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A vibrating-sample magnetometer (VSM) (also referred to as a Foner magnetometer) is a scientific instrument that measures magnetic properties based on Faraday’s Law of Induction. Simon Foner at MIT Lincoln Laboratory invented VSM in 1955 and reported it in 1959.^[1] Also it was mentioned by G.W. Van Oosterhout^[2] and by P.J Flanders in 1956.^[3] A sample is first placed in a constant magnetic field and if the sample is magnetic it will align its magnetization with the external field. The magnetic dipole moment of the sample creates a magnetic field that changes as a function of time as the sample is moved up and down. This is typically done through the use of a piezoelectric material. The alternating magnetic field induces an electric field in the pickup coils of the VSM.^[4] The current is proportional to the magnetization of the sample - the greater the induced current, the greater the magnetization. As a result, typically a hysteresis curve will be recorded^[5] and from there the magnetic properties of the sample can be deduced.

The idea of vibrating sample came from D. O. Smith's^[6] vibrating-coil magnetometer.

Typical VSM overview

Parts of a typical VSM setup

Actively cooled electromagnet/power supply
Amplifier
Control Chassis
Meter
Computer interface
Sensor coils
Vibration exciter with sample holder
Hall probe (optional)

Sample Operating Procedure:^[4]

Mounting the sample in the sample holder
Turning on the VSM system
Run the computer software to initialize the system
Calibrate the system
Optimize the system for M^[4]
Calibrate the Lock-In Amplifier
Take measurements and record data

Conditions for VSM to be effective

Magnetic field must be strong enough to fully saturate the samples (or else inaccurate measurements will be taken)
Magnetic field must be uniform across the sample space (otherwise the addition of field gradients^[5]^[7] will induce force that alter the vibration once again leading to inaccurate results

Importance of pick-up coils

These allow the VSM to maximize the induced signal, reduce the noise, give a wide saddle point, minimize the volume in between the sample and electromagnet to achieve a more uniform magnetic field at the sample space.^[5] The configuration of the coils can vary depending on the type of material being studied.^[5]

Relation to Physics

The VSM relies on Faraday's law of induction, with the detection of the emf given by $\varepsilon =N{d \over dt}(BAcos\vartheta )$ ,^[7] where N is the number of wire turns, A is the area, and $\vartheta$ the angle between the normal of the coil and the B field. However, N and A are often unnecessary if the VSM is properly calibrated.^[7] By varying the strength of the electromagnet through computer software, the external field is sweeped from high to low and back to high.^[7] Typically this is automated through a computer process and a cycle of data is printed out. The electromagnet is typically attached to a rotating base^[7] so as to allow the measurements be taken as a function of angle. The external field is applied parallel to the sample length^[7] and the aforementioned cycle prints out a hysteresis loop. Then using known magnetization of the calibration material and wire volume the high field voltage signal can be converted into emu units - useful for analysis.^[7]

Advantages and Disadvantages

The precision and accuracy of VSM's are quite high even among other magnetometers and can be on the order of ~ $\displaystyle 10^{-6}$ emu.^[5] VSM's further allow for a sample to be tested at varying angles with respect to its magnetization letting researchers minimize the effects of external influences.^[8] However, VSM's are not well suited for determining the magnetization loop due to the demagnetizing effects incurred by the sample.^[8] VSM's further suffer from temperature dependence and cannot be used on fragile samples that cannot undergo acceleration (from the vibration).^[5]^[7]^[8]

References

^ Foner, Simon (1959). "Versatile and Sensitive Vibrating-Sample Magnetometer". Rev. Sci. Instrum. 30 (7): 548–557. Bibcode:1959RScI...30..548F. doi:10.1063/1.1716679.
^ Van Oosterhout, G.W. (1956). Appl. Sci. Res. B6: 101. {{cite journal}}: Missing or empty |title= (help)
^ Flanders, P.J. (1956). IEEE Special Publication, Conference on Magnetism and Magnetic Materials. T-91: 315–317. {{cite journal}}: Missing or empty |title= (help)
^ ^a ^b ^c SWT Physics Department. "Vibrating Sample Magnetometer" (PDF).
^ ^a ^b ^c ^d ^e ^f Lopez-Dominguez, V.; Quesada, A.; Guzmán-Mínguez, J. C.; Moreno, L.; Lere, M.; Spottorno, J.; Giacomone, F.; Fernández, J. F.; Hernando, A.; García, M. A. (2018-03-01). "A simple vibrating sample magnetometer for macroscopic samples". Review of Scientific Instruments. 89 (3): 034707. Bibcode:2018RScI...89c4707L. doi:10.1063/1.5017708. hdl:10261/163494. ISSN 0034-6748. PMID 29604780.
^ Smith, D. O. (1956). "Development of a Vibrating‐Coil Magnetometer". Rev. Sci. Instrum. 27 (261): 261–268. Bibcode:1956RScI...27..261S. doi:10.1063/1.1715538.
^ ^a ^b ^c ^d ^e ^f ^g ^h Burgei, Wesley; Pechan, Michael J.; Jaeger, Herbert (2003-07-10). "A simple vibrating sample magnetometer for use in a materials physics course". American Journal of Physics. 71 (8): 825–828. Bibcode:2003AmJPh..71..825B. doi:10.1119/1.1572149. ISSN 0002-9505.
^ ^a ^b ^c "Interpretation of Vibrating Sample Magnetometer (VSM) analysis". analyzetest.com. 2021-03-16. Retrieved 2021-05-14.

@@ Line 1: / Line 1: @@
 [[Image:VSM en.svg|thumb|VSM schematic]]
 [[Image:VSM.jpg|thumb|VSM setup]]
-A '''vibrating-sample magnetometer''' (VSM) is a scientific instrument that measures magnetic properties. Simon Foner at [[MIT Lincoln Laboratory]] invented VSM in 1955 and reported it in 1959.<ref>{{cite journal|last=Foner|first=Simon|title=Versatile and Sensitive Vibrating-Sample Magnetometer|journal=Rev. Sci. Instrum.|volume=30|issue=7|pages=548–557|year=1959|doi=10.1063/1.1716679|bibcode = 1959RScI...30..548F }}</ref> A sample is first magnetized in a uniform [[magnetic field]]. It is then sinusoidally vibrated, typically through the use of a [[piezoelectric]] material. Commercial systems use linear [[actuators]] of some form. Historically, these systems were developed using modified audio speakers, though this approach was dropped due to the interference through the produced in-phase magnetic noise, as the [[magnetic flux]] through a nearby pickup coil varies sinusoidally. The [[Faraday's law of induction|induced voltage]] in the pickup coil is proportional to the sample's [[magnetic moment]], but does not depend on the strength of the applied magnetic field. In a typical setup, the induced voltage is measured with a [[lock-in amplifier]] using the piezoelectric signal as a frequency reference. It is also possible to record the [[Magnetic hysteresis|hysteresis curve]] of a material by sweeping the magnetic field.
+A '''vibrating-sample magnetometer''' (VSM) (also referred to as a Foner magnetometer) is a scientific instrument that measures magnetic properties based on Faraday’s Law of Induction. Simon Foner at [[MIT Lincoln Laboratory]] invented VSM in 1955 and reported it in 1959.<ref>{{cite journal|last=Foner|first=Simon|year=1959|title=Versatile and Sensitive Vibrating-Sample Magnetometer|journal=Rev. Sci. Instrum.|volume=30|issue=7|pages=548–557|bibcode=1959RScI...30..548F|doi=10.1063/1.1716679|doi-access=free}}</ref> Also it was mentioned by G.W. Van Oosterhout<ref>{{Cite journal|last=Van Oosterhout|first=G.W.|date=1956|journal=Appl. Sci. Res.|volume=B6|pages=101}}</ref> and by P.J Flanders in 1956.<ref>{{Cite journal|last=Flanders|first=P.J.|date=1956|journal=IEEE Special Publication, Conference on Magnetism and Magnetic Materials|volume=T-91|pages=315–317}}</ref> A sample is first placed in a constant magnetic field and if the sample is magnetic it will align its magnetization with the external field. The [[Magnetic moment|magnetic dipole moment]] of the sample creates a magnetic field that changes as a function of time as the sample is moved up and down. This is typically done through the use of a [[piezoelectric]] material. The alternating magnetic field induces an electric field in the pickup coils of the VSM.<ref name=":0">{{Cite web|last=SWT Physics Department|title=Vibrating Sample Magnetometer|url=https://gato-docs.its.txstate.edu/jcr:7543b8ec-f619-49c3-888f-01c3ad13c7da/vsm.pdf}}</ref> The current is proportional to the magnetization of the sample - the greater the induced current, the greater the magnetization. As a result, typically a [[Hysteresis|hysteresis curve]] will be recorded<ref name=":1">{{Cite journal|last1=Lopez-Dominguez|first1=V.|last2=Quesada|first2=A.|last3=Guzmán-Mínguez|first3=J. C.|last4=Moreno|first4=L.|last5=Lere|first5=M.|last6=Spottorno|first6=J.|last7=Giacomone|first7=F.|last8=Fernández|first8=J. F.|last9=Hernando|first9=A.|last10=García|first10=M. A.|date=2018-03-01|title=A simple vibrating sample magnetometer for macroscopic samples|url=https://aip.scitation.org/doi/10.1063/1.5017708|journal=Review of Scientific Instruments|volume=89|issue=3|pages=034707|doi=10.1063/1.5017708|pmid=29604780 |bibcode=2018RScI...89c4707L |issn=0034-6748|hdl=10261/163494|hdl-access=free}}</ref> and from there the magnetic properties of the sample can be deduced.
-The idea of vibrating sample came from D. O. Smith's<ref>{{Cite journal|last=Smith|first=D. O.|title=Development of a Vibrating‐Coil Magnetometer|journal=Rev. Sci. Instrum.|volume=27|issue=261|pages=261|year=1956|doi=10.1063/1.1715538|bibcode=1956RScI...27..261S}}</ref> vibrating-coil magnetometer.
+The idea of vibrating sample came from D. O. Smith's<ref>{{Cite journal|last=Smith|first=D. O.|year=1956|title=Development of a Vibrating‐Coil Magnetometer|journal=Rev. Sci. Instrum.|volume=27|issue=261|pages=261–268|bibcode=1956RScI...27..261S|doi=10.1063/1.1715538|doi-access=free}}</ref> vibrating-coil [[magnetometer]].
+== Typical VSM overview ==
+=== Parts of a typical VSM setup ===
+[[File:VSM-schematic-highres.jpg|thumb|Simplified VSM schematic]]
+* Actively cooled electromagnet/power supply
+* Amplifier
+* Control Chassis
+* Meter
+* Computer interface
+* Sensor coils
+* Vibration exciter with sample holder
+* Hall probe (optional)
+=== Sample Operating Procedure:<ref name=":0" /> ===
+# Mounting the sample in the sample holder
+# Turning on the VSM system
+# Run the computer software to initialize the system
+# Calibrate the system
+# Optimize the system for [[Magnetic moment|''M'']]<ref name=":0" />
+# Calibrate the Lock-In Amplifier
+# Take measurements and record data
+=== Conditions for VSM to be effective ===
+# Magnetic field must be strong enough to fully saturate the samples (or else inaccurate measurements will be taken)
+# Magnetic field must be uniform across the sample space (otherwise the addition of field gradients<ref name=":1" /><ref name=":2">{{Cite journal|last1=Burgei|first1=Wesley|last2=Pechan|first2=Michael J.|last3=Jaeger|first3=Herbert|date=2003-07-10|title=A simple vibrating sample magnetometer for use in a materials physics course|url=https://aapt.scitation.org/doi/10.1119/1.1572149|journal=American Journal of Physics|volume=71|issue=8|pages=825–828|doi=10.1119/1.1572149|bibcode=2003AmJPh..71..825B |issn=0002-9505}}</ref> will induce force that alter the vibration once again leading to inaccurate results
+==== Importance of pick-up coils ====
+These allow the VSM to maximize the induced signal, reduce the noise, give a wide saddle point, minimize the volume in between the sample and electromagnet to achieve a more uniform magnetic field at the sample space.<ref name=":1" /> The configuration of the coils can vary depending on the type of material being studied.<ref name=":1" />
+== Relation to Physics ==
+The VSM relies on [[Faraday's law of induction]], with the detection of the emf given by <math>\varepsilon = N{d \over dt}(BAcos\vartheta)</math>,<ref name=":2" /> where ''N'' is the number of wire turns, ''A'' is the area, and <math>\vartheta</math> the angle between the normal of the coil and the B field. However, ''N'' and ''A'' are often unnecessary if the VSM is properly calibrated.<ref name=":2" /> By varying the strength of the electromagnet through computer software, the external field is sweeped from high to low and back to high.<ref name=":2" /> Typically this is automated through a computer process and a cycle of data is printed out. The electromagnet is typically attached to a rotating base<ref name=":2" />  so as to allow the measurements be taken as a function of angle. The external field is applied parallel to the sample length<ref name=":2" /> and the aforementioned cycle prints out a [[Hysteresis|hysteresis loop]]. Then using known magnetization of the calibration material and wire volume the high field voltage signal can be converted into [[Centimetre–gram–second system of units|emu]] units - useful for analysis.<ref name=":2" />
+== Advantages and Disadvantages ==
+The precision and accuracy of VSM's are quite high even among other [[Magnetometer|magnetometers]] and can be on the order of ~ <math>\displaystyle 10^ {-6}</math> emu.<ref name=":1" /> VSM's further allow for a sample to be tested at varying angles with respect to its magnetization letting researchers minimize the effects of external influences.<ref name=":3">{{Cite web|date=2021-03-16|title=Interpretation of Vibrating Sample Magnetometer (VSM) analysis|url=http://www.analyzetest.com/index.php/2021/03/16/interpretation-of-vibrating-sample-magnetometer-vsm-analysis/|access-date=2021-05-14|website=analyzetest.com|language=en-GB}}</ref> However, VSM's are not well suited for determining the magnetization loop due to the demagnetizing effects incurred by the sample.<ref name=":3" /> VSM's further suffer from temperature dependence and cannot be used on fragile samples that cannot undergo acceleration (from the vibration).<ref name=":1" /><ref name=":2" /><ref name=":3" />
 ==References==
@@ Line 10: / Line 48: @@
 == See also ==
 * [[Magnetometer]]
+*[[Alternating (Field) Gradient Magnetometer (AFGM or AGM)]]
+*[[SQUID magnetometers|SQUID Magnetometer]]
 [[Category:American inventions]]
@@ Line 15: / Line 55: @@
 [[Category:Measuring instruments]]
 [[Category:Magnetometers]]
-{{electromagnetism-stub}}