Patent Publication Number: US-9406418-B2

Title: Magnetic exchange coupled core-shell nanomagnets

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application is a continuation of and claims priority to U.S. patent application Ser. No. 13/885,371, entitled “Magnetic Exchange Coupled Core-Shell Nanomagnets” and filed on May 14, 2013, which is incorporated herein by reference. U.S. patent application Ser. No. 13/885,371 claims priority to International Application No. PCT/US11/60879, entitled “Magnetic Exchange Coupled Core-Shell Nanomagnets” and having an international filing date of Nov. 15, 2011, which is incorporated herein by reference. International Application No. PCT/US11/60879 claims priority to U.S. Provisional Patent Application No. 61/413,869, entitled “Magnetic Exchange Coupled Core-Shell Nanomagnets” and filed on Nov. 15, 2010, which is incorporated herein by reference. 
    
    
     RELATED ART 
     Permanent magnets are currently used in a variety of applications, including electric motor applications, such as electric vehicles and windmill generators. Unfortunately, the performance of many permanent magnets degrades at high temperature making them unsuitable in some applications, such as electric motor applications where temperatures often exceed 150° Celsius (C). Further, many permanent magnets have expensive materials, such as precious metals or rare-earth metals, which has limited availability. 
     As an example, several rare-earth magnets, including Nd 2 Fe 14 B, Dy-doped Nd 2 Fe 14 B, SmCo, and Sm 2 Fe 17 N 3 , have been used or considered for motors of hybrid and electric vehicles. Of such magnets, Nd 2 Fe 14 B generally provides the highest maximum energy product (BH) max . However, the operation temperature of this magnet is limited to around 150° C., which is attributed to a low Curie temperature of around 310 to 400° C. Furthermore, magnetization decreases with temperature and generally disappears at about the Curie temperature. To increase the operation temperature, Dy can be added, but this addition increases coercivity and decreases magnetization. Therefore, the substitution effect is relatively insignificant. 
     Thus, a heretofore unaddressed need exists in the art for inexpensive permanent magnets capable of efficiently operating at high temperature. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure can be better understood with reference to the following drawings. The elements of the drawings are not necessarily to scale relative to each other, emphasis instead being placed upon clearly illustrating the principles of the disclosure. Furthermore, like reference numerals designate corresponding parts throughout the several views. 
         FIG. 1  depicts an exemplary embodiment of a nanomagnet particle having a magnetically hard core surrounded by a magnetically soft shell. 
         FIG. 2  is a plot of maximum energy product (BH max ) for a nanomagnet particle having a magnetically hard core (MnAl) surrounded by a magnetically soft shell (permalloy). 
         FIG. 3  is a plot of volume fraction (f h ) of hard magnetic phase dependent (BH) max  for a nanomagnet particle having a magnetically hard core (τ-MnAl) surrounded by a magnetically soft shell at 300 Kelvin (K) where M r /M s =1 and saturation magnetization of soft shell is in the range of 1.3 to 2.2 T. 
         FIG. 4  is a plot of volume fraction (f h ) of hard magnetic phase dependent (BH) max  for a nanomagnet particle having a magnetically hard core (τ-MnAl) surrounded by a magnetically soft shell at 300 Kelvin (K) where M r /M s =0.7 and saturation magnetization of soft shell is in the range of 1.3 to 2.2 T. 
         FIG. 5  is a plot of volume fraction (f h ) of hard magnetic phase dependent (BH) max  for a nanomagnet particle having a magnetically hard core (τ-MnAl) surrounded by a magnetically soft shell at 450 Kelvin (K) where M r /M s =1 and saturation magnetization of soft shell is in the range of 1.3 to 2.2 T. 
         FIG. 6  is a plot of volume fraction (f h ) of hard magnetic phase dependent (BH) max  for a nanomagnet particle having a magnetically hard core (τ-MnAl) surrounded by a magnetically soft shell at 450 Kelvin (K) where M r /M s =0.7 and saturation magnetization of soft shell is in the range of 1.3 to 2.2 T. 
         FIG. 7  is a plot of volume fraction (f h ) of hard magnetic phase dependent (BH) max  for a nanomagnet particle having a magnetically hard core (MnBi) surrounded by a magnetically soft shell at 300 K where M r /M s =1 and saturation magnetization of soft shell is in the range of 1.3 to 2.2 T. 
         FIG. 8  is a plot of volume fraction (f h ) of hard magnetic phase dependent (BH) max  for a nanomagnet particle having a magnetically hard core (MnBi) surrounded by a magnetically soft shell at 450 K where M r /M s =1 and saturation magnetization of soft shell is in the range of 1.3 to 2.2 T. 
         FIG. 9  is a plot of volume fraction (f h ) of hard magnetic phase dependent (BH) max  for a nanomagnet particle having a magnetically hard core (BaM) surrounded by a magnetically soft shell at 300 K where M r /M s =1 and saturation magnetization of soft shell is in the range of 1.3 to 2.2 T. 
         FIG. 10  is a plot of volume fraction (f h ) of hard magnetic phase dependent (BH) max  for a nanomagnet particle having a magnetically hard core (BaM) surrounded by a magnetically soft shell at 450 K where M r /M s =1 and saturation magnetization of soft shell is in the range of 1.3 to 2.2 T. 
     
