magnetic nanomembranes - leibniz gemeinschaft: start · feedback system for the emotor ......

52
Denys Makarov Magnetic Nanomembranes M. Melzer, D. Karnaushenko, R. Streubel, F. Bahr, W. Hofmann, L. Baraban, I. Mönch, O. G. Schmidt

Upload: lamcong

Post on 29-May-2018

214 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Denys Makarov

Magnetic Nanomembranes

M. Melzer, D. Karnaushenko, R. Streubel, F. Bahr, W. Hofmann, L. Baraban, I. Mönch, O. G. Schmidt

Page 2: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

II. Magnetic sensorics

I. Magnetism on curved surfaces (tubular and spherical structures)

Outline

Page 3: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Kelley et al., Chem. Mater. (2004)

RFID-tags

Actuators

Kofod et al., Appl. Phys. Lett. (2007)

Displays

Sony (2007)

LEDs

New York Times (2009)

Solar cells

PowerFilm Solar (2010)

Arbitrary shapes after fabrication

Extended range of applications

Electronics become flexible

Page 4: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Nature Mater. 9, 929 (2010); Nature Mater. 10, 316 (2011); Nano Lett. 11, 2522 (2011)

Electronics become flexible

Page 5: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Nature Mater. 9, 929 (2010); Nature Mater. 10, 316 (2011); Nano Lett. 11, 2522 (2011)

Electronics become flexible

Page 6: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Automotive applications drive sensor sales

Applications for magnetic sensors in today’s cars (iSuppli)

Number of magnetic sensors is 9 per car (in average)

Page 7: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Consumer electronics and appliances

AMR sensors attach to the spray arm in a dishwasher to detect jamming

o Mobile phones

o White goods (washing machines, dishwashers, refrigerators, coffee machines)

o Personal electronics (cameras, camcorders, MP3 players)

o Audio / video / gaming

o Desktop and mobile PCs, external HDD

MEMS Industry GroupTM Newsletter

Courtesy Danby

Courtesy LAYAR

Electronic compass for cell phones

Page 8: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Consumer electronics and appliances

AMR sensors attach to the spray arm in a dishwasher to detect jamming

o Mobile phones

o White goods (washing machines, dishwashers, refrigerators, coffee machines)

o Personal electronics (cameras, camcorders, MP3 players)

o Audio / video / gaming

o Desktop and mobile PCs, external HDD

MEMS Industry GroupTM Newsletter

Courtesy Danby

Courtesy LAYAR

Electronic compass for cell phones

Shapeable (magneto)electronics

Page 9: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

GMR multilayer element

20 to 50 double layers of ferro- and nonmagnetic conductors

Bext

Giant Magneto-Resistance Current-in-plane measurement

Sensitive to in-plane fields GMR(Bext) = [R(Bext) – Rsat] / Rsat

[Co/Cu]50

GMR in exchange coupled multilayers

Page 10: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

GMR layers on Poly(dimethylsiloxan) (PDMS)

- by magnetron sputter deposition

Photolithographic patterning

on the PDMS coated wafer

compatible to established

micro-fabrication technologies

Four-point GMR measurement with

current-in-plane (CIP) configuration

Pealing the rubber film from the rigid silicon support

- by means of the anti-stick layer

GMR layer on a free-standing elastic membrane

Stretchable magnetoelectronics

Page 11: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Field-dependent magnetoresistance:

GMR of [Co/Cu]50 multilayer stacks

GMR layer before peel-off

PDMS

GMR film

GMR(Bext) = [R(Bext) – Rsat] / Rsat

GMR measurements on free-standing films

Melzer et al., Nano Lett. 11, 2522 (2011)

Page 12: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Field-dependent magnetoresistance:

GMR of [Co/Cu]50 multilayer stacks

GMR layer before peel-off

PDMS

GMR film

GMR(Bext) = [R(Bext) – Rsat] / Rsat

GMR measurements on free-standing films

GMR layer after peel-off

Melzer et al., Nano Lett. 11, 2522 (2011)

Page 13: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

s = 0 %

s = 0.8 %

s = 1.5 %

Piggyback setup for application of strain

Stretching of wrinkled GMR films

Melzer et al., Nano Lett. 11, 2522 (2011); Melzer et al., RSC Advances 2, 2284 (2012)

Page 14: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Melzer et al., Adv. Mater. 24, 6468 (2012)

- Two different types of wrinkling occur on the rubber substrates

- High stretchability up to 29% of tensile strain

- Increasing resistance due to crack formation, GMR ratio changes only gradually

- Parallel wrinkles represent predetermined fracturing sites to create a

meander-like pattern during stretching

Spin valve sensor

Predetermined fracture pattern

Page 15: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Melzer et al., Adv. Mater. 24, 6468 (2012)

- Two different types of wrinkling occur on the rubber substrates

- High stretchability up to 29% of tensile strain

- Increasing resistance due to crack formation, GMR ratio changes only gradually

- Parallel wrinkles represent predetermined fracturing sites to create a

meander-like pattern during stretching

Spin valve sensor

Predetermined fracture pattern

Page 16: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Melzer et al., Adv. Mater. 24, 6468 (2012); www.lmts.epfl.ch; mariakonovalenko.wordpress.com

