Cluj school, September 2007 MAGNETORESISTANCE PHENOMENA AND RELATED EFFECTS JOSE MARIA DE TERESA (CSIC - UNIVERSIDAD DE ZARAGOZA, SPAIN) -INTRODUCTION TO MAGNETORESISTANCE (MR) -LORENTZ MR, ANISOTROPIC MR, HALL EFFECT, SPIN-DISORDER MR AND COLOSSAL MR -GIANT MR -TUNNEL MR -OTHER MAGNETORESISTIVE EFFECTS -APPLICATIONS OF MAGNETORESISTIVE DEVICES *EXCHANGE-BIAS FOR SPIN VALVES *MAGNETIC RANDOM ACCESS MEMORIES
Cluj school, September 2007 SPINTRONICS / MAGNETOELECTRONICS
Cluj school, September 2007 INTRODUCTION TO MAGNETORESISTANCE: PRELIMINARY CONCEPTS
Cluj school, September 2007 GEOMETRIES FOR THE MEASUREMENT OF RESISTANCE Bulk samples are normally measured in bar-shaped geometry and four-point linear contacts. Resistivity can be determined. V *R=I/V= I 1-4 / V 2-3 S (F can be approximated to ρ = 2 , 3 F 1 in most of the situations) I d 1 , 4 I + V + V - I - Relation between conductivity ρ (ohm x cm) and resistivity σ=1/ρ σ=1/ρ σ=1/ρ σ=1/ρ (Siemens) 1 2 3 4 * Four-contact measurements eliminate the contact and lead resistances. One should be careful regarding offset signals such as thermoelectric effects, electronic offsets, electromotive forces, which can be minimised by current inversion in d.c. Typical size measurements or using a.c. measurements: is millimetric *R=(R 1 +R 2 )/2 with R 1 = I 1-4 /V 2-3 and R 2 =I 4-1 /V 3-2 *R offset =(R 1 -R 2 )/2
Cluj school, September 2007 GEOMETRIES FOR THE MEASUREMENT OF RESISTANCE *The van der Pauw method is used for bulk samples with arbitrary shape 1 . 1331 f A t ρ = + − − 1 2 ρ + ρ ( V V V V ) A 2 4 1 3 ρ = I A B 2 1 . 1331 f B t ρ = + − − ( V V V V ) B 6 8 5 7 I 3 4 t=sample thickness; I=current; V=voltages; f=f(V, arc cosh function) *V 1 : I 2-1 , V 3-4 ; V 2 : I 1-2 , V 4-3 ; V 3 : I 3-2 , V 4-1 ; V 4 : I 2-3 , V 1-4 ; *V 5 : I 4-3 , V 1-2 ; V 6 : I 3-4 , V 2-1 ; V 7 : I 1-4 , V 2-3 ; V 8 : I 4-1 , V 3-2 ; *The van der Pauw method is very useful for measurements on regular thin films π V d ρ = 1 , 2 For samples with a line of symmetry: 1 2 ln 2 I 3 , 4 3 4
Cluj school, September 2007 GEOMETRIES FOR THE MEASUREMENT OF RESISTIVITY Devices such as micro- and nano-devices (GMR spin-valves, magnetic tunnel junctions, nanoconstrictions,...) normally require lithography techniques to define the transport geometry and the contacts. *Micrometric devices are normally patterned by means of optical lithography techniques *Nanometric devices are normally patterned by means of electron-beam lithography, focused ion beam lithography, nanoimprinting, etc. Design for R, MR and Hall effect 3 4 5 measurements of a thin film 1 2 MR: I(1,2); V(3,5 ) Au Au 6 7 8 Fe 3 O 4 Fe 3 O Hall: I(1,2); V(4,7) 4
Cluj school, September 2007 GEOMETRIES FOR THE MEASUREMENT OF RESISTIVITY -Measurements in perpendicular geometry are difficult because they require several lithographic steps to define the current (which can be required for certain measurements in GMR-CPP configuration, magnetic tunnel junctions, etc.). � � Example: masks for magnetic tunnel junctions � � I - V - I + V + *In these nanodevices, one should be careful regarding geometrical effects arising with high resistive electrodes, large contact pads, etc.
