Prolog Numerical Modeling in Magnetism Macro-Magnetism: Solution of Maxwells Equations – Engineering of (electro)magnetic devices Micromagnetism: Domain Dynamics, Hysteresis MFM image Micromagnetic simulation. Atomic Magnetism: Instrinsic Magnetic Properties

Atomic Magnetism- Modeling Instrinsic Magnetic Properties Band Models Spin Polarized First Principle Methods: restricted to simple Magnetic Structures, T=0, no dynamics, no rare earth elements ... there are attempts to overcome these restrictions Localized Moment Models Ising-, Heisenberg-, xy-, Standard Model of RE-Magnetism) Exact Methods: e.g. branch and bound algorithm, transfer matrix algorithm Monte Carlo Methods Selfconsistent Mean Field Method

Atomic Magnetism- Modeling Instrinsic Magnetic Properties M. Rotter, Institut für physikalische Chemie, Universität Wien Atomic Magnetism- Modeling Instrinsic Magnetic Properties Band Models Spin Polarized First Principle Methods: restricted to simple Magnetic Structures, T=0, no dynamics, no rare earth elements ... there are attempts to overcome these restrictions Localized Moment Models Ising-, Heisenberg-, xy-, Standard Model of RE-Magnetism) Exact Methods: e.g. branch and bound algorithm, transfer matrix algorithm Monte Carlo Methods Selfconsistent Mean Field Method

The Standard Model of RE Magnetism - the Crystal Field Concept + 4f –charge density E Q Hamiltonian McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Example: NdCu2 a b c Crystal Structure of RCu2 Imma (orthorhombic) ... 9 nonzero CF Parameters you can use module pointc to calculate CF parameters by the pointcharge model + McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

NdCu2 – Crystal Field Excitations orthorhombic, TN=6.5 K, Nd3+: J=9/2, Kramers-ion McPhase can solve CF Model Calculate Intensities and Energies Calculate and Plot Charge Density ... Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Make a Crystal Field Model using McPhase Module Cfield Module simmannfit can do this again and again for you to fit the result of the calculation to your spectrum by variation of the CF-parameters Make a Crystal Field Model using McPhase Module Cfield CF Hamiltonian Example files in directory /mcphas/examples/ndcu2b_new/cf Edit file Bkq.parameter and enter CF parameters Blm Start module cfield - type: cfield –r -B View output file cfield.out: CF - energies, eigenstates, transition-matrixelements and corresponding neutron intensities Use module convolute to convolute energy vs intensity results with spectrometer resolution function McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Magnetism would be boring without a magnetic field Use module cfield to calculate magnetization type: cfield –m Hamiltonian McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Specific Heat Use module cpcalc to calculate specific heat type: cpcalc 5 30 1 Tmin=5 Tmax=30 dT=1 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Use modules chrgplot+javaview to plot 4f charge density T=100 K T=40 K T=10 K McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Use modules pointc+chrgplot+javaview T=2K H=0 Same CEF McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

The magnetically ordered State ...investigated by neutron scattering D1B ILL, Grenoble McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Magnetic Structure from McPhase - the World of Rare Earth Magnetism GdCu2 TN= 42 K M [010] TR= 10 K q = (2/3 1 0) Magnetic Structure from Neutron Scattering Rotter et.al. J. Magn. Mag. Mat. 214 (2000) 281 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Module mcphas .... do not fit moments – fit Hamiltonians ! McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Input files for module mcphas: mcphas.j (structure), mcphas.cf (single ion properties), mcphas.tst (table of initial values), mcphas.ini (H,T-range, ...) McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Do you really want to see the MF equations ? Cfield can calculate McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism GdCu2In nichtkollineare Struktur(mcphase) I(κ) [counts] McPhase - the World of Rare Earth Magnetism |κ|[Å-1] Martin Rotter - McPhase Rio de Janeiro 2007

Single Crystal Flate Cone Diffraction E2 – HMI, Berlin k τ O McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism 3 crystals (ca 120° rotated) NdCu2 τ 5τ 3τ l McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism AF2 Pattern T=4.1K H=0T McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

NdCu2 Magnetic Structures at T=0 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Pattern T=0 k 0.4 0.6 0.8 1.0 h AF1    3τ 5τ τ=(0.6 0 0) F1  2τ τ=(0.6666 0 0) 2τ F2  2τ τ=(0.625 0 0)  F3 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

