Abstract:
A magnetomechanical resonance element or marker strip with facilitated performance based on an amorphous magnetostrictive alloy ribbon is utilized in an electronic article surveillance marker. A curvature along the element&#39;s length direction is introduced during ribbon fabrication with a different radius of curvature, which increases the resonance performance with minimal loss in the magneto-mechanical circuit, and more particularly, in a marker utilizing a plurality of resonating elements or marker strips. A marker is fabricated utilizing the resonance element or elements and is utilized in an electronic article surveillance system.

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to ferromagnetic amorphous alloy ribbon and to a marker for use in an electronic article surveillance system, the marker consisting of one or a plurality of rectangular strips based on an amorphous magnetostrictive material that vibrates in an alternating magnetic field mechanically at a resonant frequency varying with an applied static magnetic field, whereby the magnetomechanical effect of the marker is effectively utilized. The present invention is also directed to an electronic article surveillance system utilizing such a marker. 
   2. Background of the Invention 
   Magnetostriction of a magnetic material is a phenomenon in which a dimensional change takes place upon application of an external magnetic field on the magnetic material. When the dimensional change is such that the material elongates upon its being magnetized, the material is termed “positive-magnetostrictive”. When a material is “negative-magnetostrictive”, the material shrinks upon its magnetization. Thus in either case, a magnetic material vibrates when it is in an alternating magnetic field. When a static magnetic field is applied along with the alternating field, the frequency of the mechanical vibration of the magnetic material varies with the applied static field through magneto-elastic coupling. This is commonly known as ΔE effect, which is described, for example, in “Physics of Magnetism” by S. Chikazumi (John Wiley &amp; Sons, New York, 1964, page 435). Here E(H) stands for Young&#39;s modulus, which is a function of applied magnetic field H, and the material&#39;s vibrational or resonance frequency f r  is related to E(H) through
 
 f   r =(½ l )[ E ( H )/ρ] 1/2 ,   (1)
 
where l is the length of the material and ρ is the mass density of the material.
 
