[PPT] - Magnetic moments, dipoles and fields Richard F L Evans ESM 2018 PowerPoint Presentation

SLIDE 1

Magnetic moments, dipoles and fields

Richard F L Evans ESM 2018

SLIDE 2

Overview

Origin of magnetic moments Magnetic fields and demagnetising factors Units in magnetism

SLIDE 3

Useful References

J. M. D. Coey; Magnetism and Magnetic Magnetic Materials. Cambridge

University Press (2010) 614 pp

Stephen Blundell Magnetism in Condensed Matter, Oxford 2001
D. C. Jiles An Introduction to Magnetism and Magnetic Magnetic

Materials, CRC Press 480 pp

J. D. Jackson Classical Electrodynamics 3rd ed, Wiley, New York 1998

SLIDE 4

Magnetic moments

SLIDE 5

What is a magnet?

“A magnet is a material or object that produces a magnetic field”

Wikipedia

SLIDE 6

What is a magnet?

“A magnet is a material or object that produces a magnetic field”

Wikipedia

SLIDE 7

What is a magnetic field?

An invisible vector field that interacts with other magnets

https://education.pasco.com/epub/PhysicsNGSS/BookInd-515.html

SLIDE 8

What is a magnetic field?

An invisible vector field that interacts with other magnets

SLIDE 9

What is a magnetic field?

An invisible vector field that interacts with other magnets

SLIDE 10

Magnetic field, Øersted 1820

Oersted discovered in 1820 that a

current carrying wire was able to rotate a compass needle

Current and field are related by

Ampere’s Law

Example for I = 1A, integral

around the loop is 2𝜌r, r = 2 mm H ~ 80 A/m

Earth’s magnetic field ~ 40 A/m

H

δl

r I

I = ∫ Hdl

SLIDE 11

Interaction of two current-carrying wires, Ampere 1825

Two current carrying wires (one longer than the
ther) are attracted to each other for parallel

current, and repel for anti-parallel current.

The parallel wires “look like” magnets in the

perpendicular direction

Weird but central to electromagnetism (E and B

fields in light)

Different from electrostatics as this is a dynamic

effect from the motion of charge

F l = μ0 2π I1I2 r

I1 I2 F

SLIDE 12

Equivalence of currents and magnetic moments

So currents look like magnets… do magnets look like currents?
Can express a current loop as an effective moment, ie a source of

magnetic field

What kind of currents do we need compared to typical magnetic fields?

m I

m = I⊥A

A

SLIDE 13

Comparison of current magnitudes and magnets

Using the equivalence of current loops and magnetic moments we can

compare the effective currents for a typical small magnet

Moment given by for a single loop and a solenoid respectively, where n is the

number of turns of the coil

For a small magnet
At small sizes, magnets generate much larger fields -> applications in motors

10 mm 1 Am2 1 A 10,000 turns 10,000 A 1 turns

m = I⊥A m = nI⊥A

SLIDE 14

Difference between magnetic moment and magnetisation

Magnetic moment is specific to the sample (bigger magnet, bigger field)
Magnetization is the moment density
Magnetisation is a property of the material
Moment is a property of a magnet
Magnetisation is scale independent

3 mm 10 mm 25 mm 0.027 Am2 1 Am2 15.6 Am2 m = MV Assume NdFeB Ms ~ 1 MA/m

SLIDE 15

Vectorial nature of magnetic moments

A magnetic moment generates a field around it
Interaction with non-magnets is weak
Interaction with magnets is stronger but orientation dependent

Weak repulsion Strong attraction

SLIDE 16

Physical origin of magnetization and magnetic moment

At the atomic scale the magnetic moments fluctuate strongly in time and

space due to the electrons ‘orbiting’ nuclei

Use a continuous medium approximation to calculate an average

magnetisation <M> (moment/volume)

