# Magnetic Materials and Magnetism

8
How can I calculate force between permanent magnet and electromagnet?

I need to calculate force between Permanent magnet (NdFeb) and electromagnet for different voltages(5-24). They are 5 mm apart in the device.

Currently I had measure the Magnetic field  for Permanent magnet in terms of Magnetic Fled Vs Distance  (197 mT at 5 mm) and for electromagnet in terms on Magnetic Field Vs Voltage (134 mT for 12V at contact).

Any suggestions will be highly appreciated.

Please have a look at the recent paper:

Parametric resonance induced chaos in magnetic damped driven pendulum by Giorgi Khomeriki, http://arxiv.org/abs/1511.04593

The calculations presented there are simplified but nevertheless quite useful for the situation described, similar to yours.

8
What is the substrate influence on the magnetic domains formation in the case of thin films?

Magnetic microstructure  What is the substrate influence on the magnetic domains formation in the case of thin films?

3
What is the magnetic moment of NdMnO3 thin films in terms of bohr magneton?

I am working in NdMnO3 thin films, and recently started studying about the Magnetization in NdMnO3 films

I had a question about How to calculate Magnetization M in terms of Bohr magneton in case of thin films?

In case of bulk we can consider the mass of the sample in grams and calculate on the basis of emu/g but in case of thin film as per my knowledge the volume term is considered and the value here will be in emu/cc, this means no mass term present.

So I have a query of how to calculate the value of magnetic moment for the film in terms of Bohr magneton?

I think that the number f.e. per unit cell for NdMnO3 is the same as for LaMnO3, because it is a matter of one structural type (perovskite). I believe that to understand the different kinds of magnetization it will be a useful the answer to the question “What is the difference between magnetic moment(m), magnetization (M)?” from me and Sami Mahmood. See in: https://www.researchgate.net/post/What_is_the_difference_between_magnetic_momentm_magnetizationM

3
Can anyone make me clear regarding the calculating molar effective magnetic moment from Curie-Weiss law?

I know the curie -Weiss law  χm = Cm/(T − Θ).

In the paramagnetic region, I fitted experimental data with a linear fit and extracted the Θ  (Weiss temperature) and Cm (molar Curie constant) in units of  K and K.Cm3/mol.

Effective paramagnetic momentum µeff = (3KBCm/N)1/2,

I used the all the constant values and

B= 0.927 ×10−20 erg/Oe.

Finally, I come up with

µeff =2.83(Cm)1/2µB .

The above relation is valid for unit cell or formula unit?

In my unit cell, two formula units are there.

Kindly, clarify the above doubt.

.

From  above eqation HOW DID YOU calculated N value N is number of magnetic atoms per unit volume right...

17
Bohr magnetons
How to calculate the value for Bohr magneton per formula unit? I have got the value of saturation magnetization in emu.
1. Magnetometer gives you the total moment of the specimen (usually in emu). Convert that to Bohr magnetons. If your sample is saturated, then this is the saturation moment. If there is some diamagnetic contribution from the substrate [negative slope at high fields when film is saturated] (or another substrate contribution, which you would have to characterize), then subtract that first. Unless you know exactly what to subtract, this is a prime source for uncertainty in magnetometry on thin films. [Look into the linked publication for a trick to compensate the substrate contribution, esp. page 480]
2. If you have the film area of your sample then since you know the thickness you have the volume of the film. From this (and 1.) you can determine the magnetization in Bohr magnetons per unit of volume.
3. To make units of Bohr magnetons per atom useful, you need to put in some knowledge about the film material. If it is a single element, then take its density (default: bulk value; better: determined for your film [XRD or whatever]) in terms of atoms/volume and you will obtain the (average) moment in bohr magnetons per atom. Discard "average" if you KNOW the film is magnetically homogeneous (interface and surface layers may [and will, especially if the film is not protected] be different form the inner part!).
4. In case the film is an alloy, a mixture or some compound, then think first about which atoms potentially carry magnetic moments and restrict the above calculation to their density to determine their (average!!) moments per atom. Use your knowledge about the material to possibly make more useful assignments than a simple average.
• Source
##### Article: Nanoscaled alloy formation from self-assembled elemental Co nanoparticles on top of Pt films
[Hide abstract]
ABSTRACT: The thermally activated formation of nanoscale CoPt alloys was investigated, after deposition of self-assembled Co nanoparticles on textured Pt(111) and epitaxial Pt(100) films on MgO(100) and SrTiO(3)(100) substrates, respectively. For this purpose, metallic Co nanoparticles (diameter 7 nm) were prepared with a spacing of 100 nm by deposition of precursor-loaded reverse micelles, subsequent plasma etching and reduction on flat Pt surfaces. The samples were then annealed at successively higher temperatures under a H(2) atmosphere, and the resulting variations of their structure, morphology and magnetic properties were characterized. We observed pronounced differences in the diffusion and alloying of Co nanoparticles on Pt films with different orientations and microstructures. On textured Pt(111) films exhibiting grain sizes (20-30 nm) smaller than the particle spacing (100 nm), the formation of local nanoalloys at the surface is strongly suppressed and Co incorporation into the film via grain boundaries is favoured. In contrast, due to the absence of grain boundaries on high quality epitaxial Pt(100) films with micron-sized grains, local alloying at the film surface was established. Signatures of alloy formation were evident from magnetic investigations. Upon annealing to temperatures up to 380 °C, we found an increase both of the coercive field and of the Co orbital magnetic moment, indicating the formation of a CoPt phase with strongly increased magnetic anisotropy compared to pure Co. At higher temperatures, however, the Co atoms diffuse into a nearby surface region where Pt-rich compounds are formed, as shown by element-specific microscopy.
Beilstein Journal of Nanotechnology 01/2011; 2(1):473-85. DOI:10.3762/bjnano.2.51
1
How can I simulate a permanent magnet in Comsol?

