skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Size- and temperature-dependent magnetization of iron nanoclusters

Abstract

In this paper, the magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated by means of spin dynamics simulations coupled to molecular dynamics, using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, going beyond the cluster and bulk Curie temperatures. Comparison is made with experimental data and with theoretical models based on the mean-field Ising model adapted to small clusters, and taking into account the influence of low coordinated spins at free surfaces. Our results for the temperature dependence of the average magnetization per atom M (T), including the thermalization of the transnational lattice degrees of freedom, are in very good agreement with available experimental measurements on small Fe nanoclusters. In contrast, significant discrepancies with experiment are observed if the translational degrees of freedom are artificially frozen. The finite-size effects on M (T) are found to be particularly important near the cluster Curie temperature. Simulated magnetization above the Curie temperature scales with cluster size as predicted by models assuming short-range magnetic ordering. Analytical approximations to the magnetizationmore » as a function of temperature and size are proposed.« less

Authors:
 [1]; ORCiD logo [2];  [2];  [3];  [4];  [5]; ORCiD logo [6]
  1. Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States)
  2. CONICET Mendoza Technological Scientific Center (Argentina); Mendoza Univ. (Argentina)
  3. National Univ. of San Luis (Argentina)
  4. CONICET Mendoza Technological Scientific Center (Argentina)
  5. Univ. of Kassel (Germany)
  6. CONICET Mendoza Technological Scientific Center (Argentina); Mendoza Univ. (Argentina); Univ. Mayor, Santiago (Chile)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1738927
Report Number(s):
SAND-2020-13513J
Journal ID: ISSN 2469-9950; 692730
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 102; Journal Issue: 18; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Tranchida, Julien Guy, Dos Santos, Gonzalo, Aparicio, Romina, Linares, D., Miranda, E. N., Pastor, Gustavo M., and Bringa, Eduardo M.. Size- and temperature-dependent magnetization of iron nanoclusters. United States: N. p., 2020. Web. https://doi.org/10.1103/physrevb.102.184426.
Tranchida, Julien Guy, Dos Santos, Gonzalo, Aparicio, Romina, Linares, D., Miranda, E. N., Pastor, Gustavo M., & Bringa, Eduardo M.. Size- and temperature-dependent magnetization of iron nanoclusters. United States. https://doi.org/10.1103/physrevb.102.184426
Tranchida, Julien Guy, Dos Santos, Gonzalo, Aparicio, Romina, Linares, D., Miranda, E. N., Pastor, Gustavo M., and Bringa, Eduardo M.. Fri . "Size- and temperature-dependent magnetization of iron nanoclusters". United States. https://doi.org/10.1103/physrevb.102.184426. https://www.osti.gov/servlets/purl/1738927.
@article{osti_1738927,
title = {Size- and temperature-dependent magnetization of iron nanoclusters},
author = {Tranchida, Julien Guy and Dos Santos, Gonzalo and Aparicio, Romina and Linares, D. and Miranda, E. N. and Pastor, Gustavo M. and Bringa, Eduardo M.},
abstractNote = {In this paper, the magnetic behavior of bcc iron nanoclusters, with diameters between 2 and 8 nm, is investigated by means of spin dynamics simulations coupled to molecular dynamics, using a distance-dependent exchange interaction. Finite-size effects in the total magnetization as well as the influence of the free surface and the surface/core proportion of the nanoclusters are analyzed in detail for a wide temperature range, going beyond the cluster and bulk Curie temperatures. Comparison is made with experimental data and with theoretical models based on the mean-field Ising model adapted to small clusters, and taking into account the influence of low coordinated spins at free surfaces. Our results for the temperature dependence of the average magnetization per atom M (T), including the thermalization of the transnational lattice degrees of freedom, are in very good agreement with available experimental measurements on small Fe nanoclusters. In contrast, significant discrepancies with experiment are observed if the translational degrees of freedom are artificially frozen. The finite-size effects on M (T) are found to be particularly important near the cluster Curie temperature. Simulated magnetization above the Curie temperature scales with cluster size as predicted by models assuming short-range magnetic ordering. Analytical approximations to the magnetization as a function of temperature and size are proposed.},
doi = {10.1103/physrevb.102.184426},
journal = {Physical Review B},
number = 18,
volume = 102,
place = {United States},
year = {2020},
month = {11}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice
journal, July 2019


Short-range magnetic order near the Curie temperature iron from spin-resolved photoemission
journal, March 1985


Exact diagonalization of Hubbard clusters at finite temperatures
journal, January 2009


Critical exponents from field theory
journal, May 1980


Critical behavior of the uniaxial ferromagnetic monolayer Fe(110) on W(110)
journal, December 1996

  • Elmers, Hans-Joachim; Hauschild, Jens; Gradmann, Ulrich
  • Physical Review B, Vol. 54, Issue 21
  • DOI: 10.1103/PhysRevB.54.15224