   The magneto-elastic or magneto-mechanical effect described above is utilized in electronic article surveillance systems which were first taught in the U.S. Pat. Nos. 4,510,489 and 4,510,490 (hereinafter the &#39;489 and &#39;490 patents). Such surveillance systems are advantageous systems, in that they offer a combination of high detection sensitivity, high operating reliability and low operating costs. 
   A marker in such systems is a strip, or a plurality of strips, of known length of a ferromagnetic material, packaged with a magnetically harder ferromagnet (material with a higher coercivity) that provides a static field termed as bias field to establish peak magneto-mechanical coupling. The ferromagnetic marker material is preferably an amorphous alloy ribbon, since the efficiency of magneto-mechanical coupling in the alloys is very high. The mechanical resonance frequency, f r  is determined essentially by the length of the alloy ribbon and the bias field strength, as Equation (1) above indicates. 
   When an interrogating signal tuned to the resonance frequency is encountered in a surveillance system, the marker material responds with a large signal field which is detected by a receiver in the system. 
   Several amorphous ferromagnetic materials were considered for electronic article surveillance systems based on magnetomechanical resonance described above in the original &#39;489 and &#39;490 patents and included amorphous Fe—Ni—Mo—B, Fe—Co—B—Si, Fe—B—Si—C and Fe—B—Si alloys. Of the alloys, a commercially available amorphous Fe—Ni—Mo—B based METGLAS®2826MB alloy was used extensively until accidental triggering, by a magnetomechanical resonance marker, of other systems based on magnetic harmonic generation/detection. This occurs because a magnetomechanical resonance marker used at that time sometimes exhibited non-linear BH characteristics, resulting in generation of higher harmonics of the exciting field frequency. To avoid this problem, sometimes called a system “pollution problem,” a series of new marker materials were invented, examples of which were disclosed in U.S. Pat. Nos. 5,495,231, 5,539,380, 5,628,840, 5,650,023, 6,093,261 and 6,187,112. Although the new marker materials perform, on average, better than the materials utilized in the surveillance systems of the original &#39;489 and &#39;490 patents, somewhat better magnetomechanical performance was found in the marker materials disclosed, for example, in U.S. Pat. No. 6,299,702 (hereinafter, the &#39;702 patent). The new marker materials require complicated heat-treatment processes to achieve desired magnetomechanical properties as disclosed, for example, in the &#39;702 patent. Clearly, a new magnetomechanical marker material is needed which does not require such complicated post-ribbon fabrication processes, and the present invention provides such a marker material with high magnetomechanical performance without causing the “pollution problem” that is mentioned above. A marker strip in accordance with the &#39;702 patent is widely used for a marker with two strips, as is disclosed in U.S. Pat. No. 6,359,563. Due to the fact that the two strips have the same radius of curvature along the strip width direction since each of them was processed in exactly the same way, in accordance with the &#39;702 patent, the two strips touch each other at many points on the strip surfaces, damping the magnetomechanical vibration on the strips, and hence reducing the effectiveness of the marker. This drawback needs to be ameliorated. Furthermore, there is a need for an effective electronic article surveillance system which utilizes such a marker. 
   SUMMARY OF THE INVENTION 
   In accordance with an embodiment of the invention, a soft magnetic material is utilized for a marker of an electronic article surveillance system based on magnetomechanical resonance. 
   A marker material with enhanced overall magnetomechanical resonance properties is fabricated from an amorphous alloy ribbon. The magnetic marker material in a ribbon form having magnetomechanical resonance capability is cast on a rotating substrate as taught in the U.S. Pat. No. 4,142,571. When the as-cast ribbon width is wider than the predetermined width for a marker material, said ribbon is slit to said predetermined width. The ribbon thus prepared is cut into ductile, rectangular amorphous metal marker strips having a predetermined length to fabricate a magnetomechanical resonance marker using one or a plurality of said marker strips with at least one semi-hard magnet strip which provides a bias static magnetic field. Said magnetomechanical resonance marker does not trigger other systems based on the principle of magnetic higher harmonics generation/detection. 
   An electronic article surveillance system utilizes a marker of the present invention. The system has an article interrogation zone in which a magnetomechanical marker of the present invention is subject to an interrogating magnetic field at the resonance frequency of a marker strip, the signal response to the interrogating magnetic field excitation being detected by a receiver having a pair of antenna coils situated in the article interrogation zone. The received magnetomechanical resonance signal is then processed by a signal detection circuit which identifies the marker. 
   In accordance with an embodiment of the invention, a marker of a magnetomechanical resonant electronic article surveillance system, comprises: at least one ductile magnetostrictive strip cut from an amorphous ferromagnetic alloy ribbon that has a curvature along a ribbon length direction and exhibits magnetomechanical resonance under alternating magnetic field excitation with a static bias field, the at least one marker strip having a magnetic anisotropy direction along a direction perpendicular to a ribbon axis. 
   Where selected, a radius of curvature of the at least one ductile magnetostrictive marker strip is less than 100 cm. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy ribbon has a saturation induction ranging from 0.7 tesla to 1.1 tesla. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy ribbon has a saturation magnetostriction ranging from 8 ppm to 18 ppm. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy ribbon has a composition based on Fe a —Ni b —Mo c —B d  with 30≦a≦43, 35≦b≦48, 0≦c≦5, 14≦d≦20 and a+b+c+d=100, up to 3 atom % of Mo being optionally replaced by Co, Cr, Mn and/or Nb and up to 1 atom % of B being optionally replaced by Si and/or C. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy ribbon is an alloy having a composition of one of Fe 40.6  Ni 40.1  Mo 3.7  B 15.1  Si 0.5 , Fe 41.5  Ni  38.9  Mo 4.1  B 1.55 , Fe 41.7  Ni 39.4  Mo 3.1  B 15.8 , Fe 40.2  Ni 39.0  Mo 3.6  B 16.6  Si 0.6 , Fe 39.8  Ni 39.2  Mo 3.1  B 17.6  C 0.3 , Fe 36.9  Ni 41.3  Mo 4.1  B 17.8 , Fe 35.6  Ni 42.6  Mo 4.0  B 17.9 , Fe 40 Ni 38 Mo 4 B 18 , or Fe 38.0  Ni 38.8  Mo 3.9  B 19.3 . 
   In accordance with an embodiment of the invention, the at least one marker strip has a discrete length and exhibits magnetomechanical resonance at a length-related frequency. 
   Where selected, the at least one marker strip has a length ranging from approximately 15 to approximately 65 mm. 
   Where selected, the at least one marker strip has a marker strip width ranging from approximately 3 mm to approximately 15 mm. 
   In accordance with an embodiment of the invention, the at least one marker strip has a length-to-width ratio exceeding 3. 
   In accordance with an embodiment of the invention, the at least one marker strip has a slope of resonance frequency versus bias field ranging from approximately 4 Hz/(A/m) to approximately 14 Hz/(A/m). 
   In accordance with an embodiment of the invention, the marker comprises a plurality of marker strips with different radius of curvatures along the marker strips&#39; length direction. 
   Where selected, the plurality of marker strips are stacked or placed side-by-side. 
   In accordance with an embodiment of the invention, the marker comprises two marker strips and has a slope of resonance frequency versus bias field ranging from approximately 3.5 Hz/(A/m) to approximately 10 Hz/(A/m). 
   In accordance with an embodiment of the invention, the marker comprises three marker strips and has a slope of resonance frequency versus bias field ranging from approximately 4 Hz/(A/m) to approximately 9 Hz/(A/m). 
   In accordance with an embodiment of the invention, the marker comprises four or five marker strips and has a slope of resonance frequency versus bias field ranging from approximately 2 Hz/(A/m) to approximately 4 Hz/(A/m). 
   Where selected, at least one bias magnet strip is placed along the at least one marker strip&#39;s direction. 
   In accordance with an embodiment of the invention, the at least one marker strip is housed in a cavity separated from the bias magnet strip. 
   In accordance with an embodiment of the invention, electronic article surveillance system has a capability of detecting resonance of a marker, and comprises a surveillance system tuned to predetermined surveillance magnetic field frequencies, wherein the surveillance system detects a marker that is adapted to mechanically resonate at a preselected frequency, and has at least one ductile magnetostrictive marker strip cut from an amorphous ferromagnetic alloy ribbon that has a curvature along a ribbon length direction and exhibits magnetomechanical resonance under alternating magnetic field excitation with a static bias field, the at least one marker strip having a magnetic anisotropy direction along a direction perpendicular to a ribbon axis. 
   Where selected, a radius of curvature of the at least one ductile magnetostrictive marker strip is between approximately 20 cm and approximately 100 cm. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention will be more fully understood and further advantages will become apparent when reference is made to the following detailed description of the preferred embodiments and the accompanying drawings in which: 
