MAGNETORESISTANCE PHENOMENA IN MAGNETIC MATERIALS AND DEVICES JOSE - PowerPoint PPT Presentation

Constanta, European School on Magnetism 2005 MAGNETORESISTANCE PHENOMENA IN MAGNETIC MATERIALS AND DEVICES JOSE MARIA DE TERESA (CSIC - UNIVERSIDAD DE ZARAGOZA, SPAIN) -INTRODUCTION TO MAGNETORESISTANCE (MR) -LORENTZ MR (LMR), ANISOTROPIC MR (AMR), HALL EFFECT (OHE, EHE) -SPIN-DISORDER MR (SDMR) AND COLOSSAL MR (CMR) -GIANT MR (GMR) -TUNNEL MR (TMR) -PERSPECTIVES

PRELIMINARY CONCEPTS MAGNETORESISTANCE: INTRODUCTION TO Constanta, European School on Magnetism 2005

Constanta, European School on Magnetism 2005 GEOMETRY OF MEASUREMENT Bulk samples are normally measured in bar-shaped geometry and four-point linear contacts. The van der Pauw method is used for samples with arbitrary shape V S (F can be approximated to ρ = 2 , 3 I + V + V - I - F 1 in most of the situations) I d 1 , 4 1 2 3 4 *In this geometry one should be careful regarding offset signals such as thermoelectric effects, electronic offsets, electromotive forces,... Devices such as magnetic tunnel junctions, GMR in CPP geometry, etc. Normally require lithography techniques to define the contacts I - V - I + V + (results are normally expressed in the form of “resistance” or “resistance x surface”) *In this geometry one should be careful regarding geometrical effects arising with high resistive electrodes. ⇒ In all cases d.c. as well as a.c. measurements are possible

Constanta, European School on Magnetism 2005 TYPES OF MATERIALS IN TERMS OF CONDUCTION BEHAVIOUR superconductors ρ =0 Relation between conductivity and resistivity σ=1/ρ 10 18 10 14 10 10 10 6 10 2 10 -2 10 -6 resistivity (ohms cm) ⇒ All kinds of these materials (in terms of conductivity properties) have found applications in different technological domains ⇒ From a basic point of view, the electrical properties indirectly inform the researcher on the band structure, phase transitions, ground state, magnetic effects, impurities in the sample, etc. The dependence of the resistivity under magnetic field gives additional and important information on all these aspects

Constanta, European School on Magnetism 2005 DEFINITIONS OF MAGNETORESISTANCE (similar definitions can be given for “magnetoconductance”) *In the case of monotonous behaviour: *In the case of hysteretical behaviour: ρ (ohms Resistance R AP cm) R P 4 0 4 H(T) Field (Oe) Optimistic view: Optimistic view: ρ − ρ − ( ) H R R ∆ ρ ρ = = ∆ ρ ρ min = 100 / ; (%) 100 / MR x AP P (%) MR x ρ The MR ratio R min The MR ratio P is unlimited is unlimited Pessimistic view: Pessimistic view: − ρ − ρ R R ( ) H = 100 AP P ∆ ρ ρ = = ∆ ρ ρ (%) MR x max / ; (%) 100 / MR x ρ R The MR ratio is AP max The MR ratio is limited to 100% limited to 100%

Constanta, European School on Magnetism 2005 FERROMAGNETIC MATERIALS Magnetization Spin Polarization Half metal = ↑ − ↓ ↑ − ↓ ( ) ( ) P(E F )= ±1 M N N N E N E = F F ( ) P E ↑ + ↓ F ( ) ( ) N E N E F F FERMI FERMI LEVEL LEVEL ENERGY DENSITY OF STATES ⇒ Most of the magnetoresistive devices are built upon ferromagnetic materials and we will concentrate on them. Of course, magnetoresistive effects exist when using other kinds of magnetic and non-magnetic materials but here we will only consider such materials marginally.

Constanta, European School on Magnetism 2005 INTEREST OF MAGNETORESISTIVE SYSTEMS NOWADAYS APPLICATIONS IN: Magnetic read heads, position sensors, earth magnetic field sensing, non- contact potentiometers, non-volatile memories, detection of biological activity, spintronics,... PARADIGMATIC EXAMPLE : GMR sensors are the active elements in the detection of the magnetic information stored in the hard disks of computers 30 nm 250 nm

Constanta, European School on Magnetism 2005 RESISTIVITY OF NON-MAGNETIC METALS ρ = ρ + ρ + ρ ( ) ( ) ( , ) T T B T (Matthiessen’s rule) 0 P m caused by Magnetism caused by defects caused by phonons *Classical image of the resistivity : -Without electric field, random movement of conduction electrons with their Fermi velocity (typically ∼ c/200) but null drift velocity ⇒ no conduction -With applied electric field, a net acceleration appears and a drift velocity given by: <v>=eE τ /m* ( τ is the time between to scattering events). Then j=ne<v> and ρ = m* / n e 2 τ (with τ = λ mfp /v F ) (Drude’s formula) Mean free path ( λ mfp )= path between two consecutive scattering events Spin diffusion length (l SD )= distance between two consecutive scattering events which produce spin flip. l SD >> λ mfp *Key role played by the electrons at the Fermi level in the conduction process :

MAGNETORESISTANCE Constanta, European School on Magnetism 2005 AND HALL EFFECT ANISOTROPIC