Magnon and phonon dispersion, lifetime, and thermal conductivity of iron from spin-lattice dynamics simulations
journal, February 2018

  • Wu, Xufei; Liu, Zeyu; Luo, Tengfei
  • Journal of Applied Physics, Vol. 123, Issue 8
  • DOI: 10.1063/1.5020611

Atomistic spin model simulations of magnetic nanomaterials
journal, February 2014


Langevin-dynamics study of the dynamical properties of small magnetic particles
journal, December 1998


The design and verification of MuMax3
journal, October 2014

  • Vansteenkiste, Arne; Leliaert, Jonathan; Dvornik, Mykola
  • AIP Advances, Vol. 4, Issue 10
  • DOI: 10.1063/1.4899186

Dynamic simulation of structural phase transitions in magnetic iron
journal, September 2017


Ferromagnetic Monolayers
journal, October 1995


Spin Waves in Paramagnetic bcc Iron: Spin Dynamics Simulations
journal, August 2005


Temperature in micromagnetism: cell size and scaling effects of the stochastic Landau–Lifshitz equation
journal, July 2019


SPILADY: A parallel CPU and GPU code for spin–lattice magnetic molecular dynamics simulations
journal, October 2016


General method for atomistic spin-lattice dynamics with first-principles accuracy
journal, March 2019


On the performance of interatomic potential models of iron: Comparison of the phase diagrams
journal, June 2018


Analytical solution of the mean field Ising model for finite systems
journal, May 2012


Size dependence of the coalescence and melting of iron clusters: A molecular-dynamics study
journal, August 2004


Interatomic Exchange Interactions for Finite-Temperature Magnetism and Nonequilibrium Spin Dynamics
journal, September 2013


Multiscale model approaches to the design of advanced permanent magnets
journal, April 2018


Magnetic instability criterion for spin–lattice systems
journal, February 2015


Realistic finite temperature simulations of magnetic systems using quantum statistics
journal, January 2018


Magnetic hysteresis of epitaxially-deposited iron in the monolayer range: A Kerr effect experiment in surface magnetism
journal, January 1986


Dynamical temperature for spin systems
journal, April 2000


Surface Effects in Magnetic Crystals near the Ordering Temperature
journal, June 1971


Temperature-dependent Heisenberg exchange coupling constants from linking electronic-structure calculations and Monte Carlo simulations
journal, February 2012

  • Böttcher, D.; Ernst, A.; Henk, J.
  • Journal of Magnetism and Magnetic Materials, Vol. 324, Issue 4
  • DOI: 10.1016/j.jmmm.2011.08.053

Ab initio calculations of exchange interactions, spin-wave stiffness constants, and Curie temperatures of Fe, Co, and Ni
journal, October 2001


Large-scale simulation of the spin-lattice dynamics in ferromagnetic iron
journal, July 2008


Size Dependence of Inter- and Intracluster Interactions in Core–Shell Iron–Iron Oxide Nanoclusters
journal, June 2012

  • Kaur, Maninder; McCloy, John S.; Jiang, Weilin
  • The Journal of Physical Chemistry C, Vol. 116, Issue 23
  • DOI: 10.1021/jp301453w

Spin-Wave Theory of Ferromagnetic Thin Films
journal, June 1963


Magnetization and its temperature dependence in compositionally modulated amorphous Fe 7 0 B 3 0 ‐Ag films
journal, April 1987

  • Xiao, Gang; Chien, C. L.; Natan, M.
  • Journal of Applied Physics, Vol. 61, Issue 8
  • DOI: 10.1063/1.338458

Short-range magnetic order in Fe N and Ni N clusters
journal, November 1995


Structure and thermodynamic properties of liquid transition metals: An embedded-atom-method approach
journal, January 1996


Pressure dependence of the Curie temperature in bcc iron studied by ab initio simulations
journal, May 2009


Million-atom molecular dynamics simulations of magnetic iron
journal, February 2007


Magnetization on rough ferromagnetic surfaces
journal, November 2000


Triangular array of iron oxide nanoparticles: Simulation study of intraparticle and interparticle magnetism
journal, September 2019


Anisotropic magnetic molecular dynamics of cobalt nanowires
journal, November 2012


Magnetic Properties at Surface Boundary of a Half-Metallic Ferromagnet La 0.7 Sr 0.3 MnO 3
journal, August 1998


Phonon-magnon interactions in body centered cubic iron: A combined molecular and spin dynamics study
journal, May 2014

  • Perera, Dilina; Landau, David P.; Nicholson, Don M.
  • Journal of Applied Physics, Vol. 115, Issue 17
  • DOI: 10.1063/1.4863488

Spin Torque Efficiency and Analytic Error Rate Estimates of Skyrmion Racetrack Memory
journal, March 2019


