Theory of magnetostriction in Invar materials.S. KhmelevskyiCenter for Computational Materials Science, Vienna University of Technology

P. Mohn, A. V. Ruban, I. Turek

Phenomenon of magnetostriction..Para-processApplied field reduces thermal disorder orienting moments along field. It is the source of the volume magnetostriction in all ferromagnetsApplied field induces a band splitting.Small effect. It may be ignored for ferromagnets.H=100T ~ 1mRyHowever it is the source of para-process at T = 0K Even in non-magnetic materials!Re-orientation of the magnetization along the field spin-orbit coupling anisotropyAnomalous thermal expansion in Invar

Thermal expansion anomaly of Invar-type.lat thermal expansion due tolattice vibrations, usually well follows Gruneisen law.m magnetic contribution, which vanishes in paramagnetic state. It exists in all metallic magnetss0 spontaneous volume magnetostriction

for Fe-based Invar s0 ~1-2%s0(Fe-Ni) ~ 2.1%

Magnetic contribution to the thermal expansion can be viewed as sort of spontaneous paraprocess.

classical Invar alloys Fe-NiRECo2Experimental examples.

After M. Shiga and Y. NakamuraJ.Phys. Soc. Jap. (1979)(Zr1-xNbx)Fe2 Laves Phase compounds.

Modern measurements at low T: example (Er-Y)Co2s0 need not to be large if Tc is small.R. Hauser et al. Phys. Rev. B 61, 1198 (2000)Modern measurements at low T revealsa lot of materials with Invar type anomalyWhich has a small Tc.

Some Thermodynamics.Vonsovskyi, Shur (1948)Bean, Rodbell (1962) local moment model-effective exchange constant

s-d modelFixed Spin Moment calculations for YCo2Fd is the Helmholtz potential of the itinerant subsystemSimple example 1: RECo2 Laves Phases.

(Dy,Er)Co2

Dy3+

EMBED Equation.3

EMBED Equation.3

EMBED Equation.3

_1119967834.unknown

_1119969818.unknown

_1119966802.unknown

Stoner Co bandSpin-fluctuations includedS. Khmelevskyi, P.Mohn, JMMM, 272-276 (2003)525

Thermal expansionA. Lindbaum and M. RotterS.Khmelevskyi, I. Turek, P. Mohn, PRB 70, (2003)TB-LMTODisordered Local Moment. Partial DLM Gd(4f-up)1-xGd(4f-down)x f-electrons open core (m = 7mB). Simple example 2: hcp Gadolinium.

Intermediate conclusions. Invar anomaly is magnetovolume effect related to the spontaneous volume magnetostriction due to change of magnetization with temperature (very trivial).

Such effect exists in ALL magnetic materials (even in ALL non-magnetic in applied external field).

One need just to explain why in given Invar material such a contribution large enough to compensate (or be comparable in size to !) a thermal expansion due to lattice vibration in the temperature interval from 0K to Tc.

There is no intrinsic and unique feature of Invar materials, which is absent in normal ones. The difference between them only in quantity - related size of spontaneous magnetostrictions, Tc (and Gruneisen coefficient).

Fe-based transition metal alloys. Classical Invar systems: fcc Fe-Ni, Fe-Pt, Fe-Pd (technical Invars). bcc Fe-Co AFe2 Laves Phases.Problems.One cannot separate a system into electronic subsystems, one of which is responsible for the intrinsic temperature dependent molecular field acting on another subsystem with anomalous magnetostrictive properties.

We should have working approach to tackle with finite temperature magnetism of itinerant magnets in intermediate regime between local and weak itinerant cases (our choice is DLM Do it better if ).

Lots of additional material dependent complications: chemical disorder, antiferromagnetic interactions on frustrated lattice etc.

50 years of intensive theoretical development on Fe-Ni, which are very complex alloy.

