Non-equilibrium states of current-driven phonons and frustrated magnetic systems at nanoscale Open Access
Chen, Guanxiong (Fall 2021)
Abstract
This dissertation includes a variety of research projects focusing on nonequilibrium phenomena at the nanoscale. To be specific, two main systems are investigated. The first one is the highly nonthermal phonon system in current driven nanostructures. Our research demonstrates that at cryogenic temperature the current-driven phonon distribution in a variety of metallic microstructures is qualitatively different from that expected for Joule heating, as manifested by a weakly-singular linear dependence of resistance on current. In other words, the phonons generated by electron scattering events are far from equilibrium and may not be adequately described by a temperature as implied by the Joule's heating law. Our result suggests the possibility of further optimum of thermal dissipation in nanodevices beyond the limits set by the Joule heating law. As a follow up, we perform nonlocal electronic measurements utilizing an electrically biased metallic nanowire as a phonon source, and a separate nanowire serving as the phonon detector, to investigate the thermalization process of the nonequilibrium phonons. Analysis of the dependence on the thickness of the spacer separating the nanowires shows that these non-equilibrium phonons relax via strongly anharmonic processes that cannot be described in terms of the usual few-phonon scattering. Our findings provide insight into the mechanisms of current-driven phonon generation, transport, and relaxation at nanoscale in a vertically stacked device, which will likely facilitate new approaches to efficient Joule heat dissipation in 3D integrated circuits (IC).
The second system is ferromagnet /antiferromagnet (F/AF) structure experiencing random interfacial coupling. Here, we utilize magnetoelectronic measurements to analyze the effective exchange fields at permalloy/CoO interface. Our results cannot be explained in terms of quasi-uniform effective exchange fields but are in agreement with the random-field hypothesis of Malozemoff[Phys. Rev. B 35, 3679 (1987)]. The approach developed here also opens a new route for the quantitative analysis of effective exchange fields and anisotropies in magnetic heterostructures for memory, sensing and computing applications. For example, we demonstrate that ideal memristors—devices whose resistance is proportional to the charge that flows through them—can be realized using spin torque-driven viscous magnetization dynamics. The latter can be accomplished in the spin liquid state of thin-film F/AF heterostructures with frustrated exchange, where the memristive response is tunable by proximity to the glass transition, while current-induced Joule heating facilitates non-volatile operation and second-order memristive functionality beneficial for neuromorphic applications.
Table of Contents
1 Introduction 1
1.1 Phonon and lattice vibration . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Phonon modes in 1D spring chain . . . . . . . . . . . . . . . . . . . . 4
1.3 Dispersion of 1D chain . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 How do phonons propagate: ballistically or diffusively? . . . . . . . . 8
1.5 Magnetic order of materials . . . . . . . . . . . . . . . . . . . . . . . 10
1.6 Magnetic texture in ferromagnetic material . . . . . . . . . . . . . . . 13
1.7 Imaging techniques of magnetic texture . . . . . . . . . . . . . . . . 17
1.8 Anisotropic magnetoresistance . . . . . . . . . . . . . . . . . . . . . . 17
1.9 Giant magnetoresistance . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.10 Landau–Lifshitz–Gilbert (LLG) equation and magnetic dynamics . . 19
1.11 What is memristor? . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Nonequilibrium phonon distribution in current-driven nano- and
micro-structures 24
2.1 Joule’s heating and diffusive heat transfer . . . . . . . . . . . . . . . 24
2.2 Experimental approach . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.3 Breakdown of Joule’s heating at cryogenic temperature . . . . . . . . 28
2.4 Dependence of R(I) on temperature . . . . . . . . . . . . . . . . . . . 31
2.5 Dissipation channels of the nonequilibrium
phonons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.6 Mechanics of the breakdown of Joule’s heating . . . . . . . . . . . . . 37
2.7 Generality of the observation: the linear R(I) in Au wire . . . . . . . 40
2.8 Dependence on the substrate type . . . . . . . . . . . . . . . . . . . . 43
2.9 Dependence on the wire thickness for Pt on sapphire . . . . . . . . . 45
2.10 Dependence of resistance on current in a resistive nanocontact . . . . 46
2.11 COMSOL simulation of Joule heating . . . . . . . . . . . . . . . . . . 48
2.12 Estimation of phonon escape time from the acoustic mismatch . . . . 50
2.13 Estimation of phonon scattering time . . . . . . . . . . . . . . . . . . 52
2.14 Nonlinear dependence of resistance on large driving current . . . . . . 53
2.15 Estimation of electron-phonon scattering cross-section . . . . . . . . . 55
3 Transport and relaxation of current-generated nonequilibrium phonons
from nonlocal electronic measurements 57
3.1 Motivation: the propagation and decay of the nonequilibrium phonons 57
3.2 Experimental setup for nonlocal measurement . . . . . . . . . . . . . 58
3.3 Room temperature result . . . . . . . . . . . . . . . . . . . . . . . . . 59
3.4 Low temperature result . . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.5 Dependence on spacer thickness . . . . . . . . . . . . . . . . . . . . . . 62
3.6 Model for the thermalization of nonequilibrium phonons . . . . . . . 64
3.7 The mechanisms of secondary phonon generation . . . . . . . . . . . 65
3.8 Phonon transport and relaxation in a crystalline MgO spacer . . . . . 68
3.9 Dependence on experimental temperature . . . . . . . . . . . . . . . 70
3.10 COMSOL simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
4 Experimental demonstration and analysis of random field effects in
ferromagnet/antiferromagnet bilayers 76
4.1 Ferro-/Antiferromagnetic heterostructure . . . . . . . . . . . . . . . 76
4.2 Our approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3 Experiment setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 2d xy model of uncorrelated random field effects . . . . . . . . . . . . 88
4.5 Simulations of uncorrelated random field effects . . . . . . . . . . . . 91
4.6 Analysis of experimental results . . . . . . . . . . . . . . . . . . . . . 95
5 Ideal memristor based on viscous magnetization dynamics driven by
spin torque 100
5.1 Memristor: an electronic neuron . . . . . . . . . . . . . . . . . . . . . 100
5.2 Ideal memristor in magnetic system . . . . . . . . . . . . . . . . . . . 101
5.3 Memristive functionality of the proposed device . . . . . . . . . . . . 102
5.4 The influence of shape anisotropy . . . . . . . . . . . . . . . . . . . . 106
5.5 Neuromorphic functionality of the device:
STDP of non-overlapping pulses . . . . . . . . . . . . . . . . . . . . 108
6 Summary 112
Bibliography 117
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