Calculation of short range magnetic order in iron
journal, July 1986


Shape of Temperature Dependence of Spontaneous Magnetization of Ferromagnets: Quantitative Analysis
journal, March 2005


Switching times of nanoscale FePt: Finite size effects on the linear reversal mechanism
journal, April 2015

  • Ellis, M. O. A.; Chantrell, R. W.
  • Applied Physics Letters, Vol. 106, Issue 16
  • DOI: 10.1063/1.4919051

Critical susceptibility exponent measured from Fe/W(110) bilayers
journal, March 2004


Magnons and Magnon-Phonon Interactions in Iron
journal, September 1999


Quantum study of the spin wave spectrum of a superlattice with ferromagnetic interfacial coupling
journal, May 1992


Effect of stress on self-diffusion in bcc Fe: An atomistic simulation study
journal, July 2010


Spin dynamics of magnetic nanoparticles: Beyond Brown’s theory
journal, November 2005


The Curie temperature distribution of FePt granular magnetic recording media
journal, July 2012

  • Hovorka, O.; Devos, S.; Coopman, Q.
  • Applied Physics Letters, Vol. 101, Issue 5
  • DOI: 10.1063/1.4740075

Atomistic simulation of phonon and magnon thermal transport across the ferromagnetic-paramagnetic transition
journal, June 2020


Finite size effects in phase transitions
journal, January 1985


A comparative study on temperature dependent diffusion coefficient of liquid Fe
journal, October 2013


Size and structural dependence of the magnetic properties of small 3 d -transition-metal clusters
journal, October 1989

  • Pastor, G. M.; Dorantes-Dávila, J.; Bennemann, K. H.
  • Physical Review B, Vol. 40, Issue 11
  • DOI: 10.1103/PhysRevB.40.7642

Finite-size and surface effects in maghemite nanoparticles:  Monte Carlo simulations
journal, April 2001


Massively parallel symplectic algorithm for coupled magnetic spin dynamics and molecular dynamics
journal, November 2018


Structural Relaxation and Crystalline Phase Effects on the Exchange Bias Phenomenon in FeF 2 /Fe Core/Shell Nanoparticles
journal, July 2020

  • Velásquez, Ever A.; Mazo‐Zuluaga, Johan; Tangarife, Edwin
  • Advanced Materials Interfaces, Vol. 7, Issue 17
  • DOI: 10.1002/admi.202000862

Origin of reduced magnetization and domain formation in small magnetite nanoparticles
journal, April 2017

  • Nedelkoski, Zlatko; Kepaptsoglou, Demie; Lari, Leonardo
  • Scientific Reports, Vol. 7, Issue 1
  • DOI: 10.1038/srep45997

Collective dynamics in atomistic models with coupled translational and spin degrees of freedom
journal, January 2017


Embedded-atom potential for Fe and its application to self-diffusion on Fe(100)
journal, May 2006


Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool
journal, December 2009


Exact solution of the two-level system and the Einstein solid in the microcanonical formalism
journal, September 2011

  • Bertoldi, Dalía S.; Bringa, Eduardo M.; Miranda, E. N.
  • European Journal of Physics, Vol. 32, Issue 6
  • DOI: 10.1088/0143-0807/32/6/004

A Mechanism of Magnetic Hysteresis in Heterogeneous Alloys
journal, May 1948

  • Stoner, E. C.; Wohlfarth, E. P.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 240, Issue 826
  • DOI: 10.1098/rsta.1948.0007

Spirit : Multifunctional framework for atomistic spin simulations
journal, June 2019

  • Müller, Gideon P.; Hoffmann, Markus; Dißelkamp, Constantin
  • Physical Review B, Vol. 99, Issue 22
  • DOI: 10.1103/PhysRevB.99.224414

Accurate critical exponents from the ε-expansion
journal, January 1985


A ‘magnetic’ interatomic potential for molecular dynamics simulations
journal, October 2005


Magnetic moments of iron clusters with 25 to 700 atoms and their dependence on temperature
journal, December 1993


Finite-Difference Micromagnetic Solvers With the Object-Oriented Micromagnetic Framework on Graphics Processing Units
journal, April 2016


Effect of lattice vibrations on magnetic phase transition in bcc iron
journal, December 2012


Magnetic Anisotropy of 3 d Transition-Metal Clusters
journal, July 1995


Comparison of first-principles methods to extract magnetic parameters in ultrathin films: Co/Pt(111)
journal, June 2019


Spin dynamics in magnets: Equation of motion and finite temperature effects
journal, July 1996


Temperature-dependent magnetic properties of ultrathin Fe films: Interplay between local environment and itinerant ferromagnetism
journal, June 2006


Impact of thermal atomic displacements on the Curie temperature of 3 d transition metals
journal, May 2018


Critical exponents of the classical three-dimensional Heisenberg model: A single-cluster Monte Carlo study
journal, July 1993