NdCu2 Magnetic Phase Diagram F1    F3  c F1  b a AF1  lines=experiment output file: mcphas.xyt Use module phased or displaycontour for color plot of phasediagram McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism output file: mcphas.hkl McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Bulk Properties Calculated by module mcphas Magnetization output file: mcphas.fum McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism NdCu2 Specific Heat output file: mcphas.fum McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Spontaneous Magnetostriction Microscopic Source of Magneostriction: Strain dependence of magnetic interactions Crystal field Exchange T<TC(N) L=0, L0 „exchange-striction“ T T .... Symmetry decreases L0 + T<TC(N) T>TC(N) e- + McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Forced Magnetostriction Crystal Field Exchange Striction L0 L=0, L0 H <0 H + e- H >0 + McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Calculation of Magnetostriction Crystal Field Exchange mit Output file: mcphas.xyt Output file: mcphas.jj* + McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

NdCu2 Magnetostriction Exchange - Striction Crystal Field McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Dispersive Magnetic Excitations 153 MF - Zeeman Ansatz T=1.3 K McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism ... Spinwaves (Magnons) 153 T=1.3 K Bohn et. al. PRB 22 (1980) 5447 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Spinwaves (Magnons) 153 a T=1.3 K Bohn et. al. PRB 22 (1980) 5447 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Module Mcdisp – Calculate Magnetic Excitation Energies and the Neutron Scattering Cross Section MF-RPA McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Module Mcdisp – a novel fast algorithm for magnetic excitations M. Rotter, Comp. Mat. Sci. 38 (2006) 400 Transformation: McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism with definition: (1) all other components of Ψ are zero with definition: Generalized eigenvalue problem (analogue to dynmical matrix in the case of phonons!!) Solution gives eigenvalues and eigenvectors McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism may then be inverted to give the following expression for Ψ back transformation... +calculation of absorptive part... using Diracs formula: McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism McDisp - fast algorithm - Cookbook 1) 2) 3) ...setup Matrix 4) ...solve generalized EV Problem 5) McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

NdCu2 F3  F1  AF1 

McPhase - the World of Rare Earth Magnetism Diffuse Scattering McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism McPhase Modules McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Symmetry - CF Local Point Symmetry limits the number of nonzero Crystal Field Parameters (mind: local symmetry at rare earth position may be lower than lattice symmetry, i.e. The lattice may be cubic, but the local symmetry tetragonal) Point Group / Latt. Symmetry Coordinate Orientation Nonzero Blm O cubic xyz||abc B40,B44,B60,B64 z||111 B40,B43,B60,B63,B66 D6h hexagonal B20,B40,B60,B66 D4h tetragonal B20,B40,B44,B60,B64 C3v (no lattice) B20,B40,B43,B60,B63 C2h monoclinic B20,B40,B60,B66,B66s D3d (quasicubic in dhcp) B20,B40,B43,B60,B63,B66 D2 orthorh. B20,B22,B40,B42,B44,B60,B62,B64,B66

McPhase - the World of Rare Earth Magnetism Example: 2nd order CF terms for point symmetry mm2=C2v We choose here the basis of Racah instead of Stevens operators for the Crystal field, because these transform like the spherical harmonic functions Group elements G C2v 1E 1C2 1σy 1σx A1 1 B1 -1 A2 B2 Irr. Repr. These operators form a reducable representation T2(G) of the point group Character table of mm2 Group Theory basics taken from: Elliott&Dawber Symmetry in Physics, McMillan Press, 1979 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism The representation T2(G) can be decomposed into irreducible Representations (i.e. „the Olm can be linear combined to another Basis so that in this basis the representation T2 bas block diagonal form with each block corresponding to a irreducible representation“) The m‘s tell, how often a representation occurs. mA1 tells, how often the unit representation occurs in the decomposition, i.e. how many different independent basis vectors span this subspace, i.e. how many independent crystal field parameters will occur. A little group theoretical trick for calculating m Cp... Number of members of class p g.... Number of group elements χ.... Character of class Class p a χp E 5 C2 π 1 σy σx a... Angle of rotation McPhase - the World of Rare Earth Magnetism i.e. We expect 2 independent 2nd order CF parameters Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism The basis of the 2 A1 representation occuring in the decomposition of T2(G) can be found using the projection operator In order to calculate it, we have to epxlicitely write down the reducable representation T2: Jx‘=-Jx, Jy‘=-Jy Jy‘=-Jy Jx‘=-Jx B20 and B22 are nonzero. McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Symmetry – Bilinear Interaction Isotropic interaction (J(ij) is a scalar) Anisotropic Interaction (J(ij) is a tensor) McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism (quasi)hexagonal types of neighbors neighbors related by symmetry must have related interaction constants J(ij) CeCu2 Structure Cu Ce M. Rotter et al., Eur. Phys. J. B 14, 29 (2000) M. Rotter et al., JMMM. 214, 281 (2000) McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Anisotropic Interaction –Symmetry Considerations McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism ETC... McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Example: bc mirror plane b 1 a McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Symmetry – Quadrupolar Interaction Derivation similar to CF operator using representation T(G)=T2(G)xT2 (G) Isotropic Quadrupolar Interaction dhcp –lattice: between hexagonal sites dhcp –lattice: between quasicubic sites