    
    
     DETAILED DESCRIPTION 
     The present disclosure generally pertains to magnetic exchange coupled core-shell nanomagnets. In one exemplary embodiment, a permanent magnet is fabricated such that it has a magnetically hard core surrounded by a thin magnetically soft shell. The magnetically hard core provides a relatively high intrinsic coercivity (H ci ), and the magnetically soft shell provides a relatively high magnetic flux density (B). Due to magnetic exchange coupling between the core and shell, a relatively high maximum energy product (BH) max  is achievable over a wide temperature range, including temperatures above 150° C. Further, such effects can be achieved without using rare-earth metals or precious metals helping to keep the manufacturing costs of the magnet low. To allow sufficient exchange magnetic coupling between the core and shell, the overall shell thickness is controlled such that the width of the shell is less than two times the Bloch domain wall thickness of the core. 
       FIG. 1  depicts an exemplary core-shell nanomagnet particle  12  manufactured to have a core  14  composed of magnetically hard material and a shell  15  composed of a magnetically soft material. In one exemplary embodiment, the material of the core  14  includes Mn, Al, Bi, Sr, Pb, Fe, or O (with at least one hard magnetic element though more preferably with at least two hard magnetic elements), and the material of the shell includes Fe, Co, Ni, Al, Si, N, or O (with at least one soft magnetic element though more preferably with at least two soft magnetic elements). As an example, the magnetically hard core  14  may be composed of MnAl or M-type hexaferrite (BaFe 12 O 19 ) or MnBi, and the magnetically soft shell  15  may be composed of Fe 65 Co 35 , Permalloy (Fe 20 Ni 80 ), or Sendust (FeAlSi). However, in other embodiments, other elements and/or combination of elements are possible. 
     The shape of the core-shell particle  12 , as well as the core  14 , is generally spherical, though it can have other shapes, such as needlelike or hexagonal, in other embodiments. Further, the shell  15  forms a hollow sphere that encompasses and surrounds the core  14 , and the core  14  fills the void within the hollow sphere. In other embodiments, other shapes of the shell  15 , such as cylinder, cube, or hexagon, are possible. In one exemplary embodiment, the thickness of the shell  15  (δ s ) is between about 20 nm and 40 nm, and such thickness is less than two times the Bloch domain wall thickness of the core  14 . Further, the thickness of the shell  15  is uniform around the core  14 . However, it should be emphasized that other shapes and configurations of the core-shell particle  12  are possible in other embodiments. 
     The (BH) max  for the core-shell particle  12  can be characterized by the following formulas (assuming that M r =M s ). 
     
