Ferrite control is one of the key factors involved in order to properly design and produce the necessary deposition of sound, corrosion resistant welds in a variety of Stainless steel welds including the austenitic 347 grade and many other types of SS... So, it's not unusual to have some magnetism @ the welds themselves due to the relatively low percentage of ferrite found in the weld chemical composition, and from the coalescence of the filler metal & base/parent metal too, and this can vary depending on the choice of filler used for welding which is essentially a long casting which you'll understand better what I mean by this once you and anyone else who's interested reads this article below...

To explain in greater detail, I'll use this article from Atlas metals since it isn't too technical yet is in depth and relatively easy to understand:

MAGNETIC RESPONSE OF STAINLESS STEELS
Magnetic response – or the lack of it – is often one of the first things that people think of as a basic property of stainless steels. The response of a stainless steels to a magnet is an interesting physical property and can be a useful sorting test but it is not as clear-cut as is often thought.

WHAT ARE THE BASIC MAGNETIC PROPERTIES OF MATERIALS?this
Ferromagnetic Materials that are strongly attracted to a magnet (either permanent or electro) and that can themselves form permanent magnets. This is the usual property when a material is said to be “magnetic”. Magnetic Permeability The ease by which a magnetic material can be magnetized is expressed by the Magnetic Permeability.
Values close to 1.0 show the material is non-magnetic. Hard or Soft Magnetic Characteristics Magnetic materials can be classified as “Hard” or “Soft”. Hard magnetic materials retain a large amount of residual magnetism after exposure to a magnetic field. Soft magnetic materials can be magnetized by a relatively small magnetic field and when this is removed they revert to low residual magnetism. Non-magnetic Materials Materials that show no response to a magnet. Curie Temperature Some metals have a temperature at which they change from ferromagnetic to non-magnetic. For common carbon steels this happens at about 768°C.

WHICH METALS ARE MAGNETIC?
All common carbon steels (including mild steel), low alloy steels and tool steels are ferromagnetic. Some other metals such as nickel and cobalt are also ferromagnetic. All stainless steels grades with the exception of the austenitic grades are also magnetic – all ferritic grades (eg 430, AtlasCR12, 444, F20S), all duplex grades (eg 2205, 2304, 2101, 2507), all martensitic grades (eg 431, 416, 420, 440C) and all precipitation hardening grades (eg 630/17-4PH). Even although the duplex grades are mixtures of austenite and ferrite they are still strongly attracted to a magnet.

WHICH METALS ARE NON-MAGNETIC?
Most non-ferrous metals such as aluminium and copper and their alloys are non-magnetic. Austenitic stainless steels, both the common 300-series (Cr-Ni) and the lower nickel 200-series (Cr-Mn-Ni) are non-magnetic. It is common for wrought austenitic stainless steels to contain a very small amount of ferrite, but this is not sufficient to significantly affect magnetic performance except in very critical applications.

WELDS AND CASTINGS
Castings in austenitic stainless steels have slightly different compositions compared to their wrought counterparts. The cast version of 316L for instance is grade CF-3M. Most “austenitic” cast alloys are very deliberately made so that they have a few percent of ferrite – this helps prevent hot cracking during casting. A weld can be viewed as a small, long casting, and for the same reason as detailed above austenitic welds have about 4 – 8% ferrite. In the case of both welds and castings the small amount of ferrite results in a small amount of magnetic response, but it can be readily detected with a good hand-held magnet. With a suitable “ferrite meter” this magnetic response can in fact be used to measure the amount of ferrite in a weld. If a weld is required to be zero ferrite content special consumables are available. “Ferrite-free” plate can also be sourced, or existing stock 316 plate can be tested to confirm ferrite level. “Ferrite-free” products are specially produced for a few specific corrosive conditions, not usually for their magnetic properties.

THE EFFECT OF COLD WORK
Even although wrought austenitic stainless steels are non-magnetic in the annealed condition they may develop magnetic response when cold worked. Cold work can transform some austenite to martensite.  This has a dramatic effect on tensile strength and even more so on yield strength; a heavily cold drawn grade 304 wire can achieve a tensile strength of up to around 2000MPa. Such a highly worked 304 will also be very strongly attracted to a magnet. Grades with higher amounts of austenite forming elements – nickel, manganese, carbon, copper and nitrogen – form less martensite when cold worked, so do not become so strongly magnetic.

This can be evaluated as the ratio of austenite former elements divided by ferrite former elements, or simply as the Nickel/Chromium (Ni/Cr) ratio. Grade 316 products usually only become slightly magnetic and 310 and 904L are almost totally non-magnetic no matter how severely cold worked. Grade 301 on the other hand has a lesser amount of nickel and work hardens even more rapidly than does 304 …. and becomes strongly magnetic after even a small amount of cold work. These comparisons are shown in the graph above. Note that different heats of steels of the same grade may exhibit different magnetic responses because of minor differences in the amounts of each element.

HEAT TREATMENT
If a piece of austenitic stainless steel has been made to respond to a magnet by cold work this can be removed by a solution treatment – the standard treatment of heating to about 1050°C (depending on the grade) followed by water quenching or other rapid cooling. The high temperature allows the “strain-induced martensite” to re-form as austenite and the steel returns to being non-magnetic. It is also returned to being low strength.

