Methods Characterization and Systems Part 2 Magnetic Properties
11 Apr 2006
char 2.ppt
Methods of Characterization
Characterization methods can be categorized into several general categories. These include (but aren't limited to): 1. Physical--determination of the structural, topographical, morphological state of the sample. Includes SEM, TEM, AFM. 2. Chemical/compositional--characterization of the chemical elements or compounds present in the sample, possibly including location on the surface or with depth into the sample. Includes XRD, EDX, SIMS, XRF, XPS. 3. Electrical--measurement of the resistivity/conductivity of a sample, carrier concentration, mobility of charge carriers. Includes 4PP. 4. Optical--measurement of the optical properties or behavior of the sample. Includes ellipsometry, interference spectroscopy, FTIR, PL. 5. Magnetic--measurement of the magnetic properties or behavior of the sample. Includes VSM, Hall. 6. Mechanical--determination of the mechanical properties (strength, elastic modulus, etc) of the sample.
Characterization Techniques
Method Reflection spectrometry Ellipsometry Low-energy e- diffraction Scanning electron microscopy Electron microprobe Transmission electron microscopy Secondary ion mass spectroscopy X-ray diffraction X-ray fluorescence X-ray photoelectron spectroscopy
Name
Primary Beam V / UV photon Vis photon
Detected Signal V / UV photon Vis photon e- e- x-ray e- ion x-ray x-ray e-
Energy Range
Uses Film thickness t, refractive index n Film thickness, index
LEED SEM EDX TEM SIMS XRD XRF XPS
e- e- e- e- ion x-ray x-ray x-ray
20--200 eV ~0.3--50 keV 1--30 keV 50--400 keV 1--15 keV > 1 keV > 1 keV > 1 keV
Surface structure Surface morphology Surface composition High-resolution atomic structure Composition vs depth Crystal structure, composition Composition near surface Surface composition
Method
Name
Primary Beam or Probe solid probe tip RF signal I I
Detected Signal probe height RF response V V V
Energy Range
Uses
Atomic force microscopy Vibrating sample magnetometer Current-voltage measurement Hall measurement Four-point probe
AFM VSM IV
Surface topography Magnetization, coercivity, hysteresis R, , RS, R ne, nh, & mobility Sheet R
4PP
I
Dipoles
A magnetic dipole is composed of 2 magnetic "charges" or poles, 1 north pole An electric dipole is composed of 2 electric charges, 1 positive and 1 negative.and 1 south pole. Atoms can exhibit magnetic properties that sometimes mimic this simple bar magnet behavior.
N S
E B
This gives bulk materials magnetic behavior.
The electric field of of the magnetic dipole looks identical to the electric dipole. magnetic field the electric dipole looks like this.
Magnetic Materials
Magnetic materials are formed by collecting a large number of atoms that display this inherent magnetism. A bulk piece of a magnetic material
Its constituent magnetic atoms Replace the bar magnets with dipole vectors magnets) (viewed as bar
In this example, all the dipoles are aligned (perhaps by an external magnetic field). In the more general case, the dipoles may be all randomly oriented. These magnetic dipoles (at the atomic level) are represented by i. Since these are vector quantities, the total magnetic moment total is found by a vector sum of the individual atomic magnetic moments.
Magnetic Materials
The total magnetization of a material is defined as the magnetic dipole density in a total material
M =
V
The total magnetic field in a material with an external field B0 is given by
B = B0 + 0 M
The magnetic field intensity in the presence of a magnetic material is given by
B0 H= +M 0
The magnetic permeability of a material is given by
= K m 0
where Km is the relative permeability. The magnetic susceptibility of the material is given by
m = Km -1 M = mH In a linear material, we have
For paramagnetic & diamagnetic materials, Km ~ 1. Ferromagnetic materials have very large Km values. For non-magnetic materials, Km = 1 and m = 0.
Recall the variety of magnetic behaviors that materials & films may exhibit. 1. Diamagnetic--these materials have magnetic susceptibilities that oppose the application of an external B field. This can be viewed as the opposition of e in their orbitals to the varying Bext as required by Lenz's Law. Diamagnetic materials have negative susceptibilities. All materials are inherently diamagnetic to some degree, but other behavior may dominate. Conductors are strongly diamagnetic in the presence of alternating fields. Superconductors, lacking electrical resistance to current flow, are perfectly diamagnetic and expel external B fields from their interiors. Material m ( 105) Bismuth Mercury Silver Carbon (diamond) Carbon (graphite) Lead Sodium chloride Copper Water 16.6 (1.66 104) 2.9 2.6 2.1 1.6 1.8 1.4 1.0 0.91
M
H
2. Paramagnetic--when an external field is applied, these materials are magnetized in the same direction as B. This can be caused by e laying outside closed shells. They exhibit a magnetization that is directly proportional to the applied B field. These materials obey Curie's Law
B ( B, T ) = C T
where C is the Curie constant for the material & T is the absolute temperature. Material Iron oxide (FeO) Iron amonium alum Uranium Platinum Tungsten Cesium Aluminum Lithium Magnesium Sodium Oxygen gas m ( 105) 720 66 40 26 6.8 5.1 2.2 1.4 1.2 0.72 0.19
M
H
The Curie Law for paramagnetic materials
As the T is lowered, the susceptibility increases inversely with T.
(T)
(T ) ~
C T
0
T (K)
3. Ferromagnetic--some materials exhibit large ( >>1) in which long-range order causes unpaired e to line up inside macroscopic regions called domains. In zero external B, the domains may be randomly oriented with respect to each other. In an external B, the domains will begin to align with each other. The material will also display hysteretic effects. For ferromagnets, the susceptibility follows the Curie-Weiss Law above Tc.