I am trying to simulate a permanent magnet in COMSOL. I am aware of the example provided, but that one is axisymmetric and when I tried to repeat it in 3D I didn't get it. I have attached to examples of my trials. Can anyone help me? All I want is to simply simulate the magnetic field.

+ 1 more attachment

Start thinking as a pole of the magnet fixed.

39
How to stabilize magnetic nano-particles?
I have a problem with agglomeration of magnetic nano-particles and i don't know how to stabilize them. Does anyone have advice?

Please How can I use Oleic acid to stabilize magnetic nano-particles, but not during the preparation because I already prepared the samples. Another problem I have is crystallizes are with sizes vary from 9-15 nm but agglomerate during the extraction to bigger particles. I tried the coating with dextran but a partial sedimentation occur. So now how can i agglomerate the particles to coat them.

2
Why are current induced spin orbit torque switching studies done on Perpendicular anisotropy(PMA) materials?

Why most of current induced spin orbit torques studies done on ultra thin Ferromagnetic systems? (i am talking about HeavyMetal (HM)/ Ferromagnet(FM)/ insulator or HM).

i have a qualitative understanding about Spin Hall effect and Rashba effects resulting in spin polarised currents from HM giving rise to SOT. But my confusion is about ultra thin limits of FM when PMA appears.

Is SOT assisted magnetization reversal seen only in ultra thin FM ? is it to do with the volume/ number of FM atoms to be reversed? or is it to do with the experimental ease of monitoring the magnetisation state of PMA systems?

As Christian said, this is an interface effect. The SOT, PMA , STT etc. effective fields in the FM layer averaged over its volume  will be scaled as one over the FM layer thickness considering a pure macrospin behavior.

11
When does the VSM loop split and what can I say from this graph?
I recently conducted SQUID measurements and have got this graph with a split in the VSM graph. I would like to know as to what to deduce from the graph.

When changing the direction of the field sample has been package elaboration and therefore there is a split line in this area. This is normal and often does happen.

5
How do I create heating curves for magnetic hyperthermia of liquid and solid samples?

actually i am working on different ferrites coated with silica for magnetic hyperthermia. i got the heating measurements for liquid samples as well as for the powder samples. my question is that why the powder sample has saturation temp. reaches above 200 degree as compared to the liquid samples of different concentrations. Do we have some explanation along with physical background and reference for that.

Bruvera is absolutely correct.

12
Does anyone have experience with VSM analysis?

Herewith, the VSM result for synthesized nanoparticles is attached. Does anyone know how to analyse the graph step by step? What could be concluded? Is it superparamagnetic NPs?

Make in other sample and see the result

4
Why do the authors use law of approach to saturation in this paper?

what is the reason behind the terms used in Law of approach to saturation ?

