# Project

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## Dimensional crossover in strongly anisotropic antiferromagnets

 English title Dimensional crossover in strongly anisotropic antiferromagnets Mudry Christopher 129928 Project funding (Div. I-III) Paul Scherrer Institut Paul Scherrer Institute - PSI Condensed Matter Physics 01.05.2010 - 30.04.2011 52'206.00
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### Keywords (2)

quantum magnetism; dimensional crossover

### Lay Summary (English)

Lay summary
Magnetic materials are very often characterized by anisotropic magnetic interactions both in the internal space of the spin and on the lattice.This project is primarily concerned with quantum antiferromagnets that have strongly anisotropic magnetic interactions on the lattice.At temperatures much larger than thecharacteristic subleading magnetic interaction $J'$, magnetic fluctuations are predominantly two- or one-dimensional if the characteristic dominant antiferromagnetic coupling $J$ is an intraplane or an intrachain coupling, respectively.Upon decreasing temperature,magnetic fluctuations become more isotropic and, under suitable conditions, magnetic long-range order can appear below the critical temperature $T^{\ }_{AF}(J'/J)$.The study of such a dimensional crossover for quasi-two-dimensional frustrated antiferromagnets defined by stacking triangular lattices is the purpose of this project.
 Direct link to Lay Summary Last update: 21.02.2013

### Responsible applicant and co-applicants

Name Institute
 Mudry Christopher Paul Scherrer Institut

Name Institute

### Associated projects

Number Title Start Funding scheme
 116635 Dimensional crossover in strongly anisotropic antiferromagnets 01.05.2007 Project funding (Div. I-III)
 116635 Dimensional crossover in strongly anisotropic antiferromagnets 01.05.2007 Project funding (Div. I-III)

### Abstract

Magnetic materials are very often characterized by anisotropic magneticinteractions both in the internal space of the spin and on the lattice.This project is primarily concerned with quantum antiferromagnetsthat have strongly anisotropic magnetic interactions on the lattice.At temperatures much larger than the characteristic subleading magnetic interaction $J'$,magnetic fluctuations are predominantly two- or one-dimensionalif the characteristic dominant antiferromagnetic coupling $J$ is an intraplane or an intrachain coupling, respectively. Upon decreasing temperature,magnetic fluctuations become more isotropic and, under suitable conditions, magnetic long-range ordercan appear below the critical temperature$T^{\ }_{AF}(J'/J)$.The random phase approximation (RPA) has been a popular approximationto estimate the ordering temperature $T^{\ }_{AF}(J'/J)$in the strong anisotropic limit $J'\ll J$.Recently, the quality of this approximation hasbeen tested by the use of Monte Carlo simulationsfor the quasi-two-dimensionalquantum antiferromagnetic spin-$S$ Heisenberg modelon the cubic lattice.Remarkably, it was shown byYasuda \textit{et al}.,Phys.\ Rev.\ Lett.\ \textbf{94}, 217201 (2005),that the coordination number,a number of geometrical origin that enters the RPA approximation,is simply renormalized by an amount independent ofthe spin quantum number $S$ in the limit $J'/J\to0$.An explanation for this property was given by Hastings and Mudry,Phys.~Rev.~Lett.~\textbf{96}, 027215 (2006),who argued for the existence of three universal scaling functions of one scaling variablein the limit $J'/J\to0$ and at the ordering temperature.All three functions can be measured by neutron scattering.This project aims at improving over the RPAin the following contexts.\begin{enumerate}\item\textbf{Project on quasi-one-dimensional antiferromagnets}First, the techniques used by Hastings and Mudry do not apply to the quasi-one-dimensionalquantum antiferromagnetic spin-$S$ Heisenberg modelon the cubic lattice. This reflects the well known fact that spin-wave theory breaks down for one-dimensional antiferromagnets.Adapting the analysis from Hastings and Mudry toquasi-one-dimensional quantum antiferromagnetic spin-$S$magnets is one goal of this project.\item\textbf{Project on quasi-two-dimensional frustrated antiferromagnets}Second, the techniques used by Hastings and Mudrycan be relatively easily generalized to a physical realization different fromthe quasi-two-dimensional quantum antiferromagnetic spin-$S$ Heisenberg modelon the cubic lattice,namely to a suitable stacking of triangular lattices. On a square latticeand at zero temperature, the antiferromagnetic long-range order is collinear.On a triangular lattice and at zero temperature, the antiferromagnetic long-range orderis non-collinear as a result of a geometrical frustration of theantiferromagnetic interactions.\item\textbf{Project on anisotropic magnets with U(1) ($XY$) symmetric magnetic interaction}Third, this project aims at a critical examination of the RPAapplied to quasi-one-dimensional and quasi-two-dimensionalmagnets with a U(1) ($XY$) symmetric magnetic interaction.\item\textbf{Project on the competition between the dimensional and symmetry crossovers}The last goal of this project is to study the competition betweenthe dimensional and symmetry crossovers caused bymagnetic interactions that are both anisotropic in internal spin spaceand on the lattice.\end{enumerate}
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