Example for quadrupolar interactions: PrCu2 H + + M + + + + + McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism PrCu2 www.mcphase.de Settai et. al. JPSJ 67 (1998) 636 + GMS + + + + + + Ferroquadrupolarer (Cij>0) Austausch (durch CF-Phonon WW) Settai et. al. JPSJ 67 (1998) 636 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism PrCu2 Ferroquadrupolar (Cij>0) Interaction Settai et. al. JPSJ 67 (1998) 636 The Model describes well: the quadrupolar phasen diagram the magnetisation the magnetostriction die temperature dependence of elastic constants Whats about the Dynamics ? McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Orbital Excitations (Orbitonen) + 4f – charge density E Q Crystal field +Antiferroquadrupolar (C<0) Interaction McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism PrCu2 + + + + + + + Ferroquadrupolar (Cij>0) Interaction (via CF-Phonon coupling) McPhase - the World of Rare Earth Magnetism Settai et. al. JPSJ 67 (1998) 636 Martin Rotter - McPhase Rio de Janeiro 2007

PrCu2 Orbital Modes T=5 K, H=0 T MF-RPA Model Experiment Г 2.5 Energy (meV) ? 1 00L 2 McPhase: www.mcphase.de Rotter, JMMM 272-276 (2003) 481 Kawarazaki et. al., J. Phys. Cond. Mat. 7 (1995) 4051 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism NdCu2 PrCu2 Magnetic Excitations Rotter et. al., Europ. Phys. J. B 14 (2000) 29 NdCu2 Könnte nicht auch die Austauschwechselwirkung zu der beobachteten Dispersion führen ? Nur Quadrupolaustausch Г [Interpretation von Kawarazaki et. al., J. Phys. Cond. Mat. 7 (1995) 4051] 2.5 Energy (meV) 1 00L 2 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism PrCu2 00L Energy (meV) 2.5 + magnetic Interactions 1 2 Quadruplar Interaction only Nur Quadrupolaustausch Г nur magnetischer Austausch 2.5 Energy (meV) 1 00L 2 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

PrCu2 Orbital modes in Magnetic field T=2 K, H||a Rechnung Messung IN12(ILL) März 2004 (15 Tesla cryomagnet) McPhase: www.mcphase.de Rotter, JMMM 272-276 (2003) 481 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Quadrupolar Effects Neutrons can be scattered by 4f - Orbitons – Orbiton spectroscopy: - Determination of multipolar Interactions - Modeling of GMS Crystal field + Ferroquadrupolar (Cij>0) Interactions Settai et. al. JPSJ 67 (1998) 636 PrCu2 The model describes well: macroscopic properties and quadrupolar Phase diagram Magnitude of dispersion of orbital modes McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

How to start – the story of NdCu2 Suszeptibility: 1/χ(T) at high T ... Crystal Field Parameters B20, B22 Specific Heat Cp ...  first info about CF levels Magnetisation || a,b,c on single crystals in the paramagnetic state, ... ground state matrix elements Neutron TOF spectroscopy – CF levels ...  All Crystal Field Parameters Blm Thermal expansion in paramagnetic state – CF influence ...  Magnetoelastic parameters (dBlm/dε) Neutron diffraction: magnetic structure in fields || easy axis ...  phase diagram H||b - model ...  Jbb Neutron spectroscopy on single crystals in H||b=3T ...  Anisotropy of Jij - determination of Jaa=Jcc Magnetostriction ...  Confirmation of phase diagram models H||a,b,c, dJ(ij)/dε McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism The story of NdCu2 Inverse suszeptibility at high T ... B20=0.8 K, B22=1.1 K Hashimoto, Journal of Science of the Hiroshima University A43, 157 (1979) Θabc McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism The story of NdCu2 Specific haet Cp and entropy – first info about levels Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297 Rln2 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

How to start analysis – the story of NdCu2 Magnetization: Kramers ground state doublet |+-> matrix elements P. Svoboda et al. JMMM 104 (1992) 1329 Module cfield can also calculate magnetization using a full set of CF parameters McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