The method adopted to deduce the anisotropy constant from the hysteresis loop is questionable, although it has been adopted in some cited works on micro- and nanoparticles. The empirical law of approach to saturation is indeed a rough method to estimate anisotropy from (initial) magnetization curves of bulk polycrystalline materials. Equation (2) is an empirical law that applies to the case of a ferromagnet consisting of randomly oriented single-domain crystallites, with the initial state characterised by M=0. If the system starts from a remnant state (as in the hysteresis loops shown in this work), the numerical coefficients of the law should be different, as explained in J. F. Herbst and F. E. Pinkerton, Phys. Rev. B 57 (1998) 10733. Moreover, the adopted first numerical coefficient (0.07619) holds for the case of independent particles (not interacting).
A spurious contribution could also arise from the possible rotation of nanoparticles under the effect of an applied field. To sum up, the applicability of this analysis to the system studied in this work is uncertain, considering that the nanoparticles actually form agglomerations and thus a strong interaction between them should occur.

• ##### Article: Strain-induced high coercivity in CoFe2O4 powders
[Hide abstract]
ABSTRACT: Three cobalt ferrite (CoFe2O4) powders were used as starting materials for mechanical milling. A mechanical milling for a short time resulted in a relatively large residual strain and a high density of defects in the micrometer-sized CoFe2O4 powders. High coercivities (up to 5.1 kOe) were achieved in these samples, probably due to the stress anisotropy and pinning effects. A relatively high remanence ratio of 60% and a relatively large value of (BH)max of up to 2.0 MG Oe were obtained for the sample with the highest coercivity. A prolonged milling resulted in the formation of nanosized grains in an amorphous matrix, and the reduction of coercivity to a very low level. The initial particle/grain size played an important role in the microstructure evolution. No significant change in both microstructure and coercivity was found in the CoFe2O4 sample consisting of nanoparticles after mechanical milling.
Applied Physics Letters 01/2006; 88(4):042506-042506-3. DOI:10.1063/1.2161808

I'm sorry you can send me this job.

4
How does the magnetic property of a salt change with hydration?

I want to know how the paramagnetic property of ferrous sulphate change with hydration. Is there any general trend for this change that can be predictive for other salts?

Basically hydration will modify your possible exchange pathways, so you have to take into consideration the new structure, to see how it affects the magnetic properties of the compound.

6
How can I define hard magnet and soft magnet?

Is that any specific value of coercivity and remanence to define whether a material is hard magnet or soft magnet?

Dear Lau,
Magnetic materials can be divided into two groups, as wrote. But they are not magnetic materials soft or hard. These are materials having magnetic properties, soft or hard and this is a difference, but it is small. Generally, the division applies:
1 - 10 A / m - super-soft magnetics,
10 - 100 A / m - very soft magnetics,
100 - 1000 A / m - soft magnetics,
above are semi-hard and hard magnetic materials.

• Rukshan Thantirige asked a question:
Open
Anyone familiar with the exchange decoupling of SmCo5/Co bi-layers at low temperatures?

I measured in-plane hysteresis of SmCo5/Co bi-layers deposited on MgO(100) and glass at different T's from 300 K to 10 K. In both cases, HC rises as expected, however, an exchange de-coupling can be observed below a critical T, only for the sample made on glass. I understand that, in general, exchange decoupling can occur with lowering the T due to rise in anisotropy of the hard phase (Kh), which mandates a smaller soft phase size (LS) for effective coupling (as LS indirectly proportional to Kh), regardless the substrate you use. However, this doesn't explain why I don't observe any decoupling for the sample made on MgO(100).

I checked grain formation of Cr (under layer) and SmCo5 layers by AFM and noted that both Cr and SmCo5 grains formed on MgO(100) are smaller and have narrow size distributions, unlike on glass. XRD doesn't shed any light as both samples produce same signals with different intensities (probably due to epitaxial match/mismatch). I believe that this has something to do with the anomaly in grain formation but I just can't find an explanation. Any input is highly appreciated.

4
How to confirm the anitiferromagnetsim using M-T curve

In Ni-Sn alloy system, the material shows antiferromagnetism in room temperature hysteresis curve, i have also confirmed with ABK plot. I want to know how to confirm that antiferromagnetism using M-T curve. Do i need to take high temperature M-T curve or low temperature M-T curve to confirm that.