Avoids all the horrible details of fluctuating moments and can treat

magnetism on a continuum level

Good approximation for ferromagnets for volumes much larger than the

atomic volume

<M>

SLIDE 17

4 Be

9.01 2 + 2s0

12Mg

24.21 2 + 3s0

2 He

4.00

10Ne

20.18

24Cr

52.00

3 + 3d3 312

19K

38.21

1 + 4s0

11Na

22.99 1 + 3s0

3 Li

6.94 1 + 2s0

37Rb

85.47 1 + 5s0

55Cs

132.9 1 + 6s0

38 Sr

87.62

2 + 5s0

56Ba

137.3

2 + 6s0

59Pr

140.9 3 + 4f2

1 H

1.00

5 B

10.81

9 F

19.00

17Cl

35.45

35Br

79.90

21Sc

44.96

3 + 3d0

22Ti

47.88

4 + 3d0

23V

50.94

3 + 3d2

26Fe

55.85

3 + 3d5

1043

27Co

58.93

2 + 3d7

1390

28Ni

58.69

2 + 3d8

629

29Cu

63.55

2 + 3d9

30Zn

65.39

2 + 3d10

31Ga

69.72

3 + 3d10

14Si

28.09

32Ge

72.61

33As

74.92

34Se

78.96

6 C

12.01

7 N

14.01

15P

30.97

16S

32.07

18Ar

39.95

39 Y

88.91

2 + 4d0

40 Zr

91.22

4 + 4d0

41 Nb

92.91

5 + 4d0

42 Mo

95.94

5 + 4d1

43 Tc

97.9

44 Ru

101.1

3 + 4d5

45 Rh

102.4

3 + 4d6

46 Pd

106.4

2 + 4d8

47 Ag

107.9

1 + 4d10

48 Cd

112.4

2 + 4d10

49 In

114.8

3 + 4d10

50 Sn

118.7

4 + 4d10

51 Sb

121.8

52 Te

127.6

53 I

126.9

57La

138.9

3 + 4f0

72Hf

178.5

4 + 5d0

73Ta

180.9

5 + 5d0

74W

183.8

6 + 5d0

75Re

186.2

4 + 5d3

76Os

190.2

3 + 5d5

77Ir

192.2

4 + 5d5

78Pt

195.1

2 + 5d8

79Au

197.0

1 + 5d10

61Pm

145

70Yb

173.0 3 + 4f13

71Lu

175.0 3 + 4f14

90Th

232.0 4 + 5f0

91Pa

231.0 5 + 5f0

92U

238.0 4 + 5f2

87Fr

223

88Ra

226.0

2 + 7s0

89Ac

227.0

3 + 5f0

62Sm

150.4 3 + 4f5

105

66Dy

162.5 3 + 4f9 179 85

67Ho

164.9 3 + 4f10 132 20

68Er

167.3 3 + 4f11 85 20

58Ce

140.1 4 + 4f0

13

Ferromagnet TC > 290K Antiferromagnet with TN > 290K 8 O

16.00 35

65Tb

158.9 3 + 4f8 229 221

64Gd

157.3 3 + 4f7 292

63Eu

152.0 2 + 4f7 90

60Nd

144.2 3 + 4f3 19

66Dy

162.5 3 + 4f9 179 85

Atomic symbol Atomic Number Typical ionic change Atomic weight Antiferromagnetic TN(K) Ferromagnetic TC(K) Antiferromagnet/Ferromagnet with TN/TC < 290 K Metal Radioactive

Magnetic Periodic Table

80Hg

200.6

2 + 5d10

93Np

238.0 5 + 5f2

94Pu

244

95Am

243

96Cm

247

97Bk

247

98Cf

251

99Es

252

100Fm

257

101Md

258

102No

259

103Lr

260

36Kr

83.80

54Xe

83.80

81Tl

204.4

3 + 5d10

82Pb

207.2

4 + 5d10

83Bi

209.0

84Po

209

85At

210

86Rn

222

Nonmetal Diamagnet Paramagnet BOLD Magnetic atom 25Mn

55.85

2 + 3d5

96

20Ca

40.08

2 + 4s0

13Al

26.98

3 + 2p6

69Tm

168.9 3 + 4f12 56

Which elements are magnetic

From Coey

SLIDE 18

Bohr magneton

Can consider an electron ‘orbiting’ an

atom

A moving charge looks like a ‘current’,

generating an effective magnetic moment

In Bohr’s quantum theory, orbital angular

momentum l is quantized in units of ︎ℏ; h is Planck’s constant, 6.6226 10-34 Js;︎ℏ=h/ 2︎𝜌=1.05510-34 Js

The orbital angular momentum is l =

mer︎∧v

It is the z-component of lz that is quantized

in units of ︎ℏ, taking a value ml︎  ml is a quantum number, an integer with no units. Eliminating r in the expression for m

μB is the Bohr magneton, the basic unit of

atomic magnetism

e

m m l

m = IA = − evr 2 m = − e 2me I = eℏ 2me ml = mlμB μB = eℏ 2me = 9.274 × 10−24Am2|JT−1

*

* electrons travel in the opposite direction to currents

SLIDE 19

Non-integer magnetic moments

Transition metal magnets tend to

have non-integer magnetic moments, eg Fe ~ 2.2 μB, Co ~ 1.72 μB, Ni ~ 0.6 μB

If electrons carry quanta of angular

momentum, how is this possible?