( B, T ) =
C T - TC
For T > Tc, the material is paramagnetic. For T < Tc, it is ferromagnetic. Material Tc (K) Fe Co Ni Gd Dy Cu2MnAl Fe2B MnB 1043 1388 627 293 85 630 1015 578
The Curie-Weiss Law for ferromagnetic materials
As the T is lowered, the susceptibility increases inversely with T. There is a critical temperature at Tc for the onset of ferromagnetic behavior. The FM is the low temperature phase while the high temperature phase is PM. ferro (T) Curie-Weiss complex hysteretic behavior Tc para
0
T (K)
Hysteresis, Remanence, & Coercivity of Ferromagnetic Materials
remanent magnetization = M0 coercivity = Hc
"hard" ferromagnetic material has a large M0 and large Hc.
"soft" ferromagnetic material has both a small M0 and Hc.
Coercivities & Remanence of Various Materials
Material BaFe12O19 Alnico IV Alnico V Alcomax I MnBi Ce(CuCo)5 SmCo5 Sm2Co17 Nd2Fe14B
Hc (T) 0.36 0.07 0.07 0.05 0.37 0.45 1.0 0.6 1.2
M0 (T) 0.36 0.6 1.35 1.2 0.48 0.7 0.83 1.15 1.2
(BB0/ 0)max (kJ/m3) 25 10.3 55 27.8 44 92 160 215 260
(This is a quality factor for permanent magnets. The higher it is, the greater the flux that can be obtained pe unit volume of magnet.)
Magnetoresistance
Magnetoresistance is the variation of a material's (or film's) resistance electrical with the applied B field. The resistance can increase or decrease, typically by a few percent for ordinary materials. In a semiconductor with a single carrier type, the MR is proportional to (1 + (B)2) where is the carrier mobility (m2/V-sec). The Giant Magnetoresistance Effect (GMR) is a quantum mechanical effect observed in thin film structures composed of alternating ferromagnetic and nonmagnetic metal layers. The variation can be large. In zero field the magnetization of adjacent ferromagnetic layers are antiparallel due to a weak anti-ferromagnetic coupling between layers. This gives rise to a zero-field resistivity. When a field is applied to the film, a lower resistance appears when the magnetization of the adjacent layers align. The spin of the electrons of the nonmagnetic metal align parallel or antiparallel with an applied magnetic field in equal numbers. These suffer less magnetic scattering when the M of the ferromagnetic layers are parallel.
An example of GMR in Fe/Cr layers. Note how the effect increases as the film thicknesses are varied.
Fe (FM) Cr Fe (FM) t (nm)
Colossal Magnetoresistance
Colossal magnetoresistance (CMR) is a property of some materials, mostly manganese-based perovskite oxides, that enables them to dramatically change their electrical resistance in the presence of a magnetic field. The resistivity can change by orders of magnitude. There is no theory to explain this so far.
Magnetostriction of Ferromagnetic Materials
Magnetostriction is the change in any dimension (expansion or contraction) of a ferromagnetic material caused by a change in the magnetic field threading it.
The magnetostriction coefficient is given as the fractional change in size when M goes from zero to saturation.
=
L L
If the object gets larger with B, then > 0; if it gets smaller then < 0.
Magnetostriction of Ferromagnetic Materials
saturation material crystal axis magnetostriction (x 10-5) +(1.1-2.0) -(1.3-2.0) -0.8 -(5.0-5.2) -2.7 -(2.5-4.7) -(5.0-6.0)
Fe Fe Fe Ni Ni Ni Co
100 111 polycrystal 100 111 polycrystal polycrystal
A common observation of magnetostriction occurs with transformers or fluorescent light ballasts. The noise they may make (a humming sound) happens at 120 Hz since the iron material associated with the transformer core responds to the 60 Hz alternating magnetic field impressed on it (maximum expansion/contraction occurs twice per 60 Hz cycle). Magnetostriction is used to create mechanical or vibratory motion in devices. It can also be used to generate ultrasonic waves.)
Magnetic Measurements-Vibrating Sample Magnetometer
The vibrating sample magnetometer (VSM) is a basic instrument to determine magnetic properties of a sample. It is (perhaps) the most widely used magnetometer today. It offers the best combination of capabilities and can handle samples with a wide variety of properties.
vibration unit
sample
The VSM uses a DC magnetic field provided by an electromagnet, a vibration mechanism to move (oscillate) the sample in the Bdc, and detector coils to detect and measure the AC response of the sample. VSM's can be built operate over a T range from 2.0 to 1050 K If higher fields are needed (> 3 T), more advanced systems may use a superconducting magnet (a solenoid). Powders, bulk and thin films can be measured.
detection coils
magnet
VSM Operation Principle: If a sample of any material is placed in a uniform magnetic field, created between the poles of a electromagnet, a dipole moment will be induced. If the sample vibrates with sinusoidal motion a sinusoidal electrical signal can be induced in suitable placed pick-up coils. The signal has the same frequency of vibration and its amplitude will be proportional to the magnetic moment, amplitude, and relative position with respect to the pick-up coils system. magnetic sample
sample oscillation
detector coils
external DC B0
Vibrating Sample Magnetometer
The system is computer-controlled. The applied B field may be operated using current control (to the magnet) or field control, either in a feedback mode. Field control is preferred since the magnet may exhibit hysteresis, giving a complicated field-current relationship. The field feedback must be low noise to get the required field resolution, ~ 0.001 Oe. This level is required for magnetoresistive materials or films with ...