Spin valve sensor

Technology might be useful for the artificial muscles

Direct measurement of strain using magnetic sensorics

Page 17: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Elastic GMR sensor for fluidic applications

Melzer et al., RSC Advances 2, 2284 (2012)

Page 18: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Stretchable GMR sensors

Melzer et al., Nano Lett. 11, 2522 (2011)

Page 19: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

fahrrad-ro.de

buildaroo.com

o Angle positioning in rotary motors

Flexible magnetic field sensor provides:

o 3D magnetic field profile of eMotor

Optimization of the eMotor performance

Feedback system for the eMotor

sportrider.com integratedsoft.com

Measuring and Monitoring eMotors

Page 20: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

STATORPOLE

ROTOR < 500 µm

< 200 µm

(b)(a) 500 µm

Tomography of a commercial Hall sensor (TUD)

Commercially available Hall sensors are too thick to fit into the gap between stator and rotor

Thin and flexible Hall sensors

Flux control of magnetic bearings

Strong magnetic fields of ~20 kOe

Bismuth Hall sensors

Task: Increase of dynamic stiffness of

magnetic bearing systems

Flexible Hall sensors

Page 21: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

o All-flexible sensor

o No rigid components in the air gap

o Flexible PCB + magnetic sensor

STATORPOLE

ROTOR < 0.5 mm

< 0.2 mm

STATORPOLE

Rotor

Stator Sensor

Flexible Hall sensors

Page 22: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Stretchable magnetoelectronics Fabrication of GMR powder

Step 1: Deposition of GMR stack on polymer Fabrication is the same as for stretchable

GMR sensors, but instead of pealing of

the substrate the polymer is dissolved in

acetone.

Step 2: Pealing GMR sensors of the substrate

GMR powder

GMR multilayers and Polymers

Melzer et al., Nano Lett. 11, 2522 (2011); Karnaushenko et al., Adv. Mater. 24, 4518 (2012)

Page 23: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Stretchable magnetoelectronics Fabrication of GMR powder

Step 1: Deposition of GMR stack on polymer Fabrication is the same as for stretchable

GMR sensors, but instead of pealing of

the substrate the polymer is dissolved in

acetone.

Step 2: Pealing GMR sensors of the substrate

GMR powder Binder

GMR multilayers and Polymers

Melzer et al., Nano Lett. 11, 2522 (2011); Karnaushenko et al., Adv. Mater. 24, 4518 (2012)

Page 24: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

• Sensitivity • Ambient conditions

Paints

Pastes

Inks Magnetic powder

Binder solution

Fabrication and characterisation

Printable magnetoelectronics

Page 25: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Karnaushenko et al., Adv. Mater. 24, 4518 (2012)

Magnetic sensor printed on various substrates

• Big and isotropic sensitivity

• Suitable electrical parameters

• Stable at ambient conditions

• Applicable to virtually any surface

• Flexibility and bendability

Page 26: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Motivation

Resistors Capacitors LED`s Conductors

Printable electronics

Page 27: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

+ - + -

LED OFF

LED ON

Printed magnetic switch

Karnaushenko et al., Adv. Mater. 24, 4518 (2012)

Page 28: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

+ - + -

LED OFF

LED ON

Printed magnetic switch

Karnaushenko et al., Adv. Mater. 24, 4518 (2012)

Page 29: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

+ -

LED OFF

LED ON

Magnetic sensor +

Amplifier =

Magnetic Switch

Printed magnetic switch

Karnaushenko et al., Adv. Mater. 24, 4518 (2012)

Page 30: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Elastic GMR sensor for fluidic applications

Melzer et al., RSC Advances 2, 2284 (2012)

Page 31: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Rolled-up technology

Mei et al., Adv. Mater. 20, 4085 (2008)

Page 32: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

o Size of the sensor has to be adjusted to the size of the object

o Integration of the magnetic sensor in a microfluidic channel

o Rolled-up technology can be applied

Concept: rolled-up GMR sensor in fluidic channel

Mönch et al., ACS Nano 5, 7436 (2011)

Page 33: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Single sensor elements are measured independently

o GMR ratio is slightly better for the planar sensor

o Sensitivity of the planar and rolled-up sensors is similar

Rolled-up sensor: Diameter: 60 um

Length: 1000 um

Planar vs. Rolled-up sensor

Page 34: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

In-flow detection of magnetic particles

o Successful in-flow (dynamic) detection of magnetic particles

o Size of particle is adjusted to the size of the channel

Mönch et al., ACS Nano 5, 7436 (2011) Collaboration: Larysa Baraban (IfWW-TUD);

Rolled-up magnetic sensor

Page 35: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Magnetic nanoparticles in living cells

Co nanoparticles in SiO2 shell (80 nm) are uptaken

by living cells (HeLa)

Collaboration: Wang Xi, Samuel Sanchez (IIN-IFW); Larysa Baraban (IfWW-TUD)