       FIG. 1A  illustrates a side view of a marker strip cut from an amorphous alloy ribbon in accordance with an embodiment of the present invention and having a bias magnet, and  FIG. 1B  illustrates a view of a conventional marker strip with a bias magnet; 
       FIG. 2  illustrates magnetomechanical resonance characteristics of a single strip marker of the present invention and magnetomechanical resonance characteristics of a conventional single strip marker, showing resonance frequency as a function of bias field; 
       FIG. 3  illustrates resonance signals of a single strip marker in accordance with an embodiment of the present invention and resonance signals of a conventional strip marker, showing resonance signal amplitudes as a function of bias field; 
       FIG. 4  illustrates a BH loop taken at 60 Hz on a marker strip of an embodiment of the present invention having a length of approximately 38 mm, a width of approximately 6 mm and a thickness of about 28 μm; 
       FIG. 5A  illustrates a magnetomechanical resonant marker of an embodiment of the present invention with one marker strip of  FIG. 1A , and  FIG. 5B  illustrates a conventional marker with the strip of  FIG. 1B ; 
       FIGS. 6A-1  and  6 A- 2  illustrate a comparison of a physical profile of an embodiment of a magnetomechanical resonant marker of the present invention with two marker-strips whose side view is shown in element  122 , and  FIGS. 6B-1  and  6 B- 2  illustrates a comparison of a conventional marker with two conventional art strips whose angled view is shown in element  222 ; 
       FIG. 7  illustrates magnetomechanical resonance characteristics of a two-strip marker of an embodiment of the present invention and a two-strip conventional marker, showing resonance signals as a function of bias field; 
       FIG. 8  illustrates magnetomechanical resonance signal decay of a two-strip marker of an embodiment of the present invention and a two-strip conventional marker, showing resonance response signal as a function of time after termination of excitation; 
       FIG. 9  illustrates magnetomechanical resonance characteristics of a three-strip marker of an embodiment of the present invention, showing resonance frequency and response signals as a function of bias field; 
       FIG. 10  illustrates resonance signal amplitudes, V 0max  and V 1max , as a function of the number of marker strips; 
       FIG. 11  is a schematic illustration of an electronic article surveillance system of an embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   A marker material with enhanced overall magnetomechanical resonance properties is fabricated from an amorphous alloy ribbon. The magnetic marker material in a ribbon form having magnetomechanical resonance capability is cast on a rotating substrate as taught in the U.S. Pat. No. 4,142,571. When the as-cast ribbon width is wider than the predetermined width for a marker material, the ribbon is slit to the predetermined width. The ribbon thus prepared is cut into ductile, rectangular amorphous metal strips having a predetermined length to fabricate a magnetomechanical resonance marker using one or a plurality of the strips with at least one semi-hard magnet strip which provides a bias static magnetic field. The magnetomechanical resonance marker does not trigger other systems based on the principle of magnetic higher harmonics generation/detection. 
   In one embodiment of the present invention, the amorphous ferromagnetic alloy utilized to form a ribbon for the marker strip has a composition based on Fe a —Ni b —Mo c —B d  with 30≦a≦43, 35≦b≦48, 0≦c≦5, 14≦d≦20 and a+b+c+d=100, up to 3 atom % of Mo being optionally replaced by Co, Cr, Mn and/or Nb and up to 1 atom % of B being optionally replaced by Si and/or C. 
   In certain embodiments of the present invention, the amorphous ferromagnetic alloy utilized to form a ribbon for the marker strip has a composition of one of Fe 40.6  Ni 40.1  Mo 3.7  B 15.1  Si 0.5 , Fe 41.5  Ni 38.9  Mo 4.1  B 15.5 , Fe 41.7  Ni 39.4  Mo 3.1  B 15.8 , Fe 40.2  Ni 39.0  Mo 3.6  B 16.6  Si 0.6 , Fe 39.8  Ni 39.2  Mo 3.1  B 17.6  C 0.3 , Fe 36.9  Ni 41.3  Mo 4.1  B 17.8 , Fe 35.6  Ni 42.6  Mo 4.0  B 17.9 , Fe 40 Ni 38 Mo 4 B 18 , or Fe 38.0  Ni 38.8  Mo 3.9  B 19.3 . 
   Thus, an amorphous magnetostrictive alloy having a chemical composition similar to a chemical composition of a commercially available amorphous METGLAS®2826MB ribbon was cast in accordance with the invention described in the U.S. Pat. No. 4,142,571. The amorphous alloy had a saturation induction of about 0.88 Tesla and a saturation magnetostriction of about 12 ppm. The cast ribbon had widths of about 100 mm and about 25 mm, and its thickness was about 28 μm. The ribbon was then slit into narrower ribbons with different widths. The slit ribbon then was cut into ductile, rectangular strips having a length ranging from about 15 mm to about 65 mm. Each strip had a slight curvature reflecting ribbon casting wheel surface curvature. During slitting, the original curvature was modified. The curvature of a slit and cut strip was determined as described in Example 1.  FIG. 1A  illustrates the physical appearance of a marker strip  10  of an embodiment of the present invention having a bias magnet  12 , and  FIG. 1B  illustrates the physical appearance of a conventional strip  20  produced in accordance with a complex heat-treatment method disclosed in the U.S. Pat. No. 6,299,702. As indicated in  FIG. 1A , magnetic flux lines  11  are more closed in a resonance marker-bias strip configuration of an embodiment of the present invention than the magnetic flux lines  21  of a conventional strip as is illustrated in  FIG. 1B . This enables better coupling between a marker strip  10  of an embodiment of the present invention and a bias magnet strip  12  than is achieved by a conventional strip  20  and a bias magnet  22 , which results in less flux leakage at the two ends of a resonance marker strip of the embodiment of the present invention. Each resonance marker strip of the embodiment of the present invention and the conventional strip was examined in light of magnetomechanical resonance performance using a characterization method of Example 2. 
     FIG. 2  compares the resonance frequency as a function of bias field for a single strip marker  330  of an embodiment of the present invention and the resonance frequency of a conventional strip  331 , both of which had a width of about 6 mm and a length of about 38 mm.  FIG. 2  indicates that the resonance frequency change as a function of bias field is about the same for both cases. The resonance characteristics depicted in  FIG. 2  are important in designing a resonance marker with deactivation capability because deactivation is accomplished by a change in the resonance frequency by changing bias field strength. During deactivation, the slope of the resonance frequency f r  with respect to bias field H b , i.e., df r /dH b , determines the effectiveness of deactivation, and therefore is an important factor for an effective resonance marker strip. 
   Comparison of the resonance response between the two cases is illustrated in  FIG. 3 , in which V 0  is the response signal amplitude when the exciting field is turned off, and V 1  is the signal amplitude at 1 msec after the termination of the exciting field. Clearly, a higher V 1 /V 0  ratio is preferred for a better performance of a resonance marker. Both of the signal amplitudes are therefore used in industry as part of the figure of merit for a magnetomechanical resonance marker.  FIG. 3  indicates that the signal amplitude V 0    441  and V 1    442  become maximum at a bias field of H b0 =500 A/m and H b1 =400 A/m, respectively, for a resonance marker strip of an embodiment of the present invention, and V 0    443  and V 1    444  become maximum at bias fields of H b0 =460 A/m and H b1 =400 A/m, respectively, for a conventional resonance marker strip. In addition,  FIG. 3  indicates that the ratio of V 1 /V 0  at these maximum points is higher for a resonance marker strip of an embodiment of the present invention than for a conventional marker strip, illustrating that signal retention in a marker strip of an embodiment of the present invention is better than in a conventional marker. 
   Table I summarizes a comparison of parameters critical for the performance of a marker strip as a magnetomechanically resonating element between representative conventional marker strips and examples from the marker strips of an embodiment of the present invention. It is noted that the performance of the marker strips of the embodiment of the present invention is close to, or superior to, the performance of conventional marker strips. All of the marker strips of embodiment of the present invention in Table I are acceptable for use in markers of the embodiment of the present invention with each of the strip&#39;s height h, as defined in  FIG. 1A , between about 0.18 mm and about 0.64 mm, which corresponds to the strip&#39;s length direction radius of curvature between about 28 cm and about 100 cm as given in Table I. 
   In Table I, maximum signal voltage for V 0  and V 1  measured at bias field strength, H b0  and H b1 , respectively, and the resonance frequency slope, df r /dH b , measured at H b1  for marker strips of the embodiment of the present invention with strip curvature h, as defined in  FIG. 1A , were compared with corresponding characteristics for ten conventional marker strips, randomly selected. 
   The length, l of the strips were all about 38 mm, and their widths were about 6 mm. A radius of curvature for each marker strip was calculated from h and l. The resonance frequency of each strip was about 58 kHz. 
   
     
       
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE I 
             
           
           
             
                 
             
             
               Magnetomechanical Resonance Characteristics 
             
           
        
         
             
                 
                 
                 
                 
                 
                 
                 
               Radius of 
             
             
                 
               V 0max   
               H b0   
               V 1max   
               H b1   
               df r /dH b   
               h 
               Curvature 
             
             
               Marker 
               (mV) 
               (A/m) 
               (mV) 
               (A/m) 
               [Hz/(A/m)] 
               (mm) 
               (cm) 
             
             
                 
             
             
               Conventional 
               140~180 
               440~500 
               60~102 
               360~420 
               5.60~11.5 
               — 
               — 
             
             
               Present 
               167 
               490 
               97 
               400 
               12.0 
               0.18 
               100 
             
             
               Invention 
             
             
               No. 1 
             
             
               No. 2 
               156 
               470 
               86 
               410 
               9.50 
               0.18 
               100 
             
             
               No 3 
               159 
               490 
               84 
               410 
               12.5 
               0.20 
               90 
             
             
               No. 4 
               167 
               490 
               94 
               400 
               11.8 
               0.20 
               90 
             
             
               No. 5 
               183 
               458 
               110 
               390 
               11.8 
               0.23 
               78 
             
             
               No. 6 
               165 
               488 
               94 
               370 
               12.5 
               0.23 
               78 
             
             
               No. 7 
               178 
               471 
               106 
               391 
               12.3 
               0.28 
               65 
             
             
               No. 8 
               160 
               460 
               92 
               379 
               10.8 
               0.28 
               65 
             
             
               No. 9 
               157 
               461 
               87 
               351 
               9.10 
               0.36 
               50 
             
             
               No. 10 
               147 
               420 
               76 
               391 
               10.3 
               0.64 
               28 
             
             
                 
             
           
        
       
     
   
   Table I contains data for a marker strip width of about 6 mm, which is presently widely used. It is one aspect of the present invention to provide marker strips with widths different than about 6 mm. Marker strips with different widths were slit from the same ribbon used in Table I, and their magnetomechanical resonance characteristics were determined. The results are summarized in Table II. The resonance signal voltages, V 0 max  and V 1max  decreased with decreasing width, as expected. The decrease in the characteristic field values, H b0  and H b1 , with decreasing width is due to demagnetizing effects. Thus, a bias field magnet must be selected accordingly. A marker with a smaller width is suited for a smaller article surveillance area, whereas a marker with a larger width is suited for a larger article surveillance area because resonance signals are larger from larger marker strips, as Table II indicates. Since the resonance frequency depends primarily on the strip length, as Equation (1) indicates, the strip width change does not affect the resonance frequency of the article surveillance system used. 
   Table II shows the magnetomechanical resonance characteristics of marker strips of an embodiment of the present invention with strip height h, as defined in  FIG. 1A , and with different strip widths. The definitions for V 0 max , H b0 , V 1 max , H b1 , and df r /dH b  were the same as in Table I. The length l of the strips were all about 38 mm. A radius of curvature for each marker strip was calculated from h and l. The resonance frequency of each strip was about 58 kHz. 
   
     
       
             
           
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE II 
             
           
           
             
                 
             
             
               Magnetomechanical Resonance Characteristics 
             
           
        
         
             
               Marker 
                 
               H b0   
                 
                 
               df r /dH b   
                 
               Radius of 
             
             
               Width 
               V 0max   
               (A/ 
               V 1max   
               H b1   
               [Hz/ 
               h 
               Curvature 
             
             
               (mm) 
               (mV) 
               m) 
               (mV) 
               (A/m) 
               (A/m)] 
               (mm) 
               (cm) 
             
             
                 
             
           
        
         
             
               4 
               107 
               310 
               56 
               330 
               4.69 
               0.61 
               30 
             
             
               5 
               153 
               300 
               76 
               300 
               6.05 
               0.41 
               44 
             
             
               9 
               194 
               500 
               101 
               440 
               4.84 
               0.81 
               22 
             
             
               14 
               321 
               590 
               174 
               511 
               4.86 
               0.84 
               21 
             
             
                 
             
           
        
       
     
   
   Another aspect of the present invention is to provide a variety of available markers operated under different conditions. For this purpose, magnetomechanical resonance characteristics were varied by changing the chemical composition of the amorphous magnetic alloy ribbon from which marker strips were produced. The chemical compositions of the alloys examined are listed in Table III, in which values of the saturation induction and magnetostrictions for the alloys are given. The results of the magnetomechanical resonance properties of these alloys are given in Table IV below. 
   Table III shows examples of magnetostrictive amorphous alloys with their compositions, saturation inductions, B s , and saturation magnetostrictions, λ s , for magnetomechanical resonance markers of an embodiment of the present invention. The values of B s  were determined from DC BH loop measurements of Example 3, and the values of λ s  were calculated by using an empirical formula λ s =k B s   2 , with k=15.5 ppm/tesla 2 , following S. Ito et al.,  Applied Physics Letters,  vol. 37, p. 665 (1980). 
   
     
       
             
           
             
             
             
             
           
             
             
             
             
           
         
             
               TABLE III 
             
           
           
             
                 
             
             
               Magnetostrictive Amorphous Alloy 
             
           
        
         
             
                 
                 
               Saturation 
               Saturation 
             
             
               Alloy 
               Marker Chemical Composition 
               Induction 
               Magnetostriction 
             
             
               No. 
               (numbers in atom %) 
               B s (tesla) 
               λ s (ppm) 
             
             
                 
             
           
        
         
             
               A 
               Fe 40.6 Ni 40.1 Mo 3.7 B 15.1 Si 0.5   
               0.88 
               12 
             
             
               B 
               Fe 41.5 Ni 38.9 Mo 4.1 B 15.5   
               0.98 
               15 
             
             
               C 
               Fe 41.7 Ni 39.4 Mo 3.1 B 15.8   
               1.03 
               16 
             
             
               D 
               Fe 40.2 Ni 39.0 Mo 3.6 B 16.6 Si 0.6   
               0.93 
               13.5 
             
             
               E 
               Fe 39.8 Ni 39.2 Mo 3.1 B 17.6 C 0.3   
               0.94 
               14 
             
             
               F 
               Fe 36.9 Ni 41.3 Mo 4.1 B 17.8   
               0.83 
               10.5 
             
             
               G 
               Fe 35.6 Ni 42.6 Mo 4.0 B 17.9   
               0.81 
               10 
             
             
               H 
               Fe 39.6 Ni 38.3 Mo 4.1 B 18.0   
               0.88 
               12 
             
             
               I 
               Fe 38.0 Ni 38.8 Mo 3.9 B 19.3   
               0.84 
               11 
             
             
                 
             
           
        
       
     
   
   Table IV shows the magnetomechanical resonance characteristics of marker strips having different chemical compositions listed in Table III of an embodiment of the present invention with strip height h as defined in  FIG. 1A . The definitions for V 0 max , H b0 , V 1 max  and df r /dH b  were the same as in Table I. The length l of the strips were all about 38 mm. A radius of curvature for each marker strip was calculated from h and l. The resonance frequency of each strip was about 58 kHz. 
   
     
       
             
           
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
           
         
             
               TABLE IV 
             
           
           
             
                 
             
             
               Magnetomechanical Resonance Characteristics of the Alloys in Table III 
             
           
        
         
             
                 
                 
                 
                 
                 
                 
               Radius of 
             
             
               Alloy 
               V 0max   
               H b0   
               V 1max   
               H b1   
               df r /dH b   
               Curvature 
             
             
               No. 
               (mV) 
               (A/m) 
               (mV) 
               (A/m) 
               [Hz/(A/m)] 
               (cm) 
             
             
                 
             
           
        
         
             
               A 
               184 
               370 
               94 
               330 
               8.10 
               71 
             
             
               B 
               174 
               490 
               89 
               348 
               10.4 
               36 
             
             
               C 
               188 
               471 
               70 
               368 
               13.0 
               33 
             
             
               D 
               158 
               580 
               83 
               580 
               4.85 
               33 
             
             
               E 
               160 
               320 
               72 
               300 
               8.80 
               25 
             
             
               F 
               160 
               341 
               84 
               329 
               7.06 
               34 
             
             
               G 
               154 
               420 
               94 
               389 
               8.51 
               36 
             
             
               H 
               171 
               472 
               85 
               351 
               9.73 
               27 
             
             
               I 
               146 
               352 
               60 
               250 
               13.4 
               30 
             
             
                 
             
           
        
       
     
   
   All of the chemistries examined yielded magnetomechanical resonance signals such as V 0  and V 1  close to, or greater than, corresponding values for conventional marker strips listed in Table 1. Thus, depending on the requirement of an electronic article surveillance system, a most appropriate chemical composition may be selected from the above list. 
   Furthermore, ribbons slit to about a 6 mm wide width, in accordance with Example 1, were cut into strips with different lengths, and their magnetomechanical resonance properties were examined. In addition to the properties covered in Tables I, II and IV above, a complementary test to determine the effectiveness of a magnetomechanical resonance strip was performed using the following formula:
 
 V ( t )= Vo  exp(− t/   T ),  (2)
 
wherein t is the time measured after termination of an AC field excitation and  T  is a characteristic time constant for the resonance signal decay. The values of V 1 max  in Tables I, II and IV were determined from the data for t=1 msec. The results are given in Table V, in which other parameters characterizing the resonance properties of differing strip lengths are summarized. It is noted that f r  follows the relationship of Equation (1) quite well, giving a relationship of f r =2.1906×10 6 /l Hz, where l is the length of a marker strip in mm. Also noted is the increase of  T  with increasing strip length. A larger value of  T  is preferred when a longer signal retention is desired. Thus, marker strips of the present invention listed in Table V provides opportunities for a wide variety of electronic article surveillance systems utilizing different resonance frequencies.
 
   As shown in Table V, magnetomechanical resonance characteristics of marker strips of an embodiment of the present invention with different lengths, l, were measured by using Alloy G in Table III. The width and thickness of each strip were about 6 mm and about 28 μm, respectively. The definitions of V 0 max , H b0 , V 1max , H b1  and df r /dH b  were the same as in Table I. The time constant was defined in Equation (2). Marker height h was defined in  FIG. 1A , and the radius of curvature of each strip was calculated using h and l. 
   
     
       
             
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
             
           
         
             
               TABLE V 
             
             
                 
             
             
               Strip 
               Resonance 
                 
                 
               Time 
                 
                 
                 
               Radius of 
             
             
               Length 
               Frequency 
               V 0max   
               H b0   
               Constant τ 
               V 1max   
               H b1   
               df r /dH b   
               Curvature 
             
             
               (mm) 
               (Hz) 
               (mV) 
               (A/m) 
               (msec) 
               (mV) 
               (A/m) 
               [Hz/(A/m)] 
               (cm) 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               18.01 
               120772 
               73 
               610 
               0.85 
               23 
               520 
               6.65 
               26 
             
             
               20.16 
               108536 
               68 
               550 
               0.92 
               25 
               370 
               8.07 
               22 
             
             
               24.99 
               87406 
               94 
               460 
               1.16 
               42 
               338 
               6.55 
               22 
             
             
               30.02 
               72284 
               135 
               461 
               1.35 
               69 
               342 
               9.44 
               36 
             
             
               35.03 
               61818 
               143 
               387 
               1.74 
               79 
               322 
               8.73 
               29 
             
             
               37.95 
               56782 
               160 
               389 
               1.86 
               91 
               337 
               7.89 
               31 
             
             
               41.90 
               51336 
               184 
               389 
               2.03 
               109 
               350 
               6.67 
               43 
             
             
               46.95 
               45992 
               178 
               330 
               2.49 
               116 
               320 
               5.21 
               45 
             
             
               52.12 
               41438 
               197 
               331 
               2.69 
               132 
               312 
               5.28 
               35 
             
             
               56.99 
               37900 
               187 
               292 
               3.30 
               135 
               291 
               5.93 
               37 
             
             
               62.07 
               34864 
               197 
               293 
               3.56 
               148 
               279 
               4.94 
               34 
             
             
                 
             
           
        
       
     
   
   In addition to the basic magnetic properties, such as saturation magnetic induction and magnetostriction, listed in Table III, that are required to generate magnetomechanical resonance in a marker strip of an embodiment of the present invention, the direction of magnetic anisotropy, which is the direction of easy magnetization in a marker strip, must be essentially perpendicular to the strip&#39;s length direction. This is indeed the case, as indicated in  FIG. 4 , which depicts a BH loop taken at 60 Hz using a measurement method of Example 3 on an approximately 38 mm long strip from Table V above. The BH loop of  FIG. 4  indicates that the remanent magnetic induction at H=0, i.e., B(H=0), is close to zero and the permeability defined by B/H near H=0 is linear. The shape of the BH loop shown in  FIG. 4  is typical of the BH behavior of a magnetic strip in which the average direction of the magnetic anisotropy is perpendicular to strip&#39;s length direction. A consequence of the magnetization behavior of a marker strip of an embodiment of the present invention shown in  FIG. 4  is the absence of higher harmonics generation in the strip when the strip is placed in an AC magnetic field. Thus, the system “pollution problem” as mentioned in the “Background of the Invention” section, is minimized. To further check this point, a higher harmonic signal from the marker strip of  FIG. 4  was compared with that of a marker strip of an electronic article surveillance system based on magnetic harmonic generation/detection. The results of this comparison are given in Table VI below. 
   As shown in Table VI, a magnetic higher harmonics signal comparison was made between a marker strip of an embodiment of the present invention and a marker strip based on Co-based METGLAS®2714A alloy, which is widely used in an electronic article surveillance system based on a magnetic harmonic generation/detection system. The strip size was the same for both cases and was approximately 38 mm long and approximately 6 mm wide. The fundamental excitation frequency was 2.4 kHz and the 25 th  harmonic signals were compared by using a harmonic signal detection method of Example 4. 
   
     
       
             
             
             
           
             
             
             
           
         
             
                 
               TABLE VI 
             
             
                 
                 
             
             
                 
               Marker Type 
               25 th  Harmonic Signal (mV) 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
                 
               Present Invention 
               4 
             
             
                 
               Harmonic Marker 
               40 
             
             
                 
                 
             
           
        
       
     
   
   As Table VI indicates, a negligibly small harmonic signal from a marker of an embodiment of the present invention does not trigger an electronic article surveillance system based on magnetic harmonic generation/detection. 
     FIG. 5A  illustrates a physical configuration of a magnetomechanical resonance marker of the present invention where a single marker strip in accordance with an embodiment of the present invention is utilized. The marker strip is any one of the strips listed in Table I, II, IV and V. In this figure, a marker strip  31  of the present invention is placed in a hollow area  33  in which the marker  31  is free to vibrate without physical constraints with non-magnetic casing materials  30  and  32  enclosing the marker strip  31 . A bias magnet  34  is attached on the outside surface of casing  32  as an arrow indicates. In this configuration, the basic magnetic interaction between a marker strip  31  and a bias magnet  34  is that same as depicted in  FIG. 1A . As a comparison, a conventional marker configuration is shown in  FIG. 5B , in which a prior art marker strip  41  is encased a cavity area  43  between item  40  and  42 , with a bias magnet  44  attached on the outside surface of casing  42 . 
   Two marker-strips for embodiments of the present invention were selected randomly from a number of strips characterized in Table I, II, and V with the same dimension, but with slightly different curvatures or two strips having the same chemical composition with the same dimension and with slightly different curvatures are mounted on top of each other, and a marker was made as in  FIG. 6A-1 , wherein strips  110  and  111  were marker strips of an embodiment of the present invention being housed in a cavity region  102  created between outside casing material  100  and  101 , and a bias magnet  120  was attached on the outside surface of a casing material  101  as indicated by an arrow in the figure.  FIG. 6A-2  illustrates a side view of the two maker-strips of an embodiment of the present invention, showing the two strips with slightly different curvatures touching along one line across the strip&#39;s width direction. For comparison, a marker configuration for two conventional marker-strips is shown in  FIG. 6B-1 , wherein conventional marker strips  210  and  211  are placed in a cavity region  202  between outer casings  200  and  201 , and a bias magnet  220  is attached to the outside surface of casing  201 , as indicated by an arrow in the figure.  FIG. 6B-2  illustrates a view of the two conventional strips from an angle, showing the two strips touching face-to-face because the strip&#39;s curvature along their width direction is the same due to the specific annealing method used in preparing the conventional marker-strips, as described in the &#39;702 patent. 
   The magnetomechanical resonance behavior, using V 0    771  and V 1   772 , of this two-strip marker of an embodiment of the present invention is compared in  FIG. 7  with the magnetomechanical resonance behavior, using V 0    773  and V 1    774 , of a conventional two-strip marker. A further comparison of the resonance characteristics between two-strip markers of an embodiment of the present invention and representative conventional two-strip markers is summarized in Table VII, in which strips Nos. 11–18 were made from an amorphous alloy ribbon of an embodiment of the present invention. The peak signal amplitude V 1 max  at H b1  and the resonance frequency slope of the marker of an embodiment of the present invention are about the same as, or slightly greater than, that of a conventional two-strip marker. Table VII also indicates that the frequency-bias slope, df r /dH b , may be adjusted to a preferred magnitude depending on the requirement of a surveillance system. The advantage of two-strip marker configuration of an embodiment of the present invention over that of a conventional two-strip marker is further demonstrated in Table VIII, in which an average signal amplitude &lt;V 0 max &gt; of each individual marker and that of a two strip marker, V 0 max , using the two marker-strips are compared. It is noted that the ratio V 0 max /&lt;V 0 max &gt; for two-strip markers of an embodiment of the present invention is centered around 1.65 with a very small variation from marker to marker, whereas the same ratio varies widely from 1.4 to 1.9 for conventional two-strip markers. The reason for the improved performance of a two-strip marker of an embodiment of the present invention is given as follows: As depicted in  FIG. 6A-2 , each of the two marker strips of an embodiment of the present invention has a curvature along the strip length direction and touch on one line in the center generally as indicated in numeral  122 , whereas the two resonator strips of prior art touch at many points in the strip&#39;s surfaces between the two strips as indicated in numeral  222  in  FIG. 6B-2 , introducing more damping in mechanical vibration in the latter than the former. 
   As shown in Table VII, resonance characteristics were measured of two-strip markers of an embodiment of the present invention with a length of about 38 mm, a width of about 6 mm and a thickness of about 28 μm. The values for conventional markers with five samples had ranges as shown. The resonance frequency of each marker was about 58 kHz. The definitions of V 0 max , H b0 , V 1 max , H b1  and df r /dH b  were the same as in Table 1. 
   
     
       
             
             
             
             
             
             
           
         
             
               TABLE VII 
             
             
                 
             
             
                 
                 
                 
                 
                 
               df r /dH b   
             
             
                 
               V 0max   
                 
               V 1max   
                 
               [Hz/ 
             
             
               Marker 
               (mV) 
               H b0  (A/m) 
               (mV) 
               H b1  (A/m) 
               (A/m)] 
             
             
                 
             
           
           
             
               Conventional 
               266~306 
               590~620 
               157~190 
               499~569 
               7.16~8.24 
             
             
               Present 
               257 
               680 
               153 
               500 
               6.84 
             
             
               Invention 
             
             
               No. 11 
             
             
               No. 12 
               269 
               692 
               153 
               529 
               8.96 
             
             
               No. 13 
               279 
               645 
               173 
               535 
               9.78 
             
             
               No. 14 
               280 
               689 
               152 
               559 
               9.93 
             
             
               No. 15 
               250 
               558 
               174 
               538 
               4.44 
             
             
               No. 16 
               238 
               541 
               150 
               521 
               4.44 
             
             
               No. 17 
               251 
               540 
               160 
               520 
               4.53 
             
             
               No. 18 
               241 
               560 
               161 
               540 
               3.66 
             
             
                 
             
           
        
       
     
   
   As shown in Table VIII, effects of marker strip shape on the magnetomechanical performance of a two-strip marker in accordance with an embodiment of the present invention and that of conventional two-strip marker were examined. The resonance frequency of each marker was about 58 kHz. 
   
     
       
             
           
             
             
             
             
           
             
             
             
             
           
         
             
               TABLE VIII 
             
           
           
             
                 
             
             
               Characteristics of two-strip markers of the present invention. 
             
           
        
         
             
                 
                 
               Average 
                 
             
             
                 
                 
               V 0max  of individual 
                 
             
             
                 
                 
               marker strip 
               Ratio 
             
             
                 
               V 0max  (mV) 
               &lt;V 0max &gt; (mV) 
               V 0max /&lt;V 0max &gt; 
             
             
                 
                 
             
           
        
         
             
               Double Strip 
                 
                 
                 
             
             
               Marker of an 
             
             
               Embodiment of 
             
             
               Present Invention 
             
             
               No. 19 
               257 
               152 
               1.65 
             
             
               No. 20 
               249 
               151 
               1.65 
             
             
               No. 21 
               269 
               162 
               1.67 
             
             
               No. 22 
               279 
               167 
               1.68 
             
             
               No. 23 
               280 
               170 
               1.65 
             
             
               Conventional 
             
             
               A 
               266 
               167 
               1.61 
             
             
               B 
               275 
               195 
               1.41 
             
             
               C 
               293 
               187 
               1.57 
             
             
               D 
               306 
               158 
               1.94 
             
             
               E 
               293 
               183 
               1.61 
             
             
                 
             
           
        
       
     
   
   The aspect of reduced mechanical damping in a two-strip marker of an embodiment of the present invention was examined and is demonstrated in  FIG. 8 , where resonance signal amplitude is plotted against time after the termination of an alternating field which initiates the magnetomechanical resonance for a two-strip marker  801  of an embodiment of the present invention and for a conventional two-strip marker  802 . It is clear that the resonance phenomenon persists much longer in a two-strip marker of an embodiment of the present invention than a conventional two-strip marker because the two marker-strips of the embodiment of the present invention touch only on one line across the strip&#39;s width direction, whereas the two conventional marker-strips touch face-to-face with each other. The data given in  FIG. 8  was further analyzed by using Equation (2) given above. Table IX compares values of  T  thus obtained for two-strip markers of an embodiment of the present invention and conventional markers. 
   As shown in Table IX, time constants  T  are listed for resonance signal decay for two-strip markers, samples No. 24 through No. 29, of an embodiment of the present invention and for conventional samples A through E, which are the same as those found in Table VIII. The signal decay data were fitted to Equation (2) above with the parameters V 0 max  and  T  given below. The resonance frequency of each marker was about 58 kHz. 
   