How to start analysis – the story of NdCu2 Neutron TOF spectroscopy – CF levels ... Blm Gratz et. al., J. Phys.: Cond. Mat. 3 (1991) 9297 B20=1.35 K B22=1.56 K B40=0.0223 K B42=0.0101 K B44=0.0196 K B60=4.89x10-4 K B62=1.35x10-4 K B64=4.89x10-4 K B66=4.25 x10-3 K McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism The story of NdCu2 Thermal expansion – cf influence ... Magnetoelastic parameters (A=dB20/dε, B=dB22/dε) E. Gratz et al., J. Phys.: Condens. Matter 5, 567 (1993) McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

The story of NdCu2 Neutron diffraction+ magnetization: magstruc, phasediag H||b-> model ... Jbb M. Loewenhaupt et al., Z. Phys. B: Condens. Matter 101, 499 (1996) n(k)=sum of Jbb(ij) with ij being of bc plane k      

NdCu2 Magnetic Phase Diagram F1    F3  c F1  b a AF1  lines=experiment output file: mcphas.xyt Use module phased or displaycontour for color plot of phasediagram McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Jaa=Jcc(R) The story of NdCu2 Neutron spectroscopy on single crystals in H||b=3T ... Anisotropy of J(ij) - determination of Jaa=Jcc F3  M. Rotter et al., Eur. Phys. J. B 14, 29 (2000) McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

NdCu2 F3  F1  AF1  M. Rotter, et al. Applied Phys. A 74 (2002) s751

How to start analysis – the story of NdCu2 Magnetostriction ... Confirmation of phasediagram model for H||a,b,c, and determination of dJ(ij)/dε M. Rotter, et al. J. of Appl. Physics 91 10(2002) 8885

McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Nonsense ! „The Standard Model of Rare Earth Magnetism has been well established and can describe the magnetic properties of Rare earth compounds. There is no need for a program like McPhase.“ In very few RE systems a large number of results of the SM have been compared to experimental data: e.g. the full magneto-striction tensor has been analysed only in 1 case (NdCu2) Quadrupolar Excitations have not been compared to the SM There is a number of wrong predictions of the SM: e.g. -magnetoelastic paradoxon in L=0 AF-systems -extra magnetic modes or no modes (CeCu2, CeNi9Ge4, Nd2CuO4), -wrong saturation moments, e.g. in Eu-Skutterudite - ... McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

The magnetoelastic Paradoxon for L=0 demonstrated at GdNi2B2C Orthorhombic Distortion ? Exchange-Striction Standard Model of RE Mag ... McPhase Simulation McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism McPhase is a program package for the calculation of magnetic properties of rare earth based systems.           Magnetization                       Magnetic Phasediagrams     Magnetic Structures            Elastic/Inelastic/Diffuse                                               Neutron Scattering                                              Cross Section McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

McPhase - the World of Rare Earth Magnetism Crystal Field/Magnetic/Orbital Excitations Magnetostriction  and much more.... McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Epilog McPhase - the World of Rare Earth Magnetism McPhase runs on Linux and Windows and is available as freeware. McPhase is being developed by   M. Rotter, Institut für Physikalische Chemie, Universität Wien, Austria   M. Doerr, R. Schedler, Institut für Festkörperphysik, Technische Universität Dresden, Germany   P. Fabi né Hoffmann, Forschungszentrum Jülich, Germany   S. Rotter, Wien, Austria   M.Banks, Max Planck Institute Stuttgart, Germany Important Publications referencing McPhase: M. Rotter, S. Kramp, M. Loewenhaupt, E. Gratz, W. Schmidt, N. M. Pyka, B. Hennion, R. v.d.Kamp Magnetic Excitations in the antiferromagnetic phase of NdCu2 Appl. Phys. A74 (2002) S751     M. Rotter, M. Doerr, M. Loewenhaupt, P. Svoboda, Modeling Magnetostriction in RCu2 Compounds using McPhase J. of Applied Physics 91 (2002) 8885 M. Rotter Using McPhase to calculate Magnetic Phase Diagrams of Rare Earth Compounds J. Magn. Magn. Mat. 272-276 (2004) 481 McPhase - the World of Rare Earth Magnetism Martin Rotter - McPhase Rio de Janeiro 2007

Magnetostrictive Materials and Magnetic Refrigeration (MMMR) Workshop Magnetostrictive Materials and Magnetic Refrigeration (MMMR) 13.-15. August 2007, Vienna, Austria http://www.univie.ac.at/MMMR/