Disorder effects on the metastability of classical Heisenberg ferromagnets Moumita Naskar1Muktish Acharyya1Erol Vatansever2 3and Nikolaos G. Fytas3

2025-04-24 0 0 672.09KB 18 页 10玖币

侵权投诉

Disorder eﬀects on the metastability of classical Heisenberg

ferromagnets

Moumita Naskar,1Muktish Acharyya,1, ∗Erol Vatansever,2, 3 and Nikolaos G. Fytas3, †

1Department of Physics, Presidency University,

86/1 College Street, Kolkata-700073, India

2Department of Physics, Dokuz Eylül University, TR-35160, Izmir, Turkey

3Centre for Fluid and Complex Systems,

Coventry University, Coventry, CV1 5FB, United Kingdom

(Dated: June 28, 2023)

Abstract

In the present work, we investigate the eﬀects of disorder on the reversal time (τ) of classical

anisotropic Heisenberg ferromagnets in three dimensions by means of Monte Carlo simulations.

Starting from the pure system, our analysis suggests that τincreases with increasing anisotropy

strength. On the other hand, for the case of randomly distributed anisotropy, generated from

various statistical distributions, a set of results is obtained: (i) For both bimodal and uniform

distributions the variation of τwith the strength of anisotropy strongly depends on temperature.

(ii) At lower temperatures, the decrement in τwith increasing width of the distribution is more

prominent. (iii) For the case of normally distributed anisotropy, the variation of τwith the width

of the distribution is non-monotonic, featuring a minimum value that decays exponentially with

the temperature. Finally, we elaborate on the joint eﬀect of longitudinal (hz) and transverse (hx)

ﬁelds on τ, which appear to obey a scaling behavior of the form τhn

z∼f(hx).

∗Electronic address: muktish.physics@presiuniv.ac.in

†Electronic address: nikolaos.fytas@coventry.ac.uk

arXiv:2210.05510v2 [cond-mat.stat-mech] 27 Jun 2023

I. INTRODUCTION

The metastable behavior of a ferromagnet is an interesting ﬁeld of modern research with

important technological applications [1, 2]. It is well-known today that the so-called switch-

ing time (or reversal time τ), a critical parameter of this process, plays a key role in the speed

of recording in magnetic storage devices [3]. The whole problem of metastability dates back

to 1935, where the classical theory of nucleation was developed by Becker and Döring [4],

predicting the growth of supercritical droplets. These predictions of the diﬀerent regimes

of such growth depending on the magnitude of the applied magnetic ﬁeld were successfully

veriﬁed by extensive Monte Carlo simulations in Ising [5] and Blume-Capel ferromagnets [6],

as well as in generalized spin-sanisotropic models [7].

Over the years, most numerical approaches of reversal phenomena dealing with the growth

of supercritical clusters, the decay of metastable volume fraction, and their dependencies

on the applied ﬁeld and temperature, focused on pure ferromagnetic systems of discrete

symmetric Ising and Blume-Capel models. A straightforward extension would be then to

consider the case of continuous symmetric spin models, such as the classical Heisenberg

model. Indeed, a few papers have already shed some light in this context: The magneti-

zation switching in the classical anisotropic Heisenberg ferromagnet was studied by Monte

Carlo simulations and the dynamics of coherent spin rotation was detected in the limit of

low anisotropy [8]. Later on, the reversal properties were studied in classical anisotropic

ferromagnetic and antiferromagnetic bilayer Heisenberg models and it was observed that

the magnetization behavior is diﬀerent at each branch of the hysteresis loop as well as

the exchange-bias behavior [9]. More recently, the problem was investigated in the anti-

ferromagnetic anisotropic Heisenberg chain [10] and in a Van-der-Waals magnet where a

strain-sensitive magnetization reversal was reported [11]. This latter work indicated that

lattice deformation plays a major role in the reversal process, as it may lead to random

variations of the crystal ﬁeld (anisotropy) acting on the spins of the system.

In all aforementioned studies regarding the anisotropic classical Heisenberg ferromagnet,

uniform anisotropy was used for simplicity. At this point several intriguing questions may

be raised: (i) What will be the eﬀect of a random anisotropy on the reversal phenomena in

the classical Heisenberg ferromagnet? (ii) How does the nature of the statistical distribution

of the anisotropy aﬀect the reversal of magnetization and other properties of the system? To

the best of our knowledge, all these open fundamental aspects have not yet been addressed so

our understanding of metastable phenomena in a random environment is rather limited – see

Refs. [12, 13] for some particular exceptions. In the present work, we make one step forward

in this direction by studying via Monte Carlo simulations the three-dimensional anisotropic

classical Heisenberg ferromagnet with the disorder, generated by a set of random anisotropy

distributions.

The rest of the paper is organized as follows: Section II provides a description of the

model together with an outline of the simulation scheme. The numerical results and scaling

analysis are reported in Sec. III. This paper concludes with a summary and outlook in

Sec. IV.