       
         
           
             
               
                 
                   
                     M 
                     r 
                   
                   = 
                   
                     
                       
                         
                           f 
                           h 
                         
                         ⁢ 
                         
                           M 
                           h 
                         
                       
                       + 
                       
                         
                           f 
                           s 
                         
                         ⁢ 
                         
                           M 
                           s 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         when 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           M 
                           s 
                         
                       
                     
                     = 
                     
                       
                         M 
                         r 
                       
                       → 
                       
                         
                           
                             
                               
                                 Eq 
                                 . 
                                 
                                     
                                 
                                 ⁢ 
                                 
                                   ( 
                                   6 
                                   ) 
                                 
                               
                               , 
                               
                                 R 
                                 . 
                                 
                                     
                                 
                                 ⁢ 
                                 Skomski 
                               
                             
                           
                         
                         
                           
                             
                               
                                 P 
                                 . 
                                 
                                     
                                 
                                 ⁢ 
                                 3591. 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 E 
                                 . 
                                 
                                     
                                 
                                 ⁢ 
                                 Kneller 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         μ 
                         0 
                       
                       ⁢ 
                       
                         H 
                         N 
                       
                     
                     = 
                     
                       
                         2 
                         ⁢ 
                         
                           
                             
                               
                                 f 
                                 s 
                               
                               ⁢ 
                               
                                 K 
                                 s 
                               
                             
                             + 
                             
                               
                                 f 
                                 h 
                               
                               ⁢ 
                               
                                 K 
                                 h 
                               
                             
                           
                           
                             
                               
                                 f 
                                 s 
                               
                               ⁢ 
                               
                                 M 
                                 s 
                               
                             
                             + 
                             
                               
                                 f 
                                 h 
                               
                               ⁢ 
                               
                                 M 
                                 h 
                               
                             
                           
                         
                       
                       → 
                       
                         Eq 
                         . 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           8 
                           ) 
                         
                       
                     
                   
                   , 
                   
                     R 
                     . 
                     
                         
                     
                     ⁢ 
                     Skomiski 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   ( 
                                   BH 
                                   ) 
                                 
                                 max 
                               
                               = 
                               
                                 
                                   
                                     
                                       
                                         μ 
                                         0 
                                       
                                       ⁢ 
                                       
                                         M 
                                         r 
                                         2 
                                       
                                     
                                     4 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   for 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     H 
                                     N 
                                   
                                 
                                 &gt; 
                                 
                                   
                                     M 
                                     r 
                                   
                                   2 
                                 
                               
                             
                           
                         
                         
                           
                             
                               
                                 
                                   ( 
                                   BH 
                                   ) 
                                 
                                 max 
                               
                               = 
                               
                                 
                                   
                                     
                                       
                                         μ 
                                         0 
                                       
                                       ⁢ 
                                       
                                         H 
                                         N 
                                       
                                       ⁢ 
                                       
                                         M 
                                         r 
                                       
                                     
                                     2 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   for 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     H 
                                     N 
                                   
                                 
                                 &lt; 
                                 
                                   
                                     M 
                                     r 
                                   
                                   2 
                                 
                               
                             
                           
                         
                       
                       } 
                     
                     ⁢ 
                     
                       
                         
                           
                             
                               p 
                               . 
                               
                                   
                               
                               ⁢ 
                               15814 
                             
                             , 
                             
                               R 
                               . 
                               
                                   
                               
                               ⁢ 
                               Skomski 
                             
                           
                         
                       
                       
                         
                           
                             
                               P 
                               . 
                               
                                   
                               
                               ⁢ 
                               3588 
                             
                             , 
                             
                               E 
                               . 
                               
                                   
                               
                               ⁢ 
                               Kneller 
                             
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         M 
                         r 
                       
                       ⁢ 
                       
                         : 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       Remanence 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       of 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       hard 
                     
                     + 
                     
                       soft 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       phases 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       M 
                       s 
                     
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Saturation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     magnetization 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     soft 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     magnetic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     phase 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       M 
                       h 
                     
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Saturation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     magnetization 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     hard 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     magnetic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     phase 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       K 
                       h 
                     
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Magnetic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     anisotrophy 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     energy 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     hard 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     magnetic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     phase 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       K 
                       s 
                     
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Magnetic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     anisotrophy 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     energy 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     soft 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     magnetic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     phase 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       f 
                       h 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Volume 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     fraction 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     hard 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     magnetic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     phase 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       f 
                       s 
                     
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     Volume 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     fraction 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     of 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     soft 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     magnetic 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     phase 
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       μ 
                       0 
                     
                     ⁢ 
                     
                       : 
                     
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                     ⁢ 
                     π 
                     × 
                     
                       10 
                       
                         - 
                         7 
                       
                     
                     ⁢ 
                     N 
                     ⁢ 
                     
                       / 
                     
                     ⁢ 
                     
                       A 
                       2 
                     
                   
                 
               
               
                 
                   
                     
                       
                         ( 
                         3 
                         ) 
                       
                     
                   
                   
                     
                       
                         ( 
                         4 
                         ) 
                       
                     
                   
                 
               
             
           
         
       
         
         [Ref1] R Skomski, and J. M D Coey, “Giant energy product in nanostructured two-phase magnets”,  Phys. Rev. B.  48, 21 (1993) 
         [Ref2] E. F. Kneller, and R. Hawig, “The exchange-spring magnet: A new material principle for permanent magnets”,  IEEE Trans. Magn.  27, pp 3588-3600, (1991) 
       
    
     
       
         
           
             
               
                 
                   
                     
                       Assuming 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         M 
                         r 
                       
                     
                     = 
                     
                       0.7 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         M 
                         s 
                       
                     
                   
                   , 
                   
                     
                       B 
                       r 
                     
                     = 
                     
                       
                         μ 
                         0 
                       
                       ⁢ 
                       
                         M 
                         r 
                       
                     
                   
                   , 
                   
                     
 
                   
                   ⁢ 
                   Therefore 
                   , 
                   
                     
                       B 
                       r 
                     
                     = 
                     
                       0.7 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         μ 
                         0 
                       
                       ⁢ 
                       
                         M 
                         s 
                       
                     
                   
                   , 
                   
                     
                       B 
                       r 
                     
                     = 
                     
                       0.7 
                       ⁢ 
                       
                         B 
                         s 
                       
                     
                   
                 
               
               
                 
                     
                 
               
             
             
               
                 
                   
                     
                       M 
                       r 
                     
                     = 
                     
                       
                         
                           
                             
                               f 
                               h 
                             
                             ⁢ 
                             
                               B 
                               r_hard 
                             
                           
                           + 
                           
                             
                               f 
                               s 
                             
                             ⁢ 
                             
                               B 
                               r_soft 
                             
                           
                         
                         
                           μ 
                           0 
                         
                       
                       = 
                       
                         
                           
                             
                               
                                 
                                   f 
                                   h 
                                 
                                 ⁢ 
                                 
                                   B 
                                   r_hard 
                                 
                               
                               + 
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       f 
                                       h 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   B 
                                   r_soft 
                                 
                               
                             
                             
                               μ 
                               0 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               A 
                               ⁢ 
                               
                                 / 
                               
                               ⁢ 
                               m 
                             
                             ] 
                           
                         
                         = 
                         
                           
                             
                               0.7 
                               ⁡ 
                               
                                 [ 
                                 
                                   
                                     B 
                                     s_soft 
                                   
                                   - 
                                   
                                     
                                       f 
                                       h 
                                     
                                     ⁡ 
                                     
                                       ( 
                                       
                                         
                                           B 
                                           s_soft 
                                         
                                         - 
                                         
                                           B 
                                           s_hard 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                                 ] 
                               
                             
                             
