20 IEEE ELECTRON DEVICE LETTERS, VOL. 31, NO. 1, JANUARY 2010

Spintronic Memristor Temperature SensorXiaobin Wang, Member, IEEE, Yiran Chen, Member, IEEE, Ying Gu, and Hai Li, Member, IEEE

Abstract—Thermal fluctuation effects on the electric behaviorof a spintronic memristor based upon the spin-torque-induceddomain-wall motion are explored. Depending upon material,geometry, and electric excitation strength, the device electric be-havior can be either sensitive or insensitive to temperature change.We present temperature sensor designs that operate at a temper-ature sensitive region. The sensitivity is achieved through a com-bination of the temperature-dependent domain-wall mobility andthe positive feedback between memristor resistance and drivingstrength.

Index Terms—Domain wall, spintronic memristor, temperaturesensor, thermal fluctuations.

I. INTRODUCTION

THE MEMRISTOR concept [1] recently received signif-icant attention due to the demonstration of a practical

nanoscale memristor device based upon ionic transport in aresistive memory stack [2]. Nanoscale spintronic memristor hasbeen proposed based upon spin-torque-induced magnetizationmotion [3] and spin transport at semiconductor/ferromagnetjunction [4].

Thermal fluctuation at finite temperature has important im-plications to nanoscale magnetic devices [5], [6]. In this letter,we propose a spintronic memristor temperature sensor explor-ing thermal fluctuation effects on domain-wall motion in a spin-valve structure.

II. DEVICE THEORY

The spin-valve domain-wall memristor structure is shown inFig. 1. The spintronic memristor consists of a long spin-valvestrip which includes two ferromagnetic layers: reference andfree layers. The magnetization direction of the reference layeris fixed by coupling to a pinned magnetic layer. The free layer isdivided by a domain wall into two segments that have oppositemagnetization directions to each other. The device time domainresistance depends upon domain-wall position

R(t) = RH − (RH − RL)X(t)/D (1)

Manuscript received October 9, 2009. First published December 1, 2009;current version published December 23, 2009.

X. Wang and Y. Chen are with Seagate Technology, Bloomington, MN 55435USA (e-mail: xiaobin.wang@ieee.org; yiran.chen@ieee.org).

Y. Gu is with the St. Cloud State University, St. Cloud, MN 56301 USA(e-mail: guyingw@yahoo.com).

H. Li is with the Department of Electrical and Computer Engineering,Polytechnic Institute of New York University, Brooklyn, NY 11201 USA (e-mail: hli@poly.edu).

Color versions of one or more of the figures in this letter are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LED.2009.2035643

Fig. 1. Spin-valve magnetic domain-wall memristor.

where RH and RL are the high and low resistances of the spinvalve. D is the spin-valve length, and X is the domain-wallposition.

Domain-wall position is moved through current-induced spintorque excitation. For a ferromagnet with magnetization satura-tion Ms, exchange strength A, easy z-axis anisotropy Hk, andhard y-axis anisotropy Hp, the spin-torque-induced domain-wall motion at finite temperature is described through stochasticLandau–Lifshitz–Gilbert equation [7] with a spin torque term[8], [9]. Using rigid wall approximation [10], [11], the domain-wall motion is expressed in terms of magnetization sphericalangles Ms(sin θ cos φ, sin θ sinφ, cos θ) as

θ(x, t) = θ0 (x − X(t)) φ(x, t) = φ0(t)

where θ0(x) = arccos[tanh(x/w)] is the function of thedomain-wall shape. w =

√2A/MsHk is the domain-wall

thickness. X(t) is the domain-wall position. Domain-wallspeed is dX(t)/dt. The domain-wall position X(t) satisfies thefollowing stochastic differential equations [10], [11]:

dφ

dt+

α

w

dX

dt= ηφ

1w

dX

dt− α

dφ

dt= ω0 sin(2φ) +

vs

w+ ηX (2)

where ω0 = γHp/2 (γ being the gyro-magnetic ratio), α is thedamping parameter, and vs = PJuB/eMs is the spin torqueexcitation strength. P is the polarization efficiency, uB is theBohr magneton, and e is the elementary electron charge. ηφ(t)and ηX(t) are the φ and X component thermal fluctuation