Classic explanation is itinerant

magnetism: electrons are delocalised and form bands

First principles calculations reveal

a non-integer magnetic moment quite localised to the atom

Effect due to electrons hopping

between different d-orbitals 2670 K Schwarz et a

1

due to a dip in the state densities of the non-d spin-up electrons at the Fermi energy (Terakura and Kanamori 1971, Terakura 1977, Malozemoff et a

1 1984). When applied to

Fe, equation (1) gives a magnetic moment of M = 2.6. That it is in reality less than that is due to the magnetic weakness of Fe where the Fermi energy cuts through the spin-up d band (see figure 6). The straight line with a slope of + 45' is defined by M = Z - 2 N J

(2)

where N

' is the average number of spin-down electrons per atom. In this case the Fermi

energy is pinned in a pronounced dip in the spin-down state density, fixing the number mJ at 2.93 (see the case of Fe in figure 6). Table 2 contains the ASW partial charges per atom, the average numbers per atom of majority- and minority-spin electrons, miT and i

% " respectively, and the calculated lattice

constants. Starting with the highest magnetic moment calculated in figure 8 (Fe, CO),

we see from table 2 that both fit and 8

'

are close to the values assumed for equations (1) and

(2):

around a concentration of 25 at.% CO we have strong ferromagnetism and the Fermi energy is pinned in the dip of the minority-spin state density (see also figure 6). For CO

Table 2. ASW partial charges (in electrons per atom) for all six structures. The total includes a small f contribution. & ? and I%" are average numbers per atom of majority- and minority- spin electrons, respectively. The corresponding equilibrium lattice constants which are derived from ASW total energy calculations are given at the bottom. Fe,Co (Fe3Al) Fe FeCo FeCo FeCo, CO

( B C C )

Fe, Fe2 (CsCl) (Zintl) (Fe3AI)

( B C C )

Fe s

t 0.31

0.31 0.31 0.31 0.3

1

0.30

1 0.32

0.31 0.31 0.31 0.3 1 0.30 p

T

0.36 0.35 0.35 0.36 0.35 0.34

i 0.40

0.38 0.40 0.40 0.38 0.38 d

t 4.37

4.50 4.57 4.61 4.56 4.58

12.19

2.09

1 . 9 5 1 . 8 6

1 . 9 7

Total 5.07 5.20 5.26 5.31 5.25 1.92 5.26

~

1 2.93

2.80 2.69 2.59 2.67 2.63

~ ~

FeCo (Fe,AI) Fe Fe,Co FeCo FeCo CO

(BCC)

(Fe3AI) (CsCI) (Zintl) CO, CO,

( B C C )

C o s

T

1

P T

d

T

Total

t

1

i

4

0.32 0.33 0.32 0.31 0.32 0.31 0.34 0.33 0.34 0.33 0.33 0.32 0.37 0.37 0.37 0.35 0.36 0.35 0.44 0.4 1 0.43 0.41 0.40 0.40 4.66 4.67 4.66 4.64 4.65 4.62 2.92 2.93 2.93 5.38 5.40 5.39 5.34 5.36 5.32 3.73 3.71 3.68 3.68 3.69 3.67

~

2.93

2.94 2.90

.o

5.07 5.28 5.36 5.32 5.33 5.32

~o

2.93 2.98 3.15 3.18 3.42 3.67 a (A) 2.8 IO 5.647 2.814 5.627 5.624 2.773 K Schwarz et al 1984 J. Phys. F: Met. Phys. 14 2659

SLIDE 20

Field from a dipole

The magnetic induction (field) from a point dipole can be derived

classically (see Jackson) and is given by

B = µ0 4π !3(m· ˆ r)ˆ r−m |r|3 "

J. D. Jackson, Classical electrodynamics (2nd ed.). New York: Wiley. (1975)

m r B-field at any point from a point dipole

Ignores any distribution of magnetic ‘charge’ at the dipole (need a

multipole description)

SLIDE 21

Question: What is the size of the Earth’s magnetic moment?