                               μ 
                               0 
                             
                           
                           ⁡ 
                           
                             [ 
                             
                               A 
                               ⁢ 
                               
                                 / 
                               
                               ⁢ 
                               m 
                             
                             ] 
                           
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       For 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         H 
                         N 
                       
                     
                     &gt; 
                     
                       
                         M 
                         r 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       ( 
                       BH 
                       ) 
                     
                     max 
                   
                   = 
                   
                     
                       
                         
                           μ 
                           0 
                         
                         ⁢ 
                         
                           M 
                           r 
                           2 
                         
                       
                       4 
                     
                     = 
                     
                       
                         
                           
                             
                               μ 
                               0 
                             
                             ⁢ 
                             
                               
                                 { 
                                 
                                   
                                     0.7 
                                     ⁡ 
                                     
                                       [ 
                                       
                                         
                                           B 
                                           s_soft 
                                         
                                         - 
                                         
                                           
                                             f 
                                             h 
                                           
                                           ⁡ 
                                           
                                             ( 
                                             
                                               
                                                 B 
                                                 s_soft 
                                               
                                               - 
                                               
                                                 B 
                                                 s_hard 
                                               
                                             
                                             ) 
                                           
                                         
                                       
                                       ] 
                                     
                                   
                                   
                                     μ 
                                     0 
                                   
                                 
                                 } 
                               
                               2 
                             
                           
                           4 
                         
                         ⁡ 
                         
                           [ 
                           
                             
                               N 
                               
                                 A 
                                 2 
                               
                             
                             ⁢ 
                             
                               
                                 A 
                                 2 
                               
                               
                                 m 
                                 2 
                               
                             
                           
                           ] 
                         
                       
                       = 
                       
                           
                         
                           
                             [ 
                             
                               
                                 N 
                                 
                                   A 
                                   · 
                                   m 
                                 
                               
                               ⁢ 
                               
                                 A 
                                 m 
                               
                             
                             ] 
                           
                           = 
                           
                             
                               [ 
                               
                                 
                                   T 
                                   · 
                                   A 
                                 
                                 ⁢ 
                                 
                                   / 
                                 
                                 ⁢ 
                                 m 
                               
                               ] 
                             
                             = 
                             
                               
                                 
                                   0.49 
                                   ⁢ 
                                   
                                     
                                       π 
                                       ⁡ 
                                       
                                         [ 
                                         
                                           
                                             B 
                                             s_soft 
                                           
                                           - 
                                           
                                             
                                               f 
                                               h 
                                             
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 
                                                   B 
                                                   s_soft 
                                                 
                                                 - 
                                                 
                                                   B 
                                                   s_hard 
                                                 
                                               
                                               ) 
                                             
                                           
                                         
                                         ] 
                                       
                                     
                                     2 
                                   
                                 
                                 
                                   
                                     10 
                                     5 
                                   
                                   × 
                                   
                                     μ 
                                     0 
                                   
                                 
                               
                               = 
                               
                                 
                                   
                                     
                                       
                                         4.9 
                                         ⁢ 
                                         
                                           
                                             π 
                                             ⁡ 
                                             
                                               [ 
                                               
                                                 
                                                   B 
                                                   s_soft 
                                                 
                                                 - 
                                                 
                                                   
                                                     f 
                                                     h 
                                                   
                                                   ⁡ 
                                                   
                                                     ( 
                                                     
                                                       
                                                         B 
                                                         s_soft 
                                                       
                                                       - 
                                                       
                                                         B 
                                                         s_hard 
                                                       
                                                     
                                                     ) 
                                                   
                                                 
                                               
                                               ] 
                                             
                                           
                                           2 
                                         
                                       
                                       
                                         
                                           10 
                                           6 
                                         
                                         × 
                                         
                                           μ 
                                           0 
                                         
                                       
                                     
                                     ⁡ 
                                     
                                       [ 
                                       
                                         MG 
                                         · 
                                         Oe 
                                       
                                       ] 
                                     
                                   
                                   ⁢ 
                                   
                                     
 