DOES MAGNETIC RESPONSE MATTER?
Magnetic response has no effect on any other property. Cold drawn 304 (and to a lesser degree 316) is attracted to a magnet, but this has no effect on the corrosion resistance. Some of the most highly corrosion resistant stainless steels are strongly magnetic… examples are the duplex and super duplex grades and highly alloyed ferritic grades such as 29-4C. Cold drawn 304 also has high tensile strength, but this is not due to the magnetic response – both the magnetic response and the high strength are due to the cold work. Applications where absence of magnetic response may be required include MRI equipment and in naval mine-hunter vessels. Specialist guaranteed low magnetic response stainless steels can be sourced for such applications.

MAGNETICALLY SOFT STAINLESS STEELS
Magnetically soft steels are used in electrical applications involving changing electromagnetic induction. Solenoids and relays are typical examples, and where these components also need to have corrosion resistance a ferritic stainless steel can be a good choice. For critical applications specialist ferritic bar grades are available (subject to mill enquiry) with guaranteed magnetic properties.

SORTING OF STEELS
The magnetic response of a piece of steel is a quick and qualitative test that can be useful for sorting grades of stainless steel. Other qualitative tests are listed in Atlas Tech Note 1. Grade Sorting by Magnetic Response. What Can Be Sorted: Austenitic (both 300-Series and 200-series) stainless steels from other steels. All other steels are attracted to a magnet, including all the ferritic, duplex, martensitic and precipitation hardening stainless steels. The only other non-magnetic steels are the austenitic 13% manganese steels (eg “P8”). Method: Note response, if any, when a permanent magnet is brought close to the steel.

Tips & Traps: Some austenitic stainless steel grades, particularly 304, are to some degree attracted to a magnet when cold worked, eg by bending, forming, drawing or rolling. Stress relieving at cherry-red heat will remove this response due to cold work, but this stress relief may sensitize the steel and should not be performed on an item which is later to be used in a corrosive environment. A full anneal is acceptable, however. Even although duplex grades have only half the amount of the magnetic ferrite phase compared to fully ferritic grades such as 430, the difference in “feel” of a manual test is unlikely to be enough to enable sorting duplex steels from ferritic, martensitic or precipitation hardening grades. Austenitic stainless steel castings and welds are also usually slightly magnetic due to a deliberate inclusion of a small percentage of ferrite in the austenitic deposit. The % ferrite can be measured by the amount of magnetic response, and special instruments are available for this. Safety Precautions: No hazards associated with this test. This article is taken from: Atlas Specialty Metal Tech Note 11 "Magnetic Response of Stainless Steel." :

http://www.atlassteels.com.au/documents/TN11-Magnetic%20response%20rev%20Dec%202008.pdf

Here are some more links to similar articles and here's a lesson on stainless steel filler metals from ESAB which I think is good for your further learning & reference:

http://www.esabna.com/EUWeb/AWTC/Lesson5_2.htm

http://www.bssa.org.uk/topics.php?sub_category=31

http://www.welding-advisers.com/Welding-stainless.html

http://www.ssina.com/faq/index.html

Note: There's a a difference between being classified as magnetic and magnetic permeability so when you come across a sentence that states for instance: "Austenitic stainless steel is not magnetic" it doesn't necessarily mean that this type of stainless cannot be made to become magnetic due to an increase in the percentage of ferrite and the fact that this grade does indeed have a certain amount of magnetic permeability, magnetic response due to the relatively low amount of ferrite or iron, and the amount of nickel also found in the alloy mix.

Stainless steels are a very broad group of metals. The name was adopted as a generic term for steel alloys with a minimum of 10.5% chromium. The chromium gives the steel its 'stainless' properties - essentially corrosion resistance. On the surface of the metal, a very thin chromium-rich oxide layer is formed which is inert - i.e. it prevents the steel from rusting. The advantage of stainless steels over plated steels is that, if scratched or damaged, the steel will 'self-repair' as a new oxide layer is formed. In plated steels, scratches in the plate will often lead to corrosion of the steel underneath.

In general, the higher the proportion of chromium, the stronger the corrosion resistance of the steel. In addition to chromium, other metals are added to give the steel particular properties such as strength and malleability. Specifically nickel is used to strengthen the oxide layer.

As for whether they are magnetic, the answer is that it depends. There are several families of stainless steels with different physical properties. A basic stainless steel has a 'ferritic' structure and is magnetic. These are formed from the addition of chromium and can be hardened through the addition of carbon (making them 'martensitic') and are often used in cutlery. However, the most common stainless steels are 'austenitic' - these have a higher chromium content and nickel is also added. It is the nickel which modifies the physical structure of the steel and makes it non-magnetic.

So the answer is yes, the magnetic properties of stainless steel are very dependent on the elements added into the alloy, and specifically the addition of nickel can change the structure from magnetic to non-magnetic.

Here's a very good book to refer to regarding stainless steel weldability and welding metallurgy (Welding Metallurgy and Weldability of Stainless Steels [Hardcover]
John C. Lippold (Author), Damian J. Kotecki (Author) :

http://www.amazon.com/gp/product/0471473790?ie=UTF8&tag=weldingadvise-20&linkCode=as2&camp=1789&creative=390957&creativeASIN=0471473790

Now there's soooo much more to list but, I don't want to overwhelm you and I'm no longer going to list all of the links that are relevant to the topic at hand like I did in the past because I'm now limiting the time I take in responding to queries with information like I used to since my time is all too precious for me these days...

So I hope this will start you out with some decent reference material regarding stainless steel magnetic permeability, and some other facts pertaining to the various grades of stainless steel alloys.

Respectfully,
Henry

If you want to know how magnets work more in depth, here's the site for you:

http://www.coolmagnetman.com/maghow.htm