Assume an effective dipole at the centre of the Earth and a magnetic flux

density at the North Pole of 50 µT and REarth = 6.36 x 106 m | → B Npole| = μ0 4πR3

Earth

(3(→ μ ⋅ ^ r)^ r − → μ ) ∴ 4πR3

Earth| →

B Npole| μ0 = 3| → μ | ^ r − → μ = | → μ | 3^ r − ^ r = 2| → μ | | → μ | = 4πR3

Earth| →

B Npole| 2μ0 | → μ | = 2πR3

Earth| →

B Npole| μ0 = 2 ⋅ π ⋅ (6.38 × 106m)3 ⋅ (50 × 10−6T) (1.256 × 10−6NA−2) ∴ | → μ | ≈ 6.48 × 1022Am2

SLIDE 22

Question 2: What is the magnetization of the Earth?

MEarth = mEarth VEarth MEarth = mEarth

4π 3 R3 Earth

MEarth = 6.48 × 1022

4π 3 (6.38 × 106)3 ≈ 60A/m−1

SLIDE 23

Question 3: If the source of the magnetic field is an electrical current at the equator, what is its size?

m = IA IEquator = mEarth πR2

Earth

IEquator = 6.48 × 1022 π(6.38 × 106)2 ≈ 5 × 108A

SLIDE 24

Magnetic fields and demagnetising factors

SLIDE 25

What ranges of magnetic fields exist?

Historically a terrestrial 1T field was considered ‘large’
Today that is not generally true
Recording Media coercivity ~1T
MRI ~ 5T

1E-15 1E-12 1E-9 1E-6 1E-3 1 1000 1E6 1E9 1E12 1E15

MT

Magnetar Neutron Star Explosive Flux Compression Pulse Magnet Hybrid Magnet Superconducting Magnet Permanent Magnet Human Brain Human Heart Interstellar Space Interplanetary Space Earth's Field at the Surface Solenoid

pT µT T TT

SLIDE 26

Typical values of magnetic fields

Human Brain 1 fT Earth 50 𝜈T Permanent Magnet 0.5-1T Electromagnet 1T Magnetar 1012 T Superconducting magnet 10 T

SLIDE 27

Magnetic fields in free space

Two definitions of magnetic field
When talking about generated magnetic fields in free space, they express

the exact same physical phenomenon, and are related by

𝜈0 = 4pi 10-7 H/m is the permeability of free space
The difference between H-field and B-field is a common point of

confusion, but only when considering a magnetic medium B = 𝜈0(H+M)

B-field component arising from applied H-field is exactly

Magnetic Field H [A/m] Magnetic flux density B [T] B = 𝜈0H B = 𝜈0H

SLIDE 28

Magnetic fields in media

The actual B-field in response to media is generally more complex
Or alternatively in terms of a relative permeability or susceptibility
where the susceptibility gives the full magnetic response, or limit of small

fields (initial susceptibility)

Different media ave very different responses, ferromagnets highly non-

linear B = µ0µrH = µ0(1+ χ)H

B = µ0 (M+H)

χ = M(H) = dM dH 3 3 3

H→0

SLIDE 29

Diamagnetism and Paramagnetism

Diamagnets and paramagnets

have a weak magnetic response (𝝍 << 1), ~ 10-4 - 10-6

Response typically isotropic

with respect to the field

Diamagnets repel external

magnetic fields due to Larmor precession of bound electrons that induces a moment

pposite to the applied field
Paramagnets weakly align

with an external field

vercoming thermal

fluctuations M H Paramagnetic Diamagnetic

SLIDE 30

Ferromagnetism

Yue Cao et al, JMMM 395, 361-375 (2015)

Complex and

anisotropic behaviour of M(H)

Definition of 𝝍 =

M/H is not very sensible in most cases

Saturated case

easier to deal with!

SLIDE 31

Relation between B and H in a saturated material

Magnetic field around a

saturated magnet simple B = 𝜈0H

What about inside the

magnet?