Constanta, European School on Magnetism 2005 LORENTZ MR (LMR), ANISOTROPIC MR (AMR) AND HALL EFFECT IN THE CASE OF A POLYCRYSTAL H B = H +4 π M (1-D) z (ISOTROPIC MATERIAL) AND FROM SYMMETRY ARGUMENTS: m = M / | M | ⎡ ⎤ ρ − ρ ( ) ( ) 0 B B ⊥ H [ ] ⎢ ⎥ ∑ = ρ ρ = ρ ρ E J ( ) ( ) 0 When we B B ⎢ ⎥ ⊥ i ij j ij H apply current ⎢ ⎥ j ρ 0 0 ( ) || B ⎣ ⎦ * B ρ = ρ + ρ ( ) ( ) B ρ = ij ij ij resistivity for J parallel to M at B=0 || ρ = resistivity for J perpendicular to M at B=0 At B=0 ⊥ ρ = extraordinary Hall resistivity H ] [ ] r r r r [ r r r = ρ + ρ − ρ + ρ ( ) ( ) ( ) . ( ) E B J B B m J m B m x J ⊥ ⊥ || H Lorentz Hall effect Anisotropic magnetoresistance magnetoresistance effect Campbell and Fert, Magnetic Materials 3 (1982) 747

Constanta, European School on Magnetism 2005 LMR, AMR AND HALL EFFECT r r = ρ LORENTZ MR ( ) E B J ⊥ 1 r -DUE TO THE CURVING OF THE CARRIER TRAJECTORY BY THE r LORENTZ FORCE ( ) q v x B -VERY SMALL IN MOST METALS EXCEPT AT LOW TEMPERATURES OR FOR CERTAIN ELEMENTS -IT FOLLOWS THE DEPENDENCE ∆ρ/ρ =f(B/ ρ 0 ) (Kohler’s RULE) AND AT ∆ ρ ⎛ ⎞ ⎛ ⎞ 1 1 LOW FIELDS = ⎜ ⎟ ⎜ ne ⎟ 2 B ⎜ ⎟ ρ ρ ⎝ ⎠ ⎝ ⎠ ⇒ The fundamental quantity for LMR is ω c τ , the mean angle turned along the helical path between collisions, where ω c is the cyclotron frequency ( ω c =eB/m*c) Ferre in “Magnetisme- Fondements” (edited by PUG)

Constanta, European School on Magnetism 2005 LMR, AMR AND HALL EFFECT LORENTZ MR Bi thin films M. Kohler, Ann. Phys. 6 (1949) 18107 and J. F.Y. Yang et al., Phys. Rev. Lett. 82 (1999) 3328 Ferre in “Magnetisme-Fondements” (edited by PUG)

Constanta, European School on Magnetism 2005 LMR, AMR AND HALL EFFECT ) ( ) m r r ( r r = ρ − ρ ANISOTROPIC MR ( ) ( ) . E B B m J ⊥ 2 || -Spontaneous anisotropy of the MR (B=0): ρ − ρ ∆ ρ ⊥ = || ρ ρ + ρ ( 1 / 3 ) ( 2 / 3 ) ⊥ || (extrapolation to B=0 required) z M x J y -Angular dependence of the anisotropic M MR at magnetic saturation: Θ ρ = ρ + ρ Θ 2 cos J 0 ani ( Θ =angle between J and M ) J M ( ρ ani can be either positive or negative)

Constanta, European School on Magnetism 2005 LMR, AMR AND HALL EFFECT ANISOTROPIC MR Physical origin of the AMR : spin-orbit interaction effect: λ L.S ⇒ It is expected to be large only in systems with large spin-orbit interaction and anisotropic charge distribution Examples of the AMR behaviour : 1) It was shown in magnetoresistance measurements of rare-earth-doped gold that the AMR was large in all cases except for Gd, with L=0 (Gd +3 ⇒ 4f 7 ); ( Fert et al., Phys. Rev. B 16 (1977) 5040 )

Constanta, European School on Magnetism 2005 LMR, AMR AND HALL EFFECT ANISOTROPIC MR Examples of the AMR behaviour : 2) In transition-metal-based compounds, it is normally very small (because the orbital moment is almost quenched) except in some particular cases such as Ni-Co and Ni-Fe alloys (AMR up to 6% at 300 K). Thin films based on this kind of alloys were used for the first MR read heads. It has been found for the ∆ ρ ρ = γ α − (with γ =spin-orbit constant and α = ρ ↑ / ρ ↓ ) spontaneous AMR: / ( 1 ) 3) In magnetic oxides, AMR is also small except for systems having large orbital moment such as SrRuO 3 ( Herranz et al., J. Magn. Magn. Mater. 272-276 (2004) 517 ) T C

Constanta, European School on Magnetism 2005 LMR, AMR AND HALL EFFECT M r r r J = ρ ( ) E B m x J HALL EFFECT E 3 3 H ρ = ρ + ρ 0 EHE ( ) B B M H H H Ordinary Extraordinary Hall effect Hall effect (EHE) 1 ρ = − 0 H nec Explained by the Lorentz force (as in semiconductors). Its origin has been related to spin-orbit coupling in the presence of carrier spin polarization. Typically, it is stronger than the ordinary Hall effect. Figure from J. Ferre in “Magnetisme- Fondements” (edited by PUG)

Constanta, European School on Magnetism 2005 LMR, AMR AND HALL EFFECT EXTRAORDINARY HALL EFFECT (EHE) -An asymmetric interaction of the carriers with the scattering centers occur because the carriers have a spin. At least, two kinds of processes contribute to this effect: “skew scattering” and “jump scattering” Crepieux and Bruno, Phys. Rev. B 64 (2001) 014416 -The EHE effect is strongly temperature dependent and typically exhibits a peak below T C . Its sign can be even opposite to that of the ordinary Hall effect. EHE in La 2/3 Ca 1/3 MnO 3 , Matl et al., Phys. Rev. B 57 (1998) 10248