     
       
             
             
             
           
             
             
             
           
         
             
                 
               TABLE IX 
             
             
                 
                 
             
             
                 
               V 0max  (mV) 
               τ (msec) 
             
             
                 
                 
             
           
           
             
                 
             
           
        
         
             
               Two-Strip Marker of an 
                 
                 
             
             
               Embodiment of the Present 
             
             
               Invention 
             
             
               No. 24 
               204 
               2.58 
             
             
               No. 25 
               201 
               2.62 
             
             
               No. 26 
               251 
               2.80 
             
             
               No. 27 
               238 
               2.12 
             
             
               No. 28 
               251 
               2.10 
             
             
               No. 29 
               248 
               2.43 
             
             
               Conventional 
             
             
               A 
               266 
               1.69 
             
             
               B 
               275 
               1.75 
             
             
               C 
               293 
               1.95 
             
             
               D 
               306 
               1.38 
             
             
               E 
               293 
               2.23 
             
             
                 
             
           
        
       
     
   
   The advantages of having multiple marker-strips are further provided by an example of a three-strip marker. For this purpose, three randomly selected strips with the same length and width of an embodiment of the present invention were mounted on top of each other, and a three-strip marker was formed and tested. 
   As shown in  FIG. 9 , the magnetomechanical performance was further improved in a three-strip marker with a higher signal amplitude, V 0   901  and V 1   902 , than that shown in  FIG. 7 , obtained for a two-strip marker. Again consistency of the magnetomechanical performance from marker to marker is demonstrated in Table X in terms of small variability of the ratio V 0max /&lt;V 0max &gt;. This performance consistency arises from reduced mechanical damping of the constituent strips in a marker of an embodiment of the present invention as observed consistently in a marker having two strips of an embodiment of the present invention; see Table VIII. The performance consistency is further provided by small variations of V 0max , H b0 , V 1max , H b1  and bias slope, df r /dH b  [Hz/(A/m)] among different markers, as seen in Table X. 
   As shown in Table X, resonance characteristics of a three-strip marker of an embodiment of the present invention were examined. The definitions of the basic quantities are the same as in Table I. The resonance frequency of each three-strip maker was about 58 kHz. 
   
     
       
             
             
             
             
             
             
             
             
           
             
             
             
             
             
             
             
             
           
         
             
               TABLE X 
             
             
                 
             
             
                 
                 
                 
                 
                 
                 
               Average 
                 
             
             
                 
                 
                 
                 
                 
                 
               V 0max   
             
             
               Three- 
                 
                 
                 
                 
                 
               of Three Strips 
               Ratio of 
             
             
               Strip 
               V 0max   
               H b0   
               V 1max   
               H b1   
               df r /dH b   
               &lt;V 0max &gt; 
               V 0max / 
             
             
               Marker 
               (mV) 
               (A/m) 
               (mV) 
               (A/m) 
               [Hz/(A/m)] 
               (mV) 
               &lt;V 0max &gt; 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               No. 30 
               351 
               842 
               152 
               600 
               5.07 
               152 
               2.31 
             
             
               No. 31 
               361 
               818 
               143 
               689 
               8.03 
               165 
               2.19 
             
             
               No. 32 
               359 
               839 
               152 
               641 
               6.44 
               171 
               2.10 
             
             
               No. 33 
               390 
               833 
               160 
               627 
               7.02 
               177 
               2.20 
             
             
               No. 34 
               332 
               800 
               203 
               691 
               6.08 
               158 
               2.10 
             
             
                 
             
           
        
       
     
   
   A further aspect of the present invention is to provide an electronic article surveillance marker with enhanced detection capability. Thus markers with four and five marker strips were examined, and the results are summarized in Table XI. 
   As shown in Table XI, magnetomechanical resonance characteristics of markers with four and five marker strips of embodiments of the present invention were determined. The definitions of V 0max , H b0 , V 1max , H b1  and dfr/dHb were the same as in Table I. The resonance frequency of each marker was about 58 kHz. 
   
     
       
             
             
             
             
             
             
           
             
             
             
             
             
             
           
         
             
               TABLE XI 
             
             
                 
             
             
               Number of 
               V 0max   
               H b0   
                 
                 
               df r /dH b   
             
             
               Marker Strip 
               (mV) 
               (A/m) 
               V 1max  (mV) 
               H b1  (A/m) 
               [Hz/(A/m)] 
             
             
                 
             
           
           
             
                 
             
           
        
         
             
               4 
               341 
               800 
               257 
               800 
               2.37 
             
             
               5 
               368 
               887 
               280 
               887 
               3.14 
             
             
                 
             
           
        
       
     
   