Why do we care?
In general magnetization

processes are anisotropic and depend

n sample shape

B = µ0 (M+H)

SLIDE 32

Example: thin magnetic film

Much easier to magnetise in the plane than out-of-plane
Origin is demagnetising field - aims to minimise surface charges

M H H || to film H ⟂ to film + + + +

- - -

+ + + + + + + + + M M

SLIDE 33

Demagnetizing fields

Local effective field inside the magnet depends on surface
Since M is uniform, first (bulk) term is zero
For surface term, M.en determines surface charge density, larger surface

leads to larger field opposing magnetisation

Leads to concept of a demagnetising field

H = Happ - Hd

SLIDE 34

Demagnetization Factor

Calculating demagnetisation field is tedious (lots of boring and complicated

integrals)

Simplify - invent a “demagnetising factor” or “shape factor” N
Shape factor gives a constant of proportionality between the demagnetising

field and shape

Always between 0-1 and in general a tensor with trace 1
Known for simple geometric shapes (spheres, ellipsoids, rectangular prisms)
Is usually calculated numerically for anything complicated

Hd = -NM

Nx + Ny + Nz = 1

SLIDE 35

Demagnetization factors for different shapes

N = 0 N = 1/3

Infinite thin film Infinitely long cylinder Sphere

N = 1/2 N = 1

Infinitely long cylinder Short cylinder

SLIDE 36

Beware of non-uniformities

In general magnetization is not uniform for other shapes

Jay Shah et al, Nature Communications 9 1173 (2018)

SLIDE 37

Dipole fields and magnetostatics

Assume a lattice of dipoles in

shape of a sphere

Total dipole field at a point in

the centre summing over all

ther dipoles is zero
Where does the

demagnetising field come from?

B = µ0 4π !3(m· ˆ r)ˆ r−m |r|3 "

SLIDE 38

Classical solution: Lorentz cavity field

Divide the problem into local and macroscopic fields a << rc << rb
Suggests the local field at an atom is zero, despite global “demagnetising

field”

Bloc = 0 Bloc = Bsurface + Bcavity = +2M/3 - 2M/3 = 0

+ + + + + + + + + + +

+

+ + +

M

Bsurface = +2M/3 Bcavity = -2M/3

a rc rb

SLIDE 39

What about nanoparticles and clusters?

Small system where Lorentz

approximation is not true (a << rc << rb )

Average field for a sphere of

dipoles is zero

Where did the demagnetising

field go?

SLIDE 40

Field inside a dipole

Inside the current loop
Second term comes from

treating limiting field at origin

ver volume 𝜺(x)
Field at centre of current loop

looks like macroscopic field

BUT averaged over the volume

encompassed by the loop

J. D. Jackson, Classical electrodynamics (2nd ed.). New York: Wiley. (1975)

B = µ0 4π %3(m· ˆ r)ˆ r−m |r|3 + 8π 3 mδ(x) &

m

SLIDE 41

Reality: much more complicated

Dipole approximation is not

terrible

But large local deviations

from the average at atomic sites

Which field is needed for

spin dynamics for an atom?

A problem for both

atomistic and micromagnetic simulations

In the end its a moot point,
nly sample symmetry

matters since M x H = 0 for M || H

Electronic and magnetic structure o

f cc Fe-CO alloys

2665

2.4. Spin density Although we cannot settle the controversy between the localised and the itinerant pictures

for metallic magnetism, we nevertheless believe that a study of the spatial distribution of the spin density is quite useful. For this purpose we have chosen FeCo in the CsCl structure and have performed new band-structure calculations by the linearised augmented plane-wave (LAPW) method (Andersen 1975, Koelling and Arbman 1975), where the potentials are taken from the self-consistent ASW calculations. Since in the ASW method the potential is defined for overlapping spheres (according to the atomic-sphere approximation) but the muffin-tin form is needed for the LAPW calculation, the potential inside the smaller atomic spheres in the LAPW can be taken directly from the ASW, but for the region outside the atomic spheres a volume average of the ASW potential is used to give the constant part of the muffin-tin potential required. Since we used two different methods to calculate the energy bands, a comparison must be made between the two sets of results. It yields good agreement between the energy

Figure 4. Spin density pT(r)-pl(r) of FeCo (CsCI) in the (1 10) plane. The results are from

LAPW calculations which are based on the self-consistent ASW potentials. The peak maxima

near Fe and CO are slightly above 11 electrons A-3; zero in the contour maps is indicated by broken curves; the lowest contour has the value 0.1 electrons A-’ and adjacent contours differ by 0.3 electrons k3; the numbers are in units of 0.1 electrons A-’.