AFM does not give hysteresis. It depends on the material and reason for AFM mechanism, we can go for low temp or high temp M-T. In you system I suggest you can try M-T for high temperature and see at which temp the moment is maximum.

1
How can I calculate the magnetic couplings constants in the system with three magnetically active metal centers in linear chains?

What is the practical approach, i.e. using energy differences between ferromagnetic and antiferromagnetic states? in similar way to the Yamaguchi formula?

The question is what is the magnetic coupling mechanism?

In case of the super-exchange mechanism one can map the Heisenberg Hamiltonian into an Ising Hamiltonian and then use the "broken symmetry" method. An example of this approach applied to solid-state structures of AgCuF3 and NaCuF3 can be found in J. Tong, C. Lee, M.-H. Whangbo, R. K. Kremer, A. Simon, and J. Köhler, Solid State Sci., 2010, 12, 680–684.

5
How do barium hexaferrite particles cluster together to form plate-like structures?

I am doing studies on 325 mesh sized barium hexaferrite particles. Barium hexaferrite has a hexagonal structure with its axis of magnetization along the c-axis.

I am placing the particles in a silicone elastomer and poling the solution in a magnetic field causing the particles to align in the field. Using SEM images it has been observed the barium particles are clustering together to form thin plate-like structures. I am interested in how the axis of magnetization of the individual particles maps onto these structures, and particularly the direction of the magnetic moment of the plate structures.

Has anyone come across this clustering before with a similar material? Any suggestions on experimentally or theoretically determining the direction of magnetization of these plates is appreciated?

What type is your hexaferrite? Is it M-type, Y-type, W-type...? Depending on the experimental procedure such as the preparation method and heat treatment, hexaferrites crystallize as almost regular hexagonal platelets. Fro example see the articles:

1. Structural and magnetic properties of Cu-V substituted M-type barium hexaferrites, IOP Conf. Series: Materials Scie. Eng. 92 (2015) 012008. DOI: 10.1088/1757-899X/92/1/012008

2.  Magnetic properties and hyperfine interactions in M-type BaFe12-2xMoxZnxO19 hexaferrites, J. Appl. Math. Phys. 2 (2014) 77-87

3. Effects of heat treatment on the phase evolution, structural, and magnetic properties of Mo-Zn doped M-type hexaferrites, Solid State Phenomena, 232 (2015) 63-92.

4. Modification of the magnetic properties of Co2Y hexaferrites by divalent and trivalent metal substitutions, Solid State Phenomena 241 (2016) 93-125

M-type hexaferrite is usually uniaxial with easy c-axis perpendicular to the hexagonal layer. However, Y-type hexaferrites for example has an easy-plane with the magnetization parallel to the hexagonal plane. Switching the magnetic anisotropy from easy axis to easy plane and vice versa is possible by making special metal substitutions in the hexaferrites.

6
Any advantages of using a magnetized NdFeB sputtering target over a non-magnetized one?
I want to buy a NdFeB sputtering target and the manufacturer asked whether I'd like the magnetized or the non-magnetized version. So if I buy a magnetized target, shouldn't I need to do high temperature annealing of sputtered samples (since the material is already in its magnetic phase)? On the other hand, will magnetized targets cause sputtering difficulties?
Any input is highly appreciated.

Asif,

If you heat your magnet above its Curie temperature (typically 80-200 ºC) and then cool it you should mostly 'demagnetise' it.  What you are really doing is partially scrambling the preferred magnetisation direction of the domains in the magnet - it is still 'magnetised', just not in any preferred direction.

If you want to use this as a sputter target (as in the original thread) then there a few things to note:

You should do this heating in a controlled atmosphere or you will likely change its composition.

Does your 'magnet have a nickel coating?  If so you likely want to remove the nickel coating before using it in a sputter gun.... or you'll just get a nickel film!

Finally - the 'demagnetised' magnet is still ferromagnetic and will likely interfere with the operation of a standard sputter gun... but the best bet is to use as thin a target as you can find - certainly a quarter inch thick target would be preferred over a half inch one.

8
Why are the alkaline earth metals non-magnetic and their oxidation state is 2+?

Normally alkaline earth (AE) metals (Be, Mg, Ca, Sr.....) are non-magnetic and their oxidation state is 2+. If the oxidation state is 3+, both spin and orbital angular momentum has some values and  finally total angular momentum (J) is non zero. So it would be magnetic in 3+ state. Is it possible? Anyone please kindly clarify my doubt.

Thank you very much Dr. Maykel Manawan for a wonderful discussion

6
Is there a way (program) to plot a structure with magnetic vectors automatically, from the magnetic structure refinement results of FullProf?
One could add vectors in most of the structure visualisation programs. But this gets tedious when the magnetic structure is incommensurate. It will be great if any of the visualisation programs have the capability to read this details from any output files from the FullProf refinement.

A good news ! Now FullProf outputs 'mcif' file with magnetic structure details. This can be opened directly with the program vesta (have not tried with other structure plotting programs). At this point it works only with commensurate structures (with k=(000)).

4
Can I use a normal laboratory solenoid to investigate magnetostriction in mild steel using a strain gauge by measuring change in length?

I am currently in my final year of bachelors and my research involves investigating the effect of an externally applied magnetic field on the young's modulus of a bar of mild steel. The problem is, I have not been able to get a solenoid to produce the magnetic field to investigate this phenomenon. My question is:

1) will a normal laboratory solenoid allow magnetostriction in mild steel that can be measured using a strain gauge in terms of change in length of the specimen

2) if not, what instrument can I use in order to produce the necessary magnetic field for this experiment. Where can I buy it.

Thank you.

It is possible to measure magnetostriction with a strain gauge.  A full Wheatstone Bridge is the best bet so you can compensate for temperature effects.  You will need to identify the H-Field required to saturate the material so you can get maximum strain. It would be best if the rod is 'longer' rather than 'shorter' as the strains will be very small.  Look up the value but, at best, I guess it would be in around 10ppm.

Optical systems can work well but can be pricey if off the shelf. Do-able though.  LVdTs and Load Cells can be viable and cheap options.

One thing you did not say was what frequency you will operate at.  That can make a big difference.  As the frequency goes up you will get a drop in performance until you hit resonances.

9
Any advice on the Hysteresis loop and Permalloy ?

Hysteresis loop of permalloy is very small and its related with losses. Magnetic Permeability of permalloy is very high and good heating can be obtained due to losses. Are there any other parameters that can influence the losses ?

The losses can be reduced to zero if one prepares a nanosintered ferrite block properly.  I have observed 5 deggrees C of cooling with barium Ferrite.

4
Is there any easy-to-make p-MTJ (Magnetic Tunnel Junction) recipe ?

Hello,

Can anyone recommend me a recipe for p-MTJ that is easy to make? Performance is not an issue, and it doesnt have to be novel design either.

Regards,

Indra

Many thanks prof Gang Xiao

3
Surfactant for stable suspension of fe-based alloy powder in a organic solvents?

Is there a surfactant that is able to create a stable suspension of Fe-based alloy powder (particle size around 5 µm) in an organic solvent such as hexane, heptane or similar?

nothing else is expected for high density particles of µm size in a low density, low viscosity fluid (Stokes law). Only solution microgravity.

4
Is there any possibility to convert scandium oxide to scandium nitrate?

Dissolve Sc2O3 in quite excess of conc. HNO3 at 160-170 degree C for 30 minutes with stirring. Unlike other oxides, Sc2O3 need high temp and long time to form nitrates....

8
Is it important FMR and EDMR for caracterisation of MNP?

Due to lack of equipment I dont think I will be able to perform ferromagnetic resonance, electrically detected magnetic resonance or Nuclear magnetic resonance spectroscopy in order to characterize my magnetic nanopaticles ( range 8-22 nm). what should I do? I only can use Vibrating sample magnetometer and MRI ( magnetic resonance imaging ).

Do you think I will lack valuable data without those analysis or there are other methods to substitute them? for example site.directed spin labeling or electron spin resonance spectroscopy ( electron paramagentic resonance )

Diluting the sample will (in general) produce something threedimensional, whether spreading on a surface a two-dimensional array. For the same average distance between particles, you will have MUCH less sample in the latter case (the sample area in a magnetometer is limited). In the end it is up to you - it may or may not be easier to spread the samples on a surface than producing a threedimensional dilution. This depends on your system.

In the 2D (surface) case, you have another nice check for interactions: With no interactions (and isotropic or statistically oriented particles), the M(H) curve will be independent of whether the field is applied within the surface plane or perpendicular to it. In the presence of dipolar interactions you will have in-plane-anisotropy (the equivalent of shape anisotropy in magnetic materials).

In a case with about 15% surface coveragy by ~6nm Fe particles, we have easily observed such an anisotropy, see: hysica status solidi (b) 05/2010; 247(5):1170 - 1179. (DOI:10.1002/pssb.200945607).

What the required distance actually is will depend on the moment of the particles. The larger the individual moments, the larger the required distance between them.

7
What is the difference between Morin transition and temperature induced spin reorientation transition?

Basically, In both processes the direction of ferromagnetic vector spontaneously rotates from one direction to other. Here I'm concerning about the spin reorientation usually observed in orthoferrite systems which is a second order magnetic transition. Then what is the fundamental process of the spin flipping which makes Morin transition to be first order and different than spin reorientation?

Which orthoferrite are you talking of? HoFeO3 and TbFeO3 show spin reorientation transition and I studied them on single crystals by neutron diffraction. The other rare earth orthoferrite may also undergo such spin reorientation transition. You must note that the rare-earth orthoferrites have two magnetic sublattices, R (rare earth) and Fe. There are three different magnetic exchange interactions, Fe-Fe, Fe-R and R-R. Fe ions order at high temperatures of the order of 700 K. At lower temperatures spin the reorientation transition occur (for HoFeO3 T_R = 50 K). At even lower temerature rare earth ion orders. The three exchange interactions are of different magnitudes. Fe-Fe is the strongest, the Fe-R interaction is intermediate and R-R is the weakest. At high temperature Fe ions order due t the strong Fe-Fe nteraction. As the temperature is reduced Fe-R becomes gradualy more important causing soin reorientation transition and thn at very low temperatures the weak R-R nteraction causes ordering of the rare-earth sublattice. This is not a real spotaneous transition but can be called induced transition. This typical physics of two magnetic sublattices is common to RFeO3, RCrO3 and R2CuO4 (R = Nd). And this physics is quite different from the physics Morin transition in which Fe2O3 consists of one single magnetic sublattice.

5
How can we 'flatten out' or reduce the noise in a Hall measurement setup?

We are measuring the Hall resistance of a magnetic nanowire, the result shows that the different magnetization direction of the nanowire gives two different resistant value, as presented in the attached image.

However as we can see that the 'on' and 'off' value is not exactly constant, they change all the time and we also see a lot of noise.

Is there any electrical setup that we can add to the whole system so that the reading becomes a square wave?

Indra,

I agree with the previous answers. But, are you sure you are seing the effect of two magnetization states ? Or might it be the random telegraph signal (RTS) due to emission/capture of a single electron by a trap in your low-dimensional system?

We showed such signals occuring in quantum well GaAs-based Hall sensors, cf  the ref in the link. These are RTS signals and they look very similar to your signal. Depending on the charged or neutral state of a single trap, the current density distribution in the 1µm sized device is different, and the offset at the Hall output is different too.

• Source
##### Article: Low-frequency noise in AlGaAs/InGaAs/GaAs Hall micromagnetometers
[Hide abstract]
ABSTRACT: We report on studies aimed at understanding and improving the intrinsic noise of high-performance sensors using a 2D electron gas channel confined by a quantum well in the pseudomorphic AlGaAs/InGaAs/GaAs heterostructure. MIS gated and ungated Hall sensors shaped as a Greek cross with dimensions ranging from 100 mum down to submicrometer range have been investigated. At room temperature the predominant low frequency Hall voltage noise originates from the ensemble of trapping/detrapping events occurring within the continuum of GaAs surface states. Its power spectral density can be deduced from independent measurements of the interface trap density-of-states by applying Shockley-Read-Hall dynamics and the Fluctuation-Dissipation Theorem. In fact, theoretical spectra calculated without any adjustable fitting parameter coincide closely with the experimentally measured ones. At cryogenic temperature this interface traps noise freezes out, thus revealing a much weaker intrinsic background noise with 1/f spectrum. For small sensors the intrinsic /f noise converts into one or a few lorentzians due to the action of individual random telegraph signals (RTS). For Hall crosses with an intersection of 4x4mum2, we find statistically less than 1 fluctuator per each decade of time constant at 77 K. Due to the random distribution of the elementary fluctuators, some of these small Hall crosses may show less low-frequency noise than much larger 60x60mum2 sensors.
Proceedings of SPIE - The International Society for Optical Engineering 05/2003; 5115. DOI:10.1117/12.497001

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