# Calculation of energy-barrier lowering by incoherent switching in spin-transfer torque magnetoresistive random-access memory

## Abstract

To make a useful spin-transfer torque magnetoresistive random-access memory (STT-MRAM) device, it is necessary to be able to calculate switching rates, which determine the error rates of the device. In a single-macrospin model, one can use a Fokker-Planck equation to obtain a low-current thermally activated rate ∝exp(−E{sub eff}/k{sub B}T). Here, the effective energy barrier E{sub eff} scales with the single-macrospin energy barrier KV, where K is the effective anisotropy energy density and V the volume. A long-standing paradox in this field is that the actual energy barrier appears to be much smaller than this. It has been suggested that incoherent motions may lower the barrier, but this has proved difficult to quantify. In the present paper, we show that the coherent precession has a magnetostatic instability, which allows quantitative estimation of the energy barrier and may resolve the paradox.

- Authors:

- Center for Materials for Information Technology, University of Alabama, Tuscaloosa, Alabama 35401 (United States)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22409971

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Applied Physics

- Additional Journal Information:
- Journal Volume: 117; Journal Issue: 17; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; ENERGY DENSITY; ERRORS; FOKKER-PLANCK EQUATION; MAGNETORESISTANCE; MATHEMATICAL MODELS; PRECESSION; RANDOMNESS; SPIN; TORQUE

### Citation Formats

```
Munira, Kamaram, Visscher, P. B., E-mail: visscher@ua.edu, and Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35401.
```*Calculation of energy-barrier lowering by incoherent switching in spin-transfer torque magnetoresistive random-access memory*. United States: N. p., 2015.
Web. doi:10.1063/1.4908153.

```
Munira, Kamaram, Visscher, P. B., E-mail: visscher@ua.edu, & Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35401.
```*Calculation of energy-barrier lowering by incoherent switching in spin-transfer torque magnetoresistive random-access memory*. United States. doi:10.1063/1.4908153.

```
Munira, Kamaram, Visscher, P. B., E-mail: visscher@ua.edu, and Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35401. Thu .
"Calculation of energy-barrier lowering by incoherent switching in spin-transfer torque magnetoresistive random-access memory". United States. doi:10.1063/1.4908153.
```

```
@article{osti_22409971,
```

title = {Calculation of energy-barrier lowering by incoherent switching in spin-transfer torque magnetoresistive random-access memory},

author = {Munira, Kamaram and Visscher, P. B., E-mail: visscher@ua.edu and Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35401},

abstractNote = {To make a useful spin-transfer torque magnetoresistive random-access memory (STT-MRAM) device, it is necessary to be able to calculate switching rates, which determine the error rates of the device. In a single-macrospin model, one can use a Fokker-Planck equation to obtain a low-current thermally activated rate ∝exp(−E{sub eff}/k{sub B}T). Here, the effective energy barrier E{sub eff} scales with the single-macrospin energy barrier KV, where K is the effective anisotropy energy density and V the volume. A long-standing paradox in this field is that the actual energy barrier appears to be much smaller than this. It has been suggested that incoherent motions may lower the barrier, but this has proved difficult to quantify. In the present paper, we show that the coherent precession has a magnetostatic instability, which allows quantitative estimation of the energy barrier and may resolve the paradox.},

doi = {10.1063/1.4908153},

journal = {Journal of Applied Physics},

issn = {0021-8979},

number = 17,

volume = 117,

place = {United States},

year = {2015},

month = {5}

}