   The values of V 0 max    1001  and V 1 max    1002  from Tables I, IV,VII, X and XI are plotted against a number of marker strips in  FIG. 10 . A rapid increase of the magnetomechanical resonance signals is observed for up to three marker strips, beyond which the rate of signal increase with the strip number is gradual, but still showing the advantageous effect of increased number of marker strips for enhanced resonance signal detection. 
   A marker with one rectangular amorphous magnetostrictive alloy strip or a plurality of rectangular amorphous magnetostrictive alloy strips prepared in accordance with the present invention, such as the one exemplified in  FIG. 5A  and  FIG. 6A , respectively is utilized in an electronic article surveillance system illustrated in  FIG. 11 . As shown, an article  502  having a marker  501  of an embodiment of the present invention is placed in an interrogation zone  510  equipped with a pair of AC field excitation coils  511 , which is driven by an electronic device  512  consisting of a signal generator  513  and an AC amplifier  514 . The electronic device  512  is programmed to excite marker strips of the embodiment of the present invention up to a predetermined time period, at which time the excitation is terminated. After the termination of the excitation in coils  511 , a signal detected in the signal receiving coils  516  is fed to a signal detection circuit box  517 , which is tuned to a resonance frequency of the marker in the interrogation zone  510 . The excitation field termination and the onset of signal detection are controlled by a circuit box  515 . The signal detector  517  is connected to an identifier  518 , which conveys a result of the interrogation to an interrogator. When article  502  with an electronic surveillance marker of an embodiment of the present invention  501  exits the interrogation zone  510 , the marker is deactivated by a demagnetizing field, if desired. 
   EXAMPLE 1  
   A slit ribbon was cut into ductile and rectangular strips with a conventional metal ribbon cutter. The curvature of each strip was determined optically by measuring the height, h, of the curved surface over the strip length, l, as defined in  FIG. 1A . 
   EXAMPLE 2  
   The magnetomechanical performance was determined in a set-up in which a pair of coils supplying a static bias field and the voltage appearing in a signal detecting coil compensated by a bucking coil was measured by an oscilloscope and a voltmeter. The measured voltage therefore is detecting-coil dependent and indicates a relative signal amplitude. The exciting AC field was supplied by a commercially available function generator. The function generator was programmed to excite a marker strip or strips of the present invention for 3 msec, after which period the excitation was terminated, and the signal decay was measured with time. The data thus taken were processed and analyzed with a commercially available computer software. 
   EXAMPLE 3  
   A commercially available DC BH loop measurement equipment was utilized to measure magnetic induction B as a function of applied field H. For an AC BH loop measurement, an exciting coil-detecting coil assembly similar to that of Example 4 was used, and output signal from the detecting coil was fed into an electronic integrator. The integrated signal was then calibrated to give the value of the magnetic induction B of a sample. The resultant B was plotted against applied field H, resulting in an AC BH loop. In both AC and DC cases, the direction of the applied field and the measurement was along marker strips&#39; length direction. 
   EXAMPLE 4  
   A marker strip prepared in accordance with Example 1 was placed in an exciting AC field at a predetermined fundamental frequency, and its higher harmonics response was detected by a coil containing the strip. The exciting coil and signal detecting coil were wound on a bobbin with a diameter of about 50 mm. The number of the windings in the exciting coil and the signal detecting coil was about 180 and about 250, respectively. The fundamental frequency was chosen at 2.4 kHz and its voltage at the exciting coil was about 80 mV. The 25 th  harmonic voltages from the signal detecting coil were measured. 
   In accordance with an embodiment of the invention, a marker of a magnetomechanical resonant electronic article surveillance system, comprises: at least one ductile magnetostrictive marker strip cut from an amorphous ferromagnetic alloy ribbon that has a curvature along a ribbon length direction and exhibits magnetomechanical resonance under alternating magnetic field excitation with a static bias field, the said at least one marker strip having a magnetic anisotropy direction along a direction perpendicular to a ribbon axis. 
   Where selected, a radius of curvature of the at least one ductile magnetostrictive marker strip is less than 100 cm. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy ribbon has a saturation induction ranging from 0.7 tesla to 1.1 tesla. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy ribbon has a saturation magnetostriction ranging from 8 ppm to 18 ppm. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy ribbon has a composition based on Fe a —Ni b —Mo c —B d  with 30≦a≦43, 35≦b≦48, 0≦c≦5, 14≦d≦20 and a+b+c+d=100, up to 3 atom % of Mo being optionally replaced by Co, Cr, Mn and/or Nb and up to 1 atom % of B being optionally replaced by Si and/or C. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy ribbon is an alloy having a composition of one of Fe 40.6  Ni 40.1  Mo 3.7  B 15.1  Si 0.5 , Fe 41.5  Ni 38.9  Mo 4.1  B 15.5 , Fe 41.7  Ni 39.4  Mo 3.1  B 1.58 , Fe40.2 Ni 39.0  Mo 3.6  B 16.6  Si 0.6 , Fe 39.8  Ni 39.2  Mo 3.1  B 17.6  C 0.3 , Fe 36.9  Ni 41.3  Mo 4.1  B 17.8 , Fe 35.6  Ni 42.6  Mo 4.0  B 17.9 , Fe 40 Ni 38 Mo 4 B 18 , or Fe 38.0  Ni 38.8  Mo 3.9  B 19.3 . 
   In accordance with an embodiment of the invention, the at least one marker strip has a discrete length and exhibits magnetomechanical resonance at a length-related frequency. 
   Where selected, the at least one marker strip has a length ranging from approximately 15 to approximately 65 mm. 
   Where selected, the at least one marker strip has a marker strip width ranging from approximately 3 mm to approximately 15 mm. 
   In accordance with an embodiment of the invention, the at least one marker strip has a length-to-width ratio exceeding 3. 
   In accordance with an embodiment of the invention, the at least one marker strip has a slope of resonance frequency versus bias field ranging from approximately 4 Hz/(A/m) to approximately 14 Hz/(A/m). 
   In accordance with an embodiment of the invention, the marker comprises a plurality of marker strips with different radius of curvatures along the marker strips&#39; length direction and with the same length. 
   Where selected, the plurality of marker strips are stacked or placed side-by-side. 
   In accordance with an embodiment of the invention, the marker comprises two marker strips and has a slope of resonance frequency versus bias field ranging from approximately 3.5 Hz/(A/m) to approximately 10 Hz/(A/m). 
   In accordance with an embodiment of the invention, the marker comprises three marker strips and has a slope of resonance frequency versus bias field ranging from approximately 4 Hz/(A/m) to approximately 9 Hz/(A/m). 
   In accordance with an embodiment of the invention, the marker comprises four or five marker strips and has a slope of resonance frequency versus bias field ranging from approximately 2 Hz/(A/m) to approximately 4 Hz/(A/m). 
   Where selected, at least one bias magnet strip is placed along the at least one marker strip&#39;s direction. 
   In accordance with an embodiment of the invention, the at least one marker strip is housed in a cavity separated from the bias magnet strip. 
   In accordance with an embodiment of the invention, electronic article surveillance system has a capability of detecting resonance of a marker, and comprises a surveillance system tuned to predetermined surveillance magnetic field frequencies, wherein the surveillance system detects a marker that is adapted to mechanically resonate at a preselected frequency, and has at least one ductile magnetostrictive marker strip cut from an amorphous ferromagnetic alloy ribbon that has a curvature along a ribbon length direction and exhibits magnetomechanical resonance under alternating magnetic field excitation with a static bias field, the at least one marker strip having a magnetic anisotropy direction along a direction perpendicular to a ribbon axis. 
   Where selected, a radius of curvature of the at least one ductile magnetostrictive marker strip is between approximately 20 cm and approximately 100 cm. 
   In accordance with an embodiment of the invention, the amorphous ferromagnetic alloy has a composition based on Fe a —Ni b —Mo c —B d  with 30≦a≦43, 35≦b≦48, 0≦c≦5, 14≦d≦20 and a+b+c+d=100, up to 3 atom % of Mo being optionally replaced by Co, Cr, Mn and/or Nb and up to 1 atom % of B being optionally replaced by Si and/or C. 
   Although a few embodiments of the present invention have been shown and described, it would be appreciated by those skilled in the art that changes may be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the claims and their equivalents.