Cluj school, September 2007 DEFINITIONS OF MAGNETORESISTANCE (similar definitions can be given for “magnetoconductance”) *In the case of monotonous behaviour: *In the case of hysteretical behaviour: ρ ρ ρ 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 / ; MR (%) 100 x / = 100 AP P MR (%) x ρ The MR ratio R min The MR ratio P is unlimited is unlimited Pessimistic view: Pessimistic view: − R R ρ − ρ ( H ) = 100 AP P MR (%) x ∆ ρ ρ = = ∆ ρ ρ max / ; MR (%) 100 x / ρ R The MR ratio is AP max The MR ratio is limited to 100% limited to 100%
Cluj school, September 2007 FERROMAGNETIC MATERIALS Magnetization Spin Polarization Half metal = ↑ − ↓ ↑ − ↓ M N N N ( E ) N ( E ) P(E F )= ±1 = 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.
Cluj school, September 2007 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 (biosensors), spintronics,... PARADIGMATIC EXAMPLE : GMR and TMR sensors are the active elements in the detection of the information stored in the hard disks of computers
Cluj school, September 2007 ORIGIN OF RESISTIVITY *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 =E/J ρ = m* / n e 2 τ (with τ = λ mfp /v F ) λ mfp )= path Mean free path ( λ λ λ (Drude’s formula) between two consecutive scattering events ρ = ρ + ρ + ρ ( T ) ( T ) ( B , T ) (Matthiessen’s rule) 0 P m Normally giving caused by Magnetism caused by defects rise to small MR caused by phonons effects *Additional sources of resistivity (unveiled in nanodevices) : * They appear when the sample size is comparable to significant In some cases transport parameters such as the mean free path , the spin diffusion the MR effects length (distance between two consecutive scattering events which can be large produce spin flip), the Fermi length of the conduction electrons ,… even at low fields
Cluj school, September 2007 LORENTZ MR ANISOTROPIC MR AND HALL EFFECT
Cluj school, September 2007 LORENTZ MR (LMR), ANISOTROPIC MR (AMR) AND HALL EFFECT IN THE CASE OF A POLYCRYSTAL H B = H +4 π M (1-D) (ISOTROPIC MATERIAL) AND FROM z SYMMETRY ARGUMENTS: m = M / | M | � � ρ − ρ ( B ) ( B ) 0 ⊥ H � � [ ] � = ρ ρ = ρ ρ When we E J ( B ) ( B ) 0 � � ⊥ i ij j ij H apply current � � j ρ 0 0 || B ( ) � � * B ρ = ρ + ρ ( B ) ( ) ρ = resistivity for J parallel to M at B=0 ij ij ij || ρ = resistivity for J perpendicular to M at B=0 At B=0 ⊥ ρ = extraordinary Hall resistivity H � � � � ] [ ] [ � � � = ρ + ρ − ρ + ρ E ( B ) J ( B ) ( B ) m . J m ( B ) m x J ⊥ ⊥ || H E 3 E 1 E 2 Lorentz Hall effect Anisotropic magnetoresistance magnetoresistance effect Campbell and Fert, Magnetic Materials 3 (1982) 747
Cluj school, September 2007 LMR, AMR AND HALL EFFECT � � = ρ LORENTZ MR E ( B ) J ⊥ 1 -DUE TO THE CURVING OF THE CARRIER � � TRAJECTORY BY THE LORENTZ FORCE ( ) q v x B Ferre in “Magnetisme- -VERY SMALL IN MOST METALS EXCEPT AT LOW Fondements”, PUG TEMPERATURES OR FOR CERTAIN ELEMENTS � � � � The fundamental quantity for LMR is ω ω c τ τ , the mean ω ω τ τ angle turned along the helical path between collisions, where ω ω ω c is the cyclotron frequency ( ω ω ω ω ω c =eB/m*c) Bi thin films Resistivity ( µΩ cm) MR(%) M. Kohler, Ann. Phys. 6 (1949) 18107 F.Y. Yang et al., Phys. Rev. Lett. 82 (1999) 3328
Cluj school, September 2007 LMR, AMR AND HALL EFFECT � � ) ( ) m � � ( = ρ − ρ ANISOTROPIC MR E ( B ) ( B ) m . J ⊥ 2 || -Spontaneous anisotropy of the MR (B=0): ρ − ρ ∆ ρ ρ − ρ ∆ ρ ⊥ = || ⊥ = || ρ ρ ρ ρ + ρ ( 1 / 3 ) ( 2 / 3 ) ⊥ 0 || (extrapolation to B=0 required) z M x J y -Angular dependence of the anisotropic M MR at magnetic saturation: Θ Θ Θ 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)
Cluj school, September 2007 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 )
Recommend
More recommend