Calculated electron spin density in CoFe alloy

K Schwarz et al 1984 J. Phys. F: Met. Phys. 14 2659

SLIDE 42

Magnetic units

SLIDE 43

Magnetism units

The older Gaussian/cgs units are still common in the literature
(Some) conversion factors between the different systems

Quantity Symbol Gaussian & cgs emu Conversion factor SI Magnetic flux density B gauss (G) 10-4 tesla (T) Magnetic field strength H

ersted (Oe)

103/4𝜌 A/m Magnetization M emu/cc 103 A/m, J/T/m3 Magnetic Moment m emu 10-3 Am2, J/T Permeability of free space 𝜈0 dimensionless 4𝜌 × 10-7 H/m, T2 J-1 m3

http://www.ieeemagnetics.org/images/stories/magnetic_units.pdf

SLIDE 44

Old units

Redefinition of SI system in 2018 now makes the speed of light c and

electronic charge e fixed constants.

Now 𝜈0 is in principle a measurable quantity, defined from the fine

structure constant ~ 1/137

This breaks the previous convention fixing 𝜈0 as 4𝜌 10-7 H/m and thus

compatibility between the SI units and old CGS units

h/e2

exp = (µ0c/2)fixed · (1/α)exp

(µ0)exp =

2h/ce2

fixed · (α)exp

SLIDE 45

Magnetics has been one of the scientific disciplines most resistant to adoption of the SI. With the revised SI, the “peaceful coexistence”

f two systems of units [Silsbee 1962] is no longer feasible. The

following recommendations warrant consideration. 1) Scholarly journals that publish articles in magnetics should re- quire use of the SI and disallow EMU such as oersted, gauss, and “emu per cubic centimeter.” Authors who find the expression of magnetic field strength H in units of ampere per meter to be inconvenient could instead refer to µ0H in units of tesla (or milli-, micro-, nano-, or picotesla). Similarly, magnetization M could be expressed as µ0M or as magnetic polarization J in units of tesla or millitesla. 2) For the benefit of future generations of magneticians, professors should use SI in classroom instruction. Commercial instruments and magnetometers should be programmed to report measure- ment results in SI. 3) In writing equations, it is adequate to use phrases such as “where µ0 is the permeability of vacuum” (or “the vacuum magnetic permeability” or “the permeability of free space” or “the magnetic constant”) without giving a numerical value. This fol- lows typical usage when referring to the speed of light c, the Boltzmann constant k, or the Bohr magneton µB.

Ronald B. Goldfarb IEEE Magn. Lett. 8 1110003 (2017)

SLIDE 46

B, 𝜈0M and 𝜈0H are all defined in terms of magnetic field (intensity) in teslas (T)
Started with Superconducting and Permanent magnet communities, probably due to

avoidance of odd numerical conversions, dimensions and units

Now common in the literature, theoretical and experimental
Best way is to think about everything as current loop ‘sources’ of flux 𝜈0M and 𝜈0H
This convention leads to oddities in hysteresis - what are the units of M.B, both in

Tesla??

A recent trend to using teslas for everything

B = µ0 (M+H) Btotal = Bmagnetization +Bapplied

SLIDE 47

Not immediately obvious that this is useful
a single loop cycle should give units of

energy (density)

BUT - can easily extract the magnetization

in sensible dimensions by dividing by 𝜈0

In this case, a hysteresis cycle Int (M.B) has

units of J/m3

Same is true of Btot (H) loops but with

inverted units

Making sense of M-B loops

𝜈0M (T) 𝜈0H (T)

M(JT−1m−3) ≡ µ0M µ0 (T) (T2J−1m3)

SLIDE 48

Summary

Magnetic moments and current loops behave equivalently
Quantum mechanical origin of magnetic moments not too far from a

classical current loop

Magnetic fields are different inside and outside magnetic media
Internal magnetic fields in magnets are generally complicated
Units in magnetism are generally horrible, but always use SI
Remembering that 𝜈0 has units of T2 J-1 m3 will make you happy