from implanted diagnostics and therapeutics inside the human body).

Processing: Spin wave logic devices

Spin wave logic devices (e.g., XNOR gates) are being actively developed to allow spin-based processing to replace electron-based systems.^{Reference Bao, Zhu, Wong, Hockel, Lewis, Zhao, Wu, Amiri and Wang44,Reference Cherepov, Amiri, Alzate, Wong, Lewis, Upadhyaya, Nath, Bao, Bur, Wu, Carman, Khitun and Wang45,Reference Chen, Barra, Mal, Carman and Sepulveda67–Reference Schneider, Serga, Leven, Hillebrands, Stamps and Kostylev69} Figure 3c shows a key logic gate element, an ME spin bus.^{Reference Cherepov, Amiri, Alzate, Wong, Lewis, Upadhyaya, Nath, Bao, Bur, Wu, Carman, Khitun and Wang45} A coupled acoustic-spin wave is generated by one of the electrodes on this device and propagates to a detector on the far side. The surface plots in Figure 3f show the measured S-parameters (i.e., reflection and transmission properties). Logic gates combine multiple spin buses to constructively or destructively interfere these waves. The resulting high or low signal represents the 1 or 0 state, respectively, of the gate. The main goal with spin-based logic is to move away from inefficient transistor-based devices with large standby power that consume a sizeable fraction of the total energy.^{Reference Salehi and DeMara70,Reference Nikonov and Young71} Strain-mediated ME logic gates work analogously to purely magnetic spin wave logic,^{Reference Kostylev, Serga, Schneider, Leven and Hillebrands68,Reference Schneider, Serga, Leven, Hillebrands, Stamps and Kostylev69} however they can provide better energy efficiency, and the waves travel much longer distances before appreciable energy loss occurs.^{Reference Chen, Barra, Mal, Carman and Sepulveda67} Nikonov et al. found that ME devices have roughly three orders of magnitude smaller standby power, and one to two orders of magnitude smaller active power than almost any other existing technology.^{Reference Nikonov and Young71}