                                   
                                   ⁢ 
                                   For 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     H 
                                     N 
                                   
                                 
                                 &lt; 
                                 
                                   
                                     M 
                                     r 
                                   
                                   2 
                                 
                               
                             
                           
                         
                         ⁢ 
                         
                             
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         ( 
                         BH 
                         ) 
                       
                       max 
                     
                     = 
                     
                       
                         
                           
                             μ 
                             0 
                           
                           ⁢ 
                           
                             H 
                             N 
                           
                           ⁢ 
                           
                             M 
                             r 
                           
                         
                         2 
                       
                       = 
                       
                         
                           
                             2 
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     
                                       f 
                                       s 
                                     
                                     ⁢ 
                                     
                                       K 
                                       s 
                                     
                                   
                                   + 
                                   
                                     
                                       f 
                                       h 
                                     
                                     ⁢ 
                                     
                                       K 
                                       h 
                                     
                                   
                                 
                                 
                                   
                                     
                                       f 
                                       s 
                                     
                                     ⁢ 
                                     
                                       M 
                                       s 
                                     
                                   
                                   + 
                                   
                                     
                                       f 
                                       h 
                                     
                                     ⁢ 
                                     
                                       M 
                                       h 
                                     
                                   
                                 
                               
                               ) 
                             
                             ⁢ 
                             
                               ( 
                               
                                 
                                   
                                     f 
                                     s 
                                   
                                   ⁢ 
                                   
                                     M 
                                     s 
                                   
                                 
                                 + 
                                 
                                   
                                     f 
                                     h 
                                   
                                   ⁢ 
                                   
                                     M 
                                     h 
                                   
                                 
                               
                               ) 
                             
                           
                           2 
                         
                         = 
                         
                           
                             
                               
                                 f 
                                 s 
                               
                               ⁢ 
                               
                                 K 
                                 s 
                               
                             
                             + 
                             
                               
                                 f 
                                 h 
                               
                               ⁢ 
                               
                                 K 
                                 h 
                               
                             
                           
                           = 
                           
                             
                               
                                 
                                   ( 
                                   
                                     1 
                                     - 
                                     
                                       f 
                                       h 
                                     
                                   
                                   ) 
                                 
                                 ⁢ 
                                 
                                   K 
                                   s 
                                 
                               
                               + 
                               
                                 
                                   f 
                                   h 
                                 
                                 ⁢ 
                                 
                                   K 
                                   h 
                                 
                               
                             
                             = 
                             
                               
                                 