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WANG et al.: SPINTRONIC MEMRISTOR TEMPERATURE SENSOR 21

fields, respectively. Their magnitudes are determined throughthe fluctuation dissipation condition

〈ηφ(t)ηφ(t′)〉 = 〈ηX(t)ηX(t′)〉 =2αkBT

�Nδ(t − t′) (3)

where kB is the Boltzman constant, T is the temperature, � isthe Planck constant, and N = 2wS/a3 is the number of spinsin the domain wall with the cross-sectional surface area S anddomain-wall thickness w. a is the lattice constant.

III. DEVICE SCALING BEHAVIOR

Domain-wall mobility at finite temperature depends uponboth spin torque excitation strength and thermal fluctuationmagnitude. Equation (2) predicts that the domain-wall velocityis a function of the normalized spin torque excitation strengthand the normalized thermal fluctuation magnitude.

Spin torque excitation strength is proportional to cur-rent density. The normalized current density is defined asPJuB/eMswω0. At zero temperature, the domain wall startsto move only when the current density is above the crit-ical value, PJuB/eMswω0 = 1. At finite temperature, thedomain wall can move even when current density is belowthe critical value. The average domain-wall velocity (normal-ized by vs) as a function of the normalized current density(PJuB/eMswω0) and the normalized thermal fluctuationmagnitude (4kBT/N�ω0) can be obtained by solving the sto-chastic differential equation (2). Detailed mathematical tech-niques can be referred to [12]. Fig. 2 shows the normalizeddomain-wall velocity as a function of the normalized currentdensity for different normalized thermal fluctuation magni-tudes. Temperature sensitive and insensitive regions can beobserved. Curves with kneeling shapes are around the criticalcurrent density, where the domain-wall velocity is sensitive tothermal fluctuation magnitude.

The spin-valve low and high resistances scale as RL/Rh0 =[D/Z(h/h0)] and RH = RL(1 + GMR)RL, where Rh0 is thesheet film resistance with a thickness h0, giant magnetoresis-tance ratio (GMR) is the magnetoresistance ratio, and D, Z,and h are the ferromagnet length, width, and thickness.

IV. DEVICE OPERATION PRINCIPLE AND EXAMPLE

For temperature sensing, a biasing voltage pulse with con-stant magnitude is applied to the spintronic memristor. Resis-tance difference before and after voltage pulse is measured.This resistance difference is calibrated to the sense temperaturemagnitude. Fig. 2 shows that domain-wall mobility increases astemperature increases. Equation (1) shows that memristor resis-tance dropping is proportional to domain-wall moving distance.Thus, after applying a constant magnitude voltage pulse, deviceresistance dropping is bigger at a higher temperature.

The temperature sensing memristor is operated at a re-gion where its electric behavior is sensitive to temperaturechange. This is achieved through a combination of temperature-dependent domain-wall mobility and the positive feedbackbetween resistance and driving strength in memristor. Fig. 2shows the sensitive dependence of domain-wall velocity upontemperature at kneeling region around the critical current value.

Fig. 2. Average domain-wall velocity as a function of the normalized currentdensity for different thermal fluctuation strengths. (a) and (b) are the same figureplotted at different normalized current density scales.

The positive feedback between resistance and driving strengthis a unique property of the memristor. Memristor’s resistancedepends upon the integration of current/voltage excitation.For a constant voltage pulse driving, a higher temperatureresults to an increased domain-wall moving distance. Theincreased domain-wall moving distance results to a smallerresistance. The smaller resistance results to a higher drivingcurrent density, thus providing a positive feedback to furtherincrease domain-wall distance. This positive feedback acceler-ates domain-wall speed and reduces device resistance furtherfor constant voltage pulse driving.

We illustrate the temperature sensing working principlethrough a practical device design example. The materialproperties of the device are magnetization saturation Ms =1010 emu/cc, exchange strength A = 1.8 · 10−11 J/m, easyz-axis anisotropy Hk = 100 Oe, and hard y-axis anisotropyHp = 5000 Oe. The resistance of the sheet film is 50 Ω for a70-A thickness square thin film, and GMR is 12%. The geome-try of the device is 268 nm long, 17 nm wide, and 10 nm thick.The damping parameter is α = 0.02, and polarization efficiencyis P = 0.3. The number of spins in the domain wall is N =2.2 · 107. Using the aforementioned parameters, for Fig. 2,the normalized thermal magnitude is 4kBT/N�ω0 = 0.008 atroom temperature T = 300 K. The critical current density is

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22 IEEE ELECTRON DEVICE LETTERS, VOL. 31, NO. 1, JANUARY 2010

Fig. 3. Spintronic memristor resistance as a function of time at differenttemperatures (300, 350, and 400 K) for a constant magnitude voltage pulsedriving.

Jsc = eMswω0/PuB = 3 · 108 A/cm2. The normalized veloc-ity is PJscuB/eMs = 52 m/s at critical current density.

We use a single square wave pulse with a duration of 80 nsand a magnitude of 0.3 V to excite the device. Fig. 3 shows thedevice resistance dropping as a function of time for differenttemperatures (300, 350, and 400 K). Device resistance eventu-ally flattens out when domain wall settles to a fixed positionafter voltage pulse excitation. Solid curves on the figure arethe resistance changes for the proposed spintronic memristor atdifferent temperatures. Dash lines are the resistance droppingfor a nonmemristive device without positive feedback betweenthe resistance and the integration of the driving strength. Thedash lines are equivalent to the simulations with fixed drivingcurrent strength of 0.3 V/RHS. It can be seen that a positivefeedback between resistance and driving strength in memristorsignificantly increases the temperature sensing margin.

The material of our proposed spintronic memristor tempera-ture sensor is similar to the commercial recording head mater-ial. However, we believe that our proposed device structure isnovel: we are not aware of any applications of domain-wall mo-tion in a spin-valve strip structure in any practical devices. Thepositive feedback between domain-wall motion and accumu-lated resistance change is the key ingredient for this memristivedevice. The sensing temperature range of our proposed deviceis from 300 to 400 K, which covers the normal operation rangeof semiconductor chip. The required power supply voltage is0.3 V, with a typical power consumption of 150 μW. The linear-ity is 0.5 Ω/◦, and the surface area is 300 nm × 20 nm. Becausethe working principle of the device is based upon integrationof domain-wall motion under thermal fluctuation, the intrinsicrandom noise variations are averaged and suppressed. The de-vice provides reproducible temperature readings. Compared tothe available on-chip temperature sensors, our device requires

much lower power supply voltage (which can be even usedin the subthreshold voltage region) and power consumption(compared to some on-chip oscillation-ring-based temperaturesensor that consumes huge dynamic power), nanoscale featuresize, low cost, and the mature integration technology with theCMOS process. Please note that our device is targeting thehighly integrated on-chip thermal detection applications (e.g.,cell size < 1 μm2). Therefore, it may not be fair to compare ourdevice to any standalone or bulk thermal sensors.

We note that our main contribution in this letter is to demon-strate the theory and feasibility of a temperature sensor basedon the domain-wall motion in magnetic strip in a spin-valvestructure. The operating range and device properties can befurther tuned according to practical needs and material capabil-ities (e.g., the thermal effects in the device scale as temperatureover domain-wall thickness, as shown in Section III). Varyingdomain-wall thickness through the tuning magnetic mater-ial properties could change the device temperature operatingrange. Linearity or resolution of the device can be improvedby utilizing the magnetic stack with high GMR or even thetunneling magnetoresistance ratio stack. Also, it is well knownthat memristor has a rich dynamic behavior when excited witha dynamic current/voltage profile. Thus, device behavior canbe further optimized by examining the combined effects ofcurrent/voltage excitation and domain-wall motion.

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