Page 36: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

M. Kläui, J. Phys.: Cond. Mat. 20, 313001 (2008)

A. Brataas et al., Nature Materials 11, 372 (2012)

Head-to-head domain wall

Magnetic Vortex

Planar vs. Curved magnetic architectures

Head-to-head domain wall

M. Yan et al., Phys. Rev. Lett. 104, 057201 (2010)

Page 37: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Tube of larger diameter

Head-to-head domain wall

Magnetic Vortex

Planar vs. Curved magnetic architectures

Head-to-head domain wall

M. Yan et al., Phys. Rev. Lett. 104, 057201 (2010)

Collaboration: Jehyun Lee (Seoul NU)

Init

ial s

tate

: ra

nd

om

Remanent magnetic state (unrolled tube)

Page 38: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Collaboration: Rudolf Schäfer (IMM-IFW)

Head-to-head domain walls

Spiral-like domain walls

Azimuthal 180deg domains

SEM

M

agn

eto

-op

tica

l Ke

rr m

icro

sco

py

Magnetic pattern in a ferromagnetic rolled-up tube

Page 39: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

GMI effect

MI effect

Makhnovskiy et al., JMMM 276, 1866 (2004)

Circular magnetic domain structure

Transversal anisotropy

Longitudinal anisotropy

Hext

Magneto-impedance effect

Page 40: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

-15 -10 -5 0 5 10 15

-2

0

2

4

6

8

10

12

14

H

ext (mT)

s

0.1

10

1

00

f / M

Hz

Sensitivity

22 V/T

10 mA

Samples

5 mm

-15 -10 -5 0 5 10 15

-0,5

0,0

0,5

1,0

1,5

2,0

2,5

s

H

ext, (mT)

f / M

Hz

0.1

10

1

00

Sensitivity 2.7 V/T 10 mA

Planar sample Rolled-up sample

Py: 50 nm Cu: 200 nm Py: 50 nm SiO2: 500 nm SiO: 40 nm

Layer stack:

GMI in rolled-up architectures

Page 41: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Human – Machine interface

Page 42: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

http://www.hondanews.com

GMI sensors for encephalography

Page 43: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

http://www.hondanews.com

GMI sensors for encephalography

Page 44: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Processing steps:

• Lithography: define polymer strips

• Deposition: magnetic layer

• Delamination: self-assemble coils

Smith et al., Phys. Rev. Lett. 107, 097204 (2011); Smith et al., Soft Matter 7, 11309 (2011)

Fabrication of the coiled-up structures

Page 45: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Saturated before coil-up

In-plane magnetized

perpendicular to strip

In-plane magnetized

Parallel to strip

Out-of-plane

magnetized

Achieved magnetization configurations

Smith et al., Phys. Rev. Lett. 107, 097204 (2011); Smith et al., Soft Matter 7, 11309 (2011)

Page 46: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Hollow-bar-magnetized Corkscrew-magnetized Radial-magnetized

Magnetic configurations after coil-up

Saturated before coil-up

Achieved magnetization configurations

Smith et al., Phys. Rev. Lett. 107, 097204 (2011); Smith et al., Soft Matter 7, 11309 (2011)

Page 47: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

Möbius strip

Page 48: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

mx

x

y

z

Magnetic vortex state is stabilized similar to a tube

Magnetic Vortex

Geometry: radius = 300 nm, width = 300 nm, thickness = 30 nm

Möbius strip

Collaboration: Volodymyr Kravchuk (BITP)

Page 49: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

mx

Easy-axis anisotropy (K = 5x105 J/m3; Ms = 1 T) normal to the surface

Geometry: radius = 300 nm, width = 300 nm, thickness = 30 nm

x

y

z

Tube is radial-magnetized

mx

3 domain walls 1

2 3

Out-of-plane magnetized Möbius strip

Collaboration: Volodymyr Kravchuk (BITP)

Page 50: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

II. Magnetic sensorics

I. Magnetism on curved surfaces (tubular and spherical structures)

Summary

Page 51: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

I would like to thank:

Institute for Integrative Nanosciences; Carmine Ortix, Jeroen van den Brink (ITF); Rudolf Schäfer, Volker Neu, Ulrike Wolff, Sebastian Fähler (IMW); Mark H. Rümmeli, Alicia Bachmatiuk, Anja Wolter (IFF)

Michael Melzer, Robert Streubel, Tobias Kosub, Gungun Lin, Daniil Karnaushenko, Dmitriy Karnaushenko, Ingolf Mönch, Martin Kopte, Milan Pesic, Luyang Han, Irina Fiering, Cornelia Krien, Rainer Kaltofen, Alexander Kopylov

Falk Bahr, Wilfried Hofmann (EMA); Thomas Zerna (IAVT); Larysa Baraban, Gianaurelio Cuniberti (IfWW)

Acknowledgement

Page 52: Magnetic Nanomembranes - Leibniz Gemeinschaft: Start · Feedback system for the eMotor ... Saturated before coil-up In-plane magnetized perpendicular to strip ... Möbius strip Collaboration:

MAGNA group at the IFW Dresden