Disordered Local Moments state.Model for paramagnetic state: disordered alloy of the same sort of atoms with spin-up and spin down randomly distrubuted over the lattice sites. (Cyrot, Gyorrfy)

Alloy analogy:

A1-xBx A()1-x A()x binary metallic alloy partially ordered state with local moments

Using Coherent Potential Approximation

A()0.5 A()0.5 model paramagnetic state above Tc

Disordered Fe-PtFe74Pt26: wso(exp)=1.7% ; wso(calc)=1.9%

S. Khmelevskyi, I. Turek, P. Mohn, PRL, 91 037201 (2003)TB-LMTO, LDA spd-basisPartial DLM calculationsTc=Mloc2/(3kB) Tc=Mloc2/(3kB) Tc=Mloc2/(3kB)

fcc Fe-Pd, fcc Fe-Pt and bcc Fe-CoMaximum of the spontaneous magnetostriction corresponds to the maximum of the local Fe moment drop in paramagnetic state.Khmelevskyi and Mohn, PRB 69 (2004)

e/a=8.6e/a=9Fe70Pt30

Fe50Pt50Transition from strong ferromagnetic state at T=0K to the weak ferromagnetic state in PM region

Why local Fe moment anomalously decreases in Invar alloy composition?

Ordered and disordered Fe3PtCu3Au - structureLong-Range Order parameter:where c(Fe) is total concentration of Fe in the alloy and cI(Fe) is a concentration of Fe atoms on Pt sites.

Ordered and disordered Fe3PtKhmelevskyi, Ruban, Kakehashi, Mohn, Johansson, PRB 72 (2005)Bulk KKR-ASA, spdf basis, and Muffin tin electrostatic correctionsSpontaneous magnetostriction moderately decreases with increasing of ordering

Fe65Ni35 KKR-ASA LSDA spd-basis

D. D. Johnson, F. J. Pinski, J. B. Staunton, B. L. Gyorffy, and G.M. Stocks, in Physical Metallurgy of Controlled ExpansionInvar-type Alloys, 1990Nothing is new since there is exist nothing new. Fe-Ni case. Akai and Dederichs, PRB B 47, 8739 (1993)consistent with TB-LMTO calculations with spd-basisCrisan et al. Phys. Rev. B 66, 014416 (2002)

Problem number 1: exchange interactions in Fe-NiInter-atomic exchange interactions of Heisenberg Hamiltonian calculated using Lichtenstein Green function formalism (Magnetic Force Theorem). GGA results.INVAR alloy Fe65Ni65 become antiferromagnetic at volumes lower then experimental onesAntiferromagnetic scenario cannot be ruled out

Wang et al. JAP (1998)What is magnetic ground state of Fe65Ni35? Fe65Ni65 alloyCalculations with Local self-consistent Green Function methods (LSGF) 512 atoms super cell

Moment of Fe atoms with 11 and 12 Fe nearest neighbors oriented anti-parallel to the total magnetization.

Ruban, Khmelevskyi, Mohn, Johansson PRB 76 (2007)

Problem number 2: LSDA

Fe65Ni35 INVAR alloy.GGA, Full-Charge Density EMTO results: wso(exp)=2.2% ; wso(calc)=3.2% Calculations of effective inter-atomic chemical interactions and MC simulations shows that Fe-Ni cannot be considered as partially ordered alloy.Short-Range order effects is also very weak.

Ruban, Khmelevskyi, Mohn, Johansson PRB 76 (2007)

antiferromagnetic scenario: contra-example.(Zr1-xNbx)Fe2 Laves Phase compounds.and YFe2 non-Invar system.

KKR-ASA, spdf basis with MT-corrections, GGACalculations with DLM.

Rws(FM)a.u.Rws(DLM)a.u.s0(cal./exp.)%mFe(FM),BmFe(DLM),BmA(FM),BZrFe22.9012.8762.6 / 1.02.121.62-0.84Zr0.7Nb0.3Fe22.8722.8432.5 / 0.82.041.57-0.71YFe23.0143.0011.3 / ~0.02.242.06-0.8

Zr0.7Nb0.3Fe2

Zr0.7Nb0.3Fe2

Conclusions. The Invar effect has common origin in all Invar-type magnetic systems. Spontaneous volume magnetostriction, which large enough to compensate thermal expansion. It should be only RELATIVELY large. In all considering cases the source of large magnetostriction is decrease of the size of the local moments induced by the thermal disorder of magnetic moments.The source of this decrease may be different in different Invars.

The difference between Invar and non-Invar systems is quantitative not qualitative.

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