# Can We Still Find an Ideal Memristor?

## Abstract

**:**

## 1. Introduction

## 2. Magnetic Lump with Flux–Charge Interaction

## 3. LLG Model of Magnetic Flux Reversal

_{Z}is the component of the saturation magnetization M

_{S}in the Z axis, and a magnetic field H is applied along Z. The model is expressed as below:

_{W}is a switching coefficient, and C is a constant of integration such that $C={tanh}^{-1}{m}_{0}$ (m

_{0}is the initial value of m) if q(t = 0) = 0 (no accumulation of charge at any point).

_{0}is the permeability of free space and S is the cross-sectional area.

_{0}= −0.964 (such a value reflects the intrinsic fluctuation; otherwise,

**M**will stick to the stable equilibriums ${m}_{0}=\pm 1$).

## 4. Parasitic Inductance and Stepwise Memristance

## 5. Conclusions and Arguments

- The aforementioned memristive fingerprint hides behind a superficial inductor effect due to its inductor-like structure. It was necessary to apply a constant input current (such as a step-function or a sequence of square-wave pulses) to depress the inductor effect ($\because v=L\frac{di}{dt}=0$). Despite the existence of parasitic inductance, the structure displays memristivity; similarly, a real-world resistor is still thought to be a resistor despite the existence of an (inevitable) parasitic inductance and/or capacitance. Most importantly, the structure exhibits that its charge–flux interaction is memristive by nature.
- The structure is bistable and dynamically sweeps a continuous range of resistances. This “dynamical continuity” results from the uniaxial magnetic anisotropy of the prototype, which contains magnetic material with only one easy axis. A fully functioning ideal memristor should have multiple or an infinite number of stable states so its static memristance can be “frozen” at any intermediate point in time.

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Conformal differential transformation is similar to 3D object projection in terms of projecting something from a “high-dimensionality” space into a “low-dimensionality” space.

**Figure 2.**No hysteresis can be seen in the v-i curve for an ideal memristor with an odd-symmetric φ-q curve.

**Figure 3.**

**A nonideal memristor even has a pinched v-i hysteresis loop.**This memristor has two φ-q characteristic branches, each of which is chosen depending on the polarity of the input current. Some practical devices exhibit such q–φ curves [6].

**Figure 4.**

**The flux–charge interaction in a structure with a magnetic lump and a current-carrying conductor.**The Oersted field generated by the current i rotates or switches the magnetization

**M**inside the magnetic lump, and consequently, the switched magnetic flux φ induces a voltage v across the conductor, resulting in a changed (equivalent) memristance. The LLG model of flux reversal is also shown. If the magnetic field H

_{eff}is applied in direction Z, the saturation magnetization vector

**M**(t) follows a precession trajectory from its initial position (${m}_{0}\approx -1$) until ($m\approx 1$), i.e., the magnetization

**M(t)**reverses itself and is eventually aligned with the magnetic field H

_{eff}.

**Figure 5.**Intuitively, the S-shaped φ-q curve (Equation (4)) of this structure vividly depicts the self-limiting charge–flux interaction in a circuit element. It complies with the three new criteria for the ideal memristor [1,6]: a. nonlinear; b. continuously differentiable; c. strictly monotonically increasing.

**Figure 6.**Induced voltage vs. a step-function input current. The higher the amplitude of the current I, the shorter the switching time t

_{s}.

**Figure 8.**Cubic anisotropy energy surfaces. The magnetic moment in cobalt has a dependence of energy level towards one particular direction (the easy axis); then, it has uniaxial anisotropy. The biases in iron (

**left**) and nickel (

**right**) are toward many particular directions; then, they have multiple easy axes and possess cubic anisotropy [27].

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**MDPI and ACS Style**

Wang, F.Z.
Can We Still Find an Ideal Memristor? *Magnetism* **2024**, *4*, 200-208.
https://doi.org/10.3390/magnetism4030014

**AMA Style**

Wang FZ.
Can We Still Find an Ideal Memristor? *Magnetism*. 2024; 4(3):200-208.
https://doi.org/10.3390/magnetism4030014

**Chicago/Turabian Style**

Wang, Frank Zhigang.
2024. "Can We Still Find an Ideal Memristor?" *Magnetism* 4, no. 3: 200-208.
https://doi.org/10.3390/magnetism4030014