                                   K 
                                   s 
                                 
                                 + 
                                 
                                   
                                     f 
                                     h 
                                   
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         K 
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       FIG. 2  shows (BH) max  of a τ-phase MnAl-permalloy core-shell nanomagnet in terms of volume fraction of hard core (f h ). The hard magnetic τ-MnAl core (saturation magnetization=0.7 T; magnetic anisotropy constant K h =1 MJ/m 3 ) and soft magnetic permalloy shell (saturation magnetization=1 T; magnetic anisotropy constant K s =0.01 MJ/m 3 ) were used. 
     Equations (6) and (7) were used to calculate (BH) max  of MnAl-permalloy core-shell nanomagnet for H n &gt;M r /2 and H n &lt;M r /2, respectively. It is noted that (BH) max  is about 12 MGOe at H n =M r /2 and f h =8%, while (BH) max  of pure (f h =100%) MnAl nanomagnet is about 7 MGOe. 
     A τ-phase MnAl core-soft shell nanomagnet (i.e., a nanomagnet having τ-phase MnAl forming the hard magnetic core  14 ) where the shell  15  is composed of a soft magnetic alloy was used to calculate (BH) max  in terms of saturation magnetization (M s ) and shell thickness (δ s ) using equations (6) and (7). However, it is generally desirable for the shell thickness (δ s ) to be smaller than about 2 times the Bloch domain wall thickness of the core  14  to allow efficient exchange magnetic coupling between the core  14  and shell  15 . This is because the exchange magnetic coupling becomes weaker as the shell thickness increases over the Bloch domain wall thickness. The Bloch domain wall thickness for τ-phase MnAl is about 15 nm [G. G. Korznikova, J. of Microscopy, Vol. 239, 239, 2010]. Therefore, shell thickness is preferably thinner than 30 nm.  FIG. 3  shows the (BH) max  of MnAl—CoFe (2.2 T) core-shell nanomagnet becomes about 55 MGOe when exchange coupling exists. This high (BH) max  is attributable to the exchange coupling. 
     In another embodiment, a barium ferrite (BaM: BaFe 12 O 19 )—Fe 65 Co 35  core-shell nanomagnet was used to calculate (BH) max .  FIG. 9  shows (BH) max  of such nanomagnet as a function of volume fraction (f h ) of hard BaM core. The (BH) max  was estimated to be about 22.5 MGOe for f h  equal to 55%. About 11 nm thick shell for 100 nm barium ferrite particle is desired to provide approximately 22.5 MGOe as the Bloch domain wall thickness for barium ferrite is about 14 nm [M. Ziese and M. J. Thornton, Spin Electronics, p. 220, Spring 2001]. 
       FIGS. 4-10  depict estimate of (BH) max  for various core-shell nanomagnets for different temperatures. In particular,  FIG. 3  depicts a plot of (BH) max  at 300 K using τ-MnAl for the core  14  where M r /M s =1, and  FIG. 4  depicts a plot of (BH) max  at 300 K using τ-MnAl for the core  14  where M r /M s =0.7.  FIG. 5  depicts a plot of (BH) max  at 450 K using τ-MnAl for the core  14  where M r /M s =1, and  FIG. 6  depicts a plot of (BH) max  at 450 K using τ-MnAl for the core  14  where M r /M s =0.7.  FIG. 7  depicts a plot of (BH) max  at 300 K using MnBi for the core  14  where M r /M s =1, and  FIG. 8  depicts a plot of (BH) max  at 450 K using MnBi for the core  14  where M r /M s =1. Further,  FIG. 9  depicts a plot of (BH) max  at 300 K using BaM for the core  14  where M r /M s =1, and  FIG. 10  depicts a plot of (BH) max  BaM at 450 K using for the core  14  where M r /M s =1. 
     Note that there are various techniques that could be used to fabricate a nanomagnet, as described herein, including electroless plating, chemical and physical synthesis, and embedding core-shell nanomagnets in a polymeric matrix. 
     In one exemplary embodiment, M-type hexaferrite nanoparticles and anionic surfactant are mixed in distilled water, while mechanically stirring with argon gas purging and then washed with deionized water. The anionic surfactant allows Fe 2+  and Co 2+  cations to adhere to the core hexaferrite particles. When the anionic surfactant is dispersed in water, the hydrophilic head is likely to face to water, while the hydrophobic tail avoids water. The choice of the anionic surfactant could be sodium dodecyl sulfate (SDS), sodium laurilsulfate or sodium lauryl sulfate (SLS), though other anionic surfactants are possible. Aqueous solutions of SDS have been conventionally used for dispersing (or suspending) magnetite (Fe 3 O 4 ) particles. Note that the M-type hexaferrite core particle is already an oxide. Therefore, the hexaferrite is chemically stable, but not Fe and Co. Prior to adding FeCl 2 ·4H 2 O and CoCl 2 ·6H 2 O precursory shell materials to the solution, the anionic surfactant containing solution may be deaerated by purging with Ar gas. The purging preferably continues until the end of the coating process. Reduction agent NdBH 4  is dropped into the solution at a desired flow rate, and transition metal ions are thereby brought to their metallic state. The Co—Fe coated M-type hexaferrites is filtered and dried in an oven at about 80° C. This same process is also applicable to manufacturing of MnAl and MnBi core-shell nanoparticles under an inert atmosphere. In other embodiments, other techniques can be used for fabricating nanomagnet particles.