II. MODEL AND NUMERICS

The classical anisotropic (uniaxial and single-site) Heisenberg model with nearest-

neighbor ferromagnetic interactions in the presence of an external magnetic ﬁeld is described

by the following Hamiltonian

H=−JX

⟨ij⟩

Si·Sj−X

Di(Sz

i)2−hX

Si,(1)

where Si(Sx

i, Sy

i, Sz

i)represents a classical spin vector with |S|= 1 (or (Sx

i)2+(Sy

i)2+(Sz

i)2=

1) which is allowed to take any (unrestricted) angular orientation in the vector space. The

ﬁrst term in the Hamiltonian corresponds to nearest-neighbor (⟨ij⟩) ferromagnetic (J > 0)

spin-spin interaction. The parameter Diappearing in the second term denotes the strength

of uniaxial anisotropy favoring the z-axis alignment of the spin vector. Note that the limit

D→ ∞ corresponds to the Ising ferromagnet, whereas for D= 0 Eq. (1) reduces to the

isotropic Heisenberg Hamiltonian. Finally, the last term in the Hamiltonian (1) stands for the

interaction of individual spins with the externally applied magnetic ﬁeld vector h(hx, hy, hz).

The reversal of magnetization is studied mainly in the presence of a longitudinal ﬁeld hz

unless otherwise stated. However, in the last part of our study, we also present the inﬂuence

of an additional transverse ﬁeld (hx) on the reversal mechanism, along with the longitudinal

ﬁeld.

We used Monte Carlo simulations of Metropolis type to study the model of Eq. (1)

on simple cubic lattices with periodic boundary conditions and linear dimension L, where

typically L= 50 (more information on the numerical details is given in Appendix A). In

all our numerical experiments, L3such spin updates deﬁne one Monte Carlo step per site,

which also sets the time unit of our simulations. We also ﬁx J=kB= 1 to properly set the

temperature scale.

Finally some comments about errors and ﬁtting analysis: Unless otherwise stated, we

always perform the necessary statistical averaging to increase the accuracy of our data

(more details are given explicitly in the plots of Sec. III) and compute standard errors [15].

For the ﬁts, we implement the χ2test of goodness of ﬁt [16]. Speciﬁcally, the Qvalue of

our χ2test is the probability of ﬁnding a χ2value that is even larger than the one actually

found from our data. We consider a ﬁt as being fair only if 10% <Q<90%.

III. RESULTS AND DISCUSSION

The ﬁrst port of call in our study is to secure a rough estimate for the critical temper-

ature of the Heisenberg model so that we assure that the system lies well below its critical

temperature. Although in previous works [17] we observed no such detectable discontinuity

in the behavior of the metastable lifetime across the phase boundary of the ferromagnetic-

paramagnetic transition, still, in the present study, we follow the standard way of studying

the reversal time or the metastable lifetime below the critical temperature. As the pre-

cise determination of the critical temperature is deﬁnitely not necessary here, we follow the

simplest practice for locating an approximate estimation of the critical temperature. The

method refers to the detection of the pseudo-critical temperature, T∗

L, at which the magnetic

susceptibility χobtained via

χ=Nβ⟨m2⟩−⟨m⟩2(2)

attains a peak for a relatively large system size L. In the above Eq. (2), N=L3,β= 1/T ,

and m=pm2

x+m2

y+m2

zdenotes the magnetization of the system, where mx= (PiSx

i)/N,

my= (PiSy

i)/N, and mz= (PiSz

i)/N. Figure 1(a) presents the T-variation of χfor a

system with linear size L= 20 and for various values of Dand Fig. 1(b) clearly illustrates

that the pseudo-critical temperatures obtained increase with increasing uniform anisotropy

D. Note that the temperature is varied in steps of δT = 10−2so that the maximum error

in the T∗

L-determination is δT ∗

L∼2.10−2.

The metastable lifetime (or reversal time) τ, the crucial parameter of our analysis, is

文档加载中……请稍候！
如果长时间未打开，您也可以点击刷新试试。

下载文档到电脑，查找使用更方便

10 玖币 0人已下载

立即下载

摘要：

DisordereffectsonthemetastabilityofclassicalHeisenbergferromagnetsMoumitaNaskar,1MuktishAcharyya,1,∗ErolVatansever,2,3andNikolaosG.Fytas3,†1DepartmentofPhysics,PresidencyUniversity,86/1CollegeStreet,Kolkata-700073,India2DepartmentofPhysics,DokuzEylülUniversity,TR-35160,Izmir,Turkey3CentreforFluidand...

展开>> 收起<<

Disorder effects on the metastability of classical Heisenberg ferromagnets Moumita Naskar1Muktish Acharyya1Erol Vatansever2 3and Nikolaos G. Fytas3.pdf

共18页,预览4页

还剩页未读，继续阅读

声明：本站为文档C2C交易模式，即用户上传的文档直接被用户下载，本站只是中间服务平台，本站所有文档下载所得的收益归上传人(含作者)所有。玖贝云文库仅提供信息存储空间，仅对用户上传内容的表现方式做保护处理，对上载内容本身不做任何修改或编辑。若文档所含内容侵犯了您的版权或隐私，请立即通知玖贝云文库，我们立即给予删除！

Disorder effects on the metastability of classical Heisenberg ferromagnets Moumita Naskar1Muktish Acharyya1Erol Vatansever2 3and Nikolaos G. Fytas3

相关推荐

开通VIP享超值会员特权

作者详情

相关